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Measuring the return flux from laser guide stars Gagné, Ronald C 2013

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Measuring the Return Flux from Laser Guide Stars by Ronald C. Gagné  B.Sc., The University of British Columbia, 2010  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in The Faculty of Graduate Studies (Astronomy)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) June 2013 c Ronald C. Gagné 2013  Abstract For future extremely-large telescopes (ELT), operation at or near diffraction limited resolutions will be the norm, rather than the exception. Thus, adaptive optics systems and laser guide star facilities will be a critical component of the ELTs. The UBC Large Zenith Telescope (LZT) has conducted lidar observations to monitor the vertical distribution of sodium atoms with the goal of understanding both the abundance and evolution of sodium in the mesosphere to aid in both AO and laser guide star (LGS) return flux simulations. Access to the LZT’s high resolution lidar experiment has lead to a joint collaboration between UBC, Thirty Meter Telescope (TMT), and the Technical Institute of Physics and Chemistry of the Chinese Academy of Sciences (TIPC), to conduct upgrades of at the LZT site for sodium laser characterization tests, specifically TIPC’s prototype pulsed sodium laser. The additional facilities and instrumentation at the LZT site include: 1) a new building to be used as a laser room to house visiting groups’ lasers, corresponding control equipment and power systems, 2) optical equipment (scanning Fabry-Pérot interferometer, fast photodiode sensor, and miscellaneous optical filters) to measure the characteristics of the laser spectral format and pulse-shapes of pulsed lasers, and finally, 3) the site is now capable of directly imaging both natural stars and the LGS sodium spot with a 30 cm Ritchey-Chrétien equipped with a SBIG CCD camera to help determine the efficiency of LGS lasers. This document describes the new ancillary equipment for sodium laser characterization tests as well as a successful campaign conducted in the summer of 2012 on the UBC lidar laser. The summer campaign measured the laser pulse profile and spectral profile as well as LGS sodium spot measurements. The combined measurements which subsequently lead to an ii  Abstract estimated sodium column density ranging from 5.1 × 1013 atoms/m2 to 1.1 × 1013 − 1.5 × 1013 atoms/m2 depending on the number of laser spectral modes used in the model.  iii  Preface Parts of the figure 1.2 in chapter 1 are based on a diagram from [13] and used with consent from the publisher. Chapter 2 is based on two unpublished documents prepared by Dr. Hickson for internal analysis of the UBC lidar laser [4, 5].  iv  Table of Contents Abstract  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iv  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . .  v  Preface  List of Tables  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Abbreviations  ix  . . . . . . . . . . . . . . . . . . . . . . . . . xii  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Dedication  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi  1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.1  Properties of Atomic Sodium . . . . . . . . . . . . . . . . . .  4  1.2  Factors Affecting the Return Flux . . . . . . . . . . . . . . .  5  1.2.1  Environmental Properties . . . . . . . . . . . . . . . .  6  1.2.2  Laser Format and Propagation Parameters . . . . . .  7  1.3  . . . . . . . . . . . . . . .  9  2 LZT Laser Modelling and Expected Sodium Return . . . .  11  2.1  LZT Laser Characterization Tests  LZT Laser Characteristics  . . . . . . . . . . . . . . . . . . .  11  2.1.1  Laser Spectral Format  . . . . . . . . . . . . . . . . .  12  2.1.2  The Temporal Pulse Profile . . . . . . . . . . . . . . .  15  2.1.3  Laser Mode Coherence  16  . . . . . . . . . . . . . . . . .  v  Table of Contents 2.2  2.3  Expected Return Models  . . . . . . . . . . . . . . . . . . . .  17  2.2.1  Excitation Efficiency  . . . . . . . . . . . . . . . . . .  17  2.2.2  Beam Profile . . . . . . . . . . . . . . . . . . . . . . .  18  Sodium Return Analysis  . . . . . . . . . . . . . . . . . . . .  19  2.3.1  Saturation and Power Spectral Broadening . . . . . .  20  2.3.2  Variation in Beam Diameter  22  . . . . . . . . . . . . . .  3 Design and Operations for On-Sky Experiments  . . . . . .  23  3.1  New Laser Laboratory . . . . . . . . . . . . . . . . . . . . . .  23  3.2  Auxiliary Telescope  28  3.2.1  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  29  Auxiliary Telescope Operations . . . . . . . . . . . . . . . . .  31  3.3.1  Astro System Austria Mount . . . . . . . . . . . . . .  31  3.3.2  SBIG Camera  . . . . . . . . . . . . . . . . . . . . . .  32  3.3.3  Focuser . . . . . . . . . . . . . . . . . . . . . . . . . .  32  4 Power Calibration and Spectral Format Experiments . . .  36  3.3  4.1  4.2  4.3  4.4  Time-Average Pulse Profiles  5.2  . . . . . . . . . . . . . . . . . .  38  4.1.1  Alignment  . . . . . . . . . . . . . . . . . . . . . . . .  39  4.1.2  Data Acquisition . . . . . . . . . . . . . . . . . . . . .  42  Time-Resolved Pulse Profiles . . . . . . . . . . . . . . . . . .  43  4.2.1  Equipment Details and Layout . . . . . . . . . . . . .  43  4.2.2  Data Acquisition . . . . . . . . . . . . . . . . . . . . .  44  Power Meter Calibration  . . . . . . . . . . . . . . . . . . . .  45  4.3.1  Power Meters  . . . . . . . . . . . . . . . . . . . . . .  45  4.3.2  UBC - Power Meter Calibration . . . . . . . . . . . .  45  Focusing and De-focusing Sodium Spot  . . . . . . . . . . . .  46  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  48  Laser Spectral Format . . . . . . . . . . . . . . . . . . . . . .  48  5.1.1  Measured Temporal Pulse Profile  . . . . . . . . . . .  48  5.1.2  Time-Averaged Pulse Profile . . . . . . . . . . . . . .  51  Photon Flux Return Values . . . . . . . . . . . . . . . . . . .  53  5.2.1  55  5 Results 5.1  Auxiliary Telescope Optics and Alignment  The Effect of Varying the Laser Power  . . . . . . . .  vi  Table of Contents 5.2.2 5.3  . . . . . . . . . . . . . . . .  58  Power Meter Calibrations . . . . . . . . . . . . . . . . . . . .  58  6 Discussion  De-Focusing Experiment  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  62  6.1  Photon Return and Spectral Format . . . . . . . . . . . . . .  62  6.2  Further Sodium Spot Analysis  63  6.3  Future Return Flux Observational Techniques  . . . . . . . .  64  6.4  Immediate and Future Activities . . . . . . . . . . . . . . . .  65  Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  66  . . . . . . . . . . . . . . . . .  Appendices A Technical Drawings for the New Laser Laboratory. . .  . .  70  A.1 Main Laboratory Drawings . . . . . . . . . . . . . . . . . . .  70  A.2 Auxiliary Telescope Drawings  . . . . . . . . . . . . . . . . .  76  B Data Acquisition and Reference Stars . . . . . . . . . . . . .  80  B.1 LGS Observation Procedure  . . . . . . . . . . . . . . . . . .  B.2 AT - LGS Power Measurments Observation Log C Saturation Analysis Expanded  80  . . . . . . .  85  . . . . . . . . . . . . . . . . .  87  vii  List of Tables 1.1  Laser specifications for both the TIPC and University of British Columbia (UBC) pulse lasers. . . . . . . . . . . . . . . . . . .  3.1  Manufactures specifications for associated equipment on the Auxiliary Telescope. . . . . . . . . . . . . . . . . . . . . . . .  4.1  8  35  Properties of the scanning Fabry-Pérot interferometer (FPI) and the controller. . . . . . . . . . . . . . . . . . . . . . . . .  39  B.1 List of calibration stars used for the power measurements return flux experiment. . . . . . . . . . . . . . . . . . . . . . . .  82  B.2 Observation log of the power measurements taken during the return flux experiment. . . . . . . . . . . . . . . . . . . . . . .  83  viii  List of Figures 1.1  Sodium density profile, with the sodium mean altitude indicated by the white line . . . . . . . . . . . . . . . . . . . . . .  3  1.2  Sodium D2 hyperfine structure diagram. . . . . . . . . . . . .  5  2.1  Predicted normalized beam energy spectrum for the UBC lidar laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2.2  Predicted specific luminosity, in photons per atoms per area, of LGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2.3  20  Excitation probability, P (ν), versus frequency with expected normalized spectral power for the transmitted beam. . . . . .  2.4  14  21  Specific sodium luminosity for a range of beam diameters expected from the UBC lidar laser with a 5 W average power. .  22  3.1  Site layout of the Large Zenith Telescope (LZT) observatory.  24  3.2  The new laser laboratory exterior view. . . . . . . . . . . . .  25  3.3  New laser laboratory mosaic of the interior rooms and equipment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  27  3.4  Mosaic of Auxiliary Telescope (AT) enclosure configurations.  29  3.5  Digital image of optical tube assembly (OTA) alignment. . .  30  3.6  Quantum efficiency of the charge-coupled device (CCD) chip used in the Santa Barbara Instrument Group (SBIG) camera.  33  3.7  Transmission curve for photometric filters B,V,R and Clear. .  34  4.1  Expansion to the LZT optical table to accommodate the new measuring devices. . . . . . . . . . . . . . . . . . . . . . . . .  38  ix  List of Figures 4.2  Spectral characteristics of the Red laser used to align the Fabry-Pérot interferometer. . . . . . . . . . . . . . . . . . . .  4.3  The laboratory setup for the long term average spectral experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4.4  41 42  Digitization of the responsivity curve for the high speed photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  44  5.1  Readout of the digital oscilloscope for a single pulse profile. .  49  5.2  The autocorrelation function for an individual laser pulse. . .  50  5.3  Averaged power spectrum of 8192 individual pulse profiles. .  51  5.4  A series of 10 full FPI scans. . . . . . . . . . . . . . . . . . .  52  5.5  Time-averaged spectral profile from 2000 scans, shifted horizontally to align the peaks. . . . . . . . . . . . . . . . . . . .  5.6  Image and intensity profile of one of the standard stars imaged with the AT. . . . . . . . . . . . . . . . . . . . . . . . . . . .  5.7  53 54  The V-band magnitude residuals for 11 calibration stars are plotted with respect to air mass. . . . . . . . . . . . . . . . .  54  5.8  An example observered sodium spot . . . . . . . . . . . . . .  55  5.9  A screen shot of the matlab GUI written by Dr. Otarola to compute the expected photon flux detected by the AT. . . . .  56  5.10 The observed LGS return flux for various laser power settings with two fits. . . . . . . . . . . . . . . . . . . . . . . . . . . .  57  5.11 Images of three LGS spots created with three different relative focal positions: before, near and after. . . . . . . . . . . . . .  58  5.12 The top graph is the zeroed UBC-PM, an averaged UBC-PM value, and the scaled NPM readings overplotted. . . . . . . .  60  5.13 Calibration curve to determine the relationship between the UBC-PM and the NPM. . . . . . . . . . . . . . . . . . . . . .  61  A.1 New laser laboratory main plan, which includes an overhead view with dimensions, key features, and a profile of the subsoil and bedrock. . . . . . . . . . . . . . . . . . . . . . . . . . . .  71  x  List of Figures A.2 new laser laboratory (NLL) South-East facing elevation drawing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  72  A.3 Overall section schematic drawing of the NLL. . . . . . . . .  73  A.4 Overhead view of the framing plan for the NLL building. . .  74  A.5 The collar tie and gusset plate location on each truss, which includes type and location of fasteners. . . . . . . . . . . . . .  75  A.6 One half-section of the main framework for the AT structure.  77  A.7 Auxiliary telescope stationary pier. . . . . . . . . . . . . . . .  78  A.8 Auxiliary Telescope counterweight design by Martin O’Keane. 79  xi  List of Abbreviations AO adaptive optics AT Auxiliary Telescope ASA Astro System Austria APD avalanche photodiode CCD charge-coupled device cw continuous wave laser DEC declination D2 sodium fine structure transition 32 S1/2 → 32 P3/2 E-ELT European Extremely Large Telescope ESO European Southern Observatory FWHM full width at half maximum FSR free spectral range FPI Fabry-Pérot interferometer FOV field of view GUI graphics unit interface HEPA high-efficiency particulate air HSPD high-speed photodetector xii  List of Abbreviations LZT Large Zenith Telescope LGS laser guide star lidar light detection and ranging MCAO multi-conjugate adaptive optics NI National Instrument NGS natural guide star NPM Newport power meter NLL new laser laboratory OD optical density OTA optical tube assembly PID proportional-integral-derivative PDE photo-detected electrons RA right ascension RDP Remote Desktop Protocol RC Ritchey-Chrétien SNR signal-to-noise ratio SBIG Santa Barbara Instrument Group TT tip-tilt TMT Thirty Meter Telescope TIPC Technical Institute of Physics and Chemistry of the Chinese Academy of Sciences UBC-PM UBC power meter WFOS Wide-Field Optical Spectrometer  xiii  Acknowledgements First of all, I would like to thank my supervisor Dr. Paul Hickson for his trust and guidance on the many projects that I’ve worked on. Over the past four years working with you, there has not been a question that you were not able to answer or point me towards the solution. You have provided me with many unique challenges and projects, included the one described herein. It is your work ethic and dedication to astronomy that I will always look up to and strive for. I would like to thank Dr. Thomas Pfrommer for the many fruitful late night discussions and all the hours spent training me to eventually take over as an operator at the LZT. I also want to thank Dr. Angel Otarola. It was a pleasure working beside him and sharing my knowledge of the LZT. Thank you for all the time spent discussing the various aspects of the experiments, working through the laser characterization tests, and keeping things on track. I would like to thank Dr. Jon Nakane and Bernhard Zender for the many helpful discussions and for providing the numerous willing engineering students who helped out along the way. I would like to thank the many Engineering Physics students and the Astronomy undergraduate and graduate students who helped out with various parts of the project, especially in the construction process of both the auxiliary telescope and the new laser laboratory. In particular the help of Masen Lamb who spent a summer working with us building the new laser lab and observing. Also, I would like to thank Suzanne Tremblay for always providing Ronald-friendly snacks through the many work days and observation nights. She also kindly donated a few late nights to help out as an aircraft spotter xiv  Acknowledgements which made the most recent observations possible. I am very grateful for support of my parents, they instilled in me the desire to perpetually question how things work and why. Finally, I am eternally grateful for the love and support from my wife Jennifer. Her continual encouragement and support has allowed me to continue to pursue my goals.  xv  In memory of: Papa, Grandpa Vic, and Auntie Helen.  xvi  Chapter 1  Introduction Astronomy has always pushed the limits of humanity’s understanding of the Universe. To try and solve both the big picture questions and the basic fundamental questions, we have striven to explore objects and events beyond Earth. The invention of the telescope allowed us to look further and deeper, and as telescopes grow in size and complexity, they are continually inspiring human ingenuity and evolution in both thought and technology. Currently, the next major phase in the evolution of optical astronomy is the initiative for constructing 30+ m ground based telescopes. These large-size apertures may seem ambitious, but it is the desire to achieve diffraction-limited capabilities that is truly inspirational. The Thirty Meter Telescope (TMT) and European Extremely Large Telescope (E-ELT) projects are considered high priority on a global scale and are motivated by the scientific potential that the sensitivity of such systems could bring to Astronomy. Both projects are being conceived and designed as adaptive telescopes that will require adaptive optics (AO) and laser guide star (LGS) in most of their scientific operations. Initially, TMT will be conducting seeing limited observations with Wide-Field Optical Spectrometer (WFOS). In order to maximize the performance of these large telescopes, they must compensate for atmospheric distortions. With an optimally performing AO system on a large telescope, the advantage gained is D4 , where not only you have D2 for the light gathering area but another D2 for the simultaneous decrease in background noise contamination. Thus, to achieve the same signal-to-noise ratio (SNR) in a 10 hr exposure with an 8 m class telescope, the time can be reduced to a 3 min exposure for a 30 m telescope like TMT using AO. The use of AO requires a reference light source, either natural or ar1  Chapter 1. Introduction tificial, in order to measure the effect of the atmosphere on the wavefront from the science object. It is often the case that there is not a sufficiently bright natural star near the target to provide enough information to determine a proper correction. The critical separation angle is called the isoplanatic angle and it is the angle of which the wavefront phase variations are less than one radian. When there are no suitable natural stars, a laser can be used to create an artificial beacon. There are two types of LGS; Rayleigh-backscattered light from air molecules in the lower atmosphere [2], and resonance fluorescence of sodium atoms in the mesosphere (between ∼80 − 120 km) with a laser operating at 598 nm [12]. To help determine atmospheric distortions during observations, the next generation telescopes are planning on implementing sodium LGS systems from first light. For TMT, the LGS facility will hold a laser launch telescope behind the secondary mirror, projecting a desired asterism which contains 6 sources, one LGS on axis and the five others equally spaced on a circle of 35 arcsec angular diameter [3]. By incorporating both a natural guide star (NGS) and LGS into a multi-conjugate adaptive optics (MCAO) system, the area of diffraction-limited corrections increases from tens of arcseconds to 1-2 arcminutes [27]. One method to quantify the quality of an image is to determine the Strehl ratio, which is defined as the ratio of the central intensity with the aberration to the central intensity in the absence of aberration [25]. Strehl ratios range between 0 and 1, with 1 being a perfect system and Strehl proposed that a value above 0.8 is effectively diffraction-limited. In order to provide the desired high Strehl ratios, from the infrared to visible wavelengths, the AO system will need to operate at near-kHz frame rates using sensing subaperture sizes ranging from 20-50 cm. This requires unprecedented sodium LGS brightness [9]. Up to this point, the main means of assessing and optimizing the performance of any given type of sodium laser was through numerical simulations. The reasons for the simulations are the lack of standardized on-sky measurements, the small number of stable high power lasers operating at 589 nm, and until recently, the lack of data on the evolution and high frequency variation in the sodium layer [18, 19]. 2  Chapter 1. Introduction  Figure 1.1: Sodium column density profile, with the sodium mean altitude indicated by the white line. This 4.2 hour profile was taken by the UBC lidar system at the LZT.  With the deployment of the high-resolution sodium light detection and ranging (lidar) experiment at the University of British Columbia (UBC) Large Zenith Telescope (LZT) in Canada [7, 16], both AO simulations and the sodium laser efficiency simulations [10, 17] have evolved to incorporate the high resolution column density profiles like the one seen in figure 1.1. For the laser return flux simulations, there are two main methods used to examine the complicated interaction between the laser light and the mesospheric sodium layer; the rate equations for fluorescence of atomic sodium [8, 20], or more frequently-used Bloch equations [9, 21, 22]. Although the use of the UBC lidar data in simulations are helping to improve laser performance, there are still discrepancies between on-sky laser guide star return flux measurements and numerical simulations predictions [21]. It is for this reason that the next phase in the UBC lidar project was to develop and expand the existing facilities at the LZT to accommodate a protype sodium laser, such as the Technical Institute of Physics and Chemistry of the Chinese Academy of Sciences (TIPC) sodium laser, for full characterization and optimization assessment with the goal of maximiz3  1.1. Properties of Atomic Sodium ing the measured return flux and bridging the gap between simulations and observation. The key factor for choosing the LZT as the site for laser characterization tests is the ability to accurately measure both the sodium column density and the sodium return flux produced by the LGS simultaneously. Before expanding upon the on-sky and laboratory laser characterization assessments available at the LZT, a brief description outlining the relevant properties of atomic sodium is followed by a section which describes environmental and observation processes that affect observed LGS brightness.  1.1  Properties of Atomic Sodium  The following section describes the basic properties of atomic sodium that apply to sodium LGSs. Much of the information from this section can be found in Ungar et al. [26] and the recent document compiled by Steck [24] on alkali lidar research. Sodium’s only stable isotope is and a mass of 0.38175403 × 32 S1/2  →  32 P  3/2  23 Na. 23 Na  10−25 kg.  has a nuclear spin of I = 3/2  The sodium fine structure transition  (D2 ) is the dipole transition that is utilized in creating  sodium LGSs. The transition wavelength is approximated as the wavelength observed in a vacuum (589.158 nm) since the pressure and temperature in the sodium region are approximately 1 Pa and 190 K. The sodium D2 ground state, 2 S, has two hyperfine multiplets F = 1 and F = 2, which consists of 8 magnetic substates, separated by 1.772 GHz, with F being the total atomic angular momentum quantum number. The excited state, 2 P , consists of 4 hyperfine multiplets F 0 = 0 . . . 3, that consists of 16 magnetic substates, separated by 15.8, 34.3, and 58.3 MHz, respectively. Figure 1.2 displays the D2 fine and hyperfine structure with frequency splitting. The two possible ground state multiplets allow distinct D2a and D2b absorption lines, which are Doppler broadened by about 1 GHz in the mesosphere. This Doppler broadening creates a characteristic double-hump absorption profile which can be seen in Dr. Pfrommer’s [16] thesis, figure 4.5 (which also shows the UBC sodium laser line profile). 4  1.2. Factors Affecting the Return Flux  Figure 1.2: Sodium D2 hyperfine structure diagram. Parts of this diagram are inspired from Figure 1 in Moussaoui et al. [13].  1.2  Factors Affecting the Return Flux  By decreasing the sub-aperture sizes of the wavefront sensors with the desire to integrate over shorter time intervals, such as 1.25 ms, the number of photo-detected electrons (PDE) from the artificial beacons becomes im5  1.2. Factors Affecting the Return Flux portant. TMT is currently using an error budget of 900 PDE when the laser is pointed at the zenith and includes a safety buffer of a factor of 2 to account for on-sky rms wavefront errors that will occur depending on the observation conditions [22]. We now give a brief overview of environmental factors, properties of the various lasers, and observation conditions relevant to the effective sodium return flux from a sodium beacon.  1.2.1  Environmental Properties  First let us examine some environmental mechanisms and their respective timescales that require considerations when developing a sodium laser efficient at coupling with the mesospheric sodium. Many sodium lasers utilize circularly polarized light because it produces atomic polarization parallel to the light propagation direction. With on-sky systems, the relative direction of the laser beam with respect to the local geomagnetic field is important, as Larmor precession can counteract the atomic polarization. There are two important factors when considering the timescale and strength of this effect: 1) location and 2) the angle away from zenith, where the larger the angle, the more prominent the effect. At the LZT the local magnetic field strength is 0.525 G and the timescale at which this effect occurs at zenith is ∼2.7 µs [22]. Another important effect is collisions between Na and constituent gases like O2 and N2 . For example, the time between spin-randomized collisions with O2 have a timescale that ranges from 200-5000 µs depending on O2 concentrations. Yet sodium collisions with O2 and N2 molecules also help to reequilibrate the atomic velocity distortion by filling holes left from recoil in typically 300 µs [22]. Here, recoil is a momentum kick imparted on the atom from the photon-atom interaction and atoms are driven away from thermal equilibrium by high irradiance. Since the presence of mesospheric sodium allows us to create LGSs, understanding the process within the layer is critical to maximizing the return values for sodium beacons. As seen in figure 1.1, the evolution and abundance can be highly sporadic, with changes occurring on almost all  6  1.2. Factors Affecting the Return Flux timescales, from annual to microseconds [18]. This is why obtaining accurate sodium column densities simultaneous with sodium spot measurements is essential to determining precise return flux values. Other factors such as temperature, spontaneous decay to the ground state F = 1, and atmospheric absorption must also be considered when examining the sodium stimulation process.  1.2.2  Laser Format and Propagation Parameters  Considering now the laser design and optimization techniques, the laser is the tool that stimulates the mesospheric sodium atoms and directly affects the PDE count. There are two prominent laser types; pulsed lasers and continuous wave laser (cw) lasers. For the purpose of this document, only pulsed lasers will be discused as both the LZT lidar laser and the TIPC prototype laser are pulsed sodium lasers. Table 1.1 contains a list of laser parameters that play a role in overall PDE counts. Some parameters, such as the number of modes, mode spacing, and pulse length are expected values, to be confirmed by tests. One of the key parameters that LGS lasers can utilize is polarization. For a sodium atom that is subjected to a left-circularly polarized light resonant with the D2a transition, F = 2 → F 0 , there is a tendency to transfer the atoms to the |F = 2, m = 2i ground state through induced optical pumping. The transition from |F = 2, m = 2i → |F 0 = 3, m = 3i is the strongest of the transitions, which increases the effective absorption cross section. This also reduces spontaneous decay to the F = 1 ground state, where there is no interaction with laser photons, since atoms that are excited in the cycling transition do not spontaneously decay to the F = 1 ground state. Finally, when the |F 0 = 3, m = 3i transition fluorescences, the light is preferentially directed parallel to the source, leading to an increase in photon flux observed at the location of the light source [22]. Other parameters that must be confirmed for modelling purposes or monitored during LGS are: transmitted power, laser temperature (to moni-  7  1.2. Factors Affecting the Return Flux  Table 1.1: Laser specifications for both the TIPC and UBC pulse lasers. Here the TIPC on-sky laser power is the proposed value for one laser guide star at Mauna Kea site. Average laser power Pulse length Polarization Repetition rate Number of modes Mode spacing  LZT 5W 7 ns linear 50 Hz 5 450 MHz  TIPC 12 W 120 µs circular 800 MHz 3 150 MHz  tor stability), efficiency of optical repumping from D2a a to D2b , propagation method of laser light from laser to launch telescope and efficiency, peak wavelength, and finally, the spectral format. For the spectral format, it is useful to know the spectrum of both an individual pulse as well as an average pulse profile for many pulses. Considerations must also be made for saturation effects of the sodium layer due to the high instantaneous energy density from pulsed lasers. Saturation occurs when the fraction of sodium atoms excited to the upper state of the transition approaches 1/2, the maximum possible value. The reduction in the number of ground-state atoms leads to an increase in the number of laser photons that pass through the mesosphere without interacting. Two mechanisms that affect saturation are: 1. Sodium spot size - adjusting the sodium spot size requires optimizing the laser focus. To optimize the spot size a balance must be reached between reducing the beam divergence angle and saturation. 2. Optical repumping - optical repumping reduces saturation by stimulating the D2b transition and exploiting both D2 fine line transition groups.  Thus a sodium laser that produces both circular polarized and has a small 8  1.3. LZT Laser Characterization Tests percentage of “repumped” D2b light would be ideal for a LGS system [9, 22], but on-sky tests are required to confirm the models.  1.3  LZT Laser Characterization Tests  The original design for the TMT LGS facility called for cw lasers. Subsequently, TMT is exploring the option of using a Nd:YAG pulsed laser that is currently being developed by scientists at TIPC. In order to address concerns of the laser’s coupling efficiency to the mesospheric sodium and to assess whether the TIPC pulsed laser is a suitable replacement, TMT and UBC are collaborating to create a facility that will examine current and future sodium lasers to address on-sky LGS issues. There are three motivating factors that lead to the development of a new laser testing facility at the LZT, operated by UBC: • Access to a 6 m telescope dedicated to high resolution sodium lidar measurements. The LZT will provide accurate sodium column-density measurements, which are critical to characterizing the efficiency of a sodium laser. • This allows for a collaboration between two partners of TMT; Canada and China. • A dedicated laser characterization facility could serve other projects, such as European Southern Observatory (ESO)’s E-ELT. Not only will this aid in standardizing testing practices and techniques but it would also allow for various laser types to be examined with the end goal of further improvement of models. The new expansion implements all three parts and is discussed in more detail within this document. First is the construction of a new laser laboratory that is capable of housing visiting lasers. Second is the implementation of a 304.8 mm auxiliary telescope that will be used to directly image the sodium spot. This secondary telescope is required as the LZT is designed for lidar observations with no means of calibrating and converting the observed 9  1.3. LZT Laser Characterization Tests flux to a standardized photometric system, such as the Johnson-Morgan bands. Finally, experiments were conducted using the LZT lidar laser to identify the the laser’s critical parameters. The key parameters that are in question are: pulse length, pulse repetition rate, polarization, amount of optical repumping, sodium spot size and optimization, laser spectral format, laser power, mode structure, and coherence characteristics of the laser. Measuring all these parameters leads to a fully characterized laser with values that can be implemented in models such as Rochester et al. [22], which can be compared with on-sky observations. The original goal of field testing the TIPC laser during the summer of 2012 was delayed due to development issues with the TIPC laser. Instead, field tests were conducted using the LZT laser in order to develop and test the needed techniques. The main goals of the demonstration were to commission the auxiliary telescope and conduct the same experiments that were to be done on the TIPC laser but with the LZT laser. In addition to the determination of key laser parameters, the aim is to obtain optimal performance for LGS. Due to the short pulse length of the LZT laser, characterization tests are generally more challenging than for other sodium lasers currently being used. Also, UBC tests will be widely beneficial as the methods learned can be modified and applied to any laser that has a comparable, or longer, pulse length.  10  Chapter 2  LZT Laser Modelling and Expected Sodium Return To help anchor the simulations to the experiments, it is first important to review some of the theory and models developed to determine the expected return flux from the UBC lidar laser. With the delayed delivery of the TIPC laser, it was deemed worthwhile to examine the properties of the short pulsed UBC laser and demonstrate the readiness of the site for future sodium laser characterization and testing. The following chapter is divided into two sections: 1. Models of the spectral format for the LZT laser are examined. This is critical as these parameters need to be determined before any assessments of the return flux can be made. 2. An outline of the predicted return flux model is reviewed. Much of the chapter is based on two documents written by Dr. Hickson Hickson [4, 5] or taken from private conversations and discussions.  2.1  LZT Laser Characteristics  Dr. Hickson developed the mathematical relations to describe the spectral properties of the UBC laser as there are no standardized techniques or methods to measure the return flux or ways of determining various spectral properties of sodium lasers, especially a laser with such a short pulse length (∼7 ns). With this analysis further experiments were developed to determine the physical parameters of the laser. The parameters include the laser spectral format, the mode coherence, and the temporal pulse profile. 11  2.1. LZT Laser Characteristics  2.1.1  Laser Spectral Format  The UBC lidar laser system employs a Nd:YAG-pumped dye laser, which generates a ∼7 ns long pulse of radiation at λD = 589 nm with a repetition rate of 50 Hz. Within a laser cavity, more than one resonant mode can be excited, with each mode resulting in a different frequency, due to the different number of wavelengths within the cavity. The frequency difference between adjacent modes is ∆ν =  c , 2d  (2.1)  where d is the cavity length. The amplitude of the modes peaks at the design frequency of the resonator and decreases for frequencies that are further from the design frequency. Within a cavity, the radiation is a superposition of nodes, resulting in the amplitude of the electric vector having the form E(t) = f (t) Re  X  An exp(2πiνn t)  n  1X [An exp(2πiνn t) + A∗n exp(−2πiνn t)]. = f (t) 2 n  (2.2)  Where f (t) describes the time evolution of the laser excitation and is a dimensionless real function, and An describes the phase and the amplitude of the mode that has frequency νn . The form of equation 2.2 also describes the radiation within the laser pulse since this radiation is proportional to the fraction of radiation within the cavity that exits through the partially reflecting mirror at one end of the cavity. The Fourier transform of the electric field is proportional to the ampli-  12  2.1. LZT Laser Characteristics tude spectrum of the radiation, Z  ∞  E(t) exp(−2πiνt)dt  E(ν) = −∞  = f (ν) ∗  1X [An δ(ν − νn ) + A∗n δ(ν + νn )] 2 n  (2.3)  where ∗ denotes convolution and f (ν) is the Fourier transform of f (t). The squared modulus of this will be proportional to the spectral power, P (J/m2 /Hz), P (ν) ∝ E(ν)E ∗ (ν) 1X = [Am A∗n f (ν − νm )f (ν − νn ) + A∗m An f (ν + νm )f (ν + νn ) 4 m,n + A∗m A∗n f (ν + νm )f (ν − νn ) + Am An f (ν − νm )f (ν + νn )].  (2.4)  The amplitude spectrum of an individual mode is f (ν) and can be seen from eqn. 2.3. If we assume that the width of a mode is much smaller than the separation between modes, this equation can be reduced to P(ν) =  1X In [f 2 (ν − νn ) + f 2 (ν − νm )] 4 n  (2.5)  with In = An A∗n . To derive a model of the power spectrum, a few key parameters of the UBC laser are needed. These are: • The pulse energy of the laser is ∼0.1 J since the average power is 5 W. • The overall envelope of the energy in the transmitted modes is roughly Gaussian, with a full width at half maximum (FWHM) of about 1.2 GHz. • The laser supports several coherent modes, by means of a tunable cavity, with a frequency separation of approximately 450 MHz. Assuming that the pulses are Gaussian with a FWHM of ∆t = 7 ns, the 13  2.1. LZT Laser Characteristics spectrum will also be Gaussian with a FWHM of  ν0 =  2 ln 2 π∆t  (2.6)  with ν0 = 63 MHz. The model prediction for the specific energy of the transmitted radiation is then  ∞ X  Wν (ν) = Wν (0) exp[−4 ln 2(ν/ν2 )2 ]  exp[−4 ln 2(ν − jν1 )2 /ν02 ] (2.7)  j=−∞  where ν1 = 450 MHz and ν2 = 1200 MHz. The positive frequencies of the function Wν (ν) is shown in figure 2.1.  Figure 2.1: Predicted normalized beam energy spectrum for the UBC lidar laser. The power distribution is centred on the maximum emission. (Plot from Hickson [4]).  14  2.1. LZT Laser Characteristics The total energy per pulse, is obtained by integrating over all frequencies, Z  ∞  Wν (ν)dν  W = −∞  √ ∞ Wν (0)ν0 ν2 π X = p exp[−4 ln 2ν12 j 2 /(ν02 + ν22 )] 2 2 2 ln 2(ν0 + ν2 ) j=−∞  (2.8)  = 1.863 × 108 Wν (0). With a pulse energy of W = 0.1 J, we obtain Wν (0) = 5.367 × 10−10 JHz−1 .  2.1.2  (2.9)  The Temporal Pulse Profile  To examine the temporal pulse profile of the laser, one can digitize the signal from a high-speed sensor. The signal recorded by the sensor will be a time-averaged power value. With a response time that is much longer than 1/ν but less than 1/∆ν, the high-frequency oscillations of the field will not be present, yet any interference between modes will cause beat frequencies to appear in the signal. Thus, the profile of a single recorded pulse will be the mean of the square of equation 2.2; g(t) = hE(t)2 i (2.10) X 1 = f 2 (t) {Am A∗n exp[2πi(νm − νn )t] + A∗m An exp[−2πi(νm − νn )t]}. 4 m,n This is a sum of cosine functions having a range of amplitudes, frequencies, phases, and also includes a constant added from the diagonal terms. Taking the Fourier transform of this profile produces g(ν) = f (ν) ∗ f (ν) ∗  1X Am A∗n δ[ν − (νm − νn )]. 2 m,n  (2.11)  15  2.1. LZT Laser Characteristics The frequency given is the frequency difference between the two modes, and for every pair of modes, the function has a peak. Note that this profile is simply the convolution of the amplitude spectrum, equation 2.3, with itself as per the Fourier convolution theorem. By taking the squared modulus of g(ν), in equation 2.11, the product will be a series of peaks of which maximum values are proportional to Im In . If there are N modes in the laser radiation, there will be 2N − 1 peaks in |g(ν)|2 , corresponding to m − n = −N, ..., N . Therefore equation 2.11 can be rewritten as 2  |g(ν)| ∝  N X  Bp δ[ν − νp ]  (2.12)  p=−N  where B−N = I12 B−N +1 = 2I1 I2 B−N +2 = 2I1 I3 + I22  (2.13)  B−N +3 = 2I1 I4 + 2I2 I4 .. . 2 BN = IN .  Solving this set of equations will lead to the intensities of the modes in the Fourier transform of the observed pulse profile.  2.1.3  Laser Mode Coherence  One assumption made in the previous analysis is that the coefficients An are time independent, thus every pulse will produce the same interference pattern as all modes will be excited in the same way. Another scenario that would produce a similar power spectrum is the opposite extreme, where only one mode is excited per pulse, but different modes are excited from pulse to pulse. The difference would be seen in the pulse profiles, as there would be 16  2.2. Expected Return Models no interference patterns produced and taking the Fourier transform would produce a curve with a single peak (Eqn. 2.11). In reality the laser most likely operates in an intermediary state with several modes being excited per pulse and the amplitude and phases of each of these modes varies from pulse to pulse. By taking the long-term average of the Am A∗n , from equation 2.11, one can characterize the degree of coherence. Defining the complex degree of coherence between modes m and n by  Γmn =  hAm A∗n i hIm i1/2 hIn i1/2  (2.14)  The modulus of Γmn describes the degree of coherence between the two modes and will fall within [0, 1]. The right hand side is the product of the power corresponding mode intensities in the power spectrum (Eqn. 2.5). The two extremes are of complete coherence we obtain |Γmn | = 1, or if the modes are completely incoherent, |Γmn | = δmn .  2.2  Expected Return Models  The following section outlines the interplay between the sodium laser and the sodium atoms which will determine the final expected return flux (ie coupling efficiency of the laser to the sodium atoms).  2.2.1  Excitation Efficiency  To begin, we will first use the assumption that non-equilibrium effects such as Larmor precession, radiation pressure, and down conversion are unimportant as the collision rate of the mesosphere is much higher then the pulse repetition rate of the UBC lidar laser. The justification is that there should be sufficient time between pulses to allow the atomic population to equilibrate. Now consider a single sodium atom, with line-of-sight velocity υ. For low laser power, the probability that an atom in the ground state will be excited 17  2.2. Expected Return Models by radiation at frequency ν = υ/c is proportional to the incident specific energy surface density Φν (ν) (J m−2 Hz−1 ). The proportionality constant, denoted by α, will depend on polarization, but is independent of frequency. The differential probability of exciting an atom is therefore dP (ν) = [1 − P (ν)]αdΦν (ν). Integrating both sides produces the excitation probability for any energy density, P (ν) = 1 − exp[−αΦν (ν)].  (2.15)  Using the results from Holzlöhner et al. [11], they find that the specific return flux ψ expected from a low-power linearly polarized cw laser tuned to the peak of the sodium D2a line to be ψ ≈ 230 photons/s/sr/atom/(W/m2 ).  (2.16)  These results can be found in the middle plot of figure 3 from their paper. From this, a value for the coefficient α can be obtained. If we consider one second of illumination and assume isotropic emission, ψ ≈ 2890 photons/atom/(J/m2 ). Integrating over the line profile of the atomic transition converts this to a rate per specific energy surface density, which we take to be Lorentzian with a FWHM of 9.8 MHz (Holzlöhner et al. 2010). This produces an equivalent width of (π/2) FWHM = 15.4 MHz and we conclude that α = 4.45 × 1010 J−1 m2 Hz.  2.2.2  (2.17)  Beam Profile  The resonant cavity of the dye laser reflects the complex power pattern of the UBC lidar beam, which uses a diffraction grating to set the frequency. Although, both atmospheric turbulence and diffraction contribute in reducing fluctuations. To determine the specific energy surface density of the beam, we will assume that the beam has a circularly-symmetric Gaussian irradiance pro-  18  2.3. Sodium Return Analysis file, with FWHM r1 , at mean sodium altitude of 92 km. With an observed angular FWHM of the beam to be approximately 3.5 arcsec, and after correcting for downlink seeing, the r1 is approximately ∼1.5 m. Therefore, the specific energy surface density of the beam is Φν (ν, r) =  4 ln 2 Wν (ν) exp[−4 ln 2(r/r1 )2 ] πr12  = 0.392 Wν (ν) exp(−0.125r2 ).  2.3  (2.18)  Sodium Return Analysis  This next stage is determining an estimate for the photon return flux produced by excitation of the sodium layer. The first step is to integrate the product of the excitation probability and the sodium frequency (velocity) distribution φυ over frequency and beam area. Next is to obtain the total luminosity, L (photons/pulse), by multiplying the product of the integral by the sodium column density ND , Z  ∞  L = 2πND  Z  ∞  Z  0 ∞  dν Z  −∞ ∞  = 2πND  rdrφυ (ν)P (ν, r) rdrφυ (ν){1 − exp[−αΦν (ν, r)]}.  dν −∞  (2.19)  0  Using a mesospheric temperature of T = 185 K, a typical temperature observed at an altitude of 92 km [23], and taking the velocity distribution of sodium atoms to be a Maxwell-Boltzmann distribution produces 1 φυ = √ exp[−υ 2 /(2mkT )] 2πmkT s 4 ln 2 = exp[−4 ln 2(ν/ν3 )2 ] πν32  (2.20)  where m = 3.816 × 10−26 kg is the mass of a sodium atom. Thus, the  19  2.3. Sodium Return Analysis  Figure 2.2: Predicted specific luminosity, in photons per atoms per area, of LGS, given changes in the mean laser power throughput with a beam FWHM of 1.5 m. (Figure from Hickson [4]).  frequency FWHM of this distribution is p ν3 = 2 2 ln 2kT /m/λD = 1034 MHz.  (2.21)  Figure 2.2 shows the expected specific luminosity of the LGS (photons per shot per unit column density) as a function of laser power, for the beam profile of section 2.2.2. The mean beam width used was 1.5 m FWHM.  2.3.1  Saturation and Power Spectral Broadening  Now consider atoms interacting with photons at the centre of the beam, with a frequency at the peak of the energy spectrum (ν = 0). We can use the derived values for Wν (0) (2.9) and α (2.17) and Eqns. 2.15 and 2.18, the probability of excitation for atoms with a transition energies (ν = 0) will be:  20  2.3. Sodium Return Analysis  P (0) = 1 − exp[−αΦν (0)] = 1 − exp[−0.392αWν (0)]  (2.22)  = 0.99991. Which is clearly saturated, since αΦν (0) = 9.362. In plot figure 2.3, the effect on the spectrum of the excitation probability P (ν) as a function of frequency is shown. Note that due to saturation, the relative impact of the central peaks has been reduced and the effective width of the components has increased. Excitation probability vs frequency, for the centre of the beam. The beam energy spectrum (normalized to unity at the central frequency) is shown for comparison  Figure 2.3: Excitation probability, P (ν), versus frequency with expected normalized spectral power for the transmitted beam. (Figure 1.2 from Hickson [4]).  21  2.3. Sodium Return Analysis  2.3.2  Variation in Beam Diameter  To lower flux and reduce saturation, the transmitted beam can be defocussed, increasing the spot diameter at the sodium altitude. In this state, the beam profile is a disk that corresponds with the geometrical defocus convolved with the assumed Gaussian profile. For a large defocus, approximating the profile can be done well enough with the geometrical disk alone, and a uniform flux within the area can be assumed. Therefore, the luminosity will be Z  ∞  dνφυ (ν){1 − exp[−αWν (ν)/A]}  L = ND A  (2.23)  −∞  where the area A = πd2 /4 with d is the beam diameter at the sodium altitude. Figure 2.4 shows the specific sodium luminosity, at the maximum 5 W laser power, for a range of beam diameters.  Figure 2.4: Specific sodium luminosity for a range of beam diameters expected from the UBC lidar laser with a 5 W average power. (Plot by Hickson [4]).  22  Chapter 3  Design and Operations for On-Sky Experiments The following chapter addresses the new equipment and buildings that were assembled for the purpose of on-sky tests at the LZT observatory. The largest change to the observatory was the new laser laboratory (NLL) that was built to support any visiting group’s sodium laser. This new building is further described in section 3.1. Another addition was a 30 cm optical telescope, the Auxiliary Telescope (AT). This telescope was installed to perform photometric imaging in conjunction to the LZT lidar and is described in section 3.2. Building drawings and any extra information is included in Appendix A.  3.1  New Laser Laboratory  In order to facilitate on-sky tests for visiting lasers, a new laser laboratory building was constructed at the LZT observatory. As shown in figure 3.1, the location of the NLL is to the north east of the main observatory building. This location was chosen because it offered the most sky and the least amount of groundwork to prepare for building construction. Figure 3.2 shows the exterior of the new building, which has a metal cladding that matches the existing buildings as well as security gates to deter potential intruders. A custom roof hatch, 76.2 cm × 91.4 cm, was installed on the roof, to be used as a portal to allow the projection of visiting lasers on-sky at or near the zenith.  23  3.1. New Laser Laboratory  Figure 3.1: Site layout of the LZT observatory. The regions in blue are new buildings or support structures for the future laser characterization studies. All other buildings previously existed. 24  3.1. New Laser Laboratory  Figure 3.2: The new laser laboratory exterior view. The main door to the left leads to the smaller equipment room and the double door leads to the main room. The double door was installed to accommodate any large crates or equipment and can be sealed off once the equipment is installed. The metal gates provide extra security.  The dimensions of the building are 4.2 m × 6.1 m with an interior wall to divide the building into two rooms. Figure 3.3 shows the main features of the interior rooms. In the main room there is a 1 m × 1 m concrete pad that is separate from the main concrete pad and extends to bedrock. The concrete pad was constructed directly under the roof hatch to allow any visiting laser group to mount a laser launch telescope on a vibrationally-isolated concrete pad. This will reduce any beam broadening or wandering due to vibrations caused by any equipment accompanying the laser, such as the laser’s chiller. For climate and air quality control, the building has been equipped with a heat pump, dehumidifier, and air filters. The air filters are class 10,000 high-efficiency particulate air (HEPA) filter combined with fans to keep the large room under positive air pressure.  25  3.1. New Laser Laboratory To safely propagate any visiting lasers on-sky, users will be required to connect their laser safety shut off systems to the LZT laser interlock. The interlock is connected to a commercial radar used to detect approaching aircraft. The NLL is connected to the main LZT interlock and the new building contains an emergency shut off in each room, as well as a switch to arm the laser interlock system. In order to enable any laser, the radar system and both the LZT lidar interlocks and NLL interlocks need to be closed, thus in the enabled state. Once the interlock circuit has been opened, all lasers must either shutdown or shutter any projected light within 0.1 sec. The building contains the standard power supply of 60 Hz single-phase at 15 A/120 VAC and 20 A/240 VAC. In order to accommodate various power demands of visiting laser groups, the building has been equipped with a 20 KVA power converter, which provides three-phase 380 V at 50 Hz and 220 V single phase at 60 Hz. The power converter was installed in the smaller equipment room. The left image in figure 3.3 demonstrates the power converter operating a light source at three-phase, 50 Hz and 220 V.  26  3.1. New Laser Laboratory  Figure 3.3: New laser laboratory mosaic of the interior rooms and equipment. The upper image displays the position of the roof hatch with respect to the 1 m × 1 m concrete pier, the location of the laser emergency stop button and interlock connections, the heat pump, and the legs of the optical table that will be moved in when the visiting laser group confirms that the laser is in shipment. On the lower left is an image of the slightly ajar roof hatch that was installed to allow the propagation of visiting lasers on-sky. The chains are used to open and close the portal from the ground. The image on the lower right is taken in the smaller equipment room where the 20 KVA power converter was installed. A set of light bulbs were connected to the power converter to test the unit after it was installed. The lights are being run on three-phase, 50 Hz and 220 VAC. 27  3.2. Auxiliary Telescope  3.2  Auxiliary Telescope  The method that was chosen to determine the calibrated return photon flux from any LGS created at the UBC LZT observatory, is to directly image the sodium spots with an AT. The specifications for the equipment used to run the system are listed in table 3.1. The key features of the AT are a field of view (FOV) of 0.16◦ × 0.11◦ and resolution of 0.77 arcsecs/pixel. Initially, the telescope was mounted on a tripod that was to be moved in and out of the main LZT building each observing night. Due to difficulties obtaining a pointing model for the mount and the large start-up and shutdown time, it was decided that a fixed telescope location with an enclosure for protection would be a more practical arrangement. Figure 3.1 shows the location of the AT enclosure with respect to the main observatory building.  The southwest location was chosen for the  largest area of sky that would be available to the telescope. The enclosure was placed on a 2.1 m × 2.1 m × 15.24 cm-thick reinforced concrete pad. The tripod was replaced by a custom pier that was fabricated from schedule 40 aluminium pipe with an overall length of 0.762 m. The pier was positioned on the centre of the concrete pad such that the polar axis of the mount was within ±1◦ of the north celestial pole and levelled to within arcsecond precision. To level, expansion bolts were set into the concrete pad from which levelling nuts were used on each to adjust the relative height with respect to the ground. The final design for the enclosure consisted of two separate fixed aluminium segments that fold back to reveal the enclosed telescope, similar to a clam shell, as seen in figure 3.4. The 1.6 mm-thick aluminium walls with welded aluminium L-angle frames provide security, while the fixed hinges provide easy access to the telescope for quick initialization and telescope shut-down. The exterior cladding is 2.5 mm-thick aluminium sheets custom fitted and fastened with blind rivets that have a depth of 8 mm.  28  3.2. Auxiliary Telescope  Figure 3.4: Mosaic of AT enclosure configurations. On the left is the Auxiliary Telescope enclosure and on the right is an image of the enclosure open with the telescope in the ready position. A separate concrete pad was poured to stabilize the area around the enclosure. The enclosure is made of a welded aluminium L-angled frames with 2.46 mm-thick aluminium-sheet walls that were riveted to the frame.  3.2.1  Auxiliary Telescope Optics and Alignment  The optical tube assembly (OTA) used was a 30 cm f/8 Astro-Tech RitcheyChrétien (RC) design. The two hyperbolic quartz mirrors have dielectric optical coatings that produce a throughput of approximately 98%, as reported by the manufacturer. The RC design reduces spherical aberration and third-order coma. The dominant aberration is field curvature and to correct for this, a separate lens was purchased and used. Before the telescope was fully assembled on the pier, the mirrors and baffle of the OTA were aligned. Alignment was done by setting the OTA to face a flat, well-lit wall, and the mirrors and baffle were adjusted according to the Astro-Tech manual to produce a symmetrical image in the Cheshire alignment tool. Figure 3.5 is an image taken with a handheld digital camera  29  3.2. Auxiliary Telescope positioned at the output of the Cheshire alignment tool. A main feature to note is that the inner two dark rings are symmetrical. Also, the four outer secondary mirror spider vanes are evenly spaced and well aligned with the inner four spider vanes. This indicates that both the primary mirror and secondary optical axis are collimated which was confirmed by imaging stars.  Figure 3.5: Digital image of the OTA alignment. The image was taken with a handheld camera positioned at the output of the Cheshire alignment tool after alignment. Note that all light and dark circles are concentric, that the secondary mirror veins are symmetrical, and both inner circles are aligned with the outer ones. The top right is a sharp focused star demonstrating telescope collimation.  The back-focal distance from OTA is 288 mm and the optimal distance between the field flattener and imaging plane is 57±4 mm. In order to achieve these distances, appropriate spacers were used. Specifically, a  30  3.3. Auxiliary Telescope Operations 50.8 mm-thick, 100.1 mm-diameter spacer between the OTA and the focuser, and a 10 mm spacer after the field flattener.  3.3  Auxiliary Telescope Operations  This next section highlights the steps and equipment on the telescope used to obtain images of calibration stars as well as the LGS sodium spot. There are three items on the AT that are controlled through observation: the charge-coupled device (CCD), the mount, and the focuser. Communication to these devices is done through a National Instrument (NI) computer that is connected to the local network and accessed either through ssh or a virtual desktop. The NI computer was chosen because the operating system is Windows which is the only platform that the commercial programs Autoslew and CCDops are both compatible with. CCDops controls the Santa Barbara Instrument Group (SBIG) camera functions, while Autoslew software operates the Astro System Austria (ASA) mount.  3.3.1  Astro System Austria Mount  The ASA mount is a direct drive German Equatorial mount and requires proper initial installation and adjustment of the servo motors. The telescope was initially balanced by hand and final modifications were done using Autoslew’s integrated software with changes to the proportional-integralderivative (PID) and the counterweights. This is to eliminate any resonant modes that can occur within the motors which may cause large vibrations and potentially damage the telescope. Once the telescope was adequately balanced, the next stage was to create a pointing model in order to acquire and track calibration stars and return to the sodium spot. Due to the lack of documentation on the Autoslew program, the initial pointing models were only accurate for stars that were either all east of the meridian or all on the west. It was later determined that the Autoslew software required an extra set of parameters which allowed the  31  3.3. Auxiliary Telescope Operations mount to properly incorporate a meridian flip and acquire objects on either side, as well as return to the zenith at any time. The final pointing model had a pointing RMS-error in the right ascension (RA) of 0.5 arcmin and a 1.1 arcmin RMS-error in declination (DEC). At the beginning of each observation the motors were referenced by homing the telescope and then the instrument was guided by an observer outside watching the telescope’s movement, to an available star and finally synchronized.  3.3.2  SBIG Camera  The SBIG camera used is equipped with a Kodak KAF-0402ME CCD chip. An after-market 5 position filter wheel was added to the camera with the photometric filters V,B,R, and Clear. The final position was left empty. The Clear filter is used to eliminate the need to re-focus when a broad range spectral image is desired. The quantum efficiency reported by the manufacturer is shown in figure 3.6. These efficiencies were used in combination with the Baader filter function seen in figure 3.7 to calibrate the images and determine the final return flux measurements. The Clear filter was acquired to reduce the chance of any discrepancies between the reported filter functions and the actual transmission functions.  3.3.3  Focuser  The Moonlite focuser used has a drawtube with a 63.5 mm travel distance and a high resolution stepper motor for remote control capabilities. During the Summer 2012 tests, the focuser was not set up to be run remotely, thus, the stepper motor clutch was released and any changes to the AT focus were done manually.  32  3.3. Auxiliary Telescope Operations  Figure 3.6: Quantum efficiency of the CCD chip used in the SBIG camera. The data is a digitization of the quantum efficiency curve supplied by the manufacturer.  33  3.3. Auxiliary Telescope Operations  Figure 3.7: Transmission curve for photometric filters B,V,R, and Clear. The data is a digitization of the transmission curves supplied by the manufacturer.  34  3.3. Auxiliary Telescope Operations  Table 3.1: Manufactures specifications for associated equipment on the Auxiliary Telescope. Telescope Characteristics Optical Tube Assembly Model AT12RC, Ritchey-Chrétien M1 aperture 304.8 mm (1200 ) Focal length 2432 mm (∼f /8) Back focal length 288 mm Throughput 98% Central obscuration diameter 132 mm Effective detection area 58095 mm2 CCD Camera Model SBIG ST7XME (KAF0402ME CCD) Detector size 756 × 512 pixels (6.804 mm × 4.61 mm) Pixel size 9 µm × 9 µm Read noise 15 e− Shutter speed 120 ms minimum exposure Optical Filter B,V,R & Clear Focuser Model Moonlite 63.5 mm CSL Telescope mount Model ASA DDM85, German Eq. Direct Drive Load capacity 65 kg Maximum slew rate 15 deg/s Pointing accuracy Better than 5 arcsec Tracking accuracy (1 hour) 0.18 arcsec (180 mas) Software CCD control SBIG - CCDops ASA mount control Autoslew Image display DS9 Remote accessibility Windows Remote Desktop & Python Server scripts  35  Chapter 4  Power Calibration and Spectral Format Experiments In order to characterize the LZT lidar laser, additional optical elements were deployed on the optical table to provide a new beam line. Also, modifications to the original layout were required to accommodate new applications for some expanded on-sky tests described herein. Figure 4.1 shows the layout of the LZT lidar optical table. The five positions marked on the image are locations where modifications or important elements are located on the table. Any tests done by ancillary equipment are conducted with a fraction of the actual beam, as we employ a beam sampler, locate at position #4, which directs ∼1/1000 of the laser power toward any ancillary equipment. For the on-sky tests there are two main modifications to the optical table. Specifically, a new laser power meter was installed to monitor the laser power during observation and a linear actuator that allows an observer to vary the sodium spot size. Position #1 is the location of a neutral density filter with optical density 2 followed by a new retractable mirror. This mirror allows the operator to readily switch between on-sky tests or to conduct a series of laser characterization experiments. In normal lidar operations the mirror is folded out of the beam path so that laser power can be measured with a UBC manufactured power meter located at position #2. The UBC power meter is further described in section 4.3. Also important for regular night time observations is the new linear motor that was installed at position #5. This motor allows an operator to control the sodium spot size during observations. A detailed outline of this experiment can be found in section 4.4.  36  Chapter 4. Power Calibration and Spectral Format Experiments There were two main laser characterization tests conducted; the first obtained a long term average spectrum and the second determined the time resolved profiles. For the first experiment, the goal was to determine the average mode intensities In , from equation 2.5. The second experiment measured g(t) (equation 2.10) of many individual laser pulses, from which one can determine the degree of coherence Γmn , equation 2.14 after computing the Fourier transform g(ν). To conduct these spectral format experiments, the flip mirror at position #1 was folded into the beam line to direct the beam towards ancillary equipment at position #3. Section 4.1 and 4.2 further describe the experiments and equipment used to perform these laser characterization tests. In figure 4.1, position #4 highlights the location of a second retractable mirror which is used to switch between the 5 mW cw alignment laser operating at 653 nm (red) and the 589 nm lidar laser. The alignment laser was critical for positioning the ancillary equipment.  37  4.1. Time-Average Pulse Profiles  Figure 4.1: Expansion to the LZT optical table to accommodate the new measuring devices. Position #1 is the location of a retractable mirror and neutral density filter holder. Position #2 is the location of the power meter that was fabricated in the UBC Physics electronics lab. Position #3 is the location where ancillary devices can be placed to characterize the laser pulse profile. #4 indicates the location of a second retractable mirror. This mirror is used to switch between the 5 mW - 653 nm (red) alignment laser and the 589 nm lidar laser. #5 indicates the location of a new linear motorized stage that allows for remote focus control on the projected laser.  4.1  Time-Average Pulse Profiles  To determine the average mode intensities of the UBC laser over time intervals of seconds to minutes, a scanning confocal Fabry-Pérot interferometer (FPI) was deployed. The device used was manufactured by Thor Labora-  38  4.1. Time-Average Pulse Profiles tories, model SA200-5B. Refer to table 4.1 for a list of parameters for the instrument and controller. The free spectral range (FSR) of 1.5 GHz and resolution of 7.5 MHz was expected to be sufficient to span the frequency of all modes and discriminate between individual laser modes. Table 4.1: Properties of the scanning FPI and the controller. FPI Model Operable wavelength range FSR Resolution Cavity length Max finesse FPI Controller Scan rate Max sweep exp  4.1.1  SA200-5B 535-820 nm 1.5 GHz 7.5 MHz 50 mm 300 SA201 0.01 s - 0.1 s × 100  Alignment  In order to optimize the resolution of the FPI, one should maximize the finesse achieved within the cavity. There are four main parameters that finesse is dependent on: 1. The mirror’s reflectivity. 2. The laser alignment to the longitudinal axis of the cavity. 3. Matching the curvature of the laser E-field to the curvature of the concave mirrors in the FPI cavity. 4. An optimal beam diameter having a 600 µm waist at the centre of the confocal cavity. Only the second parameter was varied in the subsequent tests. The initial alignment was conducted using the red cw laser, with the output displayed on a digital oscilloscope. For positional adjustments, the 39  4.1. Time-Average Pulse Profiles interferometer was installed on a manual translation stage as well as a precision kinematic mount which allows pitch and yaw adjustments. The height adjustments were done manually by raising or lowering a slotted aluminium bracket which connects the kinematic mount to the translation stage. Figure 4.2 shows the spectral features of the red continuous wave laser. The main mode FWHM is 361.49 µs. This implies the frequency resolution of 6.61 MHz, thus the finesse = 1500 MHz/6.61 MHz ≈ 227. The maximum finesse allowed by the SA-200-5B is 300. With these measurements the system was considered well aligned with the red laser and the alignment was continued using the UBC sodium laser. Note that it takes takes 82 ms to cover the FSR of 1500 MHz, dF/dt = 18.293 MHz/ms. With the voltage ramp control being dV /dt = 46 mV/ms, the conversion of voltage ramp to frequency is: dF/dV ∼400 MHz/V. The short pulse length of the sodium laser proved to be a challenge since the FPI was developed for measuring cw lasers. After a discussion with engineers at ThorLabs, the solution to improve the finesse required adding a converging lens to focus the beam within the confocal cavity. It was assumed that the diameter of the collimated free space beam before the lens was ∼4 mm. The 250 mm focal length lens was then positioned at ∼220 mm in front of the flange on the interferometer. This was done to create a 600 µm diameter beam waist at the centre of the confocal cavity. Maximum finesse is achieved with a beam-width of 600 µm; any further decrease does not affect the finesse. To adjust the distance between the lens and the FPI, a rotating adjustable focusing element was implemented between the two optical elements.  40  4.1. Time-Average Pulse Profiles  Figure 4.2: Spectral characteristics of the Red laser used to align the FabryPérot interferometer. Top - The green curve is the ramp voltage applied to the piezoelectric transducers which varies the cavity length of the FPI. The yellow curve is the spectrum of the cw red alignment laser. The ramp voltage was 10 V. Bottom - The main mode of the cw laser has a FWHM of 361.49 ms; this implies the frequency resolution of 6.61 MHz and a finesse of 227. These data were acquired on August 15th 2012. 41  4.1. Time-Average Pulse Profiles  4.1.2  Data Acquisition  After a well aligned system was obtained, initial measurements of the UBC laser were conducted. To capture long term spectral features, a NI computer with an NI PXI-4472 card was used to digitize the ramp voltage of the FPI controller and pulse amplitudes. The experiment layout can be seen in figure 4.3. The 2 µs pulse output from the FPI preamplifer is recorded as AI0 and the scan voltage is measured as AI1. The measurements are triggered externally by the laser trigger.  Figure 4.3: The laboratory setup for the long term average spectral experiment. The FPI ramp voltage and FPI output signal are digitized by the PIX-4472 card. The external trigger is the 50 Hz laser and for each pulse, a series of 1000 samples are taken at a rate of 100 kHz. The samples recorded are FPI pulse amplitude and the scanning ramp voltage.  To record the digitized data from the NI computer, a python program was written by Dr. Hickson. The program acquire4472-4.py imports the Labview drivers for the NI PIX-4472 card, reads the digitized signal of the given channel, then writes it to the disk. When the routine is initiated it is  42  4.2. Time-Resolved Pulse Profiles triggered by the 50 Hz laser and acquires 1000 samples of FPI pulse amplitude and corresponding scanning voltage at a frequency of 100 kHz.  4.2  Time-Resolved Pulse Profiles  The second experiment which examines the spectral characteristics of the UBC lidar laser was designed to obtain a series of time-resolved laser pulse profiles. These measurements provide information on short term spectral variations as outlined in chapter 2, section 2.1.1.  4.2.1  Equipment Details and Layout  To capture the short LZT laser pulse of ∼7 ns, a high-speed photodetector (HSPD) model 1437 produced by New Focus was acquired. The wavelength range of the photodetector is 500-1630 nm and operates with a 25 GHz bandwidth. Also, both the photodetector and the high speed oscilloscope must have a high frequency response with f3dB  (N −1)∆ν (where N is the number of modes and ∆ν is the frequency seperation between longitudinal modes). For real-time data acquisition to digitize the HSPD signal, an oscilloscope was rented. The oscilloscope was manufacture by Agilent and is a Infinum (Q-series) model 91304A which has a frequency response of 4 GHz and sample rate of 20 GSa/s. Two main steps were taken to maximize the overall alignment and prevent damaging the sensitive photodiode. The first was that the red cw alignment laser was used to align the HSPD. The photodiode was placed on the same translation stage used as the FPI. An optical post and mount were used to adjust the pitch angle and vertical height. Adjustments were made based on maximizing the output of the detector displayed on the high speed oscilloscope. The second step was to place a white sheet of paper ∼2 cm in front of the detector to prevent damage by diffusing the laser light. This is because  43  4.2. Time-Resolved Pulse Profiles the maximum pulse power that the detector can withstand is 200 mW and the maximum safe average power is 10 mW. The FWHM impulse response is ∼6 ps. The instrument’s responsivity is 0.2 A/W, as seen in figure 4.4, and has a gain of 5 V/W at 589 nm. During the experiments, the laser power was monitored, using a portable Newport power meter (NPM), and remained below 0.3 W. The power meter is further described in 4.3.  Figure 4.4: Digitization of the responsivity curve for the high speed photodiode with a vertical line over-plotted to indicate the responsivity of 0.216 A/W at 589 nm.  4.2.2  Data Acquisition  The oscilloscope was set to trigger on the rising edge of the laser pulse trigger. Once triggered, the oscilloscope then recorded a profile consisting of 1000 samples at a rate of 20 GSa/s. A maximum of 8192 such profiles could be recorded sequentially.  44  4.3. Power Meter Calibration  4.3 4.3.1  Power Meter Calibration Power Meters  One of the parameters necessary to determine the return flux is laser power. For the experiments conducted during the summer of 2012, the main method to obtain these measurements was to insert, before and after each observation, a portable power meter. The meter is a Newport 1918C employing a Newport thermopile sensor 818P-030-18. Since the NPM was not designed for continuous data acquisition, the UBC electronics lab was asked to design a permanent solution. The instrument they fabricated is designed to recorded the laser power throughout any observation. The resulting UBC power meter (UBC-PM) was installed onto the UBC optical bench at location #2. The UBC-PM integrates the signal over ∼ 6 ms, then resets to a constant bias voltage. The maximum signal level of the device is 5 V. To prevent saturation, the power meter was installed after the beam sampler. Also, a neutral density filter with optical density (OD) 2 was necessary when the laser power was above 4.5 W as measured by the NPM. Optimally, the device measures between 2-3 V for best resolution.1 A 50 Ω resistor was installed in a series between the final operational amplifier and the output. This was done to prevent oscillations due to the capacitance of the coaxial cable leading to the control room. This is required only because the detector was not originally designed to drive a cable of that length. The UBC-PM data acquisition was implemented into a Labview program witten by Dr. Pfrommer. This program also controls a tip-tilt mirror used in an experiment not described herein. The program records ten measurements of the integrated pulse energy.  4.3.2  UBC - Power Meter Calibration  Once the UBC-PM voltages are recorded, they must be converted to power. To determine the calibration coefficients, a test was conducted on September 29th , 2012. Calibration of the UBC-PM required using the NPM with a  45  4.4. Focusing and De-focusing Sodium Spot known calibration to determine the conversion factor. To obtain the largest power range from the laser, it was run for ∼1 hour to warm up. During this time the NPM detector was positioned between the laser launch telescope and the beam sampler and the retractable mirror was moved to expose the UBC-PM to the beam-sampled laser. Data acquisition on the NPM required using the Newport 1918C handheld optical meter which saves the power reading to an internal buffer. The main function of the hand-held meter was to adjust optical power measurements made by the 818P power detector. The main adjustable parameters are: wavelength (589 nm), spot size, responsivity (6.2E-4), and the mode (cw continuous acquisition). The NPM has a measurement rate up to 4 kHz and a max stored sample size of 250,000 values. Stored data were transfered to an external usb disk and then be transfered to a computer. Once the rate and sample size is set, the only value recorded is the power reading. Newport provides software that allows control of the optical meter. This was run on the windows computer located in the laser lab. From there, a Remote Desktop Protocol (RDP) session was initiated to control the tip-tilt software. The laser was off at the beginning of the data acquisition and once both power meters were recording, the laser power was turned to full power. The laser power was decreased by ∼0.5 W increments until the laser was off, then increased by ∼0.5 W back to full power (∼4.5 W). The time spent at each power level was ∼30 s, not including the time spent for the initial adjustment jitter to settle to a stable value, which could take a few seconds. Once the final maximum laser power was attained, the laser was turned off so that both power meters would show an abrupt increase and decrease, which helped in fitting both power readings. Further data analysis is described in section 5.  4.4  Focusing and De-focusing Sodium Spot  An attempt was made to examine how variations in sodium spot size affects the return flux. To change the laser spot size on-sky requires varying the 46  4.4. Focusing and De-focusing Sodium Spot focus of the laser launch telescope. A new linear motor attached to a translation stage was installed on the UBC optical table, located at position #5 in figure 4.1. Optimally, the beam is expanded to ∼12 cm diameter by means of a concave diverging lens and convex objective lens. The launch telescope is a refracting telescope with a 15 cm clear aperture and a focal length of 1100 mm. The linear motor and controller allows the observer to vary the sodium spot size accurately by varying the distance between the diverging lens and the objective lens of the laser launch telescope. With the motorized stage in place, the beam divergence can be varied from a diffraction limited parallel beam to a few arcmin. The new linear motor, installed to control the sodium spot size, is a Newport TRA25cc DC servo motor controlled by a Newport SMC-100cc controller. The maximum safe displacement of the actuator is 25 mm and the motor has a uni-directional repeatability 2 µm. Newport provides software that allows an operator to control the motor position through serial commands. This controller interface was installed on a windows computer located in the UBC laser room and the telescope operator is able to remotely log into the windows computer through a RDP session and adjust the position of the diverging lens during an observation.  47  Chapter 5  Results This section generally follows the same layout as in previous chapters, although the laboratory tests are examined first. As well, the experiments conducted in the laser laboratory to characterize the UBC sodium laser are set apart from the on-sky experiments. The final section describes current results from the power meter calibration. These are not critical for the LZT laser characterization test but will be necessary for the TIPC laser tests.  5.1  Laser Spectral Format  For the laser characterization tests, the following results will be described here and within their respective sections. With the time-resolved pulse profile experiment, the laser pulse length, the number of modes, the FWHM of the modes, and mode coherence were examined. The time-average pulse experiment investigated the spectral stability as well as quality and relative power in higher modes. Such information is needed to reduce the relative errors in the predicted return flux.  5.1.1  Measured Temporal Pulse Profile  This section outlines the results obtained from the high-speed photodetector (HSPD) experiment, conducted on 2012/08/25, where 8192 individual laser profiles were continuously measured. This data set enable us to examine pulse length, mode spacing, number of modes, as well as assess the amount of coherence between modes. With the laser set at an average output power of 288 mW, as measured after the beam sampler with NPM, a series of individual pulse profiles were  48  5.1. Laser Spectral Format obtained. Figure 5.1 is a plot of a single resolved pulse profile. From this the measured autocorrelation function of the coherent part of the spectrum can be determined by taking the square of the Fourier transformed pulse profile, figure 5.2.  Figure 5.1: Readout of the digital oscilloscope for a single pulse profile. The output power of the dye laser was 288 mW during this observations. The red curve is average pulse profile of 8192 pulses and is bestfit with a Lorentzian function as opposed to Gaussian, which was originally assumed in the model (Figure by Dr. Otarola).  The next step was to determine an average pulse profile for the series of continuous pulses. The autocorrelation of the amplitude spectrum for the average pulse power spectrum seen in figure 5.3. This figure demonstrates that there is one main mode followed by multiple other smaller modes, with the magnitude of the main mode being over twice that of the smaller modes. The separation between the first and second was ∼370 MHz, as well as 49  5.1. Laser Spectral Format subsequent modes and using equation 2.1 implies a cavity length of 40.5 cm. The autocorrelation of the amplitude spectrum demonstrates that there is only one main coherent mode followed by many incoherent modes due to the small side lobes.  Figure 5.2: The autocorrelation function for an individual laser pulse. The spectrum was obtained by squaring the Fourier transform of 5.1. The main mode is fit with a gaussian that has a FWHM of 75.1 MHz and has a time of 5.87 ns (Figure by Dr. Otarola).  50  5.1. Laser Spectral Format  Figure 5.3: Averaged power spectrum of 8192 individual pulse profiles. The peaks of the secondary modes are located at 370 MHz intervals from the main mode.  5.1.2  Time-Averaged Pulse Profile  The time-averaged experiment was conducted largely during the first two weeks of August 2012. This experiment was designed to examine both beam quality as well as attempt to determine the number of modes and relative strengths. Since the output of the interferometer is of relative intensity and ramp voltage, any abnormalities that occur over longer time intervals can be observed. From the initial observations, both beam jitter and frequency drifts are apparent in the recorded spectra. This can be seen in figure 5.4, where a series of 10 full scans, with vertical offsets to differentiate between the individual scans, are plotted with respect to the applied ramp voltage. The frequency drifts observed are on time scales of ∼20 seconds.  51  5.1. Laser Spectral Format  Figure 5.4: A series of 10 full FPI scans. A vertical offset was applied between successive scans. Frequency drift and jitter, on a timescale of 20 seconds, is apparent. There are three distinct free spectral ranges contained within each scan (Figure by Dr. Otarola).  From a full 10 minute continuous sampling, the resulting spectrum spans three FSR and distinct three modes are observed within each FSR. This can be seen in figure 5.5 where a calibration factor of 400 MHz/V was used to align the spectra. It is hard to determine the number of modes due to the relatively large line width of the interferometer. Also, the relative power contained in the sidebands will be affected by aliasing from higher modes.  52  5.2. Photon Flux Return Values  Figure 5.5: Time-averaged spectral profile of 2000 combined scans, shifted horizontally to align the peaks. The interferometer identifies three free spectral ranges, which indicates that there may be modes that wrap-around.  5.2  Photon Flux Return Values  Once the laser characterization tests were performed, the next step was to image the LZT laser LGS spot to obtain return flux measurements. There were two tests conducted; 1. determining the return for various laser power settings and 2. examining the return with various degrees of de-focusing. Consequently, before any LGS measurements were made, a series of standard stars were observed to calibrate for extinction coefficient, determine seeing, and convert the LGS flux measurement to a V-band magnitude. Figure 5.6 shows an example of a processed standard star image used to determine the AB magnitude of the LGS. 53  5.2. Photon Flux Return Values  Figure 5.6: Image and intensity profile of one of the standard stars imaged with the AT. The pixel scale is 0.76 arcsecs/pixel and the FWHM of the stellar profile is 2.3 arcsecs. The image is a 60 sec exposure using the Vfilter and processed by subtracting the median and dividing by a flat field that has had the median dark subtracted.  Figure 5.7: The V-band magnitude residuals for 11 calibration stars are plotted with respect to air mass. Here the residual is the difference between the intrinsic magnitude and the apparent instrumental magnitude. The linear fit indicates an optical depth at zenith of 0.25 in the V-Band and a zero-point of 1.16.  54  5.2. Photon Flux Return Values  5.2.1  The Effect of Varying the Laser Power  From the calibrated images of the laser guide star images two important values were extracted: the spot size and the LGS flux (in CCD ADC units). First, the spot sizes were characterized by fitting a gaussian profile along both the x and y to obtain the FWHM for both directions using the plate scale of 0.767 arcsecs/pixel, figure 5.8. The next step was to determine the photon flux from the LGS and use this to examine the relationship between laser power and return flux. This can be done by first converting the ADC measurements to an instrumental magnitude. Calibrated magnitudes were then determined by applying the zero point and air mass corrections. These were then converted to an absolute flux in photons/m2 /s using the absolute calibration of Vega [14].  Figure 5.8: An example observered sodium spot with a FWHMx = 8.500 and FWHMy = 9.800 . Before this 60 sec exposure was acquired, the laser power was measured as 2.5 W and the wavelength was 588.9895 nm. Again, the AT was not tracking so the background stars will appear as horizontal streaks.  55  5.2. Photon Flux Return Values With these two values and the laser model parameter obtained in the previous section the sodium column density can be estimated. Dr. Otarola wrote a Matlab graphics unit interface (GUI) which uses the laser parameters determined in the previous section (ex: number of modes, mode spacing, pulse length, etc...) as well as instrumental parameters such as telescope throughput and final laser throughput power to determine the expected return flux. Alternatively, this can be used to predict the sodium column density if the return flux is known, as is the case here. The laser model used is based on the theoretical models of Dr. Hickson that was described in Chapter 2. Figure 5.9 shows the layout and possible calculations that can be done with the GUI.  Figure 5.9: A screen shot of the matlab GUI written by Dr. Otarola to compute the expected photon flux detected by the AT. This program utilizes the laser model described in the theory chapter (2) and requires as inputs: the laser parameters, aperture of the detector, CCD QE efficiency, throughput of both telescope optics and also the laser on-sky. This program also determine the sodium column density based on a given return flux measurement (Figure by Dr. Otarola).  56  5.2. Photon Flux Return Values One set of results illustrated in figure 5.10, which shows two curves fit to the observations. The difference between the two fits, are that one uses a fixed LGS having a FWHM of 16.3 arcsecs, while the other uses the observed spot sizes. This was done to examine the effects of unexpectedlylarge sodium spot sizes. The results indicate a column density ranging from 5.1 × 1013 atoms/m2 to 1.1 × 1013 − 1.5 × 1013 atoms/m2 depending on whether the laser spectrum used had a single dominate mode or a 5 mode spectrum, respectively.  Figure 5.10: The observed LGS return flux for various laser power settings with two fits. The first fit uses the observed FWHM of the LGSs while the second fit assumes a constant spot size with a FWHM of 16.3 arcsecs. The calculated sodium column density Cna and an excitation efficiency α used in the fits are 5.13 × 1013 atoms/m2 (Figure by Dr. Otarola).  57  5.3. Power Meter Calibrations  5.2.2  De-Focusing Experiment  This experiment was only attempted during the first night of on-sky experiments (2012/08/16). This data set combined with images taken while commissioning the AT demonstrated at the time an unexpected behaviour. A non-symmetrical spot elongation with changes in the focus. The asymmetric spot pattern could be caused by a combination of multiple effects: optical aberrations, alignment errors, astigmatism, or the fact that the projected beam of the laser on the sodium layer does not have a uniform flux across the entire area. The last factor is apparent when examining an old tip/tilt mirror as there are burn marks based this effect. Figure 5.11 demonstrates this effect as the variations in focal position produces an expected slightly elongated spot (elongation from NE to SW), to a elongated spot with a majority of the flux concentrated in a circular region, followed by a elongation that tends to go from NW to SE.  Figure 5.11: Images of three LGS spots created with three different relative focal positions: before, near and after. The general trend is that initially the elongation goes from from NE to SW then as the spot is closer to focus an almost circular spot is seen, finally the elongation begins the expand NW to SE. The laser power was measured to be 3.5 W during these observations. The horizontal lines are background stars passing through the field. For scale, the green circles around the LGSs have roughly a 20 pixel radius.  5.3  Power Meter Calibrations  In order to determine the conversion coefficient between the UBC-PM and the NPM, a known and calibrated power meter, a 12 min data set of simul58  5.3. Power Meter Calibrations taneous power readings was acquired for numerous laser power levels. The tip-tilt (TT) software control records the power meter readings as 10 values per laser pulse, where the first five measure the integrated pulse energy and the last five capture the baseline. First, each pulse measurement was zeroed by averaging a set of five baseline values and then subtracting the averaged baseline from the original reading; this is shown by the red plot in figure 5.12. The blue plot is an average of 20 zeroed measurements. This second step was taken due to the nature of the TT software which can capture and record the laser power before the power meter is fully charged or as it is resetting to the baseline. The conversion factor between the two power meters was determined by fitting two linear curves to figure 5.13. The relationship observed was 0.054 V/W · x − 0.02 V/W for any power reading above 0.4 W, with respect to the NPM, and 0.004 V /W · x for all power readings bellow 0.4 W. Note that 0.4 W translates to ∼0.002 V on the UBC-PM; this point was used as the junction between the two separate lines due the distinct non-linear behaviour measured around 0.4 V on the NPM. In order to scale the NPM points and find the residuals (figure 5.12), the NPM data points were linearly extrapolated to the same time values as the UBC-PM. The conversion relationships were then applied and the difference between the two meters was recorded.  59  5.3. Power Meter Calibrations  Figure 5.12: The top graph is the zeroed UBC-PM, an averaged UBC-PM value, and the scaled NPM readings overplotted. The two detectors were run simultaneously while varying the laser power for ∼30 sec intervals. The scaling factors were determined from 5.13. The bottom graph is the residual between the averaged UBC-PM reading and the scaled NPM.  60  5.3. Power Meter Calibrations  Figure 5.13: Calibration curve to determine the relationship between the UBC-PM and the NPM. The fit was done with two separate linear segments (y = mx + b), where m = 0.004 V/W and b = 0 is the solution to the black fit while m = 0.054 V/W and b = 0.02 V/W to the green. The junction point is at 0.4 W as seen on the NPM.  61  Chapter 6  Discussion At the completion of the demonstration phase, the general consensus was that the goal of demonstrating the LZT’s site as ready for testing and characterizing sodium lasers was successful. Although there is still work to be done, the new laser building is completed, the auxiliary telescope is operational, and with minor adjustments the ancillary laboratory equipment can be used on visiting sodium lasers to provide the necessary laser parameters that are required to determine the coupling efficiency to the sodium layer. As a result of these milestones, this new sodium laser testing facility will help to reduce the relative risks associated with attempting to maximize the overall efficiency and performance of future sodium laser guide star facilities.  6.1  Photon Return and Spectral Format  The main goal of the demonstration was to determine key techniques to characterize the LZT’s lidar laser, determine the photon return, and estimate the sodium column density. The current photon flux analysis demonstrates that the estimated sodium column density can vary by a factor of four or more, depending on the laser spectral format employed. During this testing phase, the lidar system was not required since the photon flux return (units photons/m2 /s) can be estimated using the laser parameters determined during testing and with the model. Future tests will require the use of the 6 m optical telescope and high resolution lidar detector, as it will provide an accurate means of measuring the mesospheric sodium atom column density (units atoms/m2 ). As previously mentioned, it is vital to obtain an accurate measure of the sodium column density when assessing the coupling efficiency of any sodium laser, which is a primary goal 62  6.2. Further Sodium Spot Analysis for the TIPC laser tests. For future LZT sodium laser return calculations, the spectral format which should be used is one that is similar to the time-averaged spectrum obtained with the Fabry-Pérot interferometer, figure 5.5. This pulse format seems plausible since the intensity ratios should be relatively unaffected by frequency drift or the line width of the interferometer, both of which would broaden the observed side lobes. There is some signal from aliased higher sidebands, although the extent is unknown. The pulse profile analysis (section 4.2) did produce an autocorrelation function with one strong central peak 5.3, which may seem to contradict the FPI results. In actuality, this method is subject to the amount of coherency between modes as the autocorrelation function demonstrates and that the side lobes are largely incoherent with the majority of the energy contained in the central mode. Before discussing the results further, two things should be mentioned. Firstly, while this document was being written, a new lidar receiver was designed and will be built and installed on the LZT as part of a separate project with ESO. This new receiver will utilize a large area avalanche photodiode (APD) to increase the FOV. With this new receiver, some of the procedures from the readiness campaign will require modifications. This new receiver provides more observational flexibility as compared to the previous lidar receiver. Secondly, one experiment that was not conducted was directly measuring the peak wavelength of the UBC laser. This can easily be done as there is a wavelength meter available which can be used for either the UBC or TIPC lasers.  6.2  Further Sodium Spot Analysis  The relative difficulty in interpreting the defocusing experiment demonstrated at least one oversimplification made in the model; that the laser produces a uniform flux across the beam area in the mesosphere. Thus, both modifications to the model and further analysis is required before this area produces legitimate results. Another area in the models that required a deeper analysis was the 63  6.3. Future Return Flux Observational Techniques effect caused by saturation. This effect was seen more prominently in the experiment with variable laser power, especially when higher laser powers were used when creating the LGS. An expanded theoretical analysis on saturation can be found in Appendix C.  6.3  Future Return Flux Observational Techniques  With the news of a new detector and the relative uncertainties in the spectral format of the UBC laser, another observational strategy was proposed which should mitigate both the uncertainty in the laser format and the effects of saturating the sodium layer. To accomplish this, three things should be done: the transmission of the beam must be attenuated by a factor of 10, the laser power should be below 2.5 W, and the laser launch telescope should be defocused such that the circular footprint on-sky has a diameter of at least 4 arcmin. This would create an unsaturated spot with an average intensity ∼1 mag above the sky brightness, with a byproduct that the return flux should increase up to 4 magnitudes (see appendix C). It is in this unsaturated regime that the excitation probability is proportional to the flux, times the atomic density, times the Einstein B12 coefficient, and as a result, the spectral format is no longer critical. The laser line profile and central wavelength should still be determined as they are required when integrating the product of the laser and sodium line profiles. However, due to the sodium ∼1 GHz doppler broadened line width, the relative uncertainties in the profile and central wavelength are less of a factor. An extreme case would be if the laser line profile is much smaller than the sodium line profile, in this regime any knowledge of the laser line profile is unnecessary. The de-focused LZT LGS would be unobservable with the AT due to both Rayleigh contamination and the sky brightness. Because the APD has a time resolution of 100 ns, the signal is expected to be quite strong since the photons all arrive in ∼100 µs. Nonetheless, the AT is still required to  64  6.4. Immediate and Future Activities calibrate the APD. Calibration can be accomplished by first observing a focused LGS with both detectors, followed by determining the flux calibration using natural stars with the AT and transferring the calibration from the AT to the APD.  6.4  Immediate and Future Activities  Once the new lidar receiver is installed, the software that runs both the TT mirror and records the UBC-PM readings will require modifications. It is at that point that the power meter calibration can be fully implemented. To improve the current conversion, more time should be allowed between changes to the laser power as it takes the NPM 36 s to settle to within 95 % of the correct reading. Implementing this change will not only simplify observations by recording the LZT laser power throughout an observation but it will enable the NPM to monitor the power of any visiting lasers during simultaneous observations. Ultimately, the end goal is to determine the best laser format in order to maximize the LGS brightness/W. Sodium return flux measurements taken with the new APD will aid in determining the degree of accuracy of laser parameters used in models. To accomplish this, one must verify the coupling efficiency and the photon flux return for various types of lasers: polarization, spectral format, cw vs. pulsed, etc. As well, the laser spectral tests conducted on the short pulsed UBC laser can be modified for longer pulsed lasers. Looking to the future, the next phase of this project is to implement the new lidar receiver (June 2013) and begin testing the TIPC laser (July and August 2013). There are also tentative plans for ESO to test a Wendelstein Raman fiber laser guide star system (summer 2014). Having the opportunity to test both lasers will lead to a better understanding of sodium laser characteristics and also lead to models that will enable us to maximize the efficiency of these lasers.  65  Bibliography [1] R. Gagné, T. Pfrommer, and P. Hickson. UBC LIDAR operations manual. Unpublished internal observatory documents email: rcgage@phas.ubc.ca for more information. [2] J. A. Georges III, T. E. Stalcup, J. R. Angel, and P. Mallik. Field tests of dynamic refocus of Rayleigh laser beacons. pages 137–148, 2003. doi: 10.1117/12.516200. URL http://dx.doi.org/10.1117/12.516200. [3] L. Gilles, L. Wang, and B. L. Ellerbroek. Impact of laser launch location on the performance of laser tomography and multiconjugate adaptive optics for extremely large telescopes. ao, 49:G114, Sept. 2010. doi: 10.1364/AO.49.00G114. [4] P. Hickson. UBC Lidar Sodium Return Analysis. Technical report, UBC, Oct. 2009. Interal UBC-TMT unpublished document. [5] P. Hickson. Estimating the coherence of pulsed laser modes by spectral and temporal analysis. Technical report, UBC, Apr. 2012. Interal UBC-TMT unpublished document. [6] P. Hickson. LZT operations manual. Unpublished internal observatory documents email: hickson@physics.ca for more information. [7] P. Hickson, T. Pfrommer, R. Cabanac, A. Crotts, B. Johnson, V. de Lapparent, K. M. Lanzetta, S. Gromoll, M. K. Mulrooney, S. Sivanandam, and B. Truax. The Large Zenith Telescope: A 6 m Liquid-Mirror Telescope. pasp, 119:444–455, Apr. 2007. doi: 10.1086/517621. 66  Bibliography [8] P. D. Hillman, J. D. Drummond, C. A. Denman, and R. Q. Fugate. Simple model, including recoil, for the brightness of sodium guide stars created from CW single frequency fasors and comparison to measurements. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, volume 7015 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, July 2008. doi: 10.1117/12.790650. [9] R. Holzlöhner, S. M. Rochester, D. Bonaccini Calia, D. Budker, J. M. Higbie, and W. Hackenberg. Optimization of cw sodium laser guide star efficiency. aap, 510:A20, Feb. 2010. doi: 10.1051/0004-6361/200913108. [10] R. Holzlöhner, S. M. Rochester, T. Pfrommer, D. Bonaccini Calia, D. Budker, J. M. Higbie, and W. Hackenberg. Laser guide star return flux simulations based on observed sodium density profiles. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, volume 7736 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, July 2010. doi: 10.1117/12.856721. [11] R. Holzlöhner, S. M. Rochester, T. Pfrommer, D. Bonaccini Calia, D. Budker, J. M. Higbie, and W. Hackenberg. Laser guide star return flux simulations based on observed sodium density profiles. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, volume 7736 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, July 2010. doi: 10.1117/12.856721. [12] R. A. Humphreys, C. A. Primmerman, L. C. Bradley, and J. Herrmann. Atmospheric-turbulence measurements using a synthetic beacon in the mesospheric sodium layer. Optics Letters, 16:1367–1369, Sept. 1991. doi: 10.1364/OL.16.001367. [13] N. Moussaoui, R. Holzlöhner, W. Hackenberg, and D. Bonaccini Calia. Dependence of sodium laser guide star photon return on the 67  Bibliography geomagnetic field. aap, 501:793–799, July 2009. doi: 10.1051/0004-6361/200811411. [14] J. B. Oke and R. E. Schild. The Absolute Spectral Energy Distribution of Alpha Lyrae. apj, 161:1015, Sept. 1970. doi: 10.1086/150603. [15] C. L. Perry, E. H. Olsen, and D. L. Crawford. A catalog of bright UVBY beta standard stars. pasp, 99:1184–1200, Nov. 1987. doi: 10.1086/132103. [16] T. Pfrommer. Mesospheric dynamics and ground-layer optical turbulence studies for the performance of ground-based telescopes. PhD thesis, University of British Columbia, 2011. [17] T. Pfrommer and P. Hickson. Mesospheric sodium structure variability on horizontal scales relevant to laser guide star asterisms. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, volume 8447 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, July 2012. doi: 10.1117/12.926056. [18] T. Pfrommer and P. Hickson. High-resolution mesospheric sodium observations for extremely large telescopes. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, volume 7736 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, July 2010. doi: 10.1117/12.857703. [19] T. Pfrommer, P. Hickson, and C.-Y. She. A large-aperture sodium fluorescence lidar with very high resolution for mesopause dynamics and adaptive optics studies. grl, 36:L15831, Aug. 2009. doi: 10.1029/2009GL038802. [20] J. P. Pique, I. C. Moldovan, and V. Fesquet. Concept for polychromatic laser guide stars: one-photon excitation of the 4P3/2 level of a sodium atom. Journal of the Optical Society of America A, 2006. 68  [21] R. Rampy, D. Gavel, S. Rochester, and R. Holzlöhner. Investigations of long pulse sodium laser guide stars. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, volume 8447 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, July 2012. doi: 10.1117/12.926621. [22] S. M. Rochester, A. Otarola, C. Boyer, D. Budker, B. Ellerbroek, R. Holzlöhner, and L. Wang. Modeling of pulsed-laser guide stars for the thirty meter telescope project. J. Opt. Soc. Am. B, 29(8): 2176–2188, Aug 2012. doi: 10.1364/JOSAB.29.002176. [23] C. Y. She, J. R. Yu, H. Latifi, and R. E. Bills. High-spectral-resolution fluorescence light detection and ranging for mesospheric sodium temperature measurements. Appl Opt., 1992. [24] D. A. Steck. Sodium D Line Data. Tech. rep., Department of Physics, Unversity of Oregon, available online at http://steck.us/alkalidata (revision 2.1.4), Dec 2010. Accessed 2013-03-10. [25] P. Török and F.-J. Kao, editors. Optical Imaging and Microscopy, 2007. [26] P. J. Ungar, D. S. Weiss, E. Riis, and S. Chu. Optical molasses and multilevel atoms: theory. Journal of the Optical Society of America B Optical Physics, 6:2058–2071, Nov. 1989. doi: 10.1364/JOSAB.6.002058. [27] L. Wang, A. Otarola, and B. Ellerbroek. Impact of laser guide star fratricide on TMT MCAO system. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, volume 7736 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, July 2010. doi: 10.1117/12.857348.  69  Appendix A  Technical Drawings for the New Laser Laboratory and Auxiliary Telescope While Chapter 3 briefly describes the new laser laboratory (NLL) and Auxiliary Telescope (AT), this appendix expands on the layout and design of both structures and includes technical drawings.  A.1  Main Laboratory Drawings  The main laser laboratory drawings are made as per the district of Maple Ridge building bylaws and permit guidelines. Figures A.1, A.2, and A.3 show the general layout, dimensions, and exterior cladding of the structure. In order to obtain final approval, the city required engineer-approved drawings for the trusses. Since the trusses were originally constructed on site by a master carpenter, we did not have pre-approval beforehand. A separate engineering firm was contacted to conduct a structural analysis on design, which proved to be insufficient in conditions of high snow load due to the altitude of the building. To accommodate for the higher snow loads, the trusses were fortified as directed by the engineer and the modifications were implemented according to figures A.4 and A.5.  70  A.1. Main Laboratory Drawings Figure A.1: Main plan for new laser laboratory, which includes an overhead view with dimensions, key features, and a profile of the subsoil and bedrock. 71  A.1. Main Laboratory Drawings  Figure A.2: NLL south-east facing elevation drawing.  72  A.1. Main Laboratory Drawings  Figure A.3: Overall schematic section drawing of the NLL.  73  A.1. Main Laboratory Drawings  Figure A.4: Overhead view of the framing plan for the NLL building.  74  A.1. Main Laboratory Drawings Figure A.5: The collar tie and gusset plate location on each truss, which includes type and location of fasteners.  75  A.2. Auxiliary Telescope Drawings  A.2  Auxiliary Telescope Drawings  As discussed in section 3.2, the main structure was built of an aluminium L-angle frame which consisted of two identical sections as seen in figure A.6. Each section has two hinges bolted to the base and these hinges were raised off the ground and secured to the concrete with expansion bolts. This design allows the two sections to fold away to reveal the telescope. The main pier that the telescope rests upon was also custom made. The pier was manufactured according to the drawings in figure A.7. Finally, three 10 kg brass counterweights were made in the UBC machine shop. The weights were designed by Martin O’Keane.  76  A.2. Auxiliary Telescope Drawings  48.000  60.000  78.000  69.000  30 .0 00  76 .8 37  622 64.  12.000  3.543  24.000  We require two of these structures Angled Alum. : 1 1/4" X 1 1/4" X 1/4"  MATERIAL FINISH  Auminum No Finish  DO NOT SCALE DRAWING  DRAWN  NAME  DATE  R. Gagne  30.06.2012  COMMENTS:  DIMENSIONS ARE IN INCHES  Auxiliary Telescope Structure SIZE  A  DWG. NO.  SCALE:1:20  REV.  AT-strucV2  WEIGHT: Unknown  1  SHEET 1 OF 3  Figure A.6: One half section of the main frame work for the AT structure.  77  4.00  SECTION N-N Top Plate  10.50  A.2. Auxiliary Telescope Drawings  0.31 6 - equally spaced tapped M8X1.0 holes 4.0 9  Top plate machined to standard machine tolerance ~0.001" and does not need to be ground to higher flatness  0.50  N  30.00  N  M 14.000  6 .1  8  14.000  Fillet represents Wielding points  0.75 Three equally spaced through hole for 3/4" bolt  10.750  M  0.50  The tube to be made of 10" schedule 20 pipe.  10.750  SECTION M-M Bottom Plate  MATERIAL FINISH  Aluminum  Anodised Black  DO NOT SCALE DRAWING  DRAWN  NAME  DATE  R. Gagne  11.02.2012  COMMENTS:  DIMENSIONS ARE IN INCHES  UBC Auxiliary Telescope Pier SIZE  A  DWG. NO.  AT-PierV4-10inch  SCALE:1:10  REV.  1  SHEET 1 OF 1  Figure A.7: Auxiliary telescope stationary pier.  78  A.2. Auxiliary Telescope Drawings  Figure A.8: Auxiliary telescope 10 kg counterweight design by Martin O’Keane.  79  Appendix B  Detailed List of Data Acquisition and Reference Stars B.1  LGS Observation Procedure  This section contains a list of tasks that were completed during the 2012.09.12 observing night. Before beginning this section, I will refer the reader to the lidar and LZT operations manuals for more information on safe operations and observing protocols [1, 6]. 1. Start-Up Open AT enclosure, connect power, and ethernet. Turn on Dell light detection and ranging (lidar) computer and begin Remote Desktop Protocol (RDP) connection to the National Instrument (NI) computer controlling the AT. 2. Flat Field Once all equipment is on and running, open the SBIG software CCDops then position the telescope towards a uniformly illuminated area of the sky at dusk. The altitude of the telescope is adjusted depending on length of exposure as well as to avoid stellar contamination. A typical laser guide star (LGS) exposure time is 60 seconds using the V-filter with approximately 10 images. The R-filter was not used because the filter does not seem to be transparent to 598 nm despite the manufacture specifications indicating that it should be. 80  B.1. LGS Observation Procedure 3. Darks Darks can be taken before or after a set of observations and each set should not exceed approximately 1 hour, the time scale which major variations in the sodium layer occur. It is best to move the telescope to a location away from any bright sources and use CCDops to take dark exposures. Again, typically 10 images are taken at 60 seconds per exposure. 4. Acquisition of calibration stars Next, the Astro System Austria (ASA) mount must be homed by pointing the optical tube towards the zenith and pressing the “homing” button in the autoslew program. After this, the tracking system can be synced to an available bright star centered on the CCD. With a star centered, adjustments to the focus are made with the correct filter in place. Assuming a working pointing model has already been determined, any star visible in the sky should be available as a calibration star. The stars chosen were at varying altitudes, ranging from a declination (DEC) of 0−90◦ and later used to determine atmospheric excitation. Table B.1 is a list of calibration stars with exposure times, right ascension (RA), and DEC. Exposure times and the filter used will depend on which experiment is being run. 5. Laser guide star spot acquisition All precautions for safe telescope operations and laser propagation must be followed according to the two observing manuals [1, 6]. With the radar on and the spotter in place, the laser can be turned on and observing can commence. Once the AT is pointed at the zenith and the tracking turned off, centering the sodium spot can be done with few fine adjustments to the mount. The two experiments conducted which examined the return flux are: (a) LGS focus changes: Using the black Dell computer in the control room, remotely log into the stealth computer located in the LZT 81  B.1. LGS Observation Procedure laser lab which controls the Newport linear motor as described in section 4.4. Exposure time is 10 seconds in the V-filter. (b) LGS power variations: This experiment ran best with two individuals in the laser lab, one to control the laser power and the other to move the Newport power meter (NPM) in and out of the beam line. This experiment will use the calibrated UBC power meter for any further tests. A full observation log can be found in section B.2. Table B.2 contains the power meter readings taken during the 2012.09.12 observing night. 6. Shut-Down At the end of an observing run, the data must be transferred from the NI-computer running the AT. An efficient way to do this is to use the program called Filezilla, an FTP client which utilizes ssh and scp. The rest of the shut-down procedures can be found in the appropriate operations manuals.  Table B.1: List of calibration stars used for the power measurements return flux experiment. All stars listed are from the Perry et al. catalogue. Note that HR 8085 and HR 8086 are in the same field. HR 7730 8060 8313 8634 7977 8454 8709 8085 8086 8551  τ (sec) 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12  RA 20 21 21 22 20 22 22 21 21 22  (2000) 13 18 04 24 44 31 41 28 48 56 09 59 54 39 06 54 06 55 27 51  DEC +46 48 57 -19 51 18 +17 21 00 +10 49 53 +46 06 51 +33 10 42 -15 49 15 +38 44 57 +38 44 30 +04 41 44  SpT A5 IIIn A5 V G5 Ib B8 V B3 Iae F5 III A3 V K5 V K7 V K0 III  Vmag 4.830 4.858 4.336 3.400 4.860 4.290 3.276 5.213 6.044 4.790  82  Table B.2 continued on following page.  B.1. LGS Observation Procedure  Table B.2: Observation log of the power measurements taken during the return flux experiment. All measurements taken used the NPM. The error quoted were fluctuations in the power meter readings. Desired NPM Before NPM After Aprox Time LGS Laser Measurement ± err Measurement ± err of Exposure Intsr. Power (W) Measurement Watts Measurement Watts PST mag. 0.2 0.20 .01 0.22 .01 10:23 14.9 0.4 0.41 .02 0.40 .02 10:25 14.4 0.6 0.60 .02 0.59 .01 10:28 14.1 0.8 0.81 .01 0.80 .03 10:31 14.3 1.0 1.02 .02 1.02 .01 10:33 13.1 1.5 1.50 .05 1.48 .04 10:37 12.6 2.0 2.02 .02 2.03 .02 10:39 12.1 2.5 2.49 .02 2.50 .02 10:42 12.0 3.0 3.05 .03 3.00 .02 10:44 11.9 3.5 3.52 .02 3.51 .01 10:47 11.7 4.0 4.02 .01 4.01 .03 10:49 11.7 4.5 4.52 .02 4.52 .02 10:51 11.2  83  Table B.2 continued from previous page.  0.8 0.6 0.4 0.2  NPM Before NPM After Measurement ± err Measurement ± err Measurement Watts Measurement Watts 4.53 .01 4.51 .02 4.02 .03 4.05 .02 3.54 .02 3.50 .03 3.01 .02 3.02 .01 2.53 .03 2.48 .02 2.00 .01 2.01 .01 1.53 .02 1.52 .02 1.01 .01 1.01 .01 Laser shutdown due to passing aircraft 0.80 .01 0.83 .03 0.61 .02 0.63 .02 0.40 .01 0.43 .02 0.20 .02 — —  Aprox Time of Exposure PST — 10:55 10:58 11:00 11:02 11:05 11:07 11:10  LGS Intsr. mag. 11.3 11.8 11.7 11.9 12.0 12.1 12.6 13.5  11:13 11:15 11:17 11:19  14.3 14.1 14.4 14.9  B.1. LGS Observation Procedure  Desired Laser Power (W) 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0  84  B.2. AT - LGS Power Measurments Observation Log  B.2  AT - LGS Power Measurments Observation Log  The following log was recorded on the observation night of 2012.09.12. The data can be found on sirius.phas.ubc.ca in the following directory: /Volumes/LaCie4 2/data/AT/2012.09.12/ Within the 2012.09.12 directory, there is a folder for each of the following: the flat fields, focus measurements, power measurements, and standard stars. 1. Flat Fields - Taken at the beginning of the night (∼7:30pm PST) with both the Clear filter and V-filter. The first is identified with a C in the file name, while the latter has a G. (The G is because the filter name is Green in the CCD standard software). Following the filter type is the exposure time *.**s, then the exposure number. ** During the observations all of the images were taken with the V-filter** 2. Focus Meas - This directory contains a few images that we used to visually identify a rough focus position. The optimal position was deemed to be 8.75 mm, which was what we used in our past observations. 3. Power Meas Once we roughly optimized the focus, we proceeded in taking LGS power measurements. The full set took roughly 60 min to complete, which contains a set with the laser power varying from 0.2 W to 4.5 W and another decreasing the laser power back down to 0.2 W. During the observations, we had a laser shutdown due to aircraft between 1.0 W and 0.8 W. The shutdown occurred in the process of adjusting the laser power so exposures were not affected. At the beginning of the observations, the power meter zero point was -0.0170 +/- 0.005 W. At the halfway point, the power meter zero point 85  B.2. AT - LGS Power Measurments Observation Log was -0.0100 +/- 0.005 W.  Table B.2 are readings off the NPM before and after each exposure. The maximum laser power for the night was observed to be around 4.53 W. The file with the lgs-****mw-1.FIT format are for ascending power measurements and lgs-****mw-2.FIT are for descending power measurements. 4. Stand Star - Once the LGS images were completed, we proceeded with standard stars and ended the night with darks. Since we had such a great pointing model, we chose stars both east and west and all from the catalogue from Perry et al. [15].  86  Appendix C  Saturation Analysis Expanded Through a series of discussions on the larger then anticipated observed full width at half maximum (FWHM) of the LGS spot sizes, Dr. Hickson provided a rough analysis. The following analysis suggests that the transmitted laser beam profile on the sodium layer is expected to be approximately 3 times smaller then the observed LGS FWHM. Since the population of sodium atoms that are in thermal equilibrium at ∼200 K, we can assume that a large majority will be in the ground state. This suggest that each laser pulse from the the UBC lidar laser encounters ground state atoms since the repetition rate of the laser is much longer then the collisional relaxation time. Thus, the absorption coefficient (at low power) is then α(ν) =  1 B12 h ν φ(ν) n1 8π  (C.1)  where n1 is the number density of Na atoms and φ is the line profile (its integral over frequency is unity), and B12 is the Einstein coefficient for for photo absorption. To account for polarization a factor of 2 has been inserted in the denominator. The optical depth of the sodium layer is Z τ (ν) = =  α(ν)dz 1 B12 ν h φ(ν) N 8π  (C.2)  87  Appendix C. Saturation Analysis Expanded where N is the sodium column density. Utilizing the relation between the Einstein coefficients g2 B12 g1 g2 c2 = A21 , g1 2hν 3  B12 =  (C.3)  where g1 and g2 are the multiplicity of states 1 and 2, A21 and B21 are the Einstein coefficients for spontaneous emission and induced emission respectively. Putting equation C.3 into equation C.2 returns τ (ν) =  1 g2 A21 λ2 φ(ν)N. 16π g1  (C.4)  For the D2 transitions, g2 /g1 = 2 and A21 = 1/20 ns, which gives: τ (ν) = 6.9 × 10−7 φ(ν) N.  (C.5)  Now, N ∼ 4 × 1013 m−2 , so τ (ν) ∼ 2.7 × 107 φ(ν). Within the D2 line, φ(ν) ∼ 1 GHz−1 so the optical depth is τ ∼ 0.03. From the radiative transfer equation, the laser intensity at the top of the sodium layer is I ∼ I0 exp(−τ ), so about 3% of the photons are absorbed. Essentially all the absorbed photons are re-radiated at 589 nm, since A−1 21  is much shorter than the timescale for collisional de-excitation. Con-  sequently, the coupling efficiency in the unsaturated regime is also about 3%. The return flux would be .03P/(4πd2 ), where P is the laser power and d is the distance to the sodium layer. If we take the flux density from Vega (m = 0) to be ∼3880 Jy, integrating this over a 100 nm bandpass in the V-band (550 nm) ∼ 1014 Hz) produces a flux of 3.9 × 10−9 W/m2 . Putting in P = 4 W and d = 92000 m, we find that an unsaturated LGS would have an apparent magnitude of approximately m ∼ −2.5 log 10(0.03 ∗ 4/4π (9.2 × 104 )2 3.8 × 10−9 ) ≈ 8.8.  (C.6) 88  Appendix C. Saturation Analysis Expanded As the observed LGS magnitude is about 13, we can conclude that the LZT laser does indeed saturate the sodium layer, since the return power is about ∼100 times smaller than if it were unsaturated. Now to determine how much larger the LGS would appear, suppose that the transmitted beam has a gaussian flux distribution at the sodium altitude. The intensity profile of an unsaturated LGS would have an intensity profile proportional to a gaussian with the same FWHM: I = I0 exp(−a r2 ).  (C.7)  Where a is related to the FWHM, w by a = 4 ln(2)/w2 . Because of saturation, the actual LGS profile will be nearly flat with a much lower intensity, that is, some fraction ‘b’ of the central intensity I0 of the unsaturated LGS. The radius of this saturated LGS will be roughly equal to the radius at which the profile becomes unsaturated, namely rs where b = exp(−a rs2 ). Thus, rs ∼ [− ln(b)/a]1/2 .  (C.8)  The flux of this saturated LGS will be Fs ∼ πrs2 bI0 compared to the unsaturated flux of F = πI0 /a. Setting this flux ratio equal to R = 1/40, we find that −b ln(b) = R, so b ∼ 0.005. From this we see that the FWHM of the actual LGS is 2 rs = 2[− ln(b)/a]1/2 = [− ln(b)/ ln(2)]1/2 w  (C.9)  ∼ 2.7 w. Therefore, the FWHM of the saturated LGS is ∼2.7 times larger than that of the transmitted beam. This ratio will depend on the beam profile and any deviations from a Gaussian will most likely result in a higher ratio. We found a FWHM of about 8 arcsec for the best-focussed LGS, which would then correspond to a FWHM of 2.13 arcsec for the beam footprint  89  Appendix C. Saturation Analysis Expanded on the sodium layer. This is about what one would expect for the seeing at the site.  90  

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