L. C. GRAHAMGoodyear Aerospace Corporation

Litchfield Park, AZ 85340

Flight Planning for Stereo RadarMappingThiS analysis indicates that, with proper selection of flightpaths, available radar systems are adequate formedium-scale stereo mapping.

INTRODUCTION

SINCE THE EARLIEST image-like radar dis­plays of terrain details, various cartog­

raphers and photogrammetrists have ex­plored the possibility of using airborne imag­ing radar data for topographic map compila­tion in order to obtain the advantages of all­weather operation. A special mapping systemwas developed and deployed by the militaryfor this purpose; however, because this sys­tem was rather complex and expensive, ef­forts fo use conventional radar images in the

tion through mensuration of radar images re­quires that two or more overlapping imagesbe acquired from different flightpaths. Ameasurement of the across-track position ofan imaged feature on a single image corres­ponds to measurement of the distance fromthe aircraft (flightpath) to the feature. Twosuch measurements "may be combinedthrough trilateration to compute the positionof the feature with respect to points along theflightpaths. This is illustrated in Figure 1 forthe commonly used mode employing parallel

ABSTRACT: Pairs of terrain-imaging radar images may be viewed andmeasured stereoscopically in order to obtain elevation data for top­ographic mapping. An analysis of the technical and economic con­siderations in selecting flight parameters for mapping projects ispresented. Both parallel and right-angle flightpaths are considered.The results indicate that systems as presently constituted have thepotential to produce data adequate for original medium-scale map­ping, and that the right-angle mode is superior to the parallel­flightpath mode under the assumptions made if psychophysical dif­ficulties in image fusion are not encountered.

stereo mode have continued. A system hav­ing suitable image detail for medium-scalemapping is now commercially available. TheGoodyear Aerospace owned-and-operatedGEMsa radar is employed in a twin jetCan;l.Velle aircraft owned and operated by theAero Service Corporation, a division ofLittonIndustries. The purpose of this paper is toexplore analytically the use of systems ofthistype in topographic mapping, with particularattention to the relationships between eleva­tion accuracy, cost, and flight parameters.

STEREO MODESTo make a measurement of terrain eleva-

a Goodyear Electronic Mapping System.

paths at the same altitude, an alternate usingparallel paths at different altitudes and a thirdusing paths oriented at right angles but at thesame altitude. Other than purely geometricaccuracy considerations, the advantages anddisadvantages of the three stereo modes willbe discussed next.

CONVERGENCE ANGLESThe convergence angles illustrated are a

prime variation in flightpath selection.Among the important accuracy limitations tobe discussed later are the accuracies ofmeasuring the distances from the flightpathsto the terrain points. As shown in Figure 2,these accuracies combine geometrically toproduce an important contribution to eleva-

PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSING,Vol. 41, No.9, September 1975, pp.1131-1138.

1131

1132 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975

tion accuracy. Small (weak) convergenceangles cause large elevation uncertainty dueto range measurement accuracy. The small­est elevation uncertainty, and thus the op­timum (strongest) convergence angle fromthis standpoint, is 90 degrees.

COMMONLY USED MODE

The mode commonly used employs paral­lel flightpaths at the same altitude. As shownin the figure, the flightpaths and look direc­tion are ordinarily chosen so that the commonarea is viewed from the same direction. Thishas the disadvantage of resulting in weakerconvergence angles than would result fromchoosing to view the area from opposite di-

rections. However, radar images viewedfrom opposite directions have dissimilaritiesdue to illuminating the terrain from the radar.Highlights and shadows are reversed. Thiscauses psychophysical difficulties in fusingthe two images into a three-dimensionalmodel. Significant improvements in accuracyare expected from the local averaging whichoccurs in visual model formation, and moreefficient data extraction is possible by usingthe anaglyphic technique rather than theanalytic technique. Furthermore, a prime useof the radar imagery is to view the terrainmodel stereoscopically in order to performgeologic terrain analysis. Therefore, it iscommon to use same-side stereo rather than

Fp·I FP·2

~'""".""'----=

TERRAIN I--- COMMON COVERAGE ·1

~TE PARALL:lIGHTPATH MOOE

TERRAIN I COMMON COVERAGE I

RIGHT ANGLE MOOE

FIG. 1. Stereo modes.

elEVATIONACCURACY

_~"'r'-_.L--

SMAll CONVERGENCE ANGLE

FIG. 2.LARGE CONVERGENCE ANGLE

Convergence angles.

FLIGHT PLANNING FOR STEREO RADAR MAPPING 1133

opposite-side stereo in collecting radar im­agery.

ALTERNATE PARALLEL FLIGHTPATH MODE

Figure 1 shows the alternate mode inwhich the parallel paths are flown at differentaltitudes and are not offset. This mode would,in some cases, produce stronger convergenceangles than the commonly used one. How­ever, it suffers from two disadvantages whichpreclude its use for most work. First, thelower depression angles cause greater terrainmasking from elevated terrain, in otherwords, longer shadows. Second, flying at sig­nificantly lower altitudes causes the aircraftto encounter much more turbulence incloud-covered areas where the radar hasgreatest utility, which may cause image de­gradation and danger to flight personnel insevere cases. The alternate mode is nottreated further here but those planning stereoflights should be aware of the possibility ofusing it, or combinations ofthe two, in specialcases. For example, in a low-reliefarea wherethe greatest vertical exaggeration possible isdesired, two flightpaths offset in both al­titude and horizontal position may be used.

RIGHT-ANGLE MODE

It has been known for some time that paral­lax resulting from any two differentflightpaths can be used to create a visual ter­rain model and to make measurements. Mr.Homer Jensen of Aero Service Corporationhas recently suggested that a special case ofnonparallel flightpaths be used in terrainanalysis and mapping, viz., the case whereoverlapping coverage is obtained fromflightpaths at right angles. This mode has asignificant advantage in that the convergenceangles are stronger.

On the other hand, the right-angle modesuffers from several disadvantages. First,shadows also fall at right angles and high­lights are different, causing difficulties in fu­sion, although probably not so great as in theopposite side case. Second, parallax, and thusvertical exaggeration and measurement accu­racy, vary over the overlap area in both hori­zontal dimensions rather than in only one(range) as in the parallel cases.

Third, and most important, any lack of or­thogonality in the image causes an elevationerror. This can be seen in Figure 1 by notingthat a deviation from orthogonality in theangle marked t/J by an amount Bt/J causes anerror in the position of the point at B in theimage of flightpath 2 by an amount RBIjJ. Ap­proximately the same error would be causedby an error of BR in the measured distance

from flightpath 1. Similarly, an error of 06 inflightpath 1 will cause an error equivalent tofiR in distance from flightpath 2. Imagingradars are inherently more accurate in dis­tance measurement than in angular meas­urement. Thus, there is a tradeoff betweenthe improved strength of the convergenceangle and the loss of accuracy due to or­thogonality. This is treated in more detail inthe following sections, where the potentialaccuracy of the 90-degree mode is shown tobe slightly superior to that of the commonlyused mode.

ERROR ESTIMATES

The following sections develop and applyconventional differential calculus estimatesfor the vertical measurement accuracy in thecommonly used parallel flightpath andright-angle modes of radar stereo elevationmeasurements. Horizontal measurement ac­curacies could be obtained easily in the samemanner. However, vertical measurementsare both more stringent in mapping specifica­tions and more difficult to obtain with radar,so that performance level is dependent onthese values. Therefore, only the verticalcomponents of terrain measurements aretreated, and it can be assumed that horizontalmeasurements are in general more accuratethan the values arrived at here.

ERROR CONTRIBUTIONS

The contributions to vertical measurementaccuracy treated here are the principallimi­tations to the technique and include locationof the aircraft in the along-track, across-track,and vertical directions, the accuracy ofmeasuring distance from the flightpath to theterrain (range measurement accuracy), and inthe right-angle case, the orthogonality ofeachimage.

HORIZONTAL FLIGHTPATH MEASUREMENT

ACCURACY

The GEMS system employs a SHORANnavigation system for measurement of aircraftposition. In this system, an airborne transmit­tertransmits pulses of radio frequency (UHF)energy simultaneously to two ground trans­ponders. The transponders amplify and re­transmit the signals back to the aircraft. Anairborne receiver and time comparator meas­ure the elapsed time, and thus distance, toeach ground station. The transponders areplaced far enough from the aircraft so that thedifference between ground distances and theslant distance measured are small, and can becorrected, if necessary, by knowing aircraftaltitude as described in the next section.

1134 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975

Similarly,

F'G. 3. Parallel flightpath measurementgeometry.

doppler signal sensing and an accuracy ofabout one-tenth of the antenna physicalbeam, or 0.1 degree is usually achieved.

PARALLEL FLIGHTPATH ELEVATION ERROR

(3)

",th,

I·

The geometry of an individual stereomeasurement is illustrated in Figure 3. Fromthe figure, the x and z position of the imagedpoint may be determined by simultaneoussolution of equations representing circles ofradius R, andR 2 centered at the flightpaths ofpositions alb, and a2b2' Thus,

R,2 = (x-a 1 )2 + (Z-b,)2R 22 = (X-a2)2 + (z-b 2)2. (1)

The effects ofvertical measurement errors inRt> R 2, at> b" a2, andb 2 may be determined byimplicit partial differentiation of Equations 1with respect to these quantities, and simul­taneous solution for dz. Treating range meas­urement accuracy first:

2R,dR, = 2(x-a 1 ) dx + 2(z-b,)dz,2R 2dR 2 = 2(X-a2) dx + 2(z-b2)dx. (2)

Eliminating dx and lettingx-a, = G"X-a2 =G2,

G 2 -G, = S,z-b, = z-b2 = h,

thend - R,G2 dR R 2G'dRz - hS 1 - hS 2'

Now if the differentials represent errors in R,which are approximately equal in magnitudebut statistically independent,

(G,2R 22 + G 22R,2)a z

2 = aR2 .h 2S 2

2 2G,2G 22

2az = h2s2 an ,

G 12+G 2 2a/= S2 ab2.

The flight parameters for the GEMS sys­tem in its normal mode are h =12 km, s =15km so that the overlap is represented by

9 km < G 2 < 31 km,24 km < G, < 46 km.

ORTHOGONALITY

3 Accuracies used here are assumed to be onesigma (lu). The sources do not always state thelevel specified and this assumption will in somecases be conservative.

VERTICAL FLIGHTPATH MEASUREMENT

ACCURACY

Aircraft altitude above the datum plane ismeasured by a differential barometric altime­ter calibrated during the flight with a radaraltimeter. In addition to basic instrument ac­curacy, the accuracy of this technique de­pends on proximity of available altitudecheck points (seashore, lakes, or plains ofknown elevation) and on the temporal andspatial variation of the isobaric surfaces.Again, accuracies of 30 meters are routinelyobtained and lO-meter accuracy is achieva­ble in special conditions.

From these two measurements, aircraft posi­tion is calculated by trilateration every mileor so along the flight track. An inertialnavigator is used to interpolate between theSHORAN "fix" points.

SHORAN system accuracy is a function ofequipment calibration, operator proficiency,and the degree to which the radio transmis­sion paths (propagation velocity) are meas­ured and used to correct the raw data. Ac­curacies of 30 meters3 or so are routinely ob­tained and 10-meter accuracy is achievable.

Ground station locations are obtained fromlocal ground control or from Transit satelliteGeoceivers and are, in general, good enoughto be neglected. The error of the inertial sys­tem interpolation can also be made smallenough to be neglected.

RADAR RANGE MEASUREMENT ACCURACY

Flightpath-to-terrain distances are meas­ured by scaling the radar imagery. Rangemarks which represent previously deter­mined distances are generated by a crystaloscillator and displayed in the imagery. Ter­rain features are measured with respect tothis scale, which may be made sufficientlyclosely spaced so that interpolation errors be­tween marks may be neglected. This is abasic time measurement and with sufficientcalibration may be made without difficulty toan accuracy equivalent to the radar's resolu­tion, or about 15 meters in the GEMS case,and to perhaps one-fifth of this value, or 3meters, with special care and calibration.

In the right-angle mode, the largest con­tributor to elevation error is the lack of com­plete orthogonality in the imagery, as discuss­ed earlier. The orthogonality is obtained by

FLIGHT PLANNING FOR STEREO RADAR MAPPING 1135

G, -I(M

FIG. 4. Elevation error, normal stereo, S = 15km.

REDUNDANT FLIGHTPATHS

The spacing between flightpaths used ingenerating Figure 4 was chosen to provideabout 60 per cent sidelap. That is, just enough

Using the accuracy estimates stated earlier,we may characterize the values convenientlyachieved as realistic and those achievablewith greater care and calibration as optimis­tic, as follows:

Error Realistic Optimisticcontribution value value

aR 15 m 3 mau, ab 30 m 10 m

Using these values in Equation 3 and takingthe RMS az (the three contributions to thevariance are summed), the curves in Figure 4are obtained, where a z is plotted as a functionof ground distance to the nearest flightpath,G 2• It may be noted that the realistic valuesproduce an average error of about 200 m andthe optimistic around 70 m. Choosing 100 mas the approximate requirement for mediumscale mapping, the predicted results areprobably too close to the optimistic end toregard this as a capability based on singlestereo measurements. However, no advan­tage has been taken of accuracy improve­ments from ground control incorporated asblock adjustments. This improvement,realizing that some of the values used in ar­riving at Figure 4 are conservative, indicatesthat available equipment is suitable formedium-scale mapping. Possible accuracyimprovement through additional or alternatedata collection and reduction are describedin the following section.

'/

/"REALISTIC!

V/

//

/'//

",.-

",.-"" "o,nrsTlc"

--

to ensure duplicate coverage of terrain withallowance for navigation errors and elevationdisplacement with the 37 km swath available.If the spacing is reduced somewhat, thenmeasurements may be made between alter­nate flightpaths and the spacing increased toabout two-th irds of the swath rather than half,thus providing a stronger convergence angle.Furthermore, the use of both adjacent andalternate flightpaths provides redundancy toimprove the accuracy even further. If theterrain is imaged n times, the maximumflightpath space is n -lin (swath). approach­ing the total swath for large n and providingn -1 redundant (but not equally accurate)measurements. More combinations offlightpaths are possible, but such measure­ments are not independent and no furtherimprovement in accuracy (except for that ofthe final measurement) will result. There­fore, the image from the path nearest theswath, of width lin, should be compared witheach remaining image and the results com­bined. In combining measurements, the re­sults should be weighted according to theinherent accuracy of each for a maximumlikelihood estimate. If the accuracy of thevarious measurements are ab a2, ... , a ll" theresulting accuracy will be:

1 1 1 1""2 =-2 + -2 +···+-2a al a2 am .

This scheme is illustrated in Figure 5 forn=4.

In order to characterize the advantageswhich may be gained from this procedure,Equations 3 were used to estimate the accu­racy attainable with n=2 (minimum stereocoverage), n =3 and n =4. If it is assumed thatdata collection and data reduction costs areabout equal in the normal data collection andreduction mode and calling this value 1, thenTable 1 defines the relationship of cost to n,using either complete data reduction, or onlythe most accurate pair. The average accuracyfor n= 2, 3, and 4 from Equations 3 is givenin Table 2.

As noted in the table, both the optimisticand realistic estimates of error contributionhave been used, and the computations havebeen made for altitudes of both 13 km and 6km. The higher altitude applies to most situa­tions and the lower to mapping ofhigh moun­tains where the terrain rises to values whicbsignificantly reduce effective convergenceangles .

To provide a graphic interpretation, thesedata have been plotted on Figure 6, alongwith an overall average curve based on arbi­trarily selecting the performance parametershalfway between those previously charac-

""..""12

JOO

l20

'00

,..,..

~i

'"o'

12.

..

..

1136

FP-1

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975

FP-4

FLIGHTPATHCOMBINATION

4-1

4-2

S(SPACING)

3W/4

\V/2

s*18.5~ 12.3, 24.6**9.25, 18.5, 27.75**

4-3 W/4

FIG. 5. Multiple flightpaths, n=4.

TABLE 1. RELATIONSHIP OF COST TO n.

Data reduction Total costData collection All Most accurate All Most accurate

n cost data data only data data only

2 0.5 0.5 0.5 1 13 0.75 0.75 0.5 1.5 1.254 1 1 0.5 2 1.5

* For simplicity, no allowance was made here for navigation and elevation displace­ment.

** Most accurate data (pair).

TABLE 2. AVERAGE ACCURACY. RIGHT-ANGLE MODE ELEVATION ERROR

Most accurate In assessing the errors of the right-anglen h All data data only mode of Figure 1, the geometry of Figure 7

2 12 km 170 170 defines the measurement problem. As shown

3 12 km 94 115 in the figure, two flightpaths of equal eleva-4 12 km 60 98 tions are assumed to cross at the coordinate2 6km 310 310 system center, Po' When the aircraft is at point3 6km 168 208 Pb an orthogonality error, t!Jb exists and simi-4 6km 106 174 lady when the aircraft is at P2 an orthogonal-2 12 km 53 53 ity error of t!J2 exists. Since the terrain point at3 12 km 29 36 PT exists in both images, it must lie on circles4 12 km 19 30 centered at PI' and P2/. It lies, therefore, on2 6 km 96 96 the circle defined approximately by the cy-3 6km 52 64 linder R I2=X2+Z2 for small t!JI and t!J2, and the4 6 km 33 54

plane Y=y I+mt!JI and also on the circle andplane: Fig

terized as optimistic and realistic, and choos­ing an average terrain elevation of about 2km. Again, no advantage was taken of possi­ble block adjustments, although to a first ap­proximation this probably could be assumedto be included in the cost basis.

R 22 = y2+Z2,

X = X2+rt!J2'

Combining these

R l 2 = Z2+(X2+Ylt!J2)2,Rl = Z2+(YI+X2t!JI)2,

(4)

(5)

FLIGHT PLANNING FOR STEREO RADAR MAPPING 1137

,.OJ=:;:::;;=;::i;==:::::j:j;======t=======+=1.14

°t,

and combining Equations 7 and 9, droppingthe flightpath subscripts

Uz = ~ [(X2+y2+2h2) UR2+2y2x2u~

+2h2ua2+(x2+y2)Ub2JIf2. (11)

Values for this relation in various terrainpositions, employing the errors and flightparameters previously used, are given inFigure 8. These values are conservative, inthat only one value was used for ulj!; viz., 0.1degree, considered realistic. For cost versusaccuracy considerations, the overall averagesgiven are for n=2. Double coverage (n=4,twice the cost) average error values are thosegiven as 1J4 area coverages, which are simpleaverages of the errors for values ofx and Y upto and includingsw/2 without redundant datareduction, again conservative.

Comparison of the individual values inFigure 8 with the curves in Figure 4 andcomparison of the averages in Figure 8 withthe curves in Figure 7 indicates a significantsuperiority of the right angle mode with re­spect to the commonly used parallel modeunder the assumptions made here. Actual ex-

FIG. 7. Right-angle mode geometry.

I .•

ACCURACY 01 - METERS

1.9

1.6

ut----\.-----\.--------Pk"---3<o,.------t---'''c----_+-----i

I.J..---+---+--¥----'lr------Jl',-------+--l

1.5

1.1

I.O~---4>--QPo'-- .......-__1~_...... '_-=OOO»-,o ~ ~ ~

1.4t--+----l.--------\:-f\------'~t------_+-----i

1.1t----\--~_+~._____'lr_--t-------"~-_+-----i

FIG. 6. Cost versus accuracy, parallel equal altitudeonly.

where ml/lt =X2lj!1 and rlj!2=Y 1lj!2, neglectingsecond order effects on the errors.

Taking differentials as before with R, lj!,and z as variables:

2R 1dR I = 2z dz+2YI(X2+Yllj!2)dlj!2,2R2dR2 = 2z dz+2x2(YI+X2lj!I)dlj!I' (6)

Combining Equations 64z dz = 2R1dR 1+2R2dR 2

-2Yl (X2+Yllj!2)dlj!2-2x2(YI +X2lj!I)dlj!1' (7)

Figure 7 shows that along-track navigationerrors do not cause an elevation error.Across-track and vertical errors do. Thesemay be projected in the direction of R 1 andR 2 • Thus

dR I =dal Rh

+db l R..!2nav I h

dR2 =da2Rh

+db2 RJl.! (8)nav 2 2'

These contributions to the elevation error ofEquation 7 are thus

dR I =2R 1 (h dal + ..:::..iRX

1 db l )nav \HI

dR2 nav =2R~(;2da2+ t db2) (9)

dR I = 2hdal +2x2db hnav

dR 2 nav = 2hda2+2Yldb2' (10)

Now, assuming all differentials representstatistically independent errors and makingthe following assumptions and approxima­tions,

Yllj!2«X2X2lj!1«YlUll 1= UR 2

ua1=ua2Ub 1=Ub 2

U""1=U""2Z = h, altitude above terrain,

1138 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975

~--.-_.----r--,-_HI_GTH_M_O_UNT"A,-IN_S-,{,6K_M...:,I_,---......_.--_~ • $W'. swn 1SW14 sw ~. .,. sw(Z JSWJ4 sw

• lU JU n.] .4.1 .... 11.1 ... 1... ........" ,U 12.. "1.4 141.1 "" .." '''' '11.J IIU "1.1 m.s..n ." 111.• 151.4 ltl.l ,.u ..n ... 14U "1.2 '''A """"" lU II,", 211.1 ZlU )51.5 """ ,tt. 1.1.1 l4U ]14.4 "U.. ".1 n'.1 "'.. ]51.5 Qt.• .. ,.... "'.. "" "u "',

OVERAll AVERAGE -IN.. OVERAll AVERAGE -1'1.5114 AREA AVERAGE • 111 1'4 AREA Avn"IOE -1...

LOWLANOS

OnlMISTIC REALISTIC

~ • ..." ...n """ ... X . ..." ...n """ ...• 'H tt. tt, ]I.' m ,u ".1 SJ.J i1l .U..." tt. ,... .... 11.5 ", ..." ".l 55.1 1U 12.' 111,1

...n "., ".1 JU 106.1 112.• ~ 53.3 13.2 n.' ll404 .ou

""" ]I.' 11.& 101.1 lotU 115.1 """ 61.l 'l.' 1l4." lSUi lUI... 4'.' ." 1]1.4 115.5 ZIU ... IU 11].1 ISl.' 111. n1.'

I AID, YAlU(J All( SIVEI HERE '1n_ Of fRAtTlOIAlINSTAlCf ACRQII THE n...."THOVERAll AVERAGE a 10.11/4 AREA AVERAGE a 31.•

OVERAll AVERAGE ·,11.5I!4ARUAVERAU· 51.5

FIG. 8. Elevation error summary, right-angle flightpath case.

5000 ELEVATIONFEET MSL

.'.,;.' .""~.L" I

4000~

,, ., ," I, . ,

'-;/,

I

/."f II , ,

3000 ,..". , , I

;/J , ,

,,~~ // I SIERRA ESTRELLA,

/1 I I Ii~ " MOUNTAINS

ff,~o /~::.:-._._!,;>"~:::::}? I , : II

~-1 1500 .~ , -~••If! DISTANCE FROM REFERENCE~

-- --::;."" . I ---........ REFERENCE POINTI POINT (STATUTE MILES) 2, ,I' I I I

1___.--: I1000 , I I , I

I I , II I I I II I , , , I, ,

500, I , , ,

, I I I I I I I I I II I , , I I I I

1

•2

• • • • • •LEGEND:- MAP PROFILE_n STEREO PROFILE (NO. 1 INTERPRETER)--- STEREO PROFILE (NO.2 INTERPRETER)

• POINT IDENTIFICATION NUMBER

FIG. 9. Terrain profile from GEMS imagery.

10

•11 12

• •

perience in collecting and reducing data withboth modes under comparable conditionswill be required to determine whether theorthogonality assumption is valid andwhether adequate fusion for efficient datareduction can be achieved.

EXPERIMENTAL RESULTS

Experimental results of data reductionstudies on radar imagery, using block ad­justments was reported separately in the1975 ASP national symposium. Some ratherpreliminary previous results are reportedhere for completeness.

Figure 9 shows a 4-mile profile taken froma map sheet, defined by 12 points along theprofile. Also shown are two profiles obtainedfrom a radar stereo pair by two radar inter­preters by using a simple mirror stereoscopeand parallax bar. Since only approximate val­ues ofexternal parameters were available, noabsolute measurements could be made.However, by matching the profiles at an ar-

bitrary point, some idea ofthe potential ofthemethod used with ground control could bemade. The result of comparing the map pro­file with the average of the two interpretersshows an average error ofabout 40 m over theline which corresponds to that portion ofFigure 4 from about 12 km to 20 km. In thisrange increment, the optimistic curve aver­ages about 50 m.

CONCLUSION

Theory and experiment indicate that cur­rently available terrain-imaging radars havethe potential of producing stereo data ade­quate to permit compilation of at leastmedium-scale topographic maps. Some ver­satility exists in choosing imaging modes andflight line spacings. A carefully controlledtest over a well-documented test area shouldbe made to further quantify the economic andtechnical variables and to identify optimumdata collection modes and reduction tech­niques.