Inapaper entitled “Standoff determination of thepar-ticle size and concentration of small optical depthclouds based on double-scattering measurements:concept and experimental validation with bioaero-sols” [1], we described and demonstrated a powerfulmethod to determine the particle size and concentra-tion of small optical depth clouds. The method relieson the measurement of the forward scattered lightthat is backscattered by the background aerosols atvariable distances at the back of a subvisible cloud.To determine the limitations of the recovery techni-que for daytime and nighttimemeasurements, takinginto account the effect of background aerosols and thelaser beam profile, we had concluded that aerosol
clouds with fixed temporal characteristics were re-quired. The generation of such clouds is, if not impos-sible, beyond our capability. As a result, we useddiffractive target plates of known etched-particle sizeand number to emulate small optical depth clouds forthis current study.Figure1 illustrates thegeometry ofthemeasurement in the presence of a cloud and in thepresence of its emulation with a diffractive targetplate.The subtle difference between the twomeasure-ments will be addressed in Section 3.
In this paper, we provide a description of the dif-fractive target plates followed by a short resume ofthe equations and the theory used to recover theetched-particle size and the cloud equivalent opticaldepth as well as the experimental setup and the ex-perimental data. Finally, we perform an in-depthanalysis of the factors limiting the recoverymethod, which allows us to determine the minimum
concentration necessary to adequately characterizesmall optical depth clouds.
2. Diffractive Target Plate Description
The target plates consist of etched metallic disks ofknown size randomly distributed over a circular areaof 15 cm in diameter. The disks are contained on afused silica substrate square of 16:9 cm held in aframe of 20:4 cm width. The number of particleshas been established so that the ratio of the area ofthe etched particles over the total surface is equalto 2%. The particles per unit area, Np, can be estab-lished as follows:
NpπD2
4¼ 0:02: ð1Þ
Target plates were made with 5, 20, and 50 μm dia-meter etched particles. Table 1 shows the diameters,the density, and the total number of particles on eachof the fused silica plates. Figure 1 exhibits the micro-scope picture of the 20 μm etched-particles targetplate. Since the total surface occupied by the parti-cles is small, no attempt was made to eliminate pos-sible superimpositions of the etched particles. Forthe reference measurements, we used a blank refer-
ence target having the same physical characteristicsas the three target plates, except that there was noetched particle on it.
The etched particles are many times larger thanthe wavelength of the laser used for probing(532nm). Their scattering efficiency is 2, and theirequivalent target optical depth (τtarget) is given by
τtarget ¼ 2NpπD2
4¼ 0:04: ð2Þ
This quantity can be easily related to the particleconcentration, since the volume sounded by the lidaris known. The particles are monodispersed and ran-domly distributed on the plates. Consequently, thescattering of an individual element can be repre-sented as the diffraction caused by a circular
Fig. 1. Experimental setup showing the geometry of the measurement and various scattering considered in the presence of a cloud and inthe presence of its emulation with a diffractive target plate.
Table 1. Diameters, Densities Np, and Total Number N of EtchedParticles on Fused Silica Plates
aperture. The etched particles are randomly dis-persed, and the suspension of the target plate witha rope induces small oscillation and vibration tothe target plate. Since the measurement is madeof the accumulation of many laser pulses, we consid-er that there is no coherent effect. Therefore, theoverall contribution of all the particles can be writtenas the sum of their individual contribution.
3. Retrieval Method Description
In a previous paper [1], we demonstrated that the re-covery of the effective size parameter can be easilyachieved by the application of a simple mathematicalformula that requires only knowledge of basic lidarinformation, such as the cloud distance and thesounding depth, as well as two measurements rea-lized with a multiple-field-of-view (MFOV) imaginglidar. The first lidar measurement must be done inthe presence of the subvisible cloud studied(αb > 0), while the second is used to quantify back-ground aerosols (αb ¼ 0). Thereafter we apply the fol-lowing equation to the experimental data:
ΔPNormðθiþ1 −θiÞ¼PDðzc;θiþ1 −θi;αb > 0Þ
Psðzc;θs;αb > 0Þ
−PDðzc;θiþ1 −θi;αb ¼ 0Þ
Psðzc;θs;αb ¼ 0Þ
¼ 2ϖ0b
Zzbza
αbΔLðr;z;βiþ1 −βiÞdz: ð3Þ
In this equation, PD corresponds to the scatteredpower in the FOV interval Δθi ¼ θiþ1 − θi comingfrom the second scattering order; Ps corresponds tothe single-scattering signal contained at an angleθs; αb corresponds to the small optical depth cloud ex-tinction coefficient simulated by the extinction coef-ficient caused by the etched particles; ϖ0b is thesingle scatter albedo for the bioaerosols; and
ΔLðr; z; βiþ1 − βiÞ≡Zβiþ1
βi
Z2π0
pðr; z; βÞ sin βdβdφ;
where pðr; z; βÞ is the value of the phase function forthe forward (β) scattering angle.The measurement ofΔPNormðθiþ1 − θiÞ can provide,
in principle, information on the particle sizes and onthe subvisible cloud concentration. For that, it is ne-cessary to parameterize the phase function with aGaussian fit by using the definition of effective dia-meter suggested by Bissonnette [2]. In this represen-tation, it is the forward scattering peak that ismodeled as a function of the effective diameter andthe wavelength, while it is independent of the parti-cle shape. The model assumes that the particles arerandomly oriented and that the forward scatteringpeak calculation is based on an average of particlesize and orientation:
pðβÞ ¼ A2
πω0by2e−A
21y
2β2 ; ð4Þ
where y ¼ πdeff=λ, A1 ¼ 0:544, A2 ¼ 0:139, anddeff ¼ 2hr3i=hr2i, with r corresponding to the particleradius. Combining Eq. (3) with Eq. (4) and using therelation β ≈ zcθ=ðzc − �zÞ, we obtain
ΔPNormðθiþ1 − θiÞ ¼ 2τA2
A21
�exp
�−A2
1y2
�zc
zc − �z
�2θi2
�
− exp�−A2
1y2
�zc
zc − �z
�2θiþ1
2
��:
ð5Þ
Here τ corresponds to the cloud optical depth. In[1], we demonstrated that the particle effective dia-meter could be found from θmax;Log, the peak positionof ΔPNormðθiþ1 − θiÞ, by applying the following equa-tion when the n rings studied are log-spaced:
deff ¼ 1:30ffiffiffi2
p λπθmax;Log
�lnð1þ CteÞ2
½ð1þ CteÞ2 − 1��0:5 zc − �z
zc:
ð6Þ
In Eq. (6), Cte ¼ ð10ðlogθn−logθ1Þ½1=ðn−1Þ� − 1Þ; θ1 and θnare the smallest and largest FOV considered;�z ¼ 0:5ðza þ zbÞ, where za and zb correspond to thelimits of the small optical depth cloud studied; andλ corresponds to the laser wavelength.
The representation of the phase function with aGaussian fit is highly justified for clouds made upof polydispersed aerosols. However, this is not thecase for monodispersed particles like those etchedon the target plates. Monodispersed particles areknown to present oscillation patterns in their phasefunctions. According to diffraction theory, a diskphase function can be perfectly represented bypðβÞ ¼ J1
2ðy sinðβÞÞ=2πsin2ðβÞ, while its related en-circled energy (L) can be expressed by the well-known expression
LðβÞ ¼ 1 − J02ðy sinðβÞÞ − J1
2ðy sinðβÞÞ: ð7Þ
So, the encircled energy in a ring between βi andβiþ1 is determined by applying
ΔLðβiþ1 − βiÞ ¼ J02ðy sinðβiÞÞ þ J1
2ðy sinðβiÞÞ− J0
2ðy sinðβiþ1ÞÞ − J02ðy sinðβiþ1ÞÞ:
ð8Þ
It can be shown [3] that the functionΔL presents amaximum at y sinðβiÞ ¼ 1:375. This is in very goodagreement with the position of the maximum ob-tained in Eq. (6) for the representation of the phasefunction with a Gaussian fit, which is 1.3.
Once the effective diameter is known, the opticaldepth can be easily obtained by using a simplemathematical formula that requires the same basic
knowledge as for the size parameter retrieval. Sinceexperimentally it is necessary to use a mask with atransmission Tmask to attenuate the first backscat-tering order in order to obtain a good dynamic rangeof the intensified CCD (ICCD) camera, the experi-mental optical depth can be retrieved after the rear-rangement of Eq. (5) by using
τtarget ¼−ΔPNormðθiþ1 − θiÞTmask
A2
A21
�exp
�−A2
1y2
�zc
zc−z
�2θi2
�− exp
�−A2
1y2
�zc
zc−z
�2θiþ1
2
�� : ð9Þ
This equation is slightly different from the expres-sion derived in [1], since the target thickness is verysmall (�z has been replaced by z) and the reciprocitytheorem [4] no longer applies for the target measure-ment as illustrated in Fig. 1. Shaded in gray, the la-ser beam path TAB corresponds to forwardscattering on an etched particle of the diffractive tar-get (T) followed by backscattering towards the tele-scope at A on background aerosols. The reciprocitytheorem stipulates that the laser beam path 123 isequivalent to the laser beam path TAB [4]. It corre-sponds to the laser beam that goes through the targetplate without interaction, and it is followed by back-scattering on background aerosols and by forwardscattering in the direction of the telescope. The pathbetween 2 and 3 is shown with a dashed line becausethis event occurs for fairly small FOVs. Since the tar-get plates are small, the FOV subtended by the tar-get is 0:61mrad (half-angle) when z ¼ 123m and0:44mrad when z ¼ 171m, while the FOV coveredby the detector is around 5mrad (half-angle). So, itis the limited target size that explains why the reci-procity theorem no longer applies for the target mea-surements. Finally, the path T10 corresponds tobackscattering at 180° at point 1 when the laserbeam goes through the target plate twice without in-teraction.Taking into account the double pass through the
target plates, the target optical depth can also be cal-culated from the simple ratio of the measured powerfor a fixed geometry (z and zc), the camera gatewidth, and the number of laser pulses accumulatedon the CCD chip, by using
where Ptargetðzc; θminÞ is the measured power in thepresence of the target plate with etched particles ina small FOV θmin in which we expect only to measuresingle scattering, and Pref ðzc; θminÞ is the same mea-surement inthepresenceof theblankreferencetarget.
4. Experimental Setup and Measurement
A. Lidar Description
The multiple-FOV lidar used is the same as in [1,5].In short, it consists of a 100Hz repetition rate Nd:YAG laser synchronized with a gated ICCD camera(G-ICCD, Andor ICCD DH 720-18U-03). The charac-
teristics of the outgoing laser beam are as follow:2:5 cm diameter, 0:15mrad divergence (half-angle in-cluding 50% of total laser energy) with a substantialamount of energy contained in 0:9mrad, linear polar-ization purity of 1=500, pulse energy of 25mJ, andpulse width of 20ns.
The primary optics consists of a 200mm diameteroff-axis parabolic mirror with a focal length of760mm. The position of the image plane is a functionof the focal length and the object position, and it isnecessary to adjust the image plane position in accor-dance with the sounding distance. An interferencefilter with a bandwidth of 10ns centered on532nm is used to reduce the amount of backgroundlight incident on the camera. A circular 0:5mm thickBK7 glass disk of 12:5mm in diameter with a 1%transmission central dot for FOVs smaller than0:65mrad surrounded by a 94% transmission regionfor FOVs larger than 0:65mrad is positioned in theimage plane for greater dynamic range.
B. Experimental Procedure
For each measurement event, we followed a proce-dure that allowed the optimization of the camera ac-quisition speed and the reduction of the noise level,especially the readout noise. Initially, we determinedthe optimum number of pulses required on the cam-era chip before reading the CCD. Typically, we aimedfor a maximum of 20,000 counts on a pixel (the sa-turation level is attained at 65,535 counts) to ensureenough lidar return on the photosensor matrix and agood linearity of the camera response. The lightbackground was thenmeasured between laser pulsesjust prior to acquiring the lidar return by opening thecamera gate the same number of times as for the li-dar measurements. Finally, the background imagewas subtracted from the image of the lidar return,and the difference in pixel sensibility is correctedby using the radial response of the whole system,which has been characterized by a flat-field measure-ment performed with a flat-field box.
Figure 1 illustrates the principle of themeasurement with diffractive target plates. The
diffracted–forward scattered light from the targetplate, located at a distance z from the lidar system,is backscattered by background aerosols at variablesounding distances zc. The targets are set at dis-tances z from the lidar system equal to 123m forthe 20 and 50 μm etched-particles target platesand 171m for the 20 and 5 μm etched-particles targetplates. The backscatter from background aerosols ismeasured at distances zc equal to 155.5 and 175:5mfor the former and at distances of 183.5 and 185:5mfor the latter. For each set of distances, we have takenin the presence of a target plate with etched particlesthree consecutive lidar measurements with a cameragate width of 20ns followed by three consecutive li-dar measurements with the camera gate width set to60ns. The same sequence of measurements was re-peated in the presence of the blank reference targetfor the background aerosol measurements.Figure 2 shows the schema of the data acquisition
and treatment, while the retrieval method steps areillustrated in Fig. 3 with the help of a typical dataset.Figure 3(a) shows the normalized lidar return onbackground aerosols obtained in the presence of thediffraction target plate containing 50 μm diameteretchedparticles.Figure3(b) shows the samemeasure-ment in the presence of the blank reference target.The center of these images has been intentionally sa-turated to let us observe the multiple scattering con-tributions more easily. Figure 3(c) represents thesubtraction of Fig. 3(b) from Fig. 3(a). Figure 3(d) de-
picts the image analysis in terms of encircled energyin logarithmic spaced rings delimited by θi and θiþ1.The effective diameter is then calculated by applyingEq. (6), using the position of theFOVcorresponding tothe maximum of scattered energy on a ring obtainedby fitting a second-order polynomial to thedata pointssurrounding the maximum, while the equivalent tar-get optical depth is calculated by using Eqs. (9)and (10).
5. Experimental Data
In this section, we show that even if the multiplescattering contributions are very low, as illustratedin Fig. 3 (note that the centers of Figs. 3(a) and 3(b)have been intentionally saturated), it is still possibleto retrieve meaningful information. For the experi-mental data analysis, we used 22 rings spaced on alogarithm scale included between 0.17 and 5:62mrad(half-angle).
Measurements were conducted in daytime and atnighttime under different background light levelsand for different wind speeds. The winds affect thetransportation of background aerosols, and conse-quently theymodify the quantity of background aero-sols present in the air as well as their sizedistribution. Four acquisition sets have been studiedmore carefully. The first one corresponds to a night-time measurement when the winds were very mild(wind speed w:s: < 4km=h). The second measure-ment was conducted under a bright cloudy sky atlow wind speed (w:s: < 4km=h). The third one was
carried under a mid-cloudy sky when the wind speedwas below 10km=h. Finally, the fourth one was ob-tainedunder conditions similar to the third oneexceptthat the wind speed was stronger (w:s:∼ 15km=h).The related background light levels and their fluctua-tionsonasmall timescalehavealsobeen calculated inphotons by gate opening included in a FOV of5:62mrad (half-angle).Figure 4 presentsΔPNormðθiþ1 − θiÞ nighttimemea-
surements as function of FOV mean ring values. Thetheoretical profile was obtained by applying Eq. (8). Itis expressed in arbitrary units, since it is the peakposition and not its amplitude that matters for theparticle size retrieval. The measurements shown inFigs. 4(a)–4(d) have been made on the 20 μm etched-particles target plate for sounding distances zc of155m [Figs. 4(a) and 4(b)] and 175m [Figs. 4(c) and4(d)] and for camera gate widths of 20ns [Figs. 4(a)and 4(c)] and 60ns [Figs. 4(b) and 4(d)]. The displace-ment of the peak position toward larger FOVs can beclearly observed in these graphs when the soundingdistance increases. Figures 4(e) and 4(f) show resultssimilar to Figs. 4(c) and 4(d), respectively, exceptthat they have been obtained with the 50 μm
etched-particles target plate and that it is possibleto distinguish them in the presence of the secondarydiffraction peak. All graphs presented in Fig. 4 showagood agreement between the measured positions ofthe maximums and their theoretical values. Similarresults have been obtained with the 5 μm etched-par-ticles target plate located 171 m away from the lidarsystem.
Figure 5 compares a nighttime with three daytimemeasurements for the 50 μm etched-particles targetplate for a sounding distance of 175m and a cameragate width of 60ns. The background intensity (b.l.) inphotons per gate opening is displayed on each graphas well as the wind speed (w.s.). Figure 5 clearlyshows that data for daytimemeasurements are muchnoisier than the nighttime measurements.
The efficiency of the retrieval size for camera gatewidths of 20 and 60ns, when the target plates were123m away from the lidar system, is presented inTables 2 and 3. For nighttime measurements, wefound that it was possible to retrieve the size ofthe etched particles with a precision better than10%. The experimental data show that it is easierto locate the position of the maximum diffraction
Fig. 3. (a) Normalized lidar return on background aerosols obtained in the presence of diffractive target with etched particles; (b) thesamemeasurement in the presence of the reference target; (c) is (a) minus (b). (d) Image analysis in terms of encircled energy in logarithmicspaced rings delimited by θi and θiþ1.
peak [θmax;Log in Eq. (6)] when the camera gatewidth is larger (60 versus 20ns) and whenθmax;Log is located in the smaller FOVs (zc ¼ 175mversus zc ¼ 155m) since the data are less noisy asillustrated in Fig. 4. For daytime measurements,it is not always possible to clearly identify the peakposition, and it is almost impossible to detect thepresence of the secondary diffraction peak. However,when it is possible, the precision on the particle-sizeretrieved value is about the same as for the night-time measurements.The optical depth retrieval values, presented in
Tables 4 and 5, are calculated by applying Eq. (9),using the size information presented in Table 2 and3. It was not quite possible to get good results by using
the single-scattering ratio [Eq. (10)] to retrieve the op-tical depth because the pulse-to-pulse laser energyfluctuations do not allow the measurement of smalltransmission loss. This is not surprising, since a var-iation of �10% of the theoretical ratio Ptarget=Pref ¼0:923 could lead to values of the retrieval opticaldepth ranging from −0:121 (negative value with nophysical meaning) to 0.28, while the theoreticaloptical depth value is 0.04 for the three diffractive tar-get plates used. Considering the nighttime and thedaytime measurements separately, we obtained thesamemean optical depth value of 0.042 for both cases;this is in very good agreement with the theoreticalvalue (0.04). The daytime retrieval extinction values
Fig. 4. Comparison of a nighttime measurement for two different camera gate widths (20 and 60ns) and sounding distances (zc ¼ 155mand zc ¼ 175m) for particle diameters of 20 and 50 μm.
span from 0.031 to 0.062, while the nighttime retrie-val extinction values range from 0.033 to 0.049.To determine the minimum optical depth required
for measuring the effective particle size and optical
depth with an acceptable precision, it is necessaryto conduct an analysis of the factors affecting themeasurement. For that, it is important to have a goodcomprehension of the noise sources coming from the
Fig. 5. Comparison of a nighttime and daytime measurement for a camera gate width of 60ns, zc ¼ 175m, and etched-particle diameter50 μm.
Table 2. Size Retrieval and Its Associated Error, Target at 123m, Gate Width 20 nsa
aThe target plate is located 123m from the lidar system for a camera gate width of 20ns. S.R., size retrieval; w.s., wind speed; b.l.,background light level in photons/gate opening included in 5:62mrad (half-angle). N.a., not available because the data are too noisy; thusit is impossible to distinguish the diffraction peak.
measurement with the G-ICCD camera on a statisti-cal basis.
6. Analysis of the Factors Limiting the Success of theRecovery Method
The precision of the size and optical depth retrievalmethod for daytime measurements depends on theamount of noise introduced by the following:.
1. The background light fluctuations between thelaser ON and OFF measurements;2. The aerosol background fluctuations between
the measurements on the target plate with etched-particles and the one on the reference target;3. The shot noise;4. The noises introduced by the camera G-ICCD;5. The energy spreading introduced by the imper-
fect optical lenses and the presence of dusts on thecollecting optics;6. The laser pulse-to-pulse energy fluctuations.
In this section, we analyze the effects of the factorslimiting the recovery method’s success.
A. Noises Associated with the Gated ICCD Camera
The G-ICCD camera introduces noise into the mea-surement. Assuming that a light signal is falling on aCCD pixel, if the charge on the pixel is read and thereadout process is repeated many times, the noisemay be estimated as the variation in the values read.The rms of these variations is often used to express avalue for noise.
Pixel noise has three main constituents: readoutnoise, shot noise from the dark signal, and shot noisefrom the light signal itself. Readout noise is causedby the amplifier and electronics: it is independent ofdark signal and signals levels, it is only very slightlydependent on temperature, and it is present in everyreading, as a result of which it sets a limit on the bestachievable noise performance. Shot noise from thedark signal is dependent on the exposure time andis very dependent on the temperature; shot noisefrom the signal is additionally dependent on thesignal level itself. A simple way to reduce readoutand dark signal noises is to cool the camera. For ex-ample, reducing the temperature of the CCD reducesthe dark signal. Typically, for every temperature
Table 3. Size Retrieval and Its Associated Error, Target at 123m, Gate Width 60 nsa
aThe target plate is located 123m from the lidar system for a camera gate width of 60ns. S.R., size retrieval; w.s., wind speed; b.l.:background light level in photons/gate opening included in 5:62mrad (half-angle). N.a.: not available because the data are too noisy; thusit is impossible to distinguish the diffraction peak.
Table 4. Optical Depth Retrieval and Its Associated Error, Target at 123m, Gate Width 20nsa
Mean value for all trials 0.0412aThe target plate is located 123m from the lidar system for a camera gate width of 20ns. w.s., wind speed; b.l., background light level in
photons/gate opening included in 5:62mrad (half-angle). N.a., not available because the data are too noisy; thus it is impossible to dis-tinguish the diffraction peak.
reduction of 7°C the dark signal is cut in half [6]. Bylowering the camera temperature to −20°C (the samevalue used for the data acquisition) and setting thecamera in complete darkness for the smallest expo-sure time allowed by the camera electronics, we ob-tained a readout level of (337� 2) counts over 20measurements. Since the readout noise is about2 counts=pixel=readprocess, it is possible to evaluatethe total amount of readout noise per laser pulse for aring by using
σread process=ring=laser pulse ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi22 × number of pixels in a ring
pnumber of laser pulses accumulated on the CCD chip
: ð11Þ
For the same experimental conditions, but for alarger exposure time (80 s), we obtain after the sub-traction of the number of counts related to the read-out process that the dark current is less than2 counts=pixel=s. Since the exposure time used forthe trials on target plates is less than 1 s, the noiseassociated with the dark current is very small. It isimportant to note that for the dark frame we have setthe exposure time to a value much higher than forour experiments to reduce the effect of the dark
Table 5. Optical Depth Retrieval and Its Associated Error, Target at 123m, Gate Width 60nsa
Mean value for all trials 0.0430aThe target plate is located 123m from the lidar system for a camera gate width of 60ns. w.s., wind speed; b.l., background light level in
photons/gate opening included in 5:62mrad (half-angle). N.a., not available because the data are too noisy; thus it is impossible to dis-tinguish the diffraction peak.
Table 6. Comparison of Mean Readout and Dark Current Noise Values in Each Ring with 1 and 100 Laser Pulses Accumulated on the CCD Chip
current shot noise, which varies with the square rootof the dark current according to Poisson statistics. Si-milarly to the readout noise, it is possible to evaluatethe total amount of dark current noise per laser pulseassociated with a ring by using
σdark current=ring=laser pulse ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidark current for a fixed exposure time × number of pixels in a ring
pnumber of laser pulses accumulated on the CCD chip during the exposure time
:
ð12Þ
In Table 6, we compare the mean readout noise va-lues and the range of dark current noise in each ringused for the data analysis presented in Section 5,when 1 and 100 laser pulses are accumulated onthe CCD matrix. The values obtained are very smallwith regard to the number of generated CCD countsfor each detected photon when the camera gainis high.Figure 6 depicts a full intensified event. It corre-
sponds to a signal with an amplitude much higherthan the standard deviation of the CCD electronicbackground signal and a lateral distribution equiva-lent to a width at 1=e of 1:5pixel (which correspondsto the camera resolution). To quantify the number ofCCD counts resulting from a single multiplication,three or four pixels centered on the event weresummed after the subtraction of the averaged num-ber of counts resulting from the CCD electronic offsetand the dark signal. Fifty intensified events were re-corded. They present an averaged amplitude and astandard deviation of 200 and 38 counts, respec-tively. Since the noise associated with the intensifi-cation process is 38 counts=photon, the totalamount of noise associated with the intensificationprocess per laser pulse associated with a ring is
Pnumber of pixels in a ringi¼1 signal on pixeli × ðin countsÞ
qnumber of laser pulses accumulated on the CCD chip
: ð13Þ
Table 7 gives the mean noise associated with theintensification process per laser pulse when dataare normalized to 1 laser pulse accumulated onthe CCD chip. Comparison of values from Tables 6and 7 shows that the noise coming from the intensi-fication process is usually the main component of thetotal noise related to the camera, except for rings inthe larger FOVs when few photons are detected. Asan example, consider the case where 100 laser pulsesare accumulated on the CCD chip before the readout
process; with the ring included, between 4.19 and4:88mrad, the readout noise per laser pulse willbe 2.07 counts, while the intensification count noiseper laser pulse will be 0.38 for a single photon detec-tion, but it will increase to 12.01 counts if the number
of photons detected in the ring is 1000. For the latestcase studied (1000 photoevents detected during 100laser pulses), if instead of summing the signal com-ing from 100 laser pulses on the CCD chip, we con-sider the case where we sum only 1 laser pulse, thereadout noise per laser pulse and the intensificationcount noise per laser pulse will increase by a factor of100, while the level of signal measured per laserpulse will stay the same. This example clearly showsthat there is a great advantage in accumulating asmany laser pulses as possible on the CCD chip beforethe reading process in order to decrease the relativeamount of noise introduced by the camera.
B. Shot Noise from the Signal Itself
The shot noise signal cannot be removed, because itsroots originate in basic physical laws. Most simplydefined, shot noise is the square root of the photonsignal according to Poisson photon statistics. So, itis necessary to increase the number of photons de-tected in each ring to reduce the shot noise. Thiscan be done in many ways: optimizing the signal-to-noise ratio on the camera by using a mask to at-tenuate the single-scattering lidar return; summingmany laser pulses on the CCD before the reading
process; increasing the camera gate width; and sum-ming many single acquisitions.
Figure 7 shows the averaged signal hΔPnormðθiþ1 −
θiÞi over three nighttime acquisitions for camera gatewidths of 20 and 60ns. This graph compares theΔPnormðθiþ1 − θiÞ standard deviation of the three ex-perimental data identified as Pnorm std (data) withthe error associated with the G-ICCD camera (cam-era noise) as well as with the standard deviation ofthe sum of the number of detected photons in the
presence of the target plate containing etched parti-cles and in the presence of the reference target ac-cording to Poisson statistics [Pnorm std (Poissonstat.)]. To compare the amplitudes of these two lastquantities with the ΔPnormðθiþ1 − θiÞ value [seeEq. (3)], we have normalized them by the single-scat-tering lidar signal, which we have fixed to correspondto the number of counts included in a small FOV of0:27mrad (half-angle). Figure 7 shows that Pnormstd (data) is practically equal to Pnorm std (Poissonstat.). Moreover, it reveals that a change from a cam-era gate width of 20ns to 60ns corresponds to an in-crease of the signal by a factor of 3 and a reduction ofthe shot noise by a factor of
ffiffiffi3
p.
On the basis of the above observations, the signalshot noise is the main source of noise in theΔPnormðθiþ1 − θiÞ calculation for the nighttime mea-surement, and one way to reduce its effect is to in-crease the number of photons detected in eachring. For example, decreasing the shot noise by sum-ming 25 acquisitions could allow us for certain day-timemeasurements to determine a range of FOVs forthe position corresponding to the peak of theΔPnormðθiþ1 − θiÞ curve as well as to observe the sec-
ondary diffraction maximum presence, while for asingle measurement the signal fluctuations weretoo prominent to allow us to do so. Figure 8 illus-trates one of this case. It corresponds to a measure-ment for a sounding distance of 175m with a cameragate width of 60ns in the presence of the 50 μmetched-particles target plate. This figure clearly de-monstrates that in the presence of a small bump ontheΔPnormðθiþ1 − θiÞ curve there is a clear advantageto summing a few acquisitions in order to confirm ordeny the presence of the diffraction peak.
C. Background Light Fluctuation
The amount of background light incident on the cam-era was reduced by using an interference filter cen-tered on the laser wavelength. In the dataacquisition process, for every measurement madewith the laser in operation (laser ON), a second mea-surement was made with the exact same camera ac-quisition parameters (gate width and number of gateopening) when the laser was not in operation (laserOFF). Under ideal conditions, the subtraction of bothsignals would eliminate the background light. How-ever, the background light fluctuations can affect thesuccess of the retrieval method for daytime measure-ments (see Fig. 2). To quantify their effect, we mea-sured the efficiency of our acquisition program in thesubtraction of the background light with the laserOFF. Three measurements separated by less than2 s were taken on a mid-cloudy day with a back-ground light level of 285� 12 photons with a gateopening inside a FOV of 5:62mrad (half-angle).The curves in Fig. 9 give the number of backgroundphotons detected by gate opening in each ring, whilethe histogram bars give the associated errors in thebackground light subtraction.We divided the graphicinto two parts to better scale the different statisticalerrors for all the FOVs covered by the detection sys-tem: Fig. 9(a) illustrates FOVs smaller than1:06mrad, and Fig. 9(b), FOVs greater than1:06mrad. The range of errors obtained is compar-able with the uncertainties related to Poisson statis-tics of photon emission. Consequently, the relativeerror in background light subtraction is significantlyhigher for FOVs smaller than 1mrad, since very fewphotons are detected in those rings by gate opening.
Figure 10 illustrates the effect of background lightsubtraction errors for the same daytime conditions asabove. In Figs. 10(a) and 10(b), the diffractive targetplate with 50 μm particles and camera gate widths of20 and 60ns have been used. In Fig. 10(c), the refer-ence target plate with a 60ns camera gate width hasbeen used. According to the specific case studied, wecan conclude that increasing the camera gate widthallows us to reduce the effect of an error on the back-ground light subtraction, since it substantially in-creases the lidar signal coming from the doublyscattered light. However, in the presence of rapidand large light background fluctuations, it could be-come advantageous to decrease the cameragate width.
Fig. 6. Representation of a photointensification event.
Table 7.
Mean Noise, Normalized to 1 LaserPulse Accumulated
No. of Photonsper Ring
σring=laser pulse(counts)
σring=laser pulse / Signal Associatedwith Photons (%)
Whatever the background light conditions, it isbetter to choose a sounding distance that locatesthe peak of diffraction toward the smaller FOVs inorder to reduce the influence of background lightfluctuations. In fact, considering that each pixel ofthe CCD matrix receives the same amount of back-ground light, the effect of a background light subtrac-tion error of 2 counts=pixel will be 21 times moreimportant for the larger FOV ring studied, whichcovered between 4.19 and 4:88mrad and contained10; 752pixels, than for the ring surrounding thesmaller FOV containing the laser profile, that is,the FOV that covered between 0.91 and 1:06mrad
and contained 508pixels. The chosen FOV must,however, be larger than the laser energy profile, sinceit is impossible to apply our retrieval technique whenthe doubly scattered light is mixed with the la-ser beam.
Some could think that it could be a good idea to uselinear spaced rings instead of logarithm spaced ringsin order to reduce the impact of background lightfluctuations in the larger FOVs. However, this isnot the case since when linear spaced rings are used,it becomes more difficult to distinguish the positionof the peak on the ΔPNormðθiþ1 − θiÞ curve since itsamplitude is lower and its width is larger. Linear
Fig. 7. Comparison of ΔPnormðθiþ1 − θiÞ standard deviation of the data with the error associated with the G-ICCD camera and the stan-dard deviation of the number of detected photons according to Poisson statistics.
spaced rings are thus more subject to noise and tobackground fluctuations effects than logarithmspaced rings as illustrated on Fig. 11. Consequently,it is usually more difficult to retrieve the particle sizeand concentration using linear spaced rings.
D. Other Sources of Errors
The algorithm developed for the small optical depthcloud characterization should be insensitive to thebackground aerosols, since their contribution tothe signal is subtracted. However, in the presenceof strong winds, precipitation, and important relativehumidity variations, we can expect background aero-sol fluctuations in amount and/or in size distributionbetween the twomeasurements, the measurement inthe presence of the subvisible cloud and the one in itsabsence. When these fluctuations occur, the sub-tracted background aerosol contribution is biased.The fluctuations will cause an increase or a decreasein the amount of scattered energy detected on thesensor, while size distribution fluctuations (usuallymuch less important than the background aerosolfluctuations) will modify the lidar return FOV depen-dency. One way to reduce background aerosol fluc-tuations is to minimize the time delay betweenboth measurements. For this reason, in all our trials,we made the measurements on the etched-particlestarget plate and on the reference plate less than afew minutes apart.The laser features such as its profile, energy pulse-
to-pulse fluctuations, and pulse width can also affectthe success of the recovery method. The most con-straining feature is the laser energy profile, sinceit is no longer possible to retrieve size informationas well as the optical depth cloud when θmax;Log issmaller than or equal to the FOV containing almostall of the laser beam energy. In fact, the informationat small FOVs is no longer available, since the doublyscattered light is mixed with the laser beam. Fortu-nately, the effect of background aerosols fluctuationsas well as the laser pulse-to-pulse energy fluctua-tions can be reduced by normalizing the quantities
in Eq. (3) with the single-scattering lidar returnand by summing many laser pulses on the CCD chipbefore the readout process.
The laser pulse width is the last but not the leastlaser feature we need to consider carefully. For in-stance, when the sounding distance is sufficientlyclose to the target plate and the camera gate widthsufficiently large, it becomes possible to measure di-rectly the interaction between the laser pulse and thetarget plate. For those cases, it is no longer possible toapply the retrieval technique developed, since the sin-gle scattering in thepresence of the targetwith etchedparticles is biased. In fact, it dependsno longer only onbackground aerosols concentration, but also on theetched-particle features. For all the results presented,the laser pulse width has not influenced our experi-mental results, since we have chosen the soundingdistances with regarding to the fact that it was20ns at half-height and about 60ns at full width.
The optical element quality can also affect the suc-cess of the recoverymethod. The lenses in the second-ary optics of the lidar detection system suffer fromoptical aberrations. Therefore, we can expect thatthe imagery performance will be worse in the largerFOVs, since the amount of aberrations and thespreading of the energy increase with the FOV.Based on an optical design performance evaluation,we can demonstrate that the energy coming from apoint located on a circle of 1mrad of radius will bespread on a ring of 0:06mrad RMS width and0:14mrad GEO width. As addition, the energy dif-fused in the FOVs coming from a point located ona circle of 5mrad of radius will be spread on a ringof 0:61mrad rms width and 1:17mrad GEO width.This example shows that the degradation of the op-tical performance is partly responsible for the poorerperformance observed when the diffraction peak islocated in the larger FOVs. This phenomenon is am-plified by the fact that coherent imaging systems arealso particularly sensitive to dust and surface de-fects. Diffracted light from dust particles, surface de-fects, or glass inhomogeneities creates diffractionpatterns that can spread out the energy and conse-quently degrade the data quality in the larger FOVs.
7. Minimal Optical Depth Required for CharacterizingSmall Optical Depth Clouds
It is not easy to select the minimal optical depth re-quired for adequately characterizing small opticaldepth clouds. As the cloud optical depth decreases,the lidar signal coming from its constituents de-creases and the relative incertitude in this signal in-creases according to Poisson statistics. The effect ofthe background aerosol fluctuations also becomesmore important, since the relative proportion ofthe energy detected coming from the double scat-tered light on background aerosols increases. Addingto those uncertainties sources, we need also to takeinto account the position of the diffraction peak onlogarithm spaced rings; the camera acquisitionparameters (gate width, number of laser pulses
Fig. 8. Comparison ofΔPnormðθiþ1 − θiÞ curve and standard devia-tion for a single measurement and the summing of 25 acquisitions.
cumulated on the CCD chip,…) as well as the back-ground light level (night, day, sunny, mid-cloud,…).For all these reasons, we have set the minimum
signal detectable to 5 times the noise level. As a re-sult, for a nighttime measurement and for a diffrac-tion peak located around 1:5mrad, we expect to beable to characterize a cloud with an optical depthas small as 0.005 for a camera gate width of 60nsand of 0.008 for a camera gate width of 20ns for asingle reading of the camera CCD chip.
For daytime measurements, to ensure the successof the retrieval method, it is important that the back-ground light fluctuations stay sensitively lower thanthe signal coming from the double-scattering mea-surement on background aerosols. According to thebackground light levels and the detection system stu-died in this paper, we can expect to characterizeclouds with an optical depth as small as 0.016 fora camera gate width of 60ns and 0.024 for a cameragate width of 20ns. However, it should probably be
Fig. 9. Measurement of the background light subtraction acquisition method’s efficiency.
Fig. 10. Effect of background light subtraction acquisition. (a) Camera gate width 20ns, zc ¼ 175m, and 50 μm diameter etched-particlestarget; (b) same as (a) with a camera gate width of 60ns; (c) same as (b) for the reference target.
possible to characterize lower optical depth clouds indaytime if a narrower interference filter is used.For a stationary cloud, the minimum optical depth
required can be lowered significantly by summingmany single acquisitions as shown in Fig. 8. Sincethe background measurement must be done betweentwo laser pulses to minimize the background lightfluctuations between the laser ON and laser OFFmeasurement, for a laser frequency of 100Hz it is im-possible to proceed to the background light subtrac-tion if more than 100 laser pulses are added togetheron the CCD chip before the reading process. Wetherefore suggest summing n acquisitions of 100 ac-cumulated laser pulses to decrease the amount ofnoise associated with the shot noise by a factor pro-portional to 1=
ffiffiffin
pwhen the presence of a diffraction
peak is suspected. This technique could work well forthe characterization of a continuous source such asthe emission of a chimney stack.
8. Conclusion
In this paper, we presented and validated a novel re-trieval method for the determination of particle sizeand concentration of small optical depth clouds basedon double-scattering measurements using three cali-brated target plates containing etched particleseither 5, 20, or 50 μm in diameter. The number of par-ticles on the target plates was established so that theratio of the area of the etched particles over the totalsurface is equal to 2%, which corresponds to anequivalent cloud optical depth of 0.04.Our experimental results clearly show that it is
possible to adequately characterize target plates,even in some cases during daytime conditions, witha precision better than 10% for size and the opticaldepth retrieval. The limitations of the techniquefor nighttime measurements are caused mainly bythe shot noise related to the signal itself, while theaerosol background fluctuations in distribution sizeand in quantity are not significant error factors. Inaddition to the shot noise factor, the daytime mea-surements are considerably affected by the back-
ground light fluctuations. The laser pulse-to-pulseenergy fluctuations as well as the noise introducedby the camera are other error sources that could af-fect the success of the retrieval technique. However,their contribution to the total noise can be neglectedif we proceed to the normalization of the quantitiesby the single-scattering return and if a large numberof laser pulses are accumulated on the CCD chip be-fore the readout process. Experimentally, this condi-tion was satisfied by using a mask attenuating thefirst scattering order, which also allowed us to max-imize the signal-to-noise ratio in the larger FOVs.
The success of the retrieval technique depends onthe capacity to determine the position of the diffrac-tion peak (θmax;Log) on logarithm spaced rings.θmax;Log is easier to pinpoint for FOVs slightly largerthan the laser energy profile, since
1. When FOVs are slightly larger than the laserenergy profile, more rings define the profile of thepeak, and its width is narrower. So, even in the pre-sence of a large discrepancy in the expected value fora ring, it could still be possible to determine the posi-tion of θmax;Log according to the general profile of theΔPnormðθiþ1 − θiÞ curve.
2. The effect of light background fluctuations isless important for the smaller FOVs, since they con-tain fewer pixels.
3. The impact of optical element aberrations andtheir effects on the energy spreading are less impor-tant for FOVs closer to the optical axis.
Finally, we have shown that it is possible to retrievethe particle size and concentration of small opticaldepth clouds for optical depths as low as 0.005 fornighttime quantification and 0.016 for daytime quan-tification. The validity of our second-scattering-ordermodel aimed at the standoff measurement of the ef-fective diameter of a very small amount of bioaerosolshas proved to be accurate and very robust. Since thedeveloped model is limited to second scattering orderand contributions from scattering orders higher than2 start to be noticeable for optical depths higher than0.3 [7], numerical simulations will be required for de-termining the corrections or adjustments needed toapply to the presentmodel for the study of cloudswithan optical depth higher than 0.3.
The authors thank Sylvain Cantin and George Mé-nard for technical assistance and DRDC Valcartierfor providing funds necessary to the research.
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