RECONSlDERATIO T OF THE QUADRUPLE CAMERA 99

or freedom from industrial barriers. Varyingt~e field-angle, aperture, focal-length, pictureSize .and shape seems to make possible chal­lenging combinations.

To make a long story short, two remarksonly will be added:

. (1) Taking as term of reference, on the leftSide of ~igure 2, a f = 6"-9" X 9" convergentcamera Instead of the single f=6"-9"X9"camera does not change the main conclusionssignificantly. One has to fly so much lower inorder ~~ secure adequate stereoscopic inter­pretabilIty and the accuracy of the settingsin the cri tical model corners, * tha t all the ad­vantage that better intersection angles secureover worse scale transfer angles, and weak-

.* A mapcanllotbe trusted better than its system­atically worse sections.

ened stereoscopic settings, is lost again.t(2) The traditional doubts about accuracy

and cost of handling composite photographyare no longer justified. \\'ith extensive calibra­tion areas aYailable, and doing aerial triangu­lation on stereocomparator and electronicCOll1pU ter, the actual (random) inner geo­metrical relationships of multilens aggregatescan be taken into account in a matter ofseconds per pass point, with extreme accu­racy. A condition for this is however using aflexible and economical method of computa­tion, like the one recently developed for theRoyal McBee LCP-30 electronic computer.As for plotting when a quadruple aggregateis used, each triangulated model happensprecisely to be conveniently halved .

t W. A. Brucklacher, Bildmessullg & Luftbild­wesen, July 1956.

A System for Projecting Printsfor Controlled Mosaicson Steep Slope/

CORTLAND r. LOHR,

andWM. WADE

INTRODUCTION

SI~CE many di~cultiesarise in the construc­tIOn of mosaiCS, due to photographic dis­

tortion and differences in scale between theindividual photos, many methods have beentried to overcome them. Even when a radialtemplate laydown has been made and a num­ber of control points have been obtained incorrect geodetic positions and with correctscale and distances between them, there stillremains the difficulty of making projectionprin ts so tha t the poin ts on these pri n ts willexactly fit all of the control points, to saynothing of portions of the prints which maybe distorted between control points. It may

1 This method was developed by Cortland P.Lohr and describe:! by Wm. Wade, both of theCartographic Unit, Soil Conservation Service,Portland, Oregon.

be said that no mosaic can be made with com­plete accuracy if there are many changes ofelevation in the area photographed, wi thou tusing an exorbitant number of control points.

A method has been developed by the U. S.Geological Survey for making prints whichare free of distortion, by a series of photo­graphic strip exposures made in conjunctionwith a stereoscopic plotting instrument. (SeeDevelopment of the Orthophotoscope, PHOTO­

GRAMMETRIC ENGINEERING, September 1955,Page 529.) I t is a remarkably ingenious meth­od, bu tin its presen t sta te of developmen t thecost of prin ts is so fan tastically high tha tit isimpractical to use the prints for the greatmajority of mosaics. Improvements in thefuture may make this method less costly. Ithas the advantage of rectifying all portions ofa photo-model instead of only a few con trolledportions.

100 PHOTOGRAMMETRIC ENGINEERING

3 Form SCS-19, #10922 dated 4/12/57. N t SanMateo County, Calif.-along the coast.

4 Form SCS-19, #16190 dated 8/22/57 for ra_tional Soil Survey-East side Davis County, Utah,adjacent to Great Salt Lake.

California.3 In both cases the land slopedsteeply up from the Pacific Ocean. These twojobs ,,"ere the cause of an experimen t and thedevelopmen t of the new method descri bed inthis write-up. This method was used success­fully for the east side of Davis County, Utaharea for a National Soil Survey Mosaic.'

FIG. 2

appear on the photo along with the usualwing points D, E, F, and G, used for radialcontrol in the side-lap areas of the adjacentphotos to the left and right. Assume that thetransparent radial control sheet (with the cor­rect geographic positions of the points) is laidover the photo with the center B coincidingwi th the con trol cen ter.

Let the correct positions D ' , A', F ' , E ' ,C' and G' be marked with an x as in Figure 3.

Since the scale of the photo is too large atC, or between E and G, the points E ' , C' , and

·c

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A NEW METHOD

It is well known that, in ratioing photos forlaying a mosaic, the ratio for one side of aphoto is often not the ratio needed for theother side due to the elevation of the groundbeing higher on one side than on the other.

In Figure 1 assume that a photo is takenvertically of a mountain slope and that theheight of the camera gives the correct scaleat the center point, E, on the photo. Thispoint is projected from E ' on the ground.Then, naturally, the scale at point A will betoo small si nce A I on the grou nd is fartheraway from the camera. In the same way thescale at C will be too large because C' is closerto the camera.

Figure 2 shows how the poin ts A, E, and C

FIG. 1

the prints to fan out larger as they are laiduphill and to cause a straight ridge parallelto the shore to form a bow with its concaveside toward the shore line. Jt has been verydifficult with the usual methods of ratioingto correct this or even to get the prints tomatch reasonably well.

Such a condition existed when a mosaicof the Kapapala Ranch2 in Hawaii was to belaid. The same problem occurred for a mosaicin the northern part of San Mateo County,

2 Form SCS-19, #8835 dated 12/19/56. Kapa­pala Ranch, Hawaii-File No. F-7065. 3 sheets.

The most suitable method, so far, for pro­jecting prints to fit control points, is by meansof a rectifying projector. This instru men t isequipped with an easel which can be so tiltedthat the projection can be reduced or en­larged in any part of the photo, thereby dis­tortion of scale due to change in elevation ortip or tilt in the original negative can be cor­rected. Of course the print is rectified in rela­tion to the given control points, but not nec­essarily in relation to every portion of thephoto as was mentioned in the precedingmethod, which is en tirely too expensive forsuch refinements.

Although the cost of the method of using arectifying projector is not excessive, the pro­jector itself is very much more expensive thanan ordinary photo projector. For this reasonof cost the majority of photo laboratories donot have the rectifying projector, bu t relysimply on the ratioing of photos to make anapproximate fit to the control, through usingthe much less expensive photo projector­abou t one-third the price.

Many cartographic offices have triedvarious methods of ratioing and projectingphotos without a tilting easel. The accuracyof resu I ts has varied. One of the most trou ble­some jobs is where the terrain rises steeplyfrom a shore line or valley and the ascent con­tinues for a long distance. Jn such cases thecontact prints will be larger in scale on theuphill side than on the downhill side. Theusual effect of this in laying a mosaic is for

PROJECTING PRINTS FOR CONTROLLED MOSAICS ON STEEP SLOPES 101

FIG. 4

that using only this method was bound toproduce difficult mismatches, because ratiosCfIonot be carried successively from one partof a photo to the next photo when slopes aresteep enough to make the scale different 00

one side of the photo that 00 the other.This methode is useful where long steep

slopes exist, liKe those which constitute alarge percen tage of mosaics in the westernstates.

8

FIG. 5

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8 XC' CIIII

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FIG. 3

G' on the con trol sheet will be closer togetherand nearer the cen ter than E, C, and G. In likemanner the correct control positions of D' A'and F' will be farther apart and farther iroI~the cen ter because the photo scale is too small.

Consider adjusting to the control only theright hand side of the photo shown in Figure 4.

A print is projected (using a regular photoprojector) on to a tracing of the board con­trol, reducing it so that the points of the tri­angle BEG on the print will very closely fitthe points of the triangle BE'G' traced fromthe board con trol. The tracing is then re­moved and replaced by sensi tized photo pa­per, exposing it 'and making the projectionprint.

In like man~er a print is projected to fit theleft hand side, as shown in Figure 5. In thisprint the triangle DBF is enlarged to fit thecontrol points approximately in triangleD'BF'.

This print is then laid with its center at Bwith the correct distance D' F'.

It has been found in practice that the smallerrors of adjustment can be taken up by thestretch in the paper and by tearing away por­tions of the prints to make the best ma tchlines.

It is also known that the method worksequally well whether the line of flight is paral­lel wi th the slope or across the slope. In ei thercase the wing points used for projection arethe two down-slope ones and the two up­slope ones for each half of the photo.

The principal feature of the method is thatonly one-half of each photo is approximatelycorrected at a time.

Many mosaics have been laid in whichmuch of the distortion was corrected by sim­ple ratioing of the prints, without consciouslythinking of any particular method. It can beunderstood, as was explained in the beginning,