Coherent focal volume mapping of a cw CO2 Doppler lidar

William D. Jones, L. Z. Kennedy, James W. Bilbro, and H. B. Jeffreys

In this paper we determine the coherent response to a 100-/Am diam spinning wire as a function of its positionwithin the focal volume of a 10.6-,.m coherent Doppler lidar and generate SNR contours both transverse to

and along the system line of sight. Application of the contours to single-particle scattering is discussed.

1. Introduction

A variety of calibration methods have been used overthe years to measure the parameters of coherent CO2Doppler lidars.1-3 These techniques have primarilyemployed either spinning disks or rotating belts ofknown reflectance as calibration targets. A recent ar-ticle by Post et al.1 discusses several of these targetsproviding recommendations for field use. Targets ofthis type are mainly used to measure the overall systemefficiency by comparing theoretically calculated valuesof SNR to those actually measured. They are also used,in the case of focused systems, to determine the axialresolution by translating the target along the optical axisand measuring the signal variation. Such targets pro-vide no indication of the variation of the coherent re-sponse within the beam itself. More detailed knowl-edge of the spatial variation of the coherent response isdesired for some coherent Doppler lidar applications.

To map the coherent response within the focal vol-ume, a small target of known reflectivity can be movedabout within the beam. A smooth rotating wire witha diameter much larger than the radiation wavelengthprovides such a target. In contrast to difficulties en-countered by Krause et al.4 in their attempts to use awire as an absolute field calibration target, we use thewire only for relative measurements in the labora-tory. 2

II. Technique

Since only relative response is required, it is onlynecessary to provide a backscatter cross section, which

W. D. Jones and J. W. Bilbro are with NASA Marshall Space Flight

Center, Marshall Space Flight Center, Alabama 35812; the otherauthors are with Applied Research, Inc., Huntsville, Alabama

35801.Received 8 June 1982.

is independent of position within the beam. This isachieved by using a smooth 100-,.m diam wire whosedimensions are large compared to the wavelength (10.6iam). To avoid end effects, the length of the wire issomewhat longer than the beam diameter.

Orientation of the wire with respect to the beam isshown in Fig. 1. The axis of rotation of the wire isnormal to a plane containing the optical axis. The insetof Fig. 1 shows the intensity distribution along the wirewhen it is passing through a position normal to the op-tical axis. The beam is focused at a distance R from theaxis of rotation of the wire.

Backscattered intensity vs time is recorded as thewire passes through a small angle about the normalposition indicated by a in Fig. 1. It is then Fourieranalyzed to provide the Doppler spectrum. Each fre-quency component of the spectrum arises from a dif-ferent portion of the wire moving with a different radial(line-of-sight) velocity component. Quantitatively, thefrequency FD associated with a fixed elevation y withinthe beam is

2V 2wyFD(Hz) = 2 = 2w

where X = radiation wavelength (in meters),V = line-of-sight velocity component of wire

segment at altitude y and angle a (in m/sec),

w = angular velocity of the wire.Since the scattering cross section of the wire is as-

sumed to be uniform along its length and since the an-gular variation during the measurement period is verysmall, the scattered intensity from each segment of wireis solely dependent upon the spatial distribution of in-tensity within the beam. Thus direct mapping canoccur from the frequency domain of the power spectrumto the spatial domain of the beam providing relativecoherent response vs position within the beam.Translating the wire along the beam axis and transverseto it permits contour plotting of the SNR within thefocal region.

730 APPLIED OPTICS / Vol. 23, No. 5 / 1 March 1984

Of

Fig. 1. Wire-beam orientation.

Fig. 2. CO2 Doppler lidar.

I1. Experiment Setup

The system used in the experiment is a conventionalfocused coherent CO2 Doppler lidar (Fig. 2) employingan 8-W cw laser, a modified Mach-Zehnder interfer-ometer, and a 15-cm diam off-axis telescope. The de-tector is a liquid nitrogen-cooled mercury cadmiumtelluride photodiode. For data recording and pro-cessing we use a high-speed analog-to-digital converter(ADC) and main frame computer.

A block diagram of this system is shown in Fig. 3.The output beam is directed along a 6-m optical rail.For the case described here, the system is focused at 20m. The wire is a 5-cm length of 6/0 gauge steel musicwire (100 Aim) mounted on the shaft of a dc motor ca-pable of 15,000 rpm, as shown in Fig. 4. The motor isfixed to an X- Y translation stage with a z -axis adjust-ment. The entire assembly is carriage mounted, placedon the optical rail, and aligned so that the axis of rota-tion of the wire is normal to the beam axis.

A LED and photodiode (also seen in Fig. 4) are posi-tioned to detect the wire passing through the beam.The resulting photodiode signal triggers the ADC, whichsamples the video output of the detector. By adjustingthe position of the photodiode, the sampling rate of theADC, and the rotation rate of the wire, it is possible todefine the area from which scatter is received. For arotation rate of 5,000 rpm, and a sample time of 410

Fig. 3. Block diagram of the experimental setup.

Fig. 4. Calibration target.

1 March 1984 / Vol. 23, No. 5 / APPLIED OPTICS 731

60

so

a

ZJf¢cf' I HV -'V -'v VV

4 TIME-. 410p S

Fig. 5. Time signature of the wire response.

yusec, the angular excursion for the duration of thesample is 12.30 centered about the normal to thebeam.

During data taking, the wire is positioned at the de-sired region within the beam. The output of the de-tector is digitized with 8-bit resolution at a 5-MHzsampling rate in 2048 word blocks by a Biomation model8100 transient recorder. The output is then transferredto a microcomputer and then to a main frame computerfor storage and processing. After sufficient data arecollected, the wire is repositioned within the beam andthe process repeated. Typically, five sets of data arecollected at each position for purposes of averaging.

IV. Results

Figure 5 shows a typical time signature of the wirebackscatter for one sample period. The power spectraldensity (PSD) of such a signature is obtained bysumming the squares of the real and quadrature am-plitude spectra calculated by a 2048-point FFT of thetime signature. Figure 6 shows a typical PSD obtainedby averaging five such spectra. This process is repeatedfor nine wire positions to provide a series of nine PSDswhich are then input to a contour plotting routine pro-ducing the plot shown in Fig. 7. This contour is for thelongitudinal response (along the beam axis). Eachsuccessive contour line represents a 1-dB decrease fromthe peak response.

Contours transverse to the focal plane are shown inFig. 8. This mapping is produced by moving the wirenormal to the line of sight of the system and makingmeasurements at nine points across the focal plane.Contour intervals are again 1 dB. The distorted regionson the right of the plot may be the result of a slightmisalignment. This area is -10 dB below the peakresponse and may be neglected for most purposes.

Taken together, these two contours provide detailedinformation about the coherent response to a target asa function of position within the focal region. Thesensitivity curves of Figs. 9 and 10 show where a givenSNR (or greater) is produced for a constant scatteringcross section over a fractional area of the focal volume.Viewed another way, these curves may be thought of asthe distribution of SNR produced by a single scattereras it passes through different regions of the focal vol-

40

FREQUENCY IMHZI

Fig. 6. Power spectral density of a typical wire response.

LONGITUDINAL DIRECTION

Fig. 7. Longitudinal contour of the coherent wire response.

1- 9 mm|

Fig. 8. Transverse contour map of the coherent wire response.

ume. It is then possible, in a probabilistic sense, torelate a distribution of detected signal levels to a scat-tering cross-section distribution and ultimately to infera volume backscatter value. This process is currentlybeing used to measure very low atmospheric backscattercoefficients.

V. Conclusions

A technique has been developed and demonstratedfor mapping the coherent response of a CO2 Dopplerlidar as a function of position within its focal volume.This information is required to extend the use of co-herent CO2 systems to single-particle (ultralow back-

732 APPLIED OPTICS / Vol. 23, No. 5 / 1 March 1984

7

U.

64

62

60

2

2

'a

58

56

54

52

50

48

LOG10 AREA)

Fig. 9. Longitudinal sensitivity.

52

50

a

48

46

42

401.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

LOG1 0 (AREA)

Fig. 10. Transverse sensitivity.

scatter) measurements at 10.6 /,m. Additionally, it maymake possible remote noninterfering particle sizemeasurements for particles 1 um and larger in diam-eter.

We would like to express our appreciation to E. A.Weaver, NASA/MSFC, and to R. Tobiason, NASAHeadquarters Office of Aeronautics and Space Tech-nology for their support of this effort. We would alsolike to thank V. Vaughan and R. Crump of AppliedResearch, Inc., for assisting in collection and reductionof the data.

References1. M. J. Post, R. A. Richter, R. J. Keeler, R. M. Hardesty, T. R.

Lawrence, and F. F. Hall, Jr., Appl. Opt. 19, 2828 (1980).2. R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, et al.,

"Development of a Laser Doppler System for the Detection,Tracking, and Measurement of Aircraft Wake Vortices," AASATech, Memo, TMX-66868, FAA-RD-74-213 (Mar. 1975).

3. R. L. Schwiesow and R. E. Cupp, Appl. Opt. 19, 3168 (1980).4. M. C. Krause, L. K. Morrison, C. E. Craven, N. A. Logan, and T.

R. Lawrence, "Development of Theory and Experiments to Im-prove Understanding of Laser Doppler Systems," LockheedMissiles and Space Company, Inc., Final Report, NASA contractNAS8-25921, George C. Marshall Space Flight Center (June1973).

Meetings Calendar continued from page 729

1984August

13-15 Photometric & Radiometric Measurements course,Boston M. McHenry, 5151 Monroe St., Suite 118W,Toledo, Ohio 43623

13-17 42nd Ann. Mtg. Electron Microscopy Soc. of America,11th Ann. Mtg. Microscopical Soc. of Canada, DetroitC. Lyman, Central Res. & Dev. Dept., E.I. du Pont deNemours & Co., Experimental Station, E356, Wil-mington, Del. 19898

13-17 6th Int. Conf. on Thin Films, Stockholm S. Berg, In-stitute of Technology, Uppsala University, Box 534,751 21 Uppsala, Sweden

13-17 Int. Conf. on Luminescence, Madison OSA Mtgs. Dept.,1816 Jefferson Pl., N. W., Wash., D.C. 20036

13-17 12th Inter. Laser Radar Conf., Aix-en-Provence ServiceD'Aeronomie du CNRS, A lAttention de Mr. G. Megieou de Mr. J. P. Granier, BP3, 91370-Verrieres LeBuisson, France

13-17 Photometric & Radiometric Measurements course,Boston Laser Inst. of Amer., 5151 Monroe St., Suite118W, Toledo, Ohio 43623

14-16 Laser/Fiber Optics Communications course, DenverEng. Tech., Inc., P.O. Box 8859, Waco, Tex. 76714

15-17 Int. Conf. on Information Processing, Christchurch R.Bates, Dept. Electrical Engineering, University ofCanterbury, Christchurch 1, New Zealand

15-17 Int. Conf. on Progress in Optical Physics, U. MelbourneI. Wilson, CSIRO Div. of Chem. Phys., P.O. Box 160,Clayton, Vic., Australia 3168

19-24

20-24

28th Ann. Int. Tech. Symp. & Exhibit, San Diego SPIE,P.O. Box 10, Bellingham, Wash. 98227

ICO-13 Optics in Modern Science & Technology, SapporoS. Fujiwara, Secretariet, ICO-13, Sapporo, co SimulInternational, Inc., Kowa Bldg. No. 9,1-8-10 Akasaka,Minato-ku, Tokyo 107, Japan

20-24 13th Congr. of the Int. Comm. for Optics, Sapporo Y.Ohtsuka, Faculty of Engineering, Hokkaido U.,Sapporo 060, Japan

20-24 5th Int. Symp. of Gas Flow & Chemical Lasers, OxfordA. Kay, Culham Lab., Abingdom, Oxfordshire X143DB, U.K.

20-24 Precision Electromagnetic Measurements Conf., DelftI. Smits, Dept. of Electrical Eng., Delft U. of Tech.,P.O. Box 5031, 2600 GA Delft, The Netherlands

26-1 Sept. Int. Conf. on the Photochemical Combustion and Storageof Solar Energy, Osaka The Society of Kinki ChemicalIndustry, 1-8-4, Utsubo-hommachi, Nishi-ku, Osaka550, Japan

27-29 8th Int. Colloquium on UV & X-ray Spectroscopy of As-trophysical & Laboratory Plasmas, Wash., D.C. R.Kreplin, Code 4175, Naval Res. Lab., Wash., D.C.20375

continued on page 745

1 March 1984 / Vol. 23, No. 5 / APPLIED OPTICS 733