THOMAS A. EPPES* JOHN W. ROUSE, JR

Texas AbM University College Station, Texas 77843

Viewing-Angle Effects in Radar Images The detectability factor of features off-normal can be improved by spatial filtering in the Fourier plane of a single look-direction image.

ABSTRACT.A quantitative determination of the effect of viewing angle on the detectability of topographic linears in radar imagery is pre- sented. Variations of azimuth and aspect angles of an imaging radar antenna relative to a topographic linear were simulated using low- angle illumination of controlled linearfeatures on polystyrene sheets. The several model surfaces represented idealized versions of surface types that may be expected in areas of geologic interest. Fourier transform spectra of the radar image simulations were obtained using a coherent-optics system. These spectra were found to correlate with a detectability factor obtained directly from the radar image simulations. Fourier transform spectra of a linear feature observed from multiple viewing angles by a K-band imaging radar were also obtained and a detectability factor was estimated which agreed closely with theoretical predictions.

INTRODUCTION at a particular point in space, and sub-

~ ~ ~ ~ ~ ~ ~ T a v ~ i l ~ b i l i t y of high quality radar sequently forms an image of the energy re- T i m a g e s terrain has generated consider- turned, or backscanered, to that point. Ter- able interest throughout the scientific corn- rain whose slope is oriented norma1 to the munity, especially among geologists. The in- incident microwave energy generally Pro- terest is based on the of radar im- vides the largest backscatter and appears ages to display geologic features, especially bright on the radar whereas terrain linears, with greater interpretability than which slopes away from the direction of the

standard photography. Unfortunately, the incident eIlergY Provides little or no back- full potential of radar sensors cannot be scatter and appears dark on.the image. This realized, especially in geology, until a better shadowing effect is of particular in

quantitative understanding of the geoscience identifying toIJographic h e a r s such as those information content of radar images is evident in the radar image of the Boston

tained. A problem of particular concern is the Mountains shown in Figure effect of sensor viewing angle on the in- The degree of detectability of linears de-

terpretation of the radar image. pends highly on the orientation of the radar

hi^ relief is enhanced or sup- antenna relative to the feature. This problem pressed in radar imagery depending on the has been investigated qualitatively by Mac-

feature orientation relative to the radar an- Donald, et (&!. (1g69) and Wise (1969). The tenna because of the unusual technique used pUwoSe of this paper is to show quantita- to record these microwave data. ~~d~~ pro- tively the effect of viewing angle on the de- vides its own illumination source originating tectability of linears in radar image data using

a spatial frequency analysis technique em- ploying a coherent-optics system.

*Now with Bendix Research Labs., he also waq formerly with Texas A&M University. This re- M~~~~~ OF I~~~~~~~~~~~~ search was supported by the National Aeronautics and Space Administration under Grant NGL Wise (1969) in a study of continental and 44-001-001. subcontinental fracture systems showed that

169

FIG. 1. ANIAPQ radar imagery ofthe southern Boston Mountains and Arkansas River Valley, Arkansas.

radar imagery can be accurately simulated in the laboratory by ordinary photographs of raised surfaces. In his experiments with low-angle illumination of plastic relief maps he found the photographs to be remarkably similar to radar images of the modeled areas. He also examined the enhancement of ran- domly oriented linears cut into polystyrene sheets. As this approach leads to a well- controlled experimental situation, it was used as a means of establishing a quantitative technique for subsequent spatial frequency analysis of radar imagery.

Four different single-feature polystyrene models were constructed which permitted a detailed analysis selectively restricted to one feature type at a time. The surface types represented an idealized version of surface topography that could be expected in areas of geologic importance. Surface Type I con- sisted of a vertical dropoff; Surface Type I1 consisted of a rectangular indention into the

surface; Surface Type I11 consisted of a rec- tangular feature mounted on top of the polystyrene sheet; and Surface Type IV con- sisted of a triangular indention into the sur- face. Radar image simulations for a variety of azimuth and incidence angles were pro- dtced by illuminating the surfaces at a low angle with collimated light and photograph- ing them from directly overhead. Figure 2 illustrates radar simulations using Surface Type I1 for azimuth angles of 94" and 6' (rela- tive to the axis of the feature) and a grazing angle of 20". Surface Type I1 consisted of a rectangular indention, and a shadow is evi- dent due to the projection of the forward wall onto the floor of the feature.

The look-direction effects present in the radar image simulations were investigated quantitatively by converting these two- dimensional data into the spatial frequency domain using an optical Fourier transform approach (Cutrona et al. 1960). In optical sys-

(a) 94'

FIG 2. Surface Type I1 for azimuth angles of 94" and 6" and a grazing angle of 20".

VIEWING-ANGLE EFFECTS IN RADAR IMAGES 171

tems, the Fourier transform of the input image exists on a plane in space properly termed the Fourier transform plane. In this plane the distance from the optical axis of the system is proportional to frequency in the Fourier transform, and the intensity at any point is approximately proportional to the magnitude contributed by that particular fre- quency component. By analyzing the simu- lated radar imagery in the spatial frequency domain, the description of the look-direction effect in t e m s of the enhancement or degra- dation of the principal frequency compo- nents of the image of the linear provided an excellent quantitative estimate of how detectable the linear was in the image.

Because of the lack of variability in the radar image simulations, the spatial fre- quency components lay essentially in one di- rection. It was to achieve this advantage that only one linear feature was constructed on each model, rather than the combination of features used by Wise. The power spectrum transparencies were scanned, using a micro- densitometer, along the line of frequencies produced by the lineation in the original image. Figure 3 illustrates the Fourier trans- form magnitude for the surface type shown in Figure 2a. Figure 4 is the microdensitometer output of the power spectrum. A distinct series of components was produced by the radar simulation which vary in amplitude as a function of both the azimuth and incidence angles of the illumination.

The power spectra generated by the optical Fourier transform provide a different but equivalent means of observing the variation of shadowing due to illumination angle changes. It was found that due to system con-

straints the behavior of the power spectrum in the region between about 200 and 400 cycleslmm provided the most accurate indi- cator of the changes in the radar simulation caused by illumination angle changes, and that an integration of the spectrum over this range yielded a single-number parameter representative of the detectability of the sur- face feature.

The detectability of'a feature displayed in a simulation was defined numerically by de- termining the ratio of the shadow width or corner reflection width to the actual feature width. The shadow width is a direct meas- urement of the geometrical shadowing zone on the radar simulations. Corner reflection is the width of bright areas facing the direction of illumination. This ratio, the detectability factor D, associated with each radar simula- tion represents the degree of enhancement of a feature due to changes in its orientation relative to the illumination source.

The detectability factor for Surface Type I1 is shown in Figure 5 as a function of illumina- tion angle over a 180' range. Also shown is the variation of the integrated power spectra for the range 200 to 400 cycles/mm. Figure 6 shows the effect of incidence angle changes on the detectability factor and the integrated power spectra. The high degree of correla-

U FIG. 3. Fourier transform magnitude of Surface Type 11 (94'azimuth angle, 20" grazing angle).

I I I I I I I I

0 100 200 300 400 500 600 700

Frequency (cycles/mm)

FIG. 4. Power spectrum using Surface Type I1 (94' illumination) for azimuth- angle variation.

PHOTOGRAMMETRIC

-94 - 7 4 - 5 4 - 3 4 -14 6 26 4 6 6 6 86

Degrees

I I I I I I I I I t

- 94 -71 - 54 - 3 4 - 14 6 2 6 46 66 86

Degrees

FIG. 5. Comparison of feature detectability with integrated power spectra for Surface Type I1 for azimuth-angle variation.

I-' U

.6 n

Y a u al al I-' !%

m v, i. Mi.

0- 20 3 0 40 5 0 60

Degrees

Degrees

FIG. 6. Comparison of feature detectability with integrated power spectra for Surface Type for grazing-angle variations.

tion evident in these two examples was evi- dent in data from a11 four radar simulations,

Having established a reliable laboratory technique for measuring the detectability of a linear feature in simulated radar imagery, the procedure was applied to actual radar image- ry. Figure 7 illustrates one of eight radar images used to substantiate the viewing angle effects. These data were taken in 1968 over Arkansas (Boston Mountains) using a horizontally-polarized K-band imaging radar system (ANIAPQ-97). These unique images represent eight different viewing angles of the same scene, each separated by about 45 degrees. The topographic structure of the linear feature shown most closely resembled that of Surface Type IV, which consisted of a triangular indention into the surface.

The power spectra of each of the actual radar images were generated in the optical system. A concentration of spatial frequen- cies along a line in the Fourier transform plane resulted similar to that seen in the radar simulations. Although somewhat dispersed because of feature nonlinearities, the fre- quency components of the linear feature were clearly observable. Figure 8 illustrates the integral of the power spectra over the range 200 to 400 cycles/mm for the various radar images.

FIG. 7. Actual radar imagery of a selected feature with the arrow denoting the viewing angle.

Degrees

FIG. 8. Illustration of the integrated power spectra for the multiple-look direction radar im- ages .

VIEWING-ANGLE EFFECTS IN RADAR IMAGES

Viewing Angle (deg rees )

FIG. 9. Predicted detectability factors for the linear feature in the actual radar images.

A comparison of the partial power spectra for the actual radar images with that of Sur- face Type IV for azimuth-angle variation re- vealed a similarity in the trends for the high- frequency region, although variations of the incidence angle in the actual radar imagery introduced some additional effects.

Based on the results of the radar simula- tions, which related the detectability factor to the partial power spectra, it was possible to predict quantitatively the detectability factors for the linear feature in the actual radar im- ages. Although the simultaneous interaction of azimuth- and incidence-angle effects were difficult to incorporate accurately, a reasona- ble estimate was possible. The predicted values for detectability factor were calcu- lated using a combinational linear transfor- mation for both azimuth and incidence angle based on the viewing angle effects found for Surface Type IV. Figure 9 is a plot of pre- dicted feature detectability factor for the linear feature shown in the radar images. Two separate aircraft overflights were made at a viewing angle of 225" and the near perfect agreement of the data, as shown in Figure 9, attests to the repeatability of the analysis ap- proach.

The viewing angle dependence of the de- tectability factor determined from the power spectra is reasonably well approximated by the function (shown in Equation 1) where @is the azimuth angle and K is a function of the incidence angle. The form of Equation 1 was implied by MacDonald's work, that is, the feature is best seen if viewed at right ang- les and least well seen if viewed along the feature. The factor K is zero at normal inci- dence (6=O0) and infinity at grazing incidence

(6590") and appears to vary as tan 8.

DzK(1 - cos 2@)

The value of optical processing for analysis of image-formatted data has been shown by previous authors (Dobrin, 1968; Nyberg, et al., 1971) in studies where the Fourier spec- trum harmonics generated by multiple- linear systems were examined. The optical Fourier transforms examined in this paper are spectra of frequency components arising from the nature of an individual linear fea- ture. Multiple-linear spectra such as shown by Nyberg, et al., are modulated by the spec- tral components associated with the charac- teristics of the individual linears.

The practical effect of the viewing-angle dependence of radar images is to reduce the accuracy of lineament maps obtained from these data. The generally accepted remedy is to obtain multiple look-direction imagery over the terrain of interest. This is an expen- sive means of improving mapping accuracy. However, it is evident that the detectability factor of features oriented off-normal can be improved by spatial filtering in the Fourier plane of a single look-direction image using a filter which has an angular variation of the form of Equation 1. The filtered spectra upon reconversion to an image would have a rela- tively uniform detectability factor for almost all azimuth angles.

The Center for Research, Inc., University of Kansas is gratefully acknowledged for pro- viding the ANIAPQ-97 radar images used in this study.

REFERENCES L. T. Cutrona, E. N. Leith, C. J. Palermo, and L. J.

Parcello, "Optical Data Processing and Filter- ing Systems," IRE Trans. on Information Theory, vol. IT-6, June 1960, p. 386.

M. B. Dobrin, "Optical Processing in the Earth Sciences,"lEEE Spectrum, September 1968, p. 59.

H. C. MacDonald, J. N. Kirk, L. F. Dellwig, ana A. J. Lewis, "The Influence of Radar Look- Direction on the Detection of Selected Geolog- ical Features," Proceedings of the Sixth Inter- national Symposium on Remote Sensing of En- vironment, October 1969, p. 657.

S. Nyberg, T. Orhaug, and H. Suensson, "Optical Processing for Pattern Properties," Photogrammetric Engineering, Vol. 37, June 1971, p. 547.

D. U. Wise, "Pseudo-Radar Topographic Shadow- ing for Detection of Sub-Continental Sized Fracture Systems," Proceedings of the Sixth International Symposium on Remote Sensing of Environment, October 1969, p. 603.