Direct-detection Doppler wind measurements with a Cabannes Mie lidar: A. Comparison between iodine vapor filter and Fabry Perot interferometer methods

Direct-detection Doppler wind measurements with a Cabannes Mie lidar: A. Comparison between iodine vapor filter and Fabry Perot interferometer methods Chiao-Yao She, 1, * Jia Yue, 1 Zhao-Ai Yan, 1, Johnathan W. Hair, 3 Jin-Jia Guo, Song-Hua Wu, and Zhi-Shen Liu 1 Department of Physics, Colorado State University, Fort Collins, Colorado 8053, USA Ocean Remote Sensing Institute, Ocean University of China, Qingdao 66003, China 3 The Atmospheric Sciences, NASA Langley Research Center, Hampton, Virginia 3681, USA *Corresponding author: joeshe@lamar.colostate.edu Received 15 March 006; revised 1 November 006; accepted 19 January 007; posted 13 February 007 (Doc. ID 68898); published 0 June 007 Atmospheric line-of-sight (LOS) wind measurement by means of incoherent Cabannes Mie lidar with three frequency analyzers with nearly the same maximum transmission of 80% that could be fielded at different wavelengths is analytically considered. These frequency analyzers are (a) a double-edge Fabry Perot interferometer (FPI) at 1064 nm (IR-FPI), (b) a double-edge Fabry Perot interferometer at 355 nm (UV-FPI), and (c) an iodine vapor filter (IVF) at 53 nm with two different methods, using either one absorption edge, single edge (se-ivf), or both absorption edges, double edge (de-ivf). The effect of the backscattered aerosol mixing ratio, R b, defined as the ratio of the aerosol volume backscatter coefficient to molecular volume backscatter coefficient, on LOS wind uncertainty is discussed. Assuming a known aerosol mixing ratio, R b, and 100,000 photons owing to Cabannes scattering to the receiver, in shotnoise-limited detection without sky background, the LOS wind uncertainty of the UV-FPI in the aerosolfree air R b 0, is lower by 16% than that of de-ivf, which has the lowest uncertainty for R b between 0.0 and 0.08; for R b 0.08, the IR-FPI yielded the lowest wind uncertainty. The wind uncertainty for se-ivf is always higher than that of de-ivf, but by less than a factor of under all aerosol conditions, if the split between the reference and measurement channels is optimized. The design flexibility, which allows the desensitization of either aerosol or molecular scattering, exists only with the FPI system, leading to the common practice of using IR-FPI for the planetary boundary layer and using UV-FPI for higher altitudes. Without this design flexibility, there is little choice but to use a single wavelength IVF system at 53 nm for all atmospheric altitudes. 007 Optical Society of America OCIS codes: 80.3640, 10.440, 80.3340, 90.1090. 1. Introduction When a monochromatic laser impinges upon moving aerosols or an air parcel, the frequency of the backscattered light is Doppler shifted by an amount that depends on the line-of-sight (LOS) wind and laser wavelength. By monitoring this frequency shift, the LOS wind can be measured. Based on this principle, various lidar Doppler wind measurement schemes have been devised. They may be classified according 0003-6935/07/04434-10$15.00/0 007 Optical Society of America to detection techniques as coherent and incoherent, employing heterodyning and direct detection, respectively. While the coherent method using lidar systems at wavelengths of 10 and m has been demonstrated to be an effective tool for wind measurements in the lower troposphere, typically in the planetary boundary layer where considerable aerosol scattering is present [1 3], advances and discussions over the past decade have concentrated on the directdetection (incoherent) technique, using lasers at shorter wavelength with higher Rayleigh scattering cross section from air molecules, for atmospheric wind measurements in the free troposphere as well 4434 APPLIED OPTICS Vol. 46, No. 0 10 July 007

Fig. 1. (Color online) Transmission functions of Fabry Perot interferometer (FPI) or iodine vapor filter (IVF) together with aerosol and Cabannes scattering spectrum for (a) IR-FPI at 1064 nm, (b) UV-FPI at 355 nm, (c) se-ivf at 53 nm, and (d) de-ivf at 53 nm. as in the stratosphere and lower mesosphere. The use of a double-edge Fabry Perot interferometer (FPI) for frequency analysis was pioneered by Chanin et al. [4] who first demonstrated the wind measurement at 53 nm. Korb et al. later performed analyses on such wind measurements first with a single [5] FPI, and later with a dual [6,7] FPI, termed the single-edge and (symmetric) double-edge technique, respectively. Since the free spectral range (FSR) of a FPI may be chosen by design, it is a common practice to use a FPI with a smaller FSR at longer laser wavelengths, e.g., 1064 nm for wind measurement when aerosol scattering dominates [8], and a FPI of larger FSR at a shorter laser wavelength, e.g., 355 nm, when molecular scattering dominates [9]. For specificity, we discuss in this paper the figure of merits of two frequency analyzers with FPIs, one at 1064 nm and the other at 355 nm, referred to as IR-FPI and UV- FPI, respectively; their transmission functions are shown in Figs. 1(a) and 1(b), respectively, and their characteristics given in Table 1. In 1995, while on leave at Colorado State University working with iodine vapor filters (IVF) for atmospheric temperature measurements, Liu et al. [10] proposed the use of IVF for frequency analysis of backscattered light from both aerosols and air molecules for tropospheric wind measurements. A laboratory demonstration was completed in China and reported in the following year [11]. In the same year, this wind measurement technique was independently demonstrated in the tropical stratosphere, where aerosol influence is negligible [1]. The use of Table 1. Parameters of the Four Analysis Methods Employed in this Comparative Study Frequency Analyzer FSR GHz a GHz b T MAX f a1 f a f c1 c UV-FPI (355) 1 1.70 7.1 0.8 0.09 0.09 0.18 0.18 0.5 0.5 IR-FPI (1064) 3 0.1 30 0.8 0.4 0.4 0.08 0.08 0.5 0.5 de-ivf (53) 1.9 0.8 0.39 0.39 0.40 0.40 0.5 0.5 se-ivf (53) 1.9 0.8 0.39 1.0 0.40 1.0 0.6 0.4 a This is the FWHM of FPI transmission or width of the well of an iodine absorption line. b Maximum transmissions of four analyzers are nearly the same. c Values based on 75 K and 0.75 atm. f c c 1max max 10 July 007 Vol. 46, No. 0 APPLIED OPTICS 4435

IVF for tropospheric wind measurements was implemented in a van as a mobile ground-based incoherent Doppler wind lidar (MIDWiL) by the group at the Ocean Remote Sensing Laboratory of the Ministry of Education of China. It is fielded to this day with the initial observations completed [13] in 000. Unlike the FPI, the location of an absorption line center of an iodine filter cannot be specifically chosen, although its linewidth may be adjusted by changing the cell length and or vapor temperature and pressure. Fortunately, since the wavelength of a modern monolithic doubled-yag laser at 53 nm can be tuned over 60 GHz, a number of iodine absorption lines [14] may be implemented at 53 nm for wind measurements. The frequency of the laser for the work cited was tuned to the midpoint of one absorption edge of the iodine filter; this direct-detection technique with IVF is hence a single-edge method, termed se-ivf. To employ the double-edge method with an IVF, the laser frequency must be shifted alternately to the midpoint of the other absorption edge of the same absorption line. Using an acousto-optic modulator in a way similar to that developed for the Na fluorescence lidar [15,16] Shibata et al. [17] and Nagasawa et al. [18] have demonstrated wind measurement by deploying a Cabannes Mie lidar with incoherent detection using IVF, and with the two edges (termed de-ivf here) nearly but not an exact mirror image of each other. Here we adopt the correct naming practice and regard Rayleigh scattering as sum of the Dopplerbroadened central peak (Cabannes scattering) and rotational Raman scattering as sidebands [19]. Since for wind measurements, only a signal from aerosol scattering and from Cabannes scattering is involved, we term the lidar Cabannes Mie Doppler lidar. We will analyze the figures of merit of both single-edge and (nearly symmetric) double-edge methods using a realistic IVF operated at 53 nm, referred to as se- IVF and de-ivf, respectively; their transmission functions and associated Cabannes Mie spectra are shown in Figs. 1(c) and 1(d), respectively, and their characteristics given in Table 1. Though the wind measurements with IVF have been demonstrated in the field, there is practically no analysis in the literature, which either evaluates the performance of the IVF technique, or compares its performance with the FPI technique. The purpose of this paper is to evaluate and compare the figures of merit of the four direct-detection methods (two based on FPI and two on IVF) for LOS wind measurements with Cabannes Mie lidar under different atmospheric conditions. In the process of comparing different methods, we examine the salient features as well as the necessary cautions associated with the use of IVF for Doppler wind measurements employing a Cabannes Mie lidar. We do not discuss the comparison between the coherent and directdetection (incoherent) methods though this was a topic of considerable interest and discussion [0,1], nor do we discuss the optimization and design of these analyzers, as these may be found in the literature [7,]. We simply take (or specify) the designs that were (or could be) fielded for atmospheric wind measurements to provide a quantitative and comparative study. Our goal is not just to compare their performances, but more so to investigate their differences and to understand the advantages in different receiving methods under various atmospheric conditions. The layout of this paper is as follows. First we give in Section the formulation and transmission function of these frequency analyzers. In Section 3 we evaluate LOS wind uncertainties, with a simple scheme to favorably divide the signal into two channels, with which we discuss and compare the figures of merit between the four methods. The result of the analysis and comparative study is given in Section 4. A discussion and conclusion follow in Sections 5 and 6, respectively.. Formulation and Transmission Functions Conceptually, we envision that the received Cabannes Mie backscatter signal is divided into two channels. For IR-FPI and UV-FPI, both channels are measurement channels, where the scattered light is each detected after passing though a FPI with transmission functions, F FPI1 and F FPI, shown in Figs. 1(a) and 1(b), respectively. For IVF cases, one of the channels (channel 1) is a measurement channel, and the other is a reference channel. The transmission function for the se-ivf will be denoted by F IVF1, while the transmission functions for the de-ivf will be centered at opposite edges alternately with respective transmission functions, F IVF1 and F IVF. The split in signal strength between measurement (m) and reference (R) channels for the se-ivf, will be chosen to optimize the signal-to-noise ratio (SNR). For the de- IVF, the signal photons will be a 10 90 split with 10% into the reference channel and 90% into the measurement channel, to pipe more photons into the measurement channel. This split is not arbitrary, and we will discuss this issue in Section 3 of the companion paper [3] by considering a range of optimum split depending on R b and wind speed. At a given altitude range bin, the received signal in photon counts, N, is split with fractions, 1 and, into N 1 and N photons, in the two channels, respectively, assuming unity quantum efficiency for the photodetectors for simplicity. In this paper, channel 1 is always a measurement channel, while channel may be either a measurement channel (for FPI) or a reference channel (for IVF). The subscripts for channel may then be denoted with m or R, respectively. For a measurement channel or a reference channel, their signal photon counts may be respectively expressed as N mi N mi a f ai c f ci ; i 1,, (1a) N R N R a c. (1b) Here, mi, and R are fractions of signal split into the respective channels, a and c are aerosol and Cabannes (molecular) backscattering coefficients, and f ai and f ci are aerosol and molecular scattering filter 4436 APPLIED OPTICS Vol. 46, No. 0 10 July 007

transmission factors to be defined below. For the IR-FPI and UV-FPI, we have two measurement channels with signal fractions m1 m 0.5. For se-ivf and de-ivf, we have one measurement and one reference channel with signal fractions 1 m, and R, along with m R 1. For the se-ivf, m m1, and optimization of SNR below dictates R 0.4, and m1 0.6. For de-ivf, on the other hand, we choose m1 m 0.9, and R 0.1. Here for de-ivf, we point out that though m 0.9, the IVF is centered on the opposite edges sequentially, having two measurement channels time shared, effectively, each with 45% of the received signal. It is well known that the Doppler frequency shift and the LOS wind is related as D V LOS, () where is the wavelength of the transmitting laser beam. In terms of the normalized Cabannes function [4], D, T, P, the filter transmissions of the FPI or the IVF, F i, and the laser lineshape function, G D, where D is the Doppler shift resulting from nonzero LOS wind, V LOS (positive when moving in the direction of laser beam propagation), the molecular (Cabannes) and aerosol transmission factors are, respectively, f ci D, T, P i D, T, P F i d ; i D, T, P d 1, f ai D, T, P G i D F i d ; G i D d 1. (3a) (3b) Here, though not explicitly indicated, the effect of laser line shape should be accounted for in Eq. (3a). The filter transmission for frequency analysis, F i, may be either IVF transmission, F IVF, or FPI transmission, F FPI. Due to the temperature, T, and pressure, P, the dependences of the normalized Cabannes function, the molecular transmission factor, f ci, also depends on T, and P. This dependence, which is a function of altitude, will affect all four methods considered here; unless otherwise stated, we shall assume T 75 K and P 0.75 atm for specificity. The laser line shape function, G is assumed to be Gaussian for the analysis of the scattered aerosol spectrum with FWHM of 40, 60, and 80 MHz, respectively for Yag lasers at 1064, 53, and 355 nm. These widths, depending on specific laser systems, are however considered to be negligible, except for the doubleedge FPI at 1064 nm (or IR-FPI), Fig. 1(a). For the FPI used as frequency analyzer, the transmitter laser is centered between two FPI transmission peaks, Figs. 1(a) and 1(b), with 1 D, T, P D, T, P D, T, P, G 1 D G D G D, F i F FPI i ; i 1,. (4a) The transmission function for the FPI is the Airy function [5]. The FPI transmission function may be expressed as F FPI i, FWHM T Max 1 where FWHM FSR 1 FSR 1 sin i sin. ; i 1, ; (4b) The transmission functions for both FPIs at 1064 nm for aerosol dominated atmosphere and at 355 nm for molecular dominated atmosphere, considered in this paper, are shown in Figs. 1(a) and 1(b), and their parameters are given in Table 1. For the IVF methods, the locations of Cabannes Mie function relative to the two edges are shown in Figs. 1(c) and 1(d) with i D, T, P D i, T, P ; i 1,, G i D G D i ; i 1,, F i F IVF i ; i 1,. (5) There is no simple analytic expression for the IVF transmission, F IVF. The simulated transmission function for the IVF [14,4] under the specified operational condition is shown in Figs. 1(c) and 1(d). The iodine Doppler-broadened spectrum was used to lock and stabilize the laser [13]. The transmission spectrum and its width is a function of cell length,, and vapor density. For a cell with given vapor pressure, temperature, and cell length, the IVF transmission of an absorption line is specified. For example, iodine absorption line 1109, which has been used in MIDWiL for LOS wind measurements, is heated to provide a line with a FWHM of 1.9 GHz. To more easily facilitate this study, we used a simulated transmission profile of iodine absorption line 1109, resulting from a vapor cell of 10 cm long, and with cell and finger temperatures of 55 C and 50 C, respectively. This simulated spectrum was shown in Figs. 1(c) and 1(d), and it is repeated in Fig. (a) for clarity. These parameters were so chosen to yield a simulated spectrum with the same width, 1.9 GHz, as the measured IVF transmission of line 1109. The maximum transmission of 0.784 80% in this case is due 10 July 007 Vol. 46, No. 0 APPLIED OPTICS 4437

Fig.. (Color online) (a) Simulated transmission function of the 1109 iodine absorption line with a 10 cm long vapor cell. The cell body and finger temperatures were chosen to yield FWHM of 1.9 GHz. (b) Signal-to-noise ratio as a function of fraction of light into the measurement channel 1 for the four analysis methods, calculated with 100,000 photons from Cabannes scattering into the receiver of UV-FPI and se-ivf, 90,000 photons into de-ivf, and 100,000 photons due to aerosol scattering (or R b 1) for IR-FPI at 1064 nm. The decimal numbers in the legend indicate the transmission factor of Cabannes scattering (aerosol for IR-FPI) at zero wind. mainly to the continuum absorption of iodine under the operational conditions [4]. For the retrieval of actual wind measurements, the measured spectrum should be used, but for this paper we elect to use the simulated spectrum to facilitate the ease of numerical calculations, and this does not significantly impact the filter performance. 3. Evaluation of Line-of-Sight Wind Uncertainty Since there will be two detection channels for the retrieval of LOS wind, whether a double-edge or a single-edge method is used, we define the ratio of signals of the two channels in question as the wind ratio function, R W (not to be confused with the normalized Cabannes function,, or backscattered aerosol mixing ratio, R b ), as the measurement metric for the retrieval of LOS wind. The wind ratio and its fractional change (due to either wind shift or photon noise fluctuations) may be given as R W D, R b N 1 D, R b N D, R b, R W R W N 1 N 1 N N. (6a) (6b) For the double-edge FPI techniques, both channels will be filtered measurement channels, i.e., N 1 N m1, and N N m. For the IVF technique, on the other hand, one filtered measurement channel and one reference (power monitoring) channel are used, i.e., N 1 N m0 or N mi for se-ivf or de-ivf, respectively, and N N R. The measurement sensitivity per unit (Doppler) frequency shift, S D, is defined as the fractional change in the wind ratio per unit change in Doppler shift, d D, resulting from LOS wind, Eq. (); it may be calculated from Eq. (6b) with R W R W dr W R W. Following the common practice, for this paper, the sensitivity and fractional change are evaluated at zero Doppler shift (thus valid for low wind conditions) as dr W D R S 1 N W 0 D d D 1 D N 1 0 D 1 N 0 N D D d D, (7a) 1 N S D 1 D 1 N D N 1 0 D N 0, (7b) D d D dr W D S D R W 0. (7c) For the single-edge method, the second term of Eqs. (7a) and (7b) would be zero because N R is independent of D. Thus the sensitivity of the symmetric (nearly symmetric) double-edge method is twice (or nearly twice) higher than the corresponding singleedge method. It is often desirable to compare measurement sensitivity on the basis of LOS wind, S VLOS, which can be related to S D easily as S VLOS S D d D dv LOS, with d D dv LOS. (8) If the fractional change in the wind ratio, R W R W R W R W, is due to photon noise fluctuations, which are independent between the two channels, Eq. (6b) gives R W N 1 N R W N 1 N N 1 N N 1 N SNR 1. (9a) Unlike in the evaluation of sensitivity, both terms will be nonzero for the double-edge or singleedge method. Assuming shot-noise-limited detection 4438 APPLIED OPTICS Vol. 46, No. 0 10 July 007

(Poisson statistics), the SNR depends on the photons actually detected in the two channels, N 1 and N : SNR 1 1 1 N 1 N N 1N. N 1 N (9b) The value of the SNR will, of course, depend on the way the received signal is divided between the two channels, i.e., the values of mi and R in Eqs. (1a) and (1b). Since aerosol scattering and the value of R b varies, we choose to determine these parameters by maximizing the SNR under the condition of Cabannes scattering alone. To compare the four methods for frequency analysis, we employed both FPI and IVF analyzers with nearly the same maximum transmission (Table 1) of 80%, and assume the photodetector has 100% quantum efficiency for simplicity, and further assume that a total of 100,000 photons, resulting from aerosol scattering for IR-FPI and from Cabannes (molecular) scattering for the other three methods, is being detected by the receiving system in question. We are free to optically split the received signal between the two channels to optimize the SNR in terms of f 1, f, 1, and as SNR N 1N N 1 N 100,000f 1 1 100,000f 1 1, 100,000 f f 1 f 1 (10) where N 1 100,000 1 f 1, N 100,000 f, and 1 1. Depending on the filter transmission factors, f 1 and f, the SNR as a function of 1 is plotted for the four methods of interest in Fig. (b). That max SNR occurs when 1 0.5 for symmetric double-edge methods is expected. For nearly symmetric de-ivf, the max SNR occurs when 1 is slightly and negligibly larger than 0.5, implying that more signal split into the weaker channel is optimal. This clearly shows that for the se-ivf (f 1 0.4 and f 1.0), the max SNR occurs at 1 0.6. For the de-ivf, we point out and account for the fact that at any given time, R 0.1 m 0.9, and the SNR for wind measurement is therefore determined from Eq. (10) with 1 0.5, and N 90,000. As can be seen in Fig. (b), this 90 10 split for the de-ivf f 1 f 0.4 yields SNR 10% lower than the IR-FPI f 1 f 0.4 and 50% higher than the UV-FPI f 1 f 0.18. The value for 1 that gives rise to the maximum SNR, 1max, may be derived analytically as 1max f f f 1. The filter transmissions and the corresponding optimum value of 1max for the four cases of interest are also given in Table 1. Using the determined 1max value, the SNR for the system including aerosol scattering may be computed as a function of the backscattered aerosol mixing ratio, R b a c by Eq. (9b), with N i 100,000 i R b f ai f ci, for i 1,, from Eqs. (1). Notice that for se-ivf detections, f a f c 1, and that for de-ivf, N 90,000. With the measurement sensitivity, S D (or, S VLOS ) and the SNR determined, the LOS wind measurement uncertainty due to photon noise fluctuations, V LOS, may be calculated in terms of them with Eqs. (7) and (8) by recognizing dr W D R W 0 R W R W 1 SNR: VLOS D R W R W S D S D SNR 1 S VLOS SNR. (11) Here V LOS,, S D, and S VLOS are expressed in m s, nm, GHz 1 ns, and m s 1, respectively. Thus, Eqs. (8), (9b), and (11) may be used, to compute measurement sensitivity, SNR, and LOS wind uncertainty, respectively, in general and for the four methods of interest in particular. This will be done in the next section. Following Korb et al. [5,6] and Flesia and Korb [7], we use the wind ratio, R W defined in Eq. (6a), as the measurement metric from which to retrieve LOS wind. The adoption of R W in this form not only permits a uniform description for all four methods considered in this paper, but also allows direct connection to more, but not all, published papers in the literature. However, other metrics have been used. Noticeably, we used the normalized wind ratio (NWR) in our earlier work on troposphere wind retrieval [13], and a different wind ratio, N 1 N N 1 N, was used by the French group [,6] to characterize the performance of their double-edge FPI. It should be pointed out that the fractional wind ratio, dr W R W, with R W defined in Eq. (6b) may be related to the NWR of Liu et al. [13] as R W R W 0 *NWR, giving rise to the same fractional change in signal, i.e., dr W R W 0 d NWR NWR, leading to the same sensitivity, S D, SNR, and LOS wind uncertainty, V LOS. The equivalency between using R W N 1 N, by Korb et al. [5,6] and Flesia and Korb [7], adopted by us in Eq. (6a), and using N 1 N N 1 N by Garnier and Chanin [] has been discussed by Mckay [7]. 4. Results and Performance Comparison with Known Aerosol Mixing Ratio As is generally practiced, we evaluate the measurement sensitivity per unit LOS wind, at zero wind, i.e., D 0, for the four frequency analysis methods. They are plotted as a function of aerosol mixing ratio, for 0 R b 10 in Fig. 3(a). For a lidar, which probes a large range of heights, the extinction would be too large to bear when R b 10 at visible wavelengths. For pure molecular scattering (stratospheric and lower mesospheric applications, i.e., R b 0, the sensitivities are 0, 0.0064, 0.0019, and 0.0038, in m s 1, respectively for IR-FPI, UV-FPI, se-ivf, and de-ivf. We expect that S VLOS to be zero for IR-FPI, as it depends only on aerosol scattering. Since the slope of the right edge is a bit larger than the left edge of the IVF, see Figs. 1(c) and 1(d), we expect the sensitivity of de-ivf to be higher than that of the se-ivf by less than 10 July 007 Vol. 46, No. 0 APPLIED OPTICS 4439

Fig. 3. (Color online) (a) Measurement sensitivity, and (b) signal-to-noise ratio for the four detection methods as functions of aerosol mixing ratio, 0 R b 10.0. a factor of. This difference, though negligible for R b 0, increases as R b increases; as a result, the ratio of the sensitivities (de-ivf to se-ivf) is 1.99, 1.63, and 1.60 for R b 0, 1.0, and 10, respectively, see Fig. 3(a). While the maximum transmission of the IVF, T max,is approximately the same as that of the FPI (see Table 1), the fractional change per LOS wind of de-ivf is smaller than that of UV-FPI. Here the Cabannes Mie scattering spectrum is centered near the wing of the FPI transmission; this attenuates the Cabannes scattering considerably and relatively more so for aerosol scattering. This increased fractional change in the transmission for Cabannes scattering, thereby, the measurement sensitivity of UV-FPI is highest at R b 0. As R b increases to 0.5, the de-ivf and the IR-FPI already are, respectively, nearly 3 and 10 times more sensitive than the UV-FPI at 355 nm. We compare the SNR of the four detection methods by assuming a fixed number of photons received in each case. Figure 3(b) shows the SNR resulting from 100,000 R b 1 photons and 90,000 R b 1 photons for de-ivf, received as a function of aerosol mixing ratio, 0 R b 10. Since the Cabannes Mie spectrum for the IVF is nearly centered at the halfway point in the iodine transmission in contrast to being centered in the wing of the FPI, the SNR of the de-ivf is higher than UV-FPI even if R b 0. Because our optimization results in more photons in the measurement channel with se-ivf, its SNR with 1max 0.6, is larger than that of the de-ivf. As R b increases, the received signal and thus the SNR increases for all four cases as expected. It is noted that the IR-FPI overtakes the UV-FPI in SNR as R b exceeds 0.57, suggesting that the IR-FPI is the choice for measurements in the planetary boundary layer. When aerosol scattering dominates, the SNR is expected to increase as the R b. It is quite clear that this is the case for IR-FPI, se-ivf, and de-ivf. The increase in SNR for the UV-FPI is much slower due to the fact that the parameters are optimized to desensitize aerosol scattering [,6]. The SNRs are comparable between IR-FPI and de-ivf for R b. The fact that the se-ivf fares better in SNR can be attributed to the result of no absorption in the reference channel, i.e., f a f c 1.0. Figure 4 shows the LOS wind uncertainty, evaluated at zero Doppler shift, D 0, resulting from the same 100,000 R b 1 collected photons for the four cases as a function of the aerosol mixing ratio, R b.in Fig. 4. (Color online) LOS wind uncertainty based on 100,000 Cabannes photons (90,000 for de-ivf) received by the receiver with 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. 4440 APPLIED OPTICS Vol. 46, No. 0 10 July 007

these figures we assume the value of R b is known, and the LOS wind uncertainty is the result of photon noise only. For clarity, we plot the range of R b in two graphs: (a) 0 R b 1, and (b) 0 R b 10. At R b 0 in the stratosphere and lower mesosphere, we see that the de-ivf and UV-FPI yielded comparable LOS wind uncertainties of.78 m s and.33 m s, respectively, while the se-ivf is higher with 4.31 m s due to lower sensitivity. The LOS wind uncertainty of the IR-FPI at 1064 nm decreased from being the highest for R b 0.06 to being the lowest for R b 0.09. Our analysis suggests that the UV-FPI at 355 nm yields 16% (46%) lower LOS wind uncertainty compared to the de-ivf (se-ivf) at R b 0, while the latter out performs the former when R b is greater than 0.03 (0.08), i.e., under the condition with aerosol. When aerosol scattering dominates, in the planetary boundary layer for example, again assuming the same number of photons received, the use of IR-FPI is desirable; at R b 0.7, it yields 0.1 m s, 54% lower LOS wind uncertainty as compared to that for the de-ivf, 0.46 m s. Compared to the de-ivf the uncertainty with se-ivf is 0.58 m s, 1% higher, while that for the UV-FPI is 1.98 m s, 4.1 times higher. Generally speaking, with the direct-detection method for LOS wind measurements, the performance of the IR-FPI is the best for the planetary boundary layer and the least desirable for stratosphere and mesosphere, see Figs. 4(a) and 4(b), and the reverse is true for the UV-FPI. The de-ivf has a more consistent performance comparison throughout various atmospheric conditions with performance differences within 50% of the best in the planetary boundary layer and in the stratosphere and mesosphere. 5. Discussion A fundamental difference between FPI and IVF lies in their differences in LOS wind uncertainty resulting from variations in aerosol scattering. In the case of IR-FPI, a ratio of aerosol scattering in two channels is employed as a signal for wind measurements, a variation in aerosol backscattering mixing ratio will affect both channels in the same way, thus its effect to the first order cancels out in the wind ratio. In the case of UV-FPI, though variations in R b will change the wind ratio, R W, somewhat, the researcher can design FPIs with parameters that minimize the impact of variations of aerosol scattering mixing ratio []. The parameters of an IVF are dictated by nature, and there is less room for different design options. Thus, unlike with FPI, there is less capability for one to desensitize either molecular scattering or aerosol scattering in the IVF. We will discuss the impact of variation in aerosol scattering on LOS wind measurements using IVF in a companion paper [3]. Since the wavelength dependence of a scattering cross section between aerosol and molecular backscattering is quite different, a lidar at 53 nm is in principle preferred when both aerosol and molecular scatterings are significant. Here, if one is willing to forego the advantage offered in the FPI system to have selective desensitization of aerosol scattering, one can select the separation between the peaks of the two FPIs and use a FPI setup to achieve lower wind uncertainty under different aerosol conditions, and at the same time require an independent determination of R b as is the case for the IVF system. This is, however, not done in practice. At 53 nm, the FSR of FPI is chosen to enhance (or desensitize) either aerosol scattering [8] or molecular scattering [,6]. As a result, Fischer et al. [8] chose FSR 1.5 GHz, FWHM 0.15 GHz and 1 at 53 nm to desensitize the molecular scattering, similar to the IR-FPI with our choice of FSR 3.0 GHz, FWHM 0.100 GHz, and 30 at 1064 nm, (Table 1), following Korb et al. [8]. Recognizing the fact that photomultiplier tubes are more sensitive in the ultraviolet, Imaki and Kobayashi [9], recently used a FPI at 355 nm with FSR 5.0 GHz, FWHM 0.59 GHz, and 8.6 for wind measurement from ground to 4 km, and they found that the sensitivity for the Mie backscatter is 4.0 10 m s 1, and it is 10 times larger than the Rayleigh Doppler lidar. This is consistent with the relative sensitivities between IR-FPI and UV-FPI shown in Fig. 3(a), where at R b 0.5, the sensitivity of IR-FPI is 4.0 10 m s 1, a factor of 6 times larger than that of UV-FPI. At R b 1.0, the sensitivity of IR-FPI is 6.0 10 m s 1, 10 times larger than UV-FPI. The French group [,6], on the other hand, designed its FPI with much larger FSR and larger separation between the transmission peaks to desensitize aerosol scattering. Fischer et al. [8] also realized this necessity to gain advantage, and stated that this technique can be used to measure Doppler wind from the molecular scattered signal by changing the plate spacing of the (highest resolution) etalon in the system. To put the laser wavelength dependence of FPI performance in perspective, we point out the existence of a natural wavelength scaling for Doppler wind measurements based on molecular scattering. Since the value of normalized Cabannes function [5,30],, T, P is proportional to wavelength, the molecular transmission factor f ci, Eq. (3a), for the same LOS wind remains constant (independent of wavelength), if an FPI with the same finesse, and a FSR scaled inversely proportional to wavelength is chosen. With this in mind, it is instructive to compare two different FPIs at 53 nm with the de-ivf here. The first FPI, termed vis-fpi_s, has FWHM 1.13 GHz, 1. 1.70 GHz, and FSR 8 GHz, scaled from the UV-FPI of Gentry et al. [9] at 355 nm with 7.1, FWHM 1.7 GHz, 1,.55 GHz and FSR 1 GHz (Table 1). This vis-fpi is similar to the one with 1. 1.67 GHz; FWHM 1.7 GHz, used by Garnier and Chanin [] with similar desensitization of aerosol scattering. In the same paper, the authors suggested that the optimum aerosol desensitization (minimal bias due to R b vaiation) can be achieved with 1..81 GHz; FWHM.44 GHz at a price of 5% lower in sensitivity (thus somewhat higher in wind uncertainty). Though employed by Souprayen et al. [6] later, we 10 July 007 Vol. 46, No. 0 APPLIED OPTICS 4441

Fig. 5. (Color online) Comparison between two FPIs at 53 nm, vis-fpi_s scaled from UV-FPI and vis-fpi_a with significant aerosol scattering, and de-ivf. (a) SNR and sensitivity, (b) LOS wind uncertainty. do not consider this choice here. Instead we consider as a second choice, a FPI with FWHM 1.13 GHz; 1. 0.565 GHz, and FSR 8 GHz, 7.1, which is aerosol sensitive. We termed it vis-fpi_a, as it depends on R b and has a performance similar to the de-ivf, since it also has 50% transmission for aerosol scattering, similar to the IVF. To shed light on the performance of the FPI at 53 nm, we compare the SNR and the sensitivity between vis-fpi_s, vis-fpi_a to those of de-ivf in Fig. 5(a) and the corresponding LOS wind measurement uncertainties in Fig. 5(b). It is clear that the sensitivity of vis-fpi_s is relatively independent of R b and that for both vis-fpi_a and de-ivf increases at higher values of R b ; the latter increases faster, reflecting the sharper slope at the IVF edges. The SNR of vis_fpi_a is comparable to that of de-ivf, and both are higher than vis_fpi_s as expected. In Fig. 5(b), we see that when compared with vis_fpi_a and de-ivf, the LOS wind uncertainty of vis-ivf_s is relatively independent of R b ; in fact, it is identical to UV-FPI, Fig. 4(b), as predicted by the wavelength scaling discussed previously. We have assumed that the detection is not only shot-noise limited but also resulted only from the signal photons. This assumption obviously breaks down under sunlit conditions since skylight background, if not properly attenuated, could be much larger than the signal. The background clear sky radiance at 53 nm [31] ranges between 0.05 and 0.1 Wm Sr 1 nm 1 ; it is approximately a factor of smaller at 1064 and 355 nm [3]. This difference makes lidar observation in the visible 53 nm under sunlit conditions somewhat more difficult. We will discuss this issue in the companion paper [3]. Here it suffices to say, though it is a challenge, Doppler wind measurements in the planetary boundary layer and troposphere beyond 10 km have been made at 53 nm under sunlit conditions with both FPI [8] and IVF [33]. 6. Conclusion We have presented system performance evaluations on three different frequency analyzers (with nearly the same maximum transmission of 80%) and four detection methods, i.e., double-edge UV-FPI at 355 nm and IR-FPI at 1064 nm, and de-ivf at 53 nm and se-ivf at 53 nm, that have been, or could be, deployed by different researchers to measure atmospheric winds by means of incoherent Cabannes Mie Doppler lidar. To simplify the comparison, we evaluated the LOS wind uncertainty by assuming a fixed signal level of 100,000 R b 1 photons, which are received and divided into two channels, each with a 100% efficient photodetector. Once the power aperture product of the lidar is known, one can translate this to a maximum measurable altitude and integration time. In the shotnoise (photon noise) limited detection, the LOS wind uncertainty can be scaled easily, e.g., 10 times larger for a signal level of 10 times smaller, e.g., from 100,000 to 10,000 photons. Assuming the value of the aerosol mixing ratio is known, we have evaluated the LOS wind uncertainty for each of the four methods. At R b 0 in the stratosphere and lower mesosphere, the de-ivf yielded LOS wind uncertainty of.78 m s, 16% higher than the UV-FPI of.33 m s, while owing to lower sensitivity, the se-ivf uncertainty of 4.31 m s is higher than de-ivf and UV-FPI by 40% and 50%, respectively. The LOS wind uncertainty of the IR-FPI at 1064 nm decreased from being the highest for R b 0.06 to being the lowest for R b 0.09. We point out that to take advantage of design flexibility with FPI to optimize the performance under aerosol versus molecular dominated atmosphere, one uses both IR-FPI and UV-FPI for wind measurements at different altitudes and under different atmospheric conditions. On the other hand, lacking this flexibility for the IVF system leads to the use of a single IVF system for different atmospheric regions, regardless of its aerosol conditions. Since shot-noise-limited detection is assumed in this paper, the result is valid for nighttime operation. For daytime observation, the use of a suitable technique to minimize sky background is essential. This issue along with the impact of R b vari- 444 APPLIED OPTICS Vol. 46, No. 0 10 July 007

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