WIDE-ANGLE CONVERGENT PHOTOGRAPHY

TABLE 1

LIST OF DATA FOR 30- AND 44.5- CONVERGENT PHOTOGRAPHY BASED UPON A PHOTO-SCALEIN THE MODEL CENTER OF 1 :50,000

789

-

30- Convergent Photography 44.5" Convergent Photography-

Picture size 9"X9" (23X23 cm.) 9"X9" (23X23 cm.)

Foeal-length 6" (15 cm.) 6" (15 cm.)

Flying Height h 23,200 ft. (7,100 m.) 21 ,800 ft. (6, 650 m.)

Base b 4.16 miles (6.7 km.) 5.1 miles (8.2 km.)

Base-ratio b: h 0.94 1.24

Width of Flight Strip 5.15 miles (8.7 km.) 4.65 miles (7 .5 km.)

Useful Model Area 21.2 miles' (55 km.') 23.6 miles' (61 km 2 )

A ngle of View v in Model Corner 47' 40.3"

Dead Spaces in lIfodel Corner 1.09 ·t.h 1.35 ·6.h

lIfaximum Angle l' of Homologous Rays 56g 70<

Variation of l' over Entire Model 13" 18"

Universal PhotogrammetricElectronic Rectifier *

CAPTAIN LEROY E. HOSS, JR.,

Rome .A ir Development Center,Griffiss A ir Force Base, N. Y.

andDR. SAMUEL W. LEVINE,

Fairchild Graphic Equipment Company,Syosset, Long Island, N. Y.

ABSTRACT: A n electronic line scanning machine is described which willline scan an oblique aerial photograph and produce a rectified print auto­matically. The machine incorporates optical-mechanical scanning andreproduces by means of an ultrasonic light modulator. The rectifier willhandle camera formats up to 9" X 18", focal lengths from ]" to 100" and tiltangles up to 80 degrees. Scanning is done at 500 lines per minute.

The basic theory of line scanning for aerial image rectification is dis­cussed and the development of the equations for the computer required forthe machine is given.

F OR many years various progressive in­dividuals involved in the rectification of

oblique aerial photographs have consideredan electronic line scanning technique forthe rectification of such photographs. In this

technique each elemental area in the obliquephotograph would be scanned point bypoint as a series of lines and each line wouldbe reproduced with dimensions distortedaccording to the mathematical relationship

* Acting for the authors, this paper was read at the Society's 24th Annual Meeting by Mr. JohnFreda of the Rome Air Development Center.

790 PHOTOGRAMMETRIC ENGINEERING

F'IG.2

RfCTlFIER SCANNER

....

between oblique and rectified photographs.In the past it has been thought that "thestate of the art" had not progressed to thepoint where it was feasible to design such amachine. 'vVith recent advances in electroniccomputers, light modulators, and line scan­ning techniques, as exemplified by televisionand facsimile machines, it is felt that thisbarrier no longer pertains.

On first consideration of the problem onemmediately wonders why a line scanning

rectifier would be advantageous. Presentoptical rectifiers perform a satisfactorytransformation of the oblique copy to recti­fied print. In order to handle the completerange of aerial photographs from variouscameras and the tilt angles and scales in­volved, a large number of rectifiers is re­quired for any complete installation. I n ad­dition, unusually long focal-length camerasrequire a special rectifier for high tilt anglesand it is necessary in some instances to gothrough intermediate stages of rectificationn order to completely process a photograph.

I t should be possible to design an elec­tronic printing rectifier which will acceptphotographs from cameras of all focallengths and all til t angles. I t is on thisJustification that the decision has been madeto proceed with the design of an electronicpri nti ng recti fier.

There are several basic approaches to linescanning. The all electronic technique usinga cathode ray tube is practiced in televisionscanning. There is the mechanical scanningtechnique as used In facsimile and wIre­photo transmission. In addition, line-by­line reproduction in a conventional opticalrectifier can be utilized as a means of recti­fication. All of these techniques were con­SIdered and a mechanical scanning methodwas selected on the basis that it was the onlypractical approach having the possibility ofproducing the required accuracy and resolu­tion of reproduction. It is not feasible withpresently available components to obtain

ElrCTRONK PRlNTING RECTIFIERr~l.l'.E ~

~_~~_ ~S-lrl"UE'I APERTURE--&

IIi

~I T••NSP.....T COpy ......

. .~ PRINCiPal UHf

'~:.:-- ~.......... FLOlRUCfNT UGHT

COPY (NEGATIVE)

the required accuracy and resolution in anall electronic scanning machine.

As is well known In an oblique aerialphotograph, there IS no change of scalealong a line perpendicular to the principalline. If advantage is taken of this charac­teristic, a machine designed to scan along adirection perpendicular to the principal linewill have linear motion. This is a definitesimplification. The Electronic Printing Rec­tifier design requires that the principal lineof the photograph be placed on the copyholder so that the scanning mechanism oper­ates in a direction perpendicular to theprincipal line.

A sketch of the machine IS shown In

Figure 1. Copy is placed on the transparent,cylindrical copy carriage at the left of themachine with the principal line parallel tothe axis of the copy carriage. The trans­parency is illuminated by a curved bluefluorescent tube underneath the copy car­riage. Scanning is accomplished by an os­cillating mirror placed above and on theaxis of the copy holder. As the oscillatingmirror scans a line, the copy carriage ad­vances and thus the entire photograph isscanned line-by-line. The information fromthe scanning mirror is passed to a photo­multiplier light detector and the lightenergy converted to an electronic signal.This electronic signal IS modified as re­quired and actuates an ultrasonic lightmodulator mounted on a carriage whichmoves parallel to the axis of the recordingcylinder.

The schematic of this system is shown inmore detail in Figures 2 and 3. In Figure 2,

UNIVERSAL PHOTOGRAMMETRIC ELECTRONIC RECTIFIER 791

APERTUFlE-+.

FIG. :5

SCAN AND RECORD ELECTRONICS

the copy is shown on the cylindrical copycarr:age with the principal line parallel tothe axis of the copy table. The lens focusesthe copy image on an aperture plate infront of a photomultiplier tube. As theoscillating mirror moves across the copyperpendicular to the principal line, theimage being viewed is passed across theaperture plate. and the information equiv­alent to a small spot on the copy passesthrough the aperture to the photomultipliertube. The greater the amount of light pass­ing through the copy at any given point,the greater will be the electrical signal fromthe photomultiplier.

There is a certain "dead" time on the re­cording cylinder where the photosensitiverecording paper is attached to the cylinder.During this part of the cycle the scanningmirror "flies back." It can thus be seen thatthe copy is scanned line-by-line and re­corded on a rotating cylinder line-by-line asthe copy carriage moves into the machine.

The electronic scanning and recordingsystem is given schematically in Figure 3.The signal from the photomultiplier isam pli fied and is then "gamma" correctedusing non-linear circuits. This "gamma"correction compresses the relatively largedensity range of the negative to the densityrange required for recording on paper. Thevideo signal thus obtained passes into theultrasonic light modulator system.

The ultrasonic light modulator has theability to produce a light signal whose in­tensity varies directly as the electrical signalinput. The video signal and an R.F. Signalgenerated in an oscillator mix in a modula­tor and the resultant signal is amplified to

operate an ultrasonic cell. The modulatedlight from this ultrasonic cell exposes photo­sensitive paper on the recording cylinder.

From this description of the machine itcan be seen that a piece of photographiccopy which is placed on the cylindrical copytable will be reproduced on the recordingcylinder in a line scan fashion.

This rectification transformation requiresdistortion of the two dimensions of thephotograph. This means that the line scan­ning mechanism must be controlled by onecomputer and the motion of the recordingcarriage by a second computer. This is ac­complished in the machine as indicatedschematically in Figure 4. It has beenpointed out previously that the oscillatingscanning mirror goes through a cycle foreach revolution of the recording cylinder. Ifthe angle of scan is increased, the speed ofscanning the copy is higher and the recordedline is thereby reduced in size. By varyingthe angle through which the scanning mirroroscillates and keeping the total cycle timeconstant, a distortion in the direction ofscan is obtained. This is accomplished in theElectronic Printing Rectifier by solving thetransformation functions relating theoblique aerial photograph to the rectifiedphotograph using computers. The informa­tion so computed actuates a servo drive toadjust the mirror scanning mechanism. In­formation that must be fed into these com­puters is resultant tilt angle, focal-length ofthe taking camera, and the scale factor.

Rectification in a direction along theprincipal line is obtained by varying the rateat which the recording carriage advancesrelative to the copy carriage. The copy

FIG. "SCHENATtC OF E lOR

792 PHOTOGRAMMETRIC ENGINEERING

table advances at a constant rate. The re­cording carriage advances at a varying ratefor each line and this is determined by solu­tion of the transformation equations.

I n the design of the Electronic Pri nti ngRectifier it was necessary to make a choicebetween constant advance of the copy car­riage and changing advance of the recordingcarriage, or varying advance of the copycarriage and constant advance of the record­ing carriage. The decision to advance thecopy table at a constant rate was based ontwo factors. I n an oblique aerial photographthe foreground has the highest ground res­olution and the background the lowestground resolution; this, of course, is due tothe geometry of oblique photography. How­ever, the resolution in lines per millimeterremains the same. Advancing the copy tableat a uniform advance rate maintains thisrelationship in regard to resolution, withthe foreground having the greater number oflines per inch recorded in the rectified imageand the background having a lesser numberof lines per inch recorded. This variation inresolution in no way degrades the rectifiedimage, but only maintains the same rela,lationship in detail definition as exists inthe original photograph.

From an electronic and photographicstandpoint, design problems are minimizedby lIsing the constant table advance scheme.

With this system the dimensions of theaperture of the photomultiplier tube re­main constant. The recording aperture mustvary in dimension according to the changein line advance. In the direction of record­ing, the aperture size remains constant foruniform exposure. In a direction perpendicu­lar to recording, the aperture changes insize according to the change in line advance.If this scheme were not used, the apertureof the photomultiplier would have to bevaried in size and in addition, the sensitivityof the photomultiplier tube would have to bechanged to conform to the change in size ofthe aperture.

The design specifications for the Elec-tronic Printing Rectifiel' are as follows:

1. Camera focal lengths-3" to 100".2. Tilt angles-0° to 80°.3. Tip angles-0° to 15°.4. Resolution-SOO lines per inch.5. Copy size--up to 9" X 18".6. Maximum reproduction size-36" X 48".7. Change of scale range--enlarge or re­

duce 3 to 1.8. Recording material-standard photo­

graphic paper.The theory of rectification by line scan­

ning was developed by use of Figure 5. Thehorizontal plane represents the ground. Thephotograph plane is projected back to theground plane so that the principal point in

o NODAL POINT OF LENS

PRINCIPAL LINEI PHOTO PLANE)

f-_..L-7--- +V

HORIZONTAL PLANE

FIG. 5OBLIQUE PHOTOGRAPHY GEOMETRY

UNIVERSAL PHOTOGRAMMETRIC ELECTRONIC RECTIFIER 793

a1"'=--­

G.b - v

In this equation

b = cos t.

An interesting graph showing the changeof resolution in an oblique aerial photo­graph is given in Figure 6. The plot ofchange of resol ution along the pri nci pal axisis described by the function N = 500/1-'2 andthe change of resolution perpendicular tothe principal axis is given by the functionN = 500/1-'. This plot is very revealing inthat it shows the deterioration of resolutionin an oblique aerial photograph due to thegeometry of oblique photography.

Visualizing an airplane taking obliquephotographs from the side, above the isolinethe resolution will be better in a directionparallel to the line of flight, and below theisoline the resolution will be better in a di­rection perpendicular to the line of flight.This plot also indicates the fast deteriorationof the photograph. If the nu merical valuesassigned are deleted, these plots are indica­tive of the characteristics of oblique aerialphotographs regardless of the means of rec­tification.

and

/a=--

sin t

cipal axis. v is the corresponding distance inthe photographic plane. f is the focal-lengthof the camera and t is the resultant tilt angle.By proper manipulation of these equationsit can be shown that the magnification in thedirection perpendicular to the principal lineis given by u and the magnification in thedirection along the principal line is given bythe function 1-'2 where I-' is the magnificationfactor and is given by the relationship:

0

~FIG 6

RESOLUTION OF RECTIFIED PHOTOGRAPMAT SCAN RESOLUTION - ~OO LINES

0PER INCH.

~N· NUMBER OF LINES PER INCH.

y. MAGNIFICATION FUNCTION.

~ lSOLlNE FOR K· I

\ '"~ PERPENOI UlARTO PRIN IPAL AXIS

~ ~

\ ~I--

~ ..- ALONG RINClPAL IS.

~

r~

N ~

'"

100

200

'00

20

the photograph coincides with its posItionon the ground. This configuration of thegeometry simplifies the derivation of themathematical relationships. From this figurethe transformation equations become:

11/ cos tU= --=---

/ cos t - v sin t

V = __p. _/ cos t - v sin t

Where U is a dimension in the map planeperpendicular to the principal axis, u is thecorresponding distance in the photo planeperpendicular to the pri nci pal axis. V is adistance in the map plane along the prin-

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