Modeling of Collection Efficiency in Lidar Spectroscopy

Transcription

1 Modeling of Collection Efficiency in Lidar Spectroscopy Barry Lienert and Shiv. K. Sharma Hawaii Inst. Geophysics & Planetology, 2525 Correa Rd, Honolulu HI Teng Chen, Frank Price and John M. J. Madey Dept. Physics & Astronomy, Univ. Hawaii at Manoa, 2505 Correa Rd, Honolulu HI ABSTRACT We performed a calibration experiment on a Spectralon Target using a wavelength of µm and a 60 cm lidar system coupled to a photon counter via a Triax 190 monochrometer. The complete system optics, including the telescope and monchromator, were modeled using a commercial ray-tracing program. Energy efficiency was calculated by generating large numbers of equal-area rays on the telescope input pupil from points in the plane of the target. The number of these rays received by the PMT cathode was then used to estimate the optical efficiency. Comparison of the calculated and observed signals gave agreement to within 30%. We discuss the possible sources of disagreement between the calculated and observed signals. Keywords: Lidar, spectroscopy, target calibration 1. INTRODUCTION Lidar (light detection and ranging) is an established technique for collecting range resolved information on the distribution of atmospheric aerosols and gases 1. The signal received by the lidar detector can be iteratively solved for elastic scattering (Mie and molecular) properties as a function of range 2. By selectively filtering the lidar data at different wavelengths, or by using a monchromator, inelastic scattering such as Raman can also be studied as a function of range 3. The effective range of a monchromator-coupled lidar system is typically very short, due to the inverse range squared dependence of the returned signal combined with the typically low optical coupling efficiency (OCE) between the lidar and the monchromator, particularly when high spectral resolution is required. To study this OCE in detail, we have utilized the capabilities of Zemax, a commercial ray-tracing package. 2. EFFICIENCY CALCULATION We define the OCE of an optical system as the ratio of the integrated output to input light. Both these integrations may be performed numerically by subdividing the input aperture of the system into equal-area segments with a light ray from any point in the object plane passing through the center of each segment. If the light intensity is assumed to be constant over the input aperture, each ray then represents a constant fraction of the input light. The rays can then be traced through the optical system using commercial ray-tracing packages such as Zemax. and the output number counted manually. Provided that the transmission characteristics of the optical elements are constant over their surfaces, the OCE is then the ratio of output to input rays (the ray-count efficiency, RCE) times the product of the individual optical element transmissions. The accuracy of the RCE can be improved to any desired degree by increasing the number of rays. Zemax also uses a ray counting method to estimate efficiency. However, its ray directions are chosen randomly, rather than having equal area and it is not clear whether they are distributed equally in area. To calculate the RCE, the telescope s unobstructed area is divided into N R equally spaced rings, each having a width R=(R 1 -R 2 )/N R (1) Lidar Remote Sensing for Environmental Monitoring VI, edited by Upendra N. Singh, Proc. of SPIE Vol (SPIE, Bellingham, WA, 2005) X/05/$15 doi: / Proc. of SPIE 58870V-1

2 where R 1 and R 2 are radii of the telescope s primary mirror and central obstruction, respectively. Each ring is then subdivided into N θ angular segments of width θ. N θ was determined for the ring by setting the mean arc length of its segments equal to R. A Fortran program was written to generate the ray coordinates in the normalized format read directly by Zemax. 3. EXPERIMENTAL CONFIGURATION The 61 cm telescope and associated optics are mounted on an optical table inside a metal shipping container. The lidar transmitted beam is produced by a frequency-doubled Nd:YAG 20 Hz pulsed laser having a wavelength of µm. The laser beam is expanded using a spherical mirror coupled to a 17.8 cm telescope. The transmitted beam has a diameter of about 15 cm and is reflected from an electronically adjustable 45 O flat mirror mounted on the telescope s secondary mirror. Both the telescope and transmitted beam are directed through the container roof using a 62 cm optical flat. Outside of the container, another adjustable 68 cm mirror is used to position the telescope and transmitted beam on the target. The transmitted beam converges to a focus on a target at a range of 210 m. At this range, the transmitted beam radius was observed to be ~0.5 cm. RMT SPEETROMETER FROM TELE0000E Figure 1. Optical layout of the receiver beam line (61 cm telescope is not shown). Fig. 1 shows the Zemax model of the receiver optics used for the target calibration experiment. These utilize a 61 cm Dall-Kirkham telescope (not shown) with a focal length of 7 m. The telescope is lens-coupled to a crossed Czerny- Turner monochrometer (Triax 190) having a focal ratio of 3.9 and focal length of 190 mm. The output of the monchromator is then coupled to a PMT using an additional lens. The telescope was modeled using mirror specifications provided by its designer which provide diffraction-limited performance (< 6 µm aberration at µm wavelength) at infinite range. The telescope s infinity back focus position was determined during its alignment using a 65 cm square optical flat and a small LED. The coupling lenses in Fig. 1 were modeled using their refractive indices and radii of curvatures from the Zemax lens catalogs. The monochrometer, a crossed Czerny-Turner Triax 190, was modeled by measuring the positions of the optical components, then choosing the radii of curvature of the two mirrors to optimize the output spot size at the blaze wavelength of 1.5 µm. This resulted in astigmatism comparable to that given by the monchromator s manufacturer, Jobin-Yvon at a wavelength of 1.5 µm. 4. RAY COLLECTION EFFICIENCY COMPARISONS Proc. of SPIE 58870V-2

3 A theoretical method has been given 4 which can be used to derive the efficiency of a telescope/transmitter/detector combination that can be compared with our calculated RCE s. 1.0 Optical Collection Efficiency Harms' Method Ray counting method Zemax efficiency Range, meters Figure 2. Comparison of RCE s calculated using Harms (1979) method (solid line), the ray-counting method described here (solid squares) using 314 rays (N=10) and the Zemax image efficiency (crosses). All results are at a wavelength of µm. Fig. 2 shows a comparison of results for a 1.5 mm radius detector 21 mm behind the telescope s focal point with the transmitted beam focused to the corresponding range of 2400 m. The Zemax geometrical image efficiency for a circular region in the object plane having a 12.5 mm radius is also shown. The results show reasonable agreement, confirming the consistency of Harms method, the ray-counting procedure and the Zemax efficiency calculation. 5. TARGET CALIBRATION The energy of the outgoing beam (8.34 mj) was measured using a power meter and a large convex lens. The transmitted beam is made parallel to the telescope s optic axis using an alignment device which reflects a portion of the outgoing beam into the telescope in a parallel direction and thus through the infinity back-focus of the telescope. This device was also used to measure the reflectivity of the primary and secondary mirrors with a power meter and a small laser. The power meter was also used to measure the reflectivity of the 62 and 68 cm turning flats. The monochrometer s 600 lines/mm grating efficiency (GE) was measured directly using a small µm laser and the monchromator slit widths set to 0.75 mm. The GE is highest closest to the grating s blaze wavelength of 1.5 µm. The transmission factors of the grating and the other optical components used for the experiment appear in Table 1. Optical Element Transmission efficiency Atmosphere (Mie plus molecular) Telescope mirrors Steerable 68 cm turning flat cm turning flat µm line filter Neutral density filter 1.00e-5 4 Lenses 0.97 (each) 5 cm turning flat 0.97 Proc. of SPIE 58870V-3

4 Diffraction grating: 1 st order nd order rd order Table 1. Optical component transmission values. The image of a flashlight at the target range of m was first located after the leftmost lens in Fig. 1. This was compared with the position predicted by the Zemax model in Fig. 1 and found to agree to within 3 mm. With the monochromator s input and output slit width set to 0.75 mm, the position of the coupling lens prior to the monochromator (Fig. 1) was then adjusted to maximize the returned signal on the PMT. For the final lens positions, the Zemax model gave a focus position that was 0.5 mm in front of the monochrometer s input slit. The PMT output was then digitized for each shot of the 20 Hz laser using a 500 Ms/s 8-bit digitizer triggered by the laser output beam using a fast photo-diode. 0.5 µs of pre-trigger data was collected in order to give an accurate estimate of the pre-trigger baseline, which was subtracted from the post-trigger data. Integrals were calculated over a 50 ns interval spanning the length of the returned pulse. A PMT anode sensitivity of 5.85e4 A/W at µm wavelength was estimated from its manufacturer s data sheet. However, the gain was checked by estimating the integrated charge of single photon pulses and comparing it to the charge on a single photoelectron. This yielded a gain that was 3.4 times larger than the nominal gain. This increased gain was combined with an assumed cathode quantum efficiency of 0.18 to yield a PMT sensitivity of 9.945e6 V/W across the 50 ohm terminating resistance. The light energy returned from the target was calculated using the equation E=εE 0 BRDF A/(4πr 2 ) (2) where ε is the OCE (the product of the transmission losses in Table 1and the RCE), BRDF is the bidirectional reflectance distribution function of the target, E 0 is the transmitted pulse energy (8.34 mj), A the telescope area (m 2 ) and r is the target range (m). If the target is assumed to be Lambertian, its BRDF is ρ/π sr -1 5, where ρ is the target s reflectivity. A value of 0.987, given by the target s manufacturer was used for ρ. Table 2 shows the resulting measured and calculated efficiencies and pulse energies for the first three diffraction orders. Diffraction order Ray Collection Efficiency Calculated Pulse Energy, J Measured Pulse Energy, J e-17 (6.8±0.2)e e-17 (5.1±0.2)e e-16 (4.8±0.2)e-16 Table 2. Efficiencies and the calculated pulse energies compared with the measured energies. The slightly larger measured value for the largest (m=3) signal may be due to the opposition effect 6, where the intensity of real targets is enhanced in the backscatter direction. A slightly lower quantum efficiency of the PMT due to water vapor condensation on its optical window may also have contributed to the slightly larger values. Overall, the agreement between measured and calculated energies is quite reasonable, confirming the ability of this optical model to predict the optical losses in this lidar system. 6. CONCLUSIONS 1. We have confirmed the consistency of the theoretical procedure 1 and the ray counting method described here for estimating telescope-detector coupling efficiency. 2. We have successfully described the optical performance of a lidar system coupled to a monchromator with a detailed model of all the optical elements. The resulting model allows us to calculate the absolute amplitude of the returned signals as well as the effect of changes in the optical configuration. Proc. of SPIE 58870V-4

5 7. ACKNOWLEDGEMENTS Distribution A. Approved for Public Release; distribution unlimited. 8. REFERENCES 1. A. Piironen and E. W. Eloranta, Convective boundary layer mean depths, cloud base altitudes, cloud top altitudes, cloud coverages, and cloud shadows obtained from Volume Imaging Lidar data, Journal of Geophysical Research, 100, D12, , J. N. Porter, B. Lienert, and S. K. Sharma, Using Horizontal and Slant Lidar measurements to Obtain Aerosol Scattering Coefficients From A Coastal Lidar In Hawaii, J. Atmos. Oceanic Techn., 17, , R. A. Ferrare, S. H. Melfi, D. Whiteman, K. D. Evans, G. Schwemmer, Y. Kaufman, and R. Ellingson, Raman lidar and sun photometer measurements of aerosols and water vapor, in Advances in Atmospheric Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux, and U. Wandinger, eds., 23 26, Springer-Verlag, Berlin, Harms, J., Lidar returns for coaxial and noncoaxial systems with central obstruction, Appl. Optics, 18, , M. Kavaya, Polarization effects on hard target calibration of lidar systems, Appl. Optics, 26, , D. A. Haner and R. T. Menzies, Reflectance characteristics of reference materials used in lidar hard target calibration, Appl. Optics, 28, , Proc. of SPIE 58870V-5