Direct-detection Doppler wind measurements with a Cabannes Mie lidar: B. Impact of aerosol variation on iodine vapor filter methods

Direct-detection Doppler wind measurements with a Cabannes Mie lidar: B. Impact of aerosol variation on iodine vapor filter methods Chiao-Yao She, 1, * Jia Yue, 1 Zhao-Ai Yan, 1,2 Johnathan W. Hair, 3 Jin-Jia Guo, 2 Song-Hua Wu, 2 and Zhi-Shen Liu 2 1 Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA 2 Ocean Remote Sensing Institute, Ocean University of China, Qingdao 266003, China 3 The Atmospheric Sciences, NASA Langley Research Center, Hampton, Virginia 23681, USA *Corresponding author: joeshe@lamar.colostate.edu Received 15 March 2006; revised 21 November 2006; accepted 19 January 2007; posted 13 February 2007 (Doc. ID 68904); published 20 June 2007 Atmospheric line-of-sight (LOS) wind measurement by means of incoherent Cabannes Mie lidar with three frequency analyzers, two double-edge Fabry Perot interferometers, one at 1064 nm (IR-FPI) and another at 355 nm (UV-FPI), as well as an iodine vapor filter (IVF) at 532 nm, utilizing either a single absorption edge, single edge (se-ivf), or both absorption edges, double edge (de-ivf), was considered in a companion paper [Appl. Opt. 46, 4434 (2007)], assuming known atmospheric temperature and aerosol mixing ratio, R b. The effects of temperature and aerosol variations on the uncertainty of LOS wind measurements are investigated and it is found that while the effect of temperature variation is small, the variation in R b can cause significant errors in wind measurements with IVF systems. Thus the means to incorporate a credible determination of R b into the wind measurement are presented as well as an assessment of the impact on wind measurement uncertainty. Unlike with IVF methods, researchers can take advantage of design flexibility with FPI methods to desensitize either molecular scattering for IR-FPI or aerosol scattering for UV-FPI. The additional wind measurement uncertainty caused by R b variation with FPI methods is thus negligible for these configurations. Assuming 100,000 photons from Cabannes scattering, and accounting for the R b measurement incorporated into the IVF method in this paper, it is found that the lowest wind uncertainty at low wind speeds in aerosol-free air is still with UV-FPI, 32% lower than with de-ivf. For 0.05 R b 0.07, the LOS wind uncertainty is lowest with de-ivf, and for R b 0.07, the IR-FPI outperforms all other methods. In addition to LOS wind uncertainty comparison under high wind speed conditions, the need of an appropriate and readily available narrowband filter for operating the wind lidar at visible wavelengths under sunlit condition is discussed; with such a filter the degradation of LOS wind measurement attributable to clear sky background is estimated to be 5% or less for practical lidar systems. 2007 Optical Society of America OCIS codes: 280.3640, 120.2440, 280.3340, 290.1090. 1. Introduction A brief review on direct-detection Doppler lidar wind measurements using both Fabry Perot interferometer (FPI) and iodine vapor filter (IVF) was given in a companion paper (paper A) [1]. In that paper, four methods using three different frequency analyzers were presented. They were (a) and (b) double-edge 0003-6935/07/204444-11$15.00/0 2007 Optical Society of America (de) Fabry Perot interferometer (FPI), at 1064 nm (IR-FPI) and at 355 nm (UV-FPI), and (c) and (d) iodine vapor filter (IVF) at 532 nm using one absorption edge, single edge (se-ivf), and both absorption edges, double edge (de-ivf), respectively. A comparative study was made for low wind speed conditions assuming known atmospheric temperature at 275 K and specified aerosol mixing ratio, R b (defined as the ratio of the aerosol volume backscatter coefficient to the molecular volume backscatter coefficient), and 100,000 R b 1 photons to the receiver. We found the 4444 APPLIED OPTICS Vol. 46, No. 20 10 July 2007

line-of-sight (LOS) wind uncertainty of UV-FPI in the aerosol-free air R b 0, is lower by 16% than that of de-ivf, which has the lowest wind uncertainty for R b between 0.02 and 0.08, and for R b 0.08, IR-FPI has the lowest wind uncertainty. In reality, atmospheric temperature and R b are typically unknown and have significant temporal and spatial variations. Owing to the flexibility in optimization and desensitization that exists with FPIs, the variation in temperature and R b does not affect LOS wind measurement much. On the other hand, the uncertainty in R b will cause wind bias and error when an IVF system is used. Briefly, in the case of an IR-FPI, a ratio of aerosol scattering signal measured by the two Fabry Perot channels is employed for wind measurement. A change in aerosol scattering mixing ratio will affect both numerator and denominator in the same way; its effect to the first order cancels in the signal ratio. The variation in aerosol scattering will change the measured signal ratio for wind retrievals for the case of UV-FPIs, yet researchers can design these FPIs with parameters to minimize this impact [2]. The parameters of an IVF, on the other hand, are dictated by nature; there is no effective way to desensitize either molecular scattering signal or aerosol scattering signal for wind measurements. Therefore, the aerosol mixing ratio needs to be known with sufficient accuracy, and its effect must be accounted for and included in the data analysis. As described in paper A [1], to execute directdetection Doppler wind measurements with a Cabannes Mie lidar, the received signal is divided into two channels. The received signal photon number of the two channels, N 1 and N 2, are functions of both R b and Doppler frequency shift, D, resulting from LOS wind, V LOS, with D 2V LOS, where is the wavelength of the lidar transmitter. A wind ratio R W was defined for LOS wind measurements as R W D, R b N 1 D, R b N 2 D, R b. (1) Variations in either D or R b will induce a fractional change in R W : dr W R W R W R W D R W R D R W R b. (2) b When R b is known or given, as in the case of paper A, the second term is zero, and the measured fractional change, dr W R W, is the product of wind induced Doppler shift, D, and measurement sensitivity, S D R W D R W, defined as the fractional change in the wind ratio per unit change in Doppler shift. This gives rise to measured LOS wind as V LOS 2 d D 2 S D 1 dr W R W. (3) Here, strictly speaking, the measurement sensitivity, S D, depends on both D and R b. To appreciate the similarities and differences in the impact of aerosol mixing ratio and atmospheric temperature on LOS wind uncertainty between the four methods with analyzers of nearly the same maximum transmission of 80%, we plot the normalized difference wind ratio (NDWR) [not to be confused with the R W or the normalized wind ratio (NWR) of Liu et al. [3], as a function of Doppler shift, D, for selected values of R b, and temperature, for the four methods, respectively, in Figs. 1(a) 1(d). The NDWR at a given temperature, T, is defined as NDWR R W D, R b R W 0, R b. (4) R W 0, R b We choose to plot the NDWR, because it is zero for zero LOS wind (or zero Doppler-shift, D 0). Whether we display the NDWR or the wind ratio R W D, R b, the sensitivity and signal-to-noise ratio (SNR) of the measurement come from the fractional change in R W D, R b, and the resultant figures of merit of the four methods will not be different. A comparative study of Fig. 1 does allow a more intuitive appreciation of relative LOS wind uncertainty due either to photon noise or to variation (or lack of knowledge) in R b. We chose different range of Doppler shifts, so that Figs. 1(b) 1(d) cover the same range of LOS wind; at 532 nm a 50 m s LOS wind corresponds to a 0.188 GHz Doppler shift. For the IR-FPI at 1064 nm, typically used in the troposphere not much higher than the planetary boundary layer, the range of LOS wind covered in Fig. 1(a), is a factor of 5 smaller. We note that the backward aerosol scattering mixing ratio is different for different wavelengths, and it is dependent on the shape, size, and composition of aerosol. Therefore R b is larger for the IR than the visible and the visible larger than the UV. The typical range for a continental daytime planetary boundary layer [4,5] is 0 R b 2, 0 R b 5, and 0 R b 40, for wavelengths of 355, 532, and 1064 nm, respectively. We also note that the R b value of 0.02 may be considered as aerosol-free. We consider these corresponding ranges of R b for atmospheric temperatures of 275 and 300 K in Fig. 1. As expected, for IR-FPI, NDWR is independent of R b and temperature. Since the parameters of the vis-fpi_s or UV-FPI discussed in paper A [1] were chosen to minimize the impact of aerosol scattering either at 532 nm [2] or at 355 nm [6,7], the NDWRs of these FPIs are essentially independent of variation in R b, as shown in Fig. 1(b) for UV-FPI. On the other hand, the use of IVF as a frequency analyzer yields a larger range of NDWR in response to the change of R b as it has a higher sensitivity to aerosol scattering. Thus the R b values must be known or provided from an independent measurement [3,8]; otherwise it could lead to error (or bias) in the LOS wind retrieval. The fact that Fig. 1(d), de-ivf, is much more asymmetric than Fig. 1(c), se-ivf, is consistent with the definition of NDWR. Though a variation in R b causes a huge change in NDWR for de-ivf, especially so for a 10 July 2007 Vol. 46, No. 20 APPLIED OPTICS 4445

Fig. 1. (Color online) Normalized difference wind ratio (NDWR) as a function of Doppler shift for the four direct-detection methods, each with three selected Rb values within the typical range of values at 275 K. (a) IR-FPI at 1064 nm, (b) UV-FPI at 355 nm, (c) se-ivf at 532 nm, and (d) de-ivf at 532 nm. In addition, the curves for two Rb values at 300 K are shown in panels (b) (d). The NDWR for IR-FPI in (a) is independent of temperature and Rb. positive Doppler shift as shown in Fig. 1(d), the variation in Rb from the Rb value experimentally determined by the same signal strength for LOS wind measurement will give a wind uncertainty less than that caused by photon noise fluctuation (as shown in Fig. 4 below). How to best incorporate an independent Rb measurement into the lidar system and how to assess the associated impact on wind measurement uncertainty under different wind conditions are the issues to be taken up in this paper. At a given wind shift, VLOS, or Doppler shift, D, in addition to the dependence on aerosol mixing ratio, Rb, the NDWRs of all four methods depend on atmospheric temperature (less so on pressure). To reveal this dependence, we plot two NDWR curves of two different Rb values at 300 K to each panel to allow a comparison of the NDWRs between two different temperatures (275 and 300 K). We use a temperature of 300 K (and a pressure of 1.0 atm) and a temperature of 275 K (and a pressure of 0.75 atm) to represent standard air at sea level and at a typical altitude of 3 4 km, respectively. The NDWR for IR-FPI is independent of molecular scattering, thus it is independent of both temperature and aerosol as can be seen in Fig. 1(a). Comparing the NDWR difference between 300 and 275 K (25 K difference) 4446 APPLIED OPTICS 兾 Vol. 46, No. 20 兾 10 July 2007 for Rb 0.0 in Figs. 1(b) 1(d), we found that at D 0.15 GHz, there is an 11% difference in the NDWR for the UV-FPI, and at a D 0.10 GHz, a 17% and a 16% difference, respectively, for the se-ivf and deivf at 532 nm. Such difference (bias) may be deemed not severe as they are 4%, 6%, and 7% per 10 K, respectively for UV-FPI, se-ivf and de-ivf. Judging from Figs. 1(b) 1(d), the fractional differences due to temperature variation for higher values of Rb should be comparable. The bias resulting from lack of knowledge in Rb is very different between the two frequency analyzers. From Fig. 1(b), we determined the bias in the NDWR, at D 0.15 GHz and Rb 0.75, for example, to be 0.1% per Rb 0.1, showing that the UV-FPI at 355 nm is indeed insensitive to aerosol scattering. Indeed, the difference between Rb 0 and Rb 2 at the same temperature is less than that between 275 and 300 K for the same Rb. On the other hand, Figs. 1(c) and 1(d) show the corresponding changes in NDWR at D 0.1 GHz and Rb 0.75 to be as much as 6% and 10% per Rb 0.1, respectively for se-ivf and de-ivf. Depending on the value of D and Rb, the bias resulting from uncertainty in Rb for se-ivf and de-ivf could be severe. Thus the main task of this paper is to perform a comparison between the four methods, along with the simultaneous aero-

sol mixing ratio measurement incorporated into the IVF methods. We discuss the LOS wind error resulting from variation in R b in Section 2, the incorporation of R b measurement in Section 3, and the results of wind uncertainty at different wind speeds due to both photon noise and R b variation for IVF systems as well as performance comparison of the four methods in Section 4. In addition, we discuss the challenge of using visible wavelengths for lidar observations under sunlit conditions, and we estimate the degradation caused by sky background in Section 5. The conclusion follows in Section 6. The estimation of time needed to accumulate 100,000 photons from Cabannes scattering with lidars of two different power aperture (PA) products is presented in Appendix A. Before we discuss the impact of R b variation, we point out that both the measurement sensitivity, S D, and the SNR due to photon noise are a function of D and R b. The wind uncertainty dependence on Doppler shift was ignored in paper A [1], following the general practice in the literature. However, if we wish to discuss the measurements of LOS wind up to 20 m s or higher, the wind speed, or D dependence, must be accounted for. In Figs. 2(a) 2(d), we plot the measurement sensitivity S D and the SNR as functions of R b at selected Doppler shifts for IR-FPI, UV-FPI, se-ivf, and de-ivf, respectively. In general the impact of wind speed difference on measurement sensitivity is higher than that on SNR. Owing to the symmetry that exists in a double-edged device, the change in measurement sensitivity due to wind speed variation for IR-FPI, UV-FPI, and de-ivf is smaller than that for se-ivf. This is especially true for UV-FPI, Fig. 2(b), and its sensitivity is nearly independent of both D and R b. In general, the impact of wind speed on both sensitivity and SNR appeared to be minor, giving rise to a small effect of wind speed on the LOS wind uncertainty resulting from photon noise. As to be shown in Fig. 4 below, the impact of wind speed on wind uncertainty resulting from R b variation is, however, much more pronounced, and it must be accounted for in the IVF systems. 2. Line-of-Sight Wind Uncertainty and Variation in Aerosol Mixing Ratio To assess the LOS wind uncertainty, dv LOS, due to uncertainty in R b, R b, we treat the fractional change in the wind ratio, dr W R W, resulting from change in aerosol mixing ratio, R b, as an equivalent Doppler wind shift, D. We then equate the two terms on the right-hand side of Eq. (2) and express d D in terms of variation in R b, leading to the wind uncertainty (or bias) due to variation in R b as V LOS 2 D 2 S D 1 R W R W R b R b. (5) Fig. 2. Dependence of LOS wind measurement sensitivity, S D, and SNR at three different Doppler shifts as a function of R b. (a) IR-FPI, (b) UV-FPI, (c) se-ivf, and (d) de-ivf. The curves were evaluated for Doppler shifts corresponding to LOS wind speeds of 0, 13.3, and 26.6 m s for (b) (d), and of 0, 5.3, and 10.6 m s for (a). 10 July 2007 Vol. 46, No. 20 APPLIED OPTICS 4447

Fig. 3. Effect of R b variation on LOS wind measurements. (a) Fractional change of R W per unity change of R b, R W R W R b, plotted as a function of R b with Doppler shifts of 0, 0.05, and 0.10 GHz for both se-ivf and de-ivf. (b) Variation and fractional variation of R b, R b, and R b R b for both se-ivf and de-ivf, based at signal levels of 100,000 R b 1. Here, R W D, R b is a function of D and R b. From Eq. (5), it is clear that the wind uncertainty, dv LOS, due to R b variation depends on the product of three factors, S 1 D, fractional change of wind ratio per unit change in R b, R W R W R b, and variation in R b, R b. Comparing Eq. (5) above with Eq. (11) of paper A [1], we can see that the product of R W R W R b and R b plays the same role of R W R W SNR 1 due to photon noise. To appreciate the dependence of R W R W R b and R b on R b and D, we plot them in Figs. 3(a) and 3(b), respectively, for both se-ivf and de-ivf. From Fig. 3(a), we see that the quantity R W R W R b decreases as R b increases, and it is negligible at zero Doppler shift and increases as wind speed increases. As will be discussed in the next section with Eq. (6), the variation in R b, R b, depends on the signal strength used for the determination of R b. We shall assume the same signal strength, 100,000 R b 1 for both wind and R b measurements, and we plot in Fig. 3(b) both R b and its fractional variation R b R b as a function of R b. We see that unlike R W R W R b, the quantity, R b, as determined from Eq. (6) in the next section, increases linearly with R b, and that with 100,000 R b 1 photons, we can determine R b to an accuracy better than 5% for R b 0.25. Though, as R b decreases further, the fractional R b variation increases to more than 5%, the LOS wind uncertainty it causes, as it turned out, is comparable to, or less than, that caused by photon noise. We confirm this statement by comparing LOS wind uncertainties due to photon noise to that due to R b variation, as a function of R b for selected Doppler shifts ( D 0, 0.05, and 0.10 GHz). This is done with Figs. 4(a) and 4(b) for se-ivf and de-ivf respectively. For the se-ivf, Fig. 4(a), the wind uncertainties due to photon noise (thin curves) vary mildly with Doppler-shift, and the three thin curves are seen to be closely spaced; at R b 0.5, the uncertainties are 0.73, 0.72, and, 0.78 m s, respectively at D 0, 0.05, and 0.10 GHz. The corresponding values due to the R b variation are 0.019, 0.142, and 0.267 m s. Though the latter set of values shows a higher fractional change (between these D values), their values are lower than those due to photon noise, suggesting Fig. 4. (Color online) LOS wind uncertainties as a function of R b due to photon noise (thin) and R b variation (thick) at three Doppler shifts, 0, 0.05, and 0.10 GHz, based on 100,000 R b 1 signal photons received for (a) se-ivf and (b) de-ivf. Notice that the uncertainty attributable to R b variation at zero Doppler shift for de-ivf in (b) is so small that it is off the scale. 4448 APPLIED OPTICS Vol. 46, No. 20 10 July 2007

that the accuracy R b determined by the same signal strength (detailed in next section) is sufficient. A similar situation is observed in Fig. 4(b) for the de-ivf. Here again the photon-noise-caused wind uncertainties depend on the Doppler shift only mildly, while the uncertainty caused by R b variation depends on Doppler shifts much more. At R b 0.5, the wind uncertainties attributable to photon noise are 0.57, 0.58, and 0.62 m s, respectively at D 0, 0.05, and 0.10 GHz, and the corresponding values due to R b variation are smaller and are respectively, 0.00075, 0.198, and 0.389 m s. At zero wind, D 0, the uncertainty due to R b variation is negligible; in fact it is off the scale for the de-ivf. The message of Fig. 4 may be summarized by stating that the wind uncertainty attributable to photon noise is only mildly dependent on Doppler shift; it increases somewhat as wind speed increases. The wind uncertainty due to R b variation on the other hand increases considerably for large Doppler shift. Even at D 0.1 GHz, the wind uncertainty attributable to R b variation with the R b value determined by the same signal level is still smaller than that due to photon noise. Therefore our proposed strategy is to implement R b measurement at the same signal level and add the associated wind uncertainty in quadrature to the wind uncertainty due to the photon noise. 3. Measurement of Aerosol Mixing Ratio, R b One good way to measure R b is to compare the signal from a total scattering channel (without filter) and that from a molecular channel with the laser frequency tuned to the center of the absorption well in a setup similar to the one the se-ivf uses. The transmission factors for this case would be f a 0 and f c 0.3 (assuming again an atmospheric temperature of 275 K) with the filter shown in Fig. 2(a) of paper A [1]. Substituting these parameters into Eqs. (1a) and (1b) of paper A, the signal received for the R b measurement would be N m N m f c and N R N R R b 1 for the measurement and reference channels, respectively. From these received signals, both the aerosol mixing ratio and the associated uncertainty can be shown to be R b mf c N R R N m 1; dr b R b 1 dn R R b R b 1 N R N m N R N m R b 1 1 N R dn m N m, 1 1 m f c R R b 1 N. (6) For N 100,000, the variation of the determined R b, R b, and R b R b, are shown in Fig. 3(b). The proposed implementation of LOS wind measurements with IVF can then be envisioned as follows. For the se-ivf setup, we tune the laser frequency alternatively to the edge (for wind measurement) and to the center (for R b measurement) of the absorption line. As discussed in paper A [1], in this case the received signal is split as m 0.6, and R 0.4. For the de-ivf, we also have a total scattering channel and a molecular channel, but with a 90% 10% split as in paper A, i.e., m 0.9, and R 0.1. That this is a good choice may be verified by considering the optimization of LOS wind uncertainty under different values of R b and wind speed (or D ). We have computed and plotted (not shown) the LOS wind uncertainty as a function of 1 m for the range of R b from 0to5at D 0, 0.05, and 0.1 GHz and found that the optimum splits fall between 80% 20% and 100% 0% depending on the values of R b and D. Thus we use a 90% 10% split and deem R 0.1 a good choice to increase the signal in the molecular channel to reduce LOS wind uncertainty due to photon noise. For the de-ivf setup, we then tune the laser frequency cyclically from one edge to the other, then to the well center of the absorption line. We then adopt a strategy to measure R b each time we measure LOS wind, i.e., using 50% of the dwell time in the se-ivf and 33% of the time in de-ivf for R b measurements. This implementation will decrease the SNR by 2 for the se-ivf, and by 1.5 for the de-ivf, thus increasing the LOS wind measurement uncertainty by factors of 1.4 and 1.2, respectively. 4. Results and Performance Comparison with Aerosol Mixing Ratio Measurement Incorporated The resulting total LOS wind uncertainties for the four methods at a signal of 100,000 Cabannes scattering photons (90,000 photons for de-ivf) accounting for the time needed for R b measurement, are shown in Fig. 5, with (a) 0 R b 1.0 and (b) 0 R b 10. Here we show wind uncertainty at both low wind speed (at V LOS 0) and high wind speed V LOS 26.6 m s, corresponding to D 0.1 GHz at 532 nm). As mentioned earlier, the wind uncertainty due to photon noise changes slightly with wind speed. In the case of FPI, the fact that wind uncertainty at low wind speed is slightly lower reflects the higher sensitivity as shown in Fig. 2(a). The curves for IR- FPI show this slight dependence nicely in Fig. 5(a), while the difference between UV-FPI curves is so small and not discernable in the figure. For IVF, since the wind uncertainty due to R b variation increases considerably with wind speed, the uncertainty at high wind speed is much higher than that at low wind speed. As a result, the total LOS wind uncertainties for se-ivf at R b 0.5 are 1.04 and 1.17 m s for D 0 and D 0.1 GHz, respectively. The corresponding values for de-ivf are 0.70 and 1.01 m s. For the FPI, the wind uncertainty is caused mainly by photon noise only, and the effect of wind speed on LOS wind uncertainty is minor; their values for R b 0.5 at zero wind and high wind (26.6 m s for UV-FPI and 10.6 m s for IR-FPI) are 2.06 and 2.07 m s for UV- FPI and 0.27 and 0.32 m s for IR-FPI. As can be seen in Fig. 5(a), the wind uncertainty of se-ivf at D 0 between R b 0.1 and R b 0.5 nearly coincides 10 July 2007 Vol. 46, No. 20 APPLIED OPTICS 4449

Fig. 5. (Color online) LOS wind uncertainty based on 100,000 Cabannes photons and ideal photodetectors for the four methods as a function of aerosol mixing ratio, R b, (a) 0 R b 1.0, and (b) 0 R b 10.0, with the effect of extra time required for R b measurement in se-ivf and de-ivf included. The wind uncertainties for both low wind speed (thin) and high wind speed (thick) in gigahertz are shown. In (a) the curve for IR-FPI at low wind speed D 0 is very slightly lower than that at high speed D 0.02, while the difference between UV-FPI curves is so small that it is not discernable in the figure. Notice that the wind uncertainty of se-ivf at D 0 between R b 0.1 and R b 0.5 is nearly coincident with that of de-ivf at D 0.1 GHz; the former exceeds the latter for R b 0.5 and approaches that of se-ivf at D 0.1 GHz for large values of R b, as in (b). with that of de-ivf at D 0.1 GHz; the former exceeds the latter for R b 0.5, and approaches that of se-ivf at D 0.1 GHz for large R b, as shown in Fig. 5(b). At R b 0, the wind uncertainty requires no R b measurement, and they were calculated in paper A to be 2.33, 2.79, 4.31 m s and for UV-FPI, de-ivf, se-ivf, and IR-FPI, respectively. From Fig. 5(a), we see that at R b 0.0, the order of LOS wind uncertainty for the four methods is the same; they are 2.33, 3.41 2.79 1.5, 6.09 4.31 2 and, and 2.35, 5.51, 6.60, and, respectively, at the low wind speed D 0 and the high wind speed limit 26.6 m s. We find that the wind uncertainty at the low wind speeds in aerosol-free air is lowest with UV-FPI, which is 32% lower than de-ivf. For 0.053 R b 0.067, the LOS wind uncertainty is lowest with de-ivf, and for R b 0.067; the IR-FPI outperforms all other methods. At high wind speed, the LOS wind uncertainty of UV-FPI and IR-FPI is lowest for R b 0.071 and for R b 0.071, respectively. For R b 0.2, the uncertainty of IVF falls between IR-FPI and UV-FPI independent of wind speed. Due to the factor of 1.5 and 2 increases in measurement time required for the R b measurement for de-ivf and se- IVF, respectively, except for the narrow range of 0.053 R b 0.067 at low wind speed, there exists no range of R b values for which the IVF method corresponds to the lowest wind uncertainty. Though the actual signal will be stronger owing to aerosol scattering, the measurement time required to receive 100,000 photons because of Cabannes backscattering (only) may be estimated. This is done in Appendix A for two lidars with PA 0.5 Wm 2, and 10 Wm 2 for 5% range resolution. For a lidar of PA 0.5 Wm 2, the estimated required measurement time, accounting for realistic detector quantum efficiency and optical losses, is less than1sat5km,and 3 s at 10 km, both with 5% vertical resolution. Because of the time spent for R b determination, the wind uncertainty will be increased by a factor of 1.4 for se-ivf and 1.2 for de-ivf. As an analysis paper, we do not compare the technical details of the pros and cons with each of the four methods to achieve a given signal level at respective wavelengths. However, we do note that though the cross section of Cabannes scattering is approximately a factor of 5 larger at 355 nm than at 532 nm, and the de-fpi method has been robustly deployed for regular observations with doubled Nd:YAG lasers at 532 nm [9,10]. Though de-ivf outperforms se-ivf, the need to shift the operation frequency from one edge to the other (by 1.92 GHz) with the de-ivf represents a technical challenge. One way is to modulate the seed laser (at 1064 nm) with a dual-pass tandem acoustooptic modulator (AOM). The acoustic modulation frequency required would be 1.92 GHz 4 480 MHz. Since the seed light is in a laser cavity, the modulating frequency must be chosen so that the exact shifted seed frequency of 960 MHz is an integer times the longitudinal mode spacing of the laser [11]. Because IR light is used, the dual-pass AOM conversion efficiency may be 20% as opposed to 60% in the visible. However, even though a more powerful seed laser may then be required, the output power of the slave pulsed laser at the shifted frequency is not reduced. Furthermore, since a reference channel is present in the de-ivf scheme, the received signal in the reference channel can and should be used to normalize the signals acquired in the measurement channel N mi, when the laser is tuned to the edges, to form wind ratio, R W, for wind measurements. We also note that depending on the seed laser used, iodine absorption lines other than 1109 can also be exploited for wind measurements [12]; line 1106 is a viable 4450 APPLIED OPTICS Vol. 46, No. 20 10 July 2007

alternative. Also further compromises could be designed with different iodine densities and cell lengths to obtain optimal performance for particular applications. 5. Observations Under Sunlit Condition Skylight background management is not only important but it is also essential for lidar operation under sunlit condition. The range of clear sky background radiance at 532 nm [13] is between 50 and 100 Wm 2 sr 1 m 1, and it is approximately a factor of 2 smaller at 1064 and 355 nm [14]. The degradation due to sky background at 355 nm (thus also at 1064 nm) was shown [14] to be acceptable for space lidar operation. In this section we discuss the method for sky background management and estimate the degradation in wind uncertainty caused by clear sky background at 532 nm. Once the photon counts resulting from sky background, N SB, in a time duration required to accumulate a particular signal count level, say N 100,000, are determined, the SNR of the measurement is simply SNR N N N SB. The decrease of SNR leads to a increase in LOS wind uncertainty by a factor of 1 N SB, giving rise to a degradation [15] N owing to sky background of 100 1 N SB N 1 %. Since like the LOS wind uncertainty, the uncertainty in the R b measurement is also inversely proportional to the SNR [see Eq. (6)] the same percent degradation applies to the R b measurement. The sky background counts received may be written as [16] N SB hc S b o A o d, (7) where is the detection efficiency taken to be 0.01, the same as in Appendix A for signal reception, and h and c are the Planck constant and speed of light. The other quantities, S b,, o, A o, and are the sky background radiance in Wm 2 sr 1 m 1, the wavelength in meters, the viewing solid angle in steradians, the telescope aperture area in square meters, and the bandwidth of the narrowband interference filter in micrometers, respectively. The integration time, d, in seconds is the same as t in Appendix A, the time needed to accumulate a particular signal count level, say N 100,000. The reduction factors, and are in Eq. (7) to account for the spectral absorption (rejection) of sky background by IVF (FPI) and the fraction of time in d that the background light is making contribution to noise fluctuation, respectively. With laser frequency and analyzers given, either FPI or IVF, the noise resulting from sky background can only be reduced, to the extent possible, by the use of a very narrowband interference filter with bandwidth and by reducing the fraction of integration time that sky background contributes to noise fluctuation,. Since for vertical resolution z, the round-trip time with lidar signal is 2 z c, the time that the sky background will contribute to noise fluctuation is 2 z c r per second, where r is the pulse repetition rate. The factor may then be expressed as 2 z c r. (8) Equation (8) suggests that it is advantageous to use higher pulse power with lower repetition rate. For this discussion, we nonetheless assume a 50 Hz system, i.e., r 50. With these parameters, we note that Doppler wind measurement under sunlit condition using a lidar of modest PA product at 532 nm has been demonstrated to an altitude greater than 10 km with either FPI 15 or IVF 17 receiving systems. In their recent work, Liu et al. [17] performed wind measurements with se-ivf at 532 nm, and used an interference filter with 0.11 nm bandwidth (76% peak transmission) and a field of view of 170 rad. Recent advances in coating technology make the custom designed narrowband interference filter with high peak transmission commercially available. Thus for this analysis, we take 0.1 nm 1.0 10 4 m, and o 2 10 4 2 4, corresponding to a field of view of 200 rad, for the estimation of N SB. Substituting these values along with 0.01, and Eq. (8) into Eq. (7), we have N SB hc S b o A o d 1.05 10 3 S b A o r d z. (9) The reduction factor of background light due to spectral absorption (rejection) of FPI (IVF),, may be estimated from the spectral response of the analyzer. For FPI, as defined in [1], is roughly 2 FWHM FSR, giving 0.067 and 0.28, for IR-FPI and UV-FPI, respectively. Iodine vapor has a great number of absorption lines [18], giving alternate transparency and opacity as a function of frequency; we may approximate 0.5 for IVF. From Appendix A we compute the time required to accumulate 100,000 Cabannes backscattered photons, t d, for a number of scenarios. For discussions here, we consider four cases: Cabannes scattering from 5 km with a lidar of PA 0.5 Wm 2, from 10 km with two lidars of PA 0.5 Wm 2 and PA 10 Wm 2, and from 30 km with lidar of PA 10 Wm 2, all with 5% range resolution. Taking S b 100 Wm 2 sr 1 m 1, and d from Appendix A for these scenarios at 532 nm and a 50 Hz systems, we can estimate clear sky background counts and percent degradation in SNR at 532 nm from Eq. (8); their results are tabulated in Table 1. A quick examination of the percent degradation in Table 1 suggests that the sky background should not be a limiting concern at 532 nm, provided a proper narrowband filter is used in the receiving system, a 10 July 2007 Vol. 46, No. 20 APPLIED OPTICS 4451

Table 1. S b ( ) a PA o Wm 2 Background Counts and Percent Degradation in SNR at 532 nm with 50 Hz System A o m 2 Alt. Percent km z m d t s N SB Degradation 100 0.5 0.1 5 250 0.5 0.8 27.9 0.014 100 0.5 0.1 10 500 0.5 3.0 209 0.10 100 10 0.5 10 500 0.5 0.15 52.4 0.03 100 10 0.5 30 1500 0.5 10.0 10,474 5.11 a Wm 2 Sr 1 m 1. We assume 0.1 nm bandwidth and 200 rad field of view. conclusion similarly reached by McGill et al. [14] when they performed a realistic simulation of nadir wind lidar at 355 nm. Our estimate in Table 1 showed a 5% degradation attributable to background from clear sky for a wind system with PA 10 Wm 2 even at a range of 30 km. This leaves room for considering sky with modest cloud coverage and the use of a narrowband filters with widths wider than 0.1 nm. For example, if we take background radiance for cloudy sky to be ten times larger, the % degradation in SNR would be 43%; in this case, we would recommend the use of a 10 Hz system, then the background counts will be reduced by a factor of 5, giving a 10% degradation. We also point out that if aerosol scattering is included in the lidar signal, the percent degradation in Table 1 would be reduced. 6. Discussion and Conclusion As in companion paper A [1], we have presented performance evaluations on three different frequency analyzers. Unlike in paper A [1], we now assume the atmospheric temperature and aerosol mixing ratio to be unknown. Within the range of temperatures encountered in the atmosphere, we found that the impact of atmospheric temperature variation on wind uncertainty is small. However, for IVF methods, though the temperature effect is still not important, the knowledge of aerosol mixing ratio, R b is crucial for the wind measurement. We then discussed the method for incorporating R b measurement and included it into the analysis of LOS wind uncertainty for the IVF systems when the performances of the four methods are compared. Unlike most earlier analytical reports, we also consider the measurement sensitivity and uncertainty of four methods at large Doppler shifts and found that the IVF methods are more sensitive to the variation in R b in this limit. In addition, we consider wind measurement under sunlit conditions and compute the degradation attributable to sky background. Though sky background radiance varies as a function of wavelength, the clear sky radiance at 532 nm is only approximately a factor of 2 higher than that at 355 and 1064 nm. We have evaluated the background counts under clear sky and the associated percentage degradation in SNR for four scenarios. As shown in Table 1, we found only 5% degradation for LOS wind measurement at a range of 30 km for a 50 Hz system at 532 nm with PA 10 Wm 2, provided a proper narrowband filter 0.1 nm is used. While the UV-FPI is desensitized against aerosol scattering, the performance of the IVF methods depends on the knowledge of the aerosol mixing ratio, R b. Our analysis showed that at the signal level of 100,000 R b 1 photons, the wind uncertainty due to R b variation is always smaller than that due to photon noise and is negligible at low wind speed. Thus though R b measurement is not necessary at low wind speed, for the proposed IVF methods, we only have to account for the extra time required for R b measurements. We also compute the uncertainty due to R b variation at high wind speed, and add it in quadrature to the photon noise uncertainty for the evaluation of LOS wind uncertainty. With this in mind, we found that in the low wind speed limit, the UV-FPI outperformed the other methods at R b 0.0, with LOS wind uncertainty of 2.33, 3.41, 6.09, and, respectively for UV-FPI, de-ivf, se-ivf, and IR-FPI, for N 100,000. For the high wind speed limit 26.6 m s, the corresponding uncertainties are 2.35, 5.51, 6.60, and. The LOS wind uncertainty from de-ivf is less than a factor of 2 lower than that of se-ivf. Although the LOS wind uncertainties for both de-ivf and se-ivf at large Doppler shifts may increase significantly, the relative order of uncertainty for the four methods remains the same: the UV FPI is the best in an atmosphere without aerosol, the IR-FPI in an atmosphere with aerosol scattering dominance. For R b 0.2, the de-ivf and se-ivf perform between the UV-FPI and IR-FPI throughout. To take advantage of design flexibility on FPI systems to desensitize molecular or aerosol scattering, one uses both IR-FPI and UV-FPI for wind measurements to cover different altitude ranges with different atmospheric conditions. On the other hand, since the flexibility for desensitization does not exist with the IVF system, a single IVF system with R b measurement incorporated is used for different atmospheric regions, regardless of its aerosol conditions. Compared with FPI filters, the ease of alignment, very high degree of spectral stability, and lower cost are attractive features with IVF. Unless the atmospheric condition of interest is known to be either aerosol-free or aerosol dominant, the IVF at 532 nm is a viable and attractive system for wind measurements. Appendix A. Estimation of Cabannes Scattering Signal at 532 nm We have employed a signal level of 100,000 photons (attributable solely to Cabannes backscattering) for the discussion and comparison of LOS wind uncertainty between the four direct-detection methods. The spatial and temporal resolutions of the LOS wind measurement to which this signal level corresponds would depend on the PA product of the lidar as well as on atmospheric conditions. To put things in perspective, we consider the backscattered signal in photon numbers, N, from a height range z, with 4452 APPLIED OPTICS Vol. 46, No. 20 10 July 2007

Table 2. Estimation of Times Needed to Accumulate a Prespecified Signal Level Range, z (km) 2 5 10 b 10 b 30 50 60 70 80 90 PA (Wm 2 ) 0.5 0.5 0.5 10 10 10 10 10 10 10 Molecular density, 2.09 E25 1.53 E25 8.60 E24 8.60 E24 3.83 E23 6.44 E21 6.44 E21 1.72 E21 3.80 E20 7.10 E19 n(z) a (m 3 ) R. bin, z (km) 0.1 0.25 0.5 0.5 1.5 2.5 3.0 3.5 4.0 4.5 Time for 100,000 photons, t (s) 2.21 E-01 7.56 E-01 2.69 E00 1.34 E-01 9.05 E00 8.98 E02 1.08 E03 4.70 E03 2.43 E04 1.47 E05 a Molecular density taken from U.S. standard air [21], 1976. b At 10 km, both small and large telescopes are considered. molecular density n z, a range resolution, z, and a time interval, t. From the lidar equation, we have N P t h A z 2 d d n z z. (A1) Here, is the detection efficiency and P the transmitting power of the lidar at the range z in question. Including the quantum efficiency of the photomultiplier tube, the passive loss in optics, the atmospheric transmission, and the use of a narrowband interference filter, we set 0.01 for simplicity. At 532 nm, the backscattering differential Cabannes cross section is 6.0 10 32 m 2 sr [19,20], and the received backscattered photons from Cabannes scattering at a height z is then PA t z N 6.0 10 32 n z 3.47 10 19 z 2 1.73 10 13 PA n z 10 6 z km 2 t z. (A2) The time that is required to receive N photons due to Cabannes backscattering at z and range resolution z would be 18 t 5.78 10 PA N z km 2 1 n z z m ; 0.01. (A3) To provide a realistic estimate, we assume a smaller system with PA 0.5 Wm 2 P 5 W and A 0.1 m 2 for the lower part of the atmosphere z 10 km, and a larger system with PA 10 Wm 2 P 20 W and A 0.5 m 2 ) for the upper part of the atmosphere z 10 km. At each altitude, we assume a range resolution of 5% and molecular air density taken from the 1976 U.S. Standard Atmosphere [21] as listed in Table 2. The estimated times that are required to receive 100,000 photons due to Cabannes backscattering (only), t, from the range z and range resolution, z, are also given in Table 2. Due to aerosol scattering, the actual signal, especially in the lower altitudes, will be larger. The results showed that to achieve the LOS wind uncertainty given in Fig. 5 up to 5 km, less than 1 s is needed, and only 3 s are needed at 10 km with a lidar of PA 0.5 Wm 2. For the mesosphere using a larger telescope with PA 10 Wm 2, the time needed to accumulate 100,000 photons with 5% spatial resolution is 0.25, 0.30, 1.31, 6.75, and 40.8 h at 50, 60, 70, 80, and 90 km, respectively. Taking these estimates as reality, such a temporal resolution would make dynamics study beyond 60 km with Doppler wind lidar difficult if not impossible. The work in Colorado State University was supported in part by NASA under grant NAG5-10076 and the NSF, under grants ATM-00-03171 and ATM-05-45221. The work in China was supported by the National Natural Science Foundation of China, projects 40427001, 60578038, 40505003, and 40505005. References 1. C.-Y. She, J. Yue, Z.-A. Yan, J. W. Hair, J.-J. Quo, S.-H. Wu, and Z.-S. Liu, Direct-detection Doppler wind measurements with a Cabannes Mie lidar: A. Comparison between iodine vapor filter and Fabry Perot interferometer methods, Appl. Opt. 46, 4434 4443 (2007). 2. A. Garnier and M. L. Chanin, Description of a Doppler Rayleigh lidar for measuring winds in the middle atmosphere, Appl. Phys. B 55, 35 40 (1992). 3. Z.-S. Liu, D. Wu, J.-T. Liu, K.-L. Zhang, W.-B. Chen, X.-O. Song, J. W. Hair, and C.-Y. She, Low-altitude atmospheric wind measurement from the combined Mie and Rayleigh backscattering by Doppler lidar with an iodine filter, Appl. Opt. 41, 7079 7086 (2002). 4. A. Papayannis, D. Balis, V. Amiridis, G. Chourdakis, G. Tsaknakis, C. Zerefos, A. D. A. Castanho, S. Nickovic, S. Kazadzis, and J. Grabowski, Measurements of Saharan dust aerosols over the Eastern Mediterranean using elastic backscatter-raman lidar, spectrophotometric and satellite observations in the frame of the EARLINET project, Atmos. Chem. Phys. 5, 2065 2079 (2005). 5. V. B. Edward, M. A. Fenn, C. F. Butler, W. B. Grant, V. G. Brackett, J. W. Hair, M. A. Avery, R. E. Newell, Y. Hu, H. E. Fuelberg, D. J. Jacob, B. E. Anderson, E. L. Atlas, D. R. Blake, W. H. Brune, J. E. Dibb, Alan Fried, B. G. Heikes, G. W. Sachse, S. T. Sandholm, H. B. Singh, R. W. Talbot, S. A. Vay, R. J. Weber, and K. B. Bartlett, Large-scale ozone and aerosol distributions, air mass characteristics, and ozone fluxes over the western Pacific Ocean in late winter early spring, J. Geophys. Res. 108, 8805 8830 (2003), doi:10.1029 2002JD003290. 6. C. Flesia and C. L. Korb, Theory of the double-edge molecular technique for Doppler lidar wind measurement, Appl. Opt. 38, 432 440 (1999). 7. B. M. Gentry, H. Chen, and S. X. Li, Wind measurements with 355 nm molecular Doppler lidar, Opt. Lett. 25, 1231 1233 (2000). 10 July 2007 Vol. 46, No. 20 APPLIED OPTICS 4453

8. J. W. Hair, L. M. Caldwell, D. A. Krueger, and C.-Y. She, High-spectral-resolution lidar with iodine-vapor filters: measurement of atmospheric-state and aerosol profiles, Appl. Opt. 40, 5280 5294 (2001). 9. C. Souprayen, A. Garnier, A. Hertzog, A. Hauchecorne, and J. Portenuve, Rayleigh Mie Doppler wind lidar for atmospheric measurements. 1. Instrumental setup, validation, and first climatological results, Appl. Opt. 38, 2410 2421 (1999). 10. U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, and K. Adolfsen, The ALOMAR Rayleigh Mie Raman lidar: Objectives, configuration, and performance, Ann. Geophys. 18, 815 833 (2000). 11. C.-Y. She, J. D. Vance, T. D. Kawahara, B. P. Williams, and Q. Wu, An all-solid-state transportable narrowband sodium lidar for mesopause region temperature and horizontal wind measurements, J. Can. Phys. 85, 111 118 (2007). 12. C. Nagasawa, Y. Shibata, M. Abo, T. Nagai, and O. Uchino, Incoherent Doppler lidar using wavelengths for wind measurement, in Lidar Remote Sensing for Industry and Environment Monitoring, U. Singh, T. Itabe, and N. Sugimoto, eds., Proc. SPIE 4153, 338 349 (2001). 13. J. A. Reagan, A. E. Galbraith, and J. D. Spinhirne, Micro pulse lidar daytime performance: simulations and observations, in Geoscience and Remote Sensing Symposium, Remote Sensing for a Sustainable Future (IEEE, 1996), pp. 683 685. 14. M. J. McGill, W. D. Hart, J. A. McKay, and J. D. Spinhirne, Modeling the performance of direct-detection Doppler lidar systems including cloud and solar background variability, Appl. Opt. 38, 6388 6397 (1999). 15. K. W. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barbes, M. J. McGill, and T. D. Irgang, Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night, Opt. Eng. 34, 499 511 (1995). 16. R. M. Measures, Laser Remote Sensing (Wiley, 1984) p. 224. 17. B.-Y. Liu, Z.-S. Liu, Z.-G. Li, Z.-A. Yan, R.-B. Wang, and Z.-B. Sun, Wind measurements with incoherent Doppler Lidar based on iodine filters at night and day, in Reviewed and Revised Papers Presented at the 23rd International Laser Radar Conference, C. Nagasawa and N. Sugimoto, eds. (2006), pp. 55 58. 18. J. N. Forkey, W. R. Lempert, and R. B. Miles, Corrected and calibrated I2 absorption model at frequency-doubled Nd: YAG laser wavelengths, Appl. Opt. 36, 6729 6738, 1997. 19. R. D. Bates, Rayleigh scattering by air, Planet. Space Sci. 32, 785 790 (1984). 20. C. Y. She, Spectral structure of laser light scattering revisited: bandwidths of nonresonant scattering lidar, Appl. Opt. 40, 4875 4884 (2001). 21. NOAA, NASA, and U.S. Air Force, U.S. Standard Atmosphere, 1976 (U.S. Government Printing Office: 1976O-588-256, 1976). 4454 APPLIED OPTICS Vol. 46, No. 20 10 July 2007