On atmospheric lidar performance comparison: from power aperture product to power aperture mixing ratio scattering cross-section product

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1 Journal of Modern Optics Vol. 52, No. 18, 15 December 2005, On atmospheric lidar performance comparison: from power aperture product to power aperture mixing ratio scattering cross-section product CHIAO-YAO SHE* Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA (Received 31 May 2005) A new performance index for atmospheric lidar, namely the power aperture mixing ratio scattering cross-section (PAMS ) product, is proposed. Unlike the index widely used at present, namely the power aperture (PA) product, the new index provides an accurate comparison between different types of lidar for measuring the same atmospheric parameters. Using a sodium resonance lidar and a Rayleigh lidar for measuring temperature and wind in the mesopause region ( km) as an example, the concept and application of PAMS are illustrated. The value of the power aperture (PA) product has been widely used as the index to compare the performance and to assess the figures of merit of atmospheric lidar. This is because the received signal, independent of the optical processes invoked, is proportional to the power P of the lidar transmitter and to the area A of the receiving telescope. It is well known that the signal received from a lidar also depends on the optical scattering process and on the concentration of the scatterers involved. Thus, with same PA product, the signals received for different types of lidar can differ by orders of magnitude, depending on the optical processes and species concentrations in question. A well-known example is that the total cross-section of rotational (vibrational) Raman scattering is (0.001) times that of Cabannes scattering [1]. Here, we adapt the terminologies proposed by Young [2] and regard Rayleigh scattering as the sum of Cabannes scattering (central peak) and pure rotational Raman scattering (sidebands). In this connection, we would consider Cabannes scattering as the optical process that dominates the signal in a broadband Rayleigh temperature lidar [3] and that provides all the signal in a narrowband Rayleigh wind lidar [4]. In the case of resonance Raman scattering and/or resonance scattering from metal atoms, there is considerable enhancement in the scattering cross-section as the incident laser frequency approaches the frequency of an allowed molecular or atomic transition. For example, the absorption cross-section of the D 2 transition in a sodium atom is about times that of * joeshe@lamar.colostate.edu Journal of Modern Optics ISSN print/issn online # 2005 Taylor & Francis DOI: /

2 2724 C.-Y. She Cabannes scattering [5]. This factor of signal enhancement, which is not accounted for by the PA product, should not be ignored when the performances of different types of lidar are compared. In addition to the scattering cross-section, the lidar signal is also proportional to the species concentration of scatterers in question. There is an obvious need to take into account the cross-section of the scattering process and the concentration of scattering species, when comparing the performance of different types of atmospheric lidar. In this short note, I propose a new metric, termed the power aperture mixing ratio scattering cross-section (PAMS ) product, that would include all the key parameters that are required to assess the signal strength of atmospheric return, and the figure of merit of a lidar. I further propose the use of Cabannes scattering of the atmosphere (both major species of nitrogen and oxygen) at 532 nm as reference and report the differential scattering cross-section and relevant species concentration of a lidar in a unit of the differential Cabannes scattering cross-section of air molecules at 532 nm, m 2 sr 1 [6] and of the atmospheric concentration (density) at the same altitude respectively, as the relative differential scattering crosssection S and mixing ratio M of the atmospheric scatterer in question. Therefore, the product of transmitter power P, receiver area A, mixing ratio M of the scattering species in question and relative differential scattering cross-section S, that is PAMS, is proposed as the figure of merit to gauge the performance of an atmospheric lidar. In this approach, both M and S are dimensionless quantities; PA and PAMS thus have the same units, that is watts per square metre. For a Rayleigh lidar (or more correctly a Cabannes lidar) at 532 nm, M ¼ S ¼ 1, and the numerical values for PA and PAMS would be the same. To emphasize this point, I show in figure 1, a photon count profile taken on 19 January 2003 from a moderate sodium resonance lidar, operated at the D 2a peak frequency of the sodium D 2 transition [5]. For this lidar, deployed since 1989 at Colorado State University (CSU), the Cabannes signal at 589 nm decreases to the noise level at an altitude of about 50 km, but the signal due to laser-induced fluorescence (or resonance scattering) between 80 and 110 km, where neutral atmospheric sodium atoms reside, is seen to be fairly strong. In fact, the photon counts at 90 km due to laser-induced fluorescence, averaging over a vertical distance of 150 m, is seen to be approximately the same as that of Cabannes scattering at 25 km, about 135 counts per 150 m range bin in 40 s integration. We can estimate this enhancement by noting that the resonance differential cross-section at the D 2a peak frequency scattered from mesopause sodium atoms at 200 K (because of Doppler broadening, the resonant scattering cross-section at a given frequency is temperature dependent) is m 2 sr 1 [5], giving S ¼ ( )/( ) ¼ Our lidar climatology of the January mean sodium density at 90 km is m 3 [7] and the air density at this altitude according to U.S. Standard Atmosphere, 1976 [8] is m 3, giving M ¼ Thus, the signal of the resonant scattering sodium lidar at 90 km is about times that of a Rayleigh lidar for the same PA product. Since this particular Cabannes scattering signal (at 589 nm) at 25 km is roughly the same as the resonant signal at 90 km (figure 1), and the molecular density at 25 km is about m 3, we can use this signal to estimate the Rayleigh lidar signal (at 532 nm) at 90 km (near the sodium layer peak height), by multiplying

3 Atmospheric lidar performance comparison Jan. 19, 2003 (ch1_file 96) Altitude (km) Photon counts per bin ~135 for 90 km & 25km Photons/150m-40s Figure 1. A raw photon profile with 150 m and 40 s resolution taken on 19 January 2003 from the sodium resonance lidar at Colorado State University (CSU). The fact that the return signal at 90 km is approximately the same as that at 25 km from the same lidar with the same PA product suggests the presence of two different scattering processes and/or species concentrations. The Rayleigh scattering at 90 km for this relatively small lidar with a telescope of 35 cm diameter is below the background level. The need to take these factors into account in comparing the performances of different atmospheric lidars is evident. it a factor of (25/90) 2 and ( )/( ) to account for the range and molecular density difference, and of (589/532) 4 to account for the 4 dependence of Rayleigh scattering, that is (1/13.0)( )(1/0.665) ¼ ( ) 1. This estimate gives an approximately 10 5 weaker Rayleigh signal at 90 km (at 532 nm) than that at 25 km (at 589 nm), consistent with the factor ( )/ ¼ estimated earlier, based on theoretical scattering cross-sections together with the climatological sodium density and standard air density. The PA product of the CSU sodium lidar that produced the resonant scattering signal shown in figure 1 is 0.05 W m 2, using a transmitter power of 0.5 W and a receiving telescope of 35 cm diameter. Comparing the performance of this lidar with a Rayleigh lidar that could be deployed with a laser with 20 W power at 532 nm and a large receiving telescope of 3.5 m diameter, a telescope available at the Starfire Optical Range (SOR), New Mexico [9], the latter has a PA value of 200 W m 2, which is 4000 times larger than the PA for the CSU lidar. If we were to compare the signal strength at 90 km in January for the CSU sodium resonance lidar at 589 nm with that of a Rayleigh lidar at 532 nm using the SOR telescope, we would calculate the PAMS values for each lidar. The Rayleigh lidar at SOR would have PAMS ¼ PA ¼ 200 W m 2. The PAMS for the CSU sodium fluorescence (resonant scattering) lidar is, however, (PA)(M)(S ) ¼ (0.05 W m 2 )( ) ( ) ¼ 3250 W m 2, about 16 times larger than that of the Rayleigh lidar at SOR. This calculation comparing the PAMS values for a Rayleigh lidar with

4 2726 C.-Y. She Table 1. Definition of PAMS, and PA versus PAMS for two lidars. Definition of parameter Rayleigh lidar with a telescope of 3.5 m diameter Sodium lidar with a telescope of 35 cm diameter Power P of transmitter (W) Area A of receiver (m 2 ) Mixing ratio M of species (90 km) Differential backscatter cross-section S (units of m 2 sr 1 ) Wavelength (nm) PA (W m 2 ) PAMS (W m 2 ) PA ¼ 200 W m 2 and a sodium resonance fluorescence lidar with PA ¼ 0.05 W m 2 is summarized in table 1. We note that, to compare the performances of lidars of the same type, the metric proposed, PAMS, is of little value, since the values of both M and S would be the same for lidars of the same type. In this case the standard metric, PA, serves the intended purpose very (or equally) well. However, when different types of lidar can be used to measure the same parameters in an atmospheric region, PAMS can be used simply and effectively for comparing their signal strengths, that is the rates of photons received. Two important examples that could benefit from PAMS comparison are Raman lidar [10] versus differential absorption lidar [11] for observing the same minor atmospheric species, for example water vapour or ozone, and Rayleigh lidar versus metal resonance lidar for measuring the mesopause region ( km) temperature and horizontal wind. I used the latter case as example for discussion (see table 1). We also note that the signal strength as indicated by PAMS and the measurement precision (of an atmospheric parameter) are different; indeed, the latter may be a better metric to gauge and evaluate lidar performance. The measurement precision depends on the signal-to-noise ratio, which in turn depends on receiver technology as well as the measurement technique used to retrieve the atmospheric parameter of interest. Although these factors should be considered, the measurement precision is generally proportional to the square root of the received photon number, and the relationship between measurement precision and signal photon rate for different measurement techniques are generally not very different. For different lidar types operated at comparable wavelengths, the detection technology is similar, and then the difference in transmitter and scattering processes dominates the difference in lidar performances. If different measurement techniques were used in comparison, their differences can usually be accounted for, at least qualitatively. To illustrate these points further, I compare nocturnal temperature and horizontal wind measurement between a Rayleigh lidar and a sodium resonance lidar. I believe that a practical and prudent approach is to start from measurement precisions already demonstrated experimentally and to scale the results to different altitudes and for systems with different PA products. French lidar at the Observatory

5 Atmospheric lidar performance comparison 2727 Table 2. Comparison of temperature and wind measurement uncertainties at 90 km. Definition of parameter Rayleigh lidar, OHP Mobile wind lidar, NASA Sodium lidar, CSU Power of transmitter (W) Telescope diameter (m) Area of receiver (m 2 ) Mixing ratio of species at 90 km S (in units of m 2 sr 1 ) 1 (532/355) 4 ¼ Wavelength (nm) PA (W m 2 ) PAMS (W m 2 ) reported Resolution reported 3 km, 3 h 0.7 km, 40 min 2.0 km,1 h Measurement (altitude) uncertainty reported 10 K (at 90 km a ) 6.5 m s 1 (at 30 km a ) 0.5 K or 1.5 m s 1 (at 90 km a ) PAMS for 80 cm telescope 10 (20 W) 12.5 b (5 W) c (0.5 W) (W m 2 ) (attainable power) Scaled uncertainty, 3 km, 1 h resolution at 90 km 9.5 K 119 m/s 0.2 K and 0.5 m s 1 a Air densities at 30, 40, 50, 60, 70, 80 and 90 km are m 3, m 3, m 3, m 3, m 3, m 3 and m 3 respectively. b Assuming 5 W power at 355 nm; PA ¼ 2.5 W m 2. c Assuming 5 W power at 355 nm; PA ¼ 0.25 W m 2. of Haute-Provence (OHP) has been measuring the middle atmospheric temperature since 1978 [12]. At 90 km, this lidar with PA ¼ 3Wm 2 was quoted to measure temperature with a 1 uncertainty of 10 K at 3 km and 3 h resolution. For Rayleigh wind measurement using (exclusively) Cabannes scattering, a recent molecular Doppler lidar [4] at 355 nm with PA ¼ 0.11 W m 2, quoted a measurement precision of 6.5 m s 1 with 0.7 km and 40 min resolution. Because of the shorter wavelength used, the PAMS for this lidar is 0.55 W m 2. These results may be compared with the nocturnal temperature and wind precision of 0.5 K and 1.5 m s 1 at 2 km and 1 h resolution from the CSU sodium lidar [13] with PA ¼ 0.05 W m 2, and PAMS ¼ 3250 W m 2. The detailed comparison is given in table 2. Note that, when scaled to the same resolution (3 km and 1 h) at 90 km, I chose an attainable telescope size (a diameter of 80 cm), and higher but attainable powers of 20, 5 and 0.5 W at 532, 355 and 589 nm respectively, giving corresponding PA products of 10, 2.5 and 0.25 W m 2. My estimated 1 measurement uncertainties are 9.5 K and 119 m s 1 for the Rayleigh lidar and 0.2 K and 0.5 ms for the sodium resonance lidar (see the last row of table 2). The square of the temperature uncertainty ratio between the Rayleigh and the sodium lidars is (9.5/0.2) 2 ¼ 2256; in view of the different types of lidar employed, this compares favourably with the ratio of the PAMS of the sodium lidar to that of the Rayleigh lidar, /10 ¼ The corresponding square of the wind uncertainty ratio is (119/0.5) 2 ¼ ; it is, however, about 44 times the corresponding PAMS ratio, =12:5 ¼ The much larger discrepancy for wind comparison is somewhat surprising, although costly spectral

6 2728 C.-Y. She analysis is required to perform a Rayleigh wind measurement. For example, with the double-edge technique [4], the received signal is typically divided into two separate channels, and each is filtered by a Fabry Pe rot interferometer, offset in the opposite direction from the centre frequency of the returned Cabannes spectrum; the two filtered signals are then compared for the determination of Doppler shift and, thereby, the line-of-sight wind. The filtered signal in each channel may be lower than the scattered return received for Rayleigh temperature measurement by a factor of as much as 10. On the other hand, the resonance scattering technique permits both temperature and line-of-sight wind to be retrieved on the same basis [14]. Thus the differences in measurement techniques are responsible for most of the discrepancy encountered between the Rayleigh wind and sodium resonance lidars. Using a telescope of 1.8 m [15] or 0.92 m [16] diameter, Rayleigh temperature measurements at 90 km appear possible. However, reported Rayleigh wind measurements [4, 15, 17] to date have yet to exceed 40 km in altitude. Scaling from the 119 m s 1 uncertainty at 90 km with 1 h and 3 km resolution of a lidar with PA ¼ 10 W m 2 to lower altitudes of 30, 40, 50, 60, 70 and 80 km with the same resolution, we obtained the respective measurement uncertainties of 0.54, 1.54, 3.80 m, 8.32, 18.8 and 45.4 m s 1. For this scaling, we used the air densities from U.S. Standard Atmosphere, 1976 [8] as listed in the footnote of table 2. The difficulty for Rayleigh wind measurements in the upper mesosphere with present technology is evident. Under sunlit conditions, the sky background dominates the noise in lidar observation at visible and soft ultraviolet wavelengths. A novel receiver technology using a Faraday filter [18], which can reject the sky background by a factor of , made a great difference. Without going into the details, PAMS provides a general guidance for comparing the figures of merit of different lidars under conditions when the background light is weak. For observations under sunlit conditions, the effectiveness in receiver technology must be exploited in addition to the PAMS consideration. In summary, I discussed the need to take the scattering process and species concentration into consideration when comparing the performances of different types of atmospheric lidar that could be used to measure the same atmospheric parameters, such as temperature and wind in the mesopause region. I proposed the use of two additional quantities, namely the relative differential scattering crosssection S and mixing ratio M, and the formation of the PAMS product as the performance index for comparing the figures of merit of atmospheric lidars. In this manner, the Rayleigh lidar at 532 nm would serve as a standard reference with PA ¼ PAMS. In general the PAMS value for a lidar may be orders of magnitude larger or smaller than its PA value. In addition to PAMS comparisons, I also pointed out the importance of measurement techniques, which in my view provided the main reason that Rayleigh wind measurement appears to be much more difficult than Rayleigh temperature measurement with current technology. Although I demonstrated the superiority of a metal resonance lidar, it unfortunately depends on the presence of atmospheric atoms, limiting its usefulness to between 80 and 110 km. This points to the challenges ahead for the lidar community to overcome the difficulties encountered in atmospheric wind measurements between 50 and 80 km in altitude.

7 Atmospheric lidar performance comparison 2729 Acknowledgment This work is supported in part by grants from the National Science Foundation, ATM and National Aeronautics and Space Administration NAG References [1] C.-Y. She, Appl. Optics (2001). [2] A.T. Young, Phys. Today (1982). [3] A. Hauchecorne and M.L. Chanin, Geophys. Res. Lett (1980). [4] B.M. Gentry, H. Chen and S.X. Li, Optics Lett (2000). [5] C.-Y. She and J.R. Yu, Appl. Optics (1995). [6] R.D. Bates, Planetary Space Sci (1984). [7] C.-Y. She, S.S. Chen, Z.L. Hu, et al., Geophys. Res. Lett (2000). [8] NOAA, NASA and US Air Force, U.S. Standard Atmosphere, 1976, Publication 1976O (US Government Printing Office, Washington, DC, 1976). [9] Y. Zhao, A. Liu and C. Gardner, J. Atmos. Solar Terrestrial Phys (2003). [10] H. Inaba and T. Kobayasi, Nature (1969). [11] R.L. Byer and M. Garbuny, Appl. Optics (1973). [12] A. Hauchecorne, M.L. Chanin and P. Keckhut, J. Geophys. Res (1991). [13] C.-Y. She, J. Atmos. Solar Terrestrial Phys (2004). [14] K.S. Arnold and C.-Y. She, Contemp. Phys (2003). [15] U. von Zahn, G. von Cossart, J. Fiedler, et al., Annls Geophys (2000). [16] J.P. Thayer, N.B. Nielsen, R.E. Warren, et al., Opt. Engng (1997). [17] C. Souprayen, A. Garnier, A. Hertzog, et al., Appl. Optics (1999). [18] H. Chen, M.A. White, D.A. Krueger, et al., Optics Lett (1996).