Polarization Effects of Scattered Coherent Light on Imagery

C. L. Rudder and R. L. Carpenter

The polarized and depolarized components of backscattered laser light are examined photographically.Effects of surface roughness and angle of incidence are determined by measuring contrasts and dynamicrange of the laser imagery. Three effective scattering surfaces are deduced from Fung's scatter theory toexplain the results.

Depolarization of electromagnetic waves scatteredfrom rough surfaces has been studied extensively formicrowave radar applications. Several theories relatethe scattered electric field to the polarization of theincident waves and the surface structure of the scat-terer.>-6 Although no explicit experimental verificationof these theories exists, the scattering mechanism de-scribed is generally accepted for interpretation ofradar data.

Other investigators have used lasers to study experi-mentally the degree of depolarization in backscatteredwaves as a function of the scattering properties of thetarget material.7 Depolarization characteristics ofcomplex surfaces were examined for other scatter anglesby Egan e al.8 The referenced authors empiricallyattribute the depolarization process primarily to multi-ple scattering.

Several applications of the laser have created a needto relate the scattering process to target signatures ob-tained in imagery, e.g., holography, remote sensing,reconnaissance, and display systems. The previousinvestigations of depolarization characteristics of roughsurfaces (for lasers and microwaves) suggest that effectsmay be observed in laser imagery that can aid in inter-pretation. The techniques are well known in the geo-science studies done by remote sensing with radar. 9 Inthis paper, we relate the scatter theory presented byFung to laser imagery.3

Fung has shown the electromagnetic field scatteredfrom a rough surface contains polarized and depolarizedcomponents.3 4 Single and multiple scattering contrib-ute to the polarized return. Only multiple scatteringgives rise to the depolarized return. This descriptionallows us to write the scattered field at a point P as

Es(P) = e (AS + AQs) + fi AD. (1)

The authors are with the Reconnaissance Laboratory, Mc-Donnell Company, St. Louis, Missouri 63166.

Received 8 July 1968.

The e and i unit vectors are in the direction of theincident electric and magnetic fields, respectively. TheAs is an integral function of the surface roughness andreflectivity. Since this contribution is due to singlescattering, the integration is performed over an effectivespecular surface. Such a surface would be defined bythe angular distribution of propagation vectors in theincident beam of light. The AQs describes the polar-ized return due to multiple scattering. The diffusesurface causes this contribution, but we label it thequasi-specular surface because of the polarization of thescattered light. Finally, AD is the integral functionover the diffuse surface describing the depolarized re-turn. For a randomly rough surface, the distribution oflight scattered from the quasi-specular surface would beindistinguishable from that scattered by the diffusesurface.

The average reflectivity is given by10

R = f Ro(X) + f2 Ro(X) + f3 Ro3(X) + * * * . (2)

where fl, f2, f3, . . . are the fractions of incident lightundergoing single, double, triple, . . . reflections. TheRo (X) is the Fresnel reflection coefficient. The fi Ro(X)is contained in A. Successive terms in R, notincluding f Ro (X), are contained in AQ and AD-Since multiply reflected light is partially absorbed ateach reflection, light scattered from AQ and AD willhave different effects on imagery than light scatteredfrom AS. We have examined these effects for thebackscatter case.

The purpose of the experimental investigation was tosee how surface roughness and reflectivity affect imag-ery made with coherent light. The two parameterswere controlled by constructing a target of gray scalesprinted on Kodak photographic papers. Papers usedwere Polycontrast F, Ektalure E, and Opal V; alternatenomenclature are gloss, matte, and rough surfaces,respectively. Profiles of these surfaces are shown inFig. 1. These data were obtained with a Tallysurfroughness measuring instrument. Average peak tovalley heights were 0.35 , (gloss), 6.66 A (matte), and

February 1969 / Vol. 8, No. 2 / APPLIED OPTICS 419

Figure 3(b) is a photograph made with the analyzeroriented perpendicular to the incident polarization torecord the depolarized return. The gray scales showthat increased dynamic range and contrast exist whenthe effect of the specular contribution is removed. Thisresult can be attributed to the partial absorption of thelight at each reflection of the multiple reflection process.

Photographic negatives were examined with a micro-densitometer to determine the increase in contrast anddynamic range with polarization filtering. Figures 4, 5,and 6 show microdensitometer traces for photographstaken at 0 equal to 0, 150, and 300. These resultsshow that the polarized return becomes less importantin backscatter for off-normal incidence. At normalincidence the single scattering process predominates,but the effect rapidly decreases with increasing S.

Fig. 1. Surface profiles.

Fig. 2. Experimental setup.

10.66 p (rough). Finally, the reflectivities were fixedby the gray steps on each target, hence, the data areobtained as contrasts.

In the experimental setup (Fig. 2), a He-Ne laseremitting light at 6328 A and a camera were placed sothat their angular separation was 50, permitting photo-graphs of the backscattered light to be taken. Datawere taken for several values of the angle 0. Theincident beam was linearly polarized perpendicular tothe plane of incidence defined by the target normal andthe direction of propagation. Polarized and depolar-ized components of the scattered field were recordedseparately by using a light polarizing film in front of thecamera lens.

For illustration, photographs of the target are shownin Fig. 3 for 0 equal to 00. Figure 3(a) was made withthe polarized return. The bright areas are attributedto the effective specular surface. The varying distri-bution of the white areas for the three surfaces is due tothe differences in the slopes of the peaks shown in Fig.1. Changing the angle 0 causes the scattering surfacesto be redefined with respect to the coordinates of theincident wave (i.e., A, AQS, and AD are changed).This alters the distribution of the specular contribution.

(a)

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Fig. 3. Photographs of the target illuminated with laser lightat 6328 A. The angle of incidence is 6 = . (a) The specularand quasi-specular components. (b) The diffuse component.

420 APPLIED OPTICS / Vol. 8, No. 2 / February 1969

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The scatter theory presented by Fung agrees with theeffects seen in imagery. Scattering due to the effectivespecular surface and diffuse surface is clearly evidentwhen polarization filtering is used. The increased con-trast and dynamic range in the imagery from the depo-larized field can be attributed to multiple reflections anddifferent reflection coefficients. Since partial absorp-tion of the light occurs at each reflection, the intensityof the depolarized light is more affected by the surfaceproperties than the polarized light. These resultsindicate that depolarization characteristics of roughsurfaces as well as reflectivities can be studied photo-grammetrically, and related to target signatures.

References1. P. Beckmann and A. Spizzichino, The Scattering of Electro-

magnetic Waves from Rough Surfaces (The Macmillan Com-pany, New York, 1963).

2. A. K. Fung, Planet. Space Sci. 14, 563 (1966).3. A. K. Fung, Planet. Space Sci. 15, 1337 (1967).4. A. K. Fung, J. Franklin Inst. 285, 125 (1968).5. R. D. Kodis, IEEE Trans. AP-14, 77 (1966).6. T. Hagfors, J. Geophys. Res. 68, 423 (1963).7. J. Renau, P. K. Cheo, and H. G. Cooper, J. Opt. Soc. Amer.

57, 459 (1967).8. W. G. Egan, J. Grusauskas, and H. B. Hallock, Appl. Opt.

7, 1529 (1968).9. R. D. Ellermeier, A. K. Fung, and D. S. Simonett, Center

for Research in Engineering Science, University of Kansas,Lawrence, CRES Rep. No. 61-10 (1966).

10. J. R. Aronson, A. G. Emslie, R. V. Allen, and H. H. Mc-Linden, J. Geophys. Res. 72, 687 (1967).

February 1969 / Vol. 8, No. 2 / APPLIED OPTICS 421

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