Large-Field Photographic Astrometry*

S. VASILEVSKIS,

Lick Observatory, Univ. of California,Mount Hamilton, Cali].

ABSTRACT: A brief review is given on (a) development of large-field astrographsfrom the Normal Ast'rograph up to the 20-inch Carnegie Astrograph of LickObservatory, (b) engines for measurement of plates, including an outline of anautomatic engine being planned for Lick Observatory, and (c) reduction ofmeasurements.

INTRODUCTION

E XPERIMENTS for using photography inastronomy started al most immediately

after the inven tion by Daguerre had beenreported to the Paris Academy of Sciences bythe French astronomer Fran<;:ois Arago, onJanuary 7, 1839. A more successful start,however, was possible only after the dryprocess had been developed.

From the very beginning the experimentswere carried out in two directions: spec­troscopy and direct photography. The im­portance of photography in astronomy rap­idly increased, and at present most astro­nomical observations are made using photog­raphy. In astrometry, i.e. determination ofpositions and proper motions of celestial ob­jects, visual observations wi th cross-hairsare still carried out for determination of ab­solute equatorial coordinates; all the dif­ferential work, however, is done almost ex­clusively by photography.

Al though reflectors occupy the most prom­inent position in astronomy as a whole, theyfind almost no use in astrometry. A parabolicmirror has a very small field of good defini­tion; although a Schmidt type reflector givesexcellen t defini tion over large fields, there is adistortion of the field which cannot be as­sumed to be stable. Recent experiments ini­tiated by the Hamburg-Bergedorf Observa­toryl have, however, indicated that Schmidttelescopes can be used in astrometry. Thisreview will be limited to refractors only.

Photographic astrometry can be subdividedin two areas: (a) long-focus or small-field,and (b) large-field astrometry. Long-focusastrometry employs photographic or visualrefractors wi th long focus, of the order of 30feet and more2 ; correspondingly the angularfield is small, of the order of one degree or

less. Long-focus instruments are used for de­termination of parallaxes, of relative propermotions, for observations of dou ble stars, andin other problems where the highest angularprecision is required without a necessity of alarge angular field.

Large-field astrometry employs photo­graphically corrected refractors, with focal­length of the order of 10 feet. The angularfield is at least two degrees square. Thesetelescopes are called astrographs. Large-fieldastrometry deals mostly wi th posi tions andabsolute proper motions of stars. For thispurpose a number of reference points isnecessary on each plate, and the field has tobe large enough to contain a sufficient numberof these references. The present review islimited to large-field photographic astromet­ry, which is more related to photogrammetrythan other branches of astrometry.

ASTROGRAPH

Towards the end of the 19th century thetwo French astronomers, the brothers Henry,were so successful in astronomical photog­raphy that an international conference toconsider the field was organized. I t took placein Paris in April, 1887, and resulted in a planfor photographic mapping of the whole skyand for determination of stellar posi tions andmagnitudes from the photographs. J The pro­cedure of the undertaking was worked outand a uniform type of instrument wasadopted. The instrument is equipped with atwo-component lens of 33 cm. aperture and343 cm. focal length. It is called the NormalAstrograph; it covers a field two degreessquare with a scale of 60" per mm. The wholesky was divided into 18 zones and assigned tothe same number of observatories. 4 Latersome observatories withdrew and the corre-

* Presented as part of the Society's symposium "Photogrammetry in Science" in conjunction withthe 125th meeting of the American Association for the Advancement of Science, Sheraton-Park Hotel,Washington, D. c., December 29, 1958.

461

462 PHOTOGRAMMETRIC ENGINEERING

sponding zones were reassigned to other ob­servatories.s In spite of an early start and ofactive international cooperation, the pro­gram, known as Astrographic Catalogue, isstill not completed. 6 One of the main reasonsfor this delay is the relatively small field.

In 1914 F. Schlesinger and C. J. Hudsonproposed to use a larger field instrument forposition determination, in order to decreasethe number of plates necessary to cover anarea and to increase the number of referencestars available on each plate.7 Positions ofreference stars are observed individually byvisual meridian circles requiring much effortand time; therefore the number of referencestars available is not very large.

Schlesinger and his collaborators repeatedphotographically a few so-called AG zones,8observed earlier visually by internationalcooperation under leadership of Astro­nomische Gesellschaft. Photographs weretaken by a four-component lens with effectiveaperture of 7.55 em. and focal length of 163. 5em. (scale: 126" per mm.), covering a fieldof 5° square. The experiment was so suc­cessful, that it was decided to continue thework on a larger scale; the result was the re­observation of many AG zones by Schlesingerand Ida Barney, published in several volumesof Transactions of Yale University Observatory.

In 1933 Schlesinger and Barney increasedthe field considerably by using a four-com­ponent lens designed by F. E. Ross.9 With anaperture of 14.3 em. and focal-length of 202.5em. a field of 10° X 14° was photographed on48 em. X58 em. plates. 1O This is the largestfield ever used for precise astrometric pur­poses, and the same astronomers found itadvisable to reduce the field. Their next lens,also by Ross, was made with 5-inch apertureand 206.7 em. focal-length (scale 99 ~ 77 permm.), covering a field 10° square on plates 17inches square.u

Schlesinger's success stimulated the Astro­nomische Gesellschaft to repeat photo­graphically all the AG zones from the Northpole to declination _2°, and at the 1921meeting of this society it was decided to workout a program. 12 The final program wasadopted in 192713 ; six German observatoriesand Pulkovo observatory determined posi­tions of reference starsl4, and only three ob­servatories carried out the photographicwork.1s The Zeiss Astrovierlinser was adoptedas objective for the astrograph; its four-com­ponent lens of 14 em. aperture and 206 em.focal length defines well a 5° square field atthe scale of 100" per mm. This type of in­strument is known as AG Astrograph.

Shortly before the war W. H. Wright, then

Director of Lick Observatory, initiated aprogram for determination of stellar propermotions with reference to faint externalgalaxies.l6 None of the existing astrographswas suited for this purpose because of smallapertures and large focal-ratios. A 20-inchfour-component lens was designed by F. E.Ross especially for the Lick Proper MotionProgram, and the construction of the astro­graph was supported by Carnegie Corpora­tion. The lens has a focal length of 146 inches(scale 55:' 1 per mm.) and it defines well a 6°square field on plates 17 inches square; theastrograph is depicted in Figure 1.

For determination of stellar proper motionstwo sets of photographs, taken at sufficientlydistant times (epochs) have to be compared.The first-epoch set was taken in the years1947 to 1954,17 The second set will be startedin about 1967.18

MEASUREMENT OF PLATES

Only glass plates are used in precise photo­graphic astrometry, and rectangular coor­dinates of objects are measured. When theAstrographic Catalogue was initiated, therewas no previous experience on precision ob­tainable from photographs. Since a shift ofemulsion during development was consideredto be one of the most dangerous sources oferrors, a precise rectangular grid, called areseau, was printed on each photograph. Thelines on the reseau were 5 mm. apart, andpositions of star images were referred to theselines by means of an eyepiece-micrometer orby a precise glass scale placed in the focal­plane of the microscope eyepiece.

Later investigations showed that there is noneed to use a reseau and instead of a printedreseau, a long scale built into engine was usedfor position reference. l9 F. Schlesinger intro­duced measuring engines with a long screw,20and since then this type is mostly used forprecise measurement of plates. Long-scale aswell as long-screw engines measure one co­ordinate at a time. After one coordinate of allstars on a plate is measured, the plate isrotated by 90° and the second coordinate ismeasured. In order to eliminate some sys­tematic errors, mainly personal ones, eachcoordinate is measured in direct and reversepositions of the plate, or an eyepiece reversingprism is used for reversing the field,

Before the war Carl Zeiss developed ameasuring engine with two glass scales per­pendicular to each other and placed so thatdirections of both scales intersect on the axisof the microscope. 21 This arrangement ofscales, according to Abbe's principle,22 elimi-

LARGE-FIELD PHOTOGRAPHIC ASTROMETRY

FIG. 1. 20-inch Carnegie Astrograph of Lick Observatory. (Lick Observatory photograph.)

463

nates errors of ways, and both coordinatesare measured simultaneously.

In order to increase the accuracy, usuallytwo settings on an image are made in eachposi tion of the plate. The errors of measure­men t are of the order of two microns, depend­ing on the quality of images. Good images areof the order of 50 microns in diameter; if theyare much larger, the precision decreases. Ifthe magni tude range of stars to be measuredis large, a coarse grating is placed in fron t ofthe objective. The grating produces shortspectra symmetrically arranged on each sideof the image, and these spectra are measuredinstead of the cen tral image.

A new approach to measurement of plateshas been pioneered by Watson Scientific Com­puting Laboratory of IBM; a conventionallong-screw engine has been converted into anautomatic machine. 23 Approximate coordi­nates of images are punched on IBM cards,and they serve as input data for automaticguiding to the image selected. The visualmicroscope is replaced by a spinning-sectorphotoelectric scanner. When the imagereaches the field of the scanner, the lattercenters automatically on the image; then theprecise coordinate is read and recorded auto­matically on the same IBM card. The ac­curacy of measurement is considerably higherthan with a visual machine. 24

The successful experiment by IBM stimu­lated the planning of an automatic engine forthe Lick Proper Motion Program, and the

machine is in process of development in ac­cordance with the following outline.

The measurement will consist of two sep­arate operations: (a) survey of plates, selec­tion of objects to be measured, and recordingof approximate coordinates of the objects se­lected for automatic setting in the process offinal measurement; (b) automatic measure­ment of positions and photographic magni­tudes. Each of these operations will require aseparate machine: (a) a surveying machine,and (b) a measuring engine.

The function of the surveying machine isto select objects for measurement and to ob­tain their approximate coordinates for auto­matic positioning in the measuring engine.The number of images measured on eachplate will be of the order of 200 to 300. Thisnumber is a very small fraction of all theimages on plate. Two plates of the same field,taken at different epochs are put into thesurveying machine, and both fields are super­imposed optically for simultaneous or alter­nating view of corresponding fields on bothplates. After an object is selected, a cross­wire is centered on the image, and its approxi­mate coordinates are read and recorded, withan accuracy of 0.1 mm. or better. Instead of avisual reading of scales and recording byhand, a reader and recorder is operated by asingle push-button, after the selection is made.

After a plate-pair has been surveyed, oneplate of the pair is put into the measuringengine, and properly centered and oriented

464 PHOTOGRAMMETRIe ENGINEERING

(1)

These equations, known as the six-con­stants formulae, include not only centering,scale and orientation errors, but also thelinear terms of spherical corrections. Before(2) can be used, the plate constants a, b, c, d,e, and f have to be determined, and this isdone as follows:

On each plate there must be a number ofreference stars with known equatorial co­ordinates. Standard coordinates of these starsare computed by formulae inverse to (1), andthen they are compared with the measuredcoordinates of the same stars, rewriting (2)in a form

(2)

(2')

X = a + bx + cy

Y = d + ex + fy

a + bx + cy = X - x

d + ex + fy = Y - Y

Each reference star provides the above twoequations with six unknowns, and a minimumof three stars permits one to compute theseunknowns. Usually more than the necessarythree reference stars are used, and the plateconstants are found from the least squaressolution.

After the plate constants a, b, etc, are com­puted, their values are inserted into (2)for each star measured, and the standardcoordinates are calculated. Then the equa­torial coordinates are found from (1).

For larger fields other corrections have

inverse problem, i.e. for computation of stand­ard coordinates from equatorial ones. Therelationship can be expressed in many dif­ferent forms depending on computationalmeans, but the problem is always a straight­forward geometrical one of the gnomonicprojection. The relationship between themeasured and standard coordinates is muchmore complicated and less definite.

Many errors and corrections have to betaken into account for reduction of measuredcoordinates to standard ones. The principalfactors to be considered are:

Instrumental errors: centering, orienta­tion, scale, tilt of the plate, optical distor­tion, curvature of the plate, distortion ofthe photographic emulsion, magnitudeequation, and color magnification.

Spherical corrections: atmospheric re­fraction, aberration of light, precession andand nutation.The number and the size of corrections in­

creases with the field, and for a small field2 degrees square most of the corrections men­tioned can be neglected, and usually the fol­lowing relationship, derived first by Turner,28is adequate

The most general problem in photographicastrometry is to calculate the equatorial co­ordinates, i5 of celestial objects from the meas­ured rectangular coordinates x, y of theirphotographic images. This reduction is donein two steps, using as a bridge so-called stand­ard coordinates26 X, Y. Standard coor­dinates are purely geometrical rectangularcoordinates with the origin at the tangentialpoint of gnomonic projection, and with Xand Y axes correctly oriented in E and Ndirections respectively. If A and D are rightascension and declination of the origin ofstandard coordinates, the relationship be­tween the standard and the equatorial co­ordinates of an object is27

X sec Dtan (O! - A) = -----

1 - YtanD

Y+tanDtan Ii = -----cos (O! - A)

1 - YtanD

Similar formulae can be written for the

From then on the measurement proceedsautomatically with the aid of the recordsproduced in the surveying process. The inputof the approximate coordinates of an imageoperates servo systems and guides a photo­electric scanner to the image. Then thescanner centers itself upon the image, andprecise rectangular coordinates, as well asthe opacity of the image, are read and re­corded automatically. After the measure­ment of one image is recorded, the machineproceeds automatically to the next image andrepeats the operation described until all theimages selected in the survey of the plate aremeasured. Then the second plate of the pairis measured with the same input data.

Normally, this process should continueautomatically until the measurement of theplate is completed, and no continuous atten­tion by an operator should be necessary. Incase of any failure in the automatic operationa signal is given to the operator at the sur­veying machine in an adjacent room.

Two calibrated scales will be used as themeasuring standards in the engine, and avariable-iris type photometer25 will be in­corporated for measurements of opacity. Theaverage interval between two successivemeasurements, including the guiding, willnot exceed 30 seconds, i.e. the speed will be atleast 10 times of that with a conventionallong-screw measuring engine. It is expectedthat the automatic measuring engine will bemanufactured and installed at Lick Observa­tory within three years.

REDUCTION OF MEASUREMENTS

LARGE-FIELD PHOTOGRAPHIC ASTROMETRY 465

where p and q are rectangular coordinatesof the tangential point. Even the most carefuladj ustmen t of the astrograph does not guar­antee that the tangential point will coincidewith and remain for a longer interval at thecenter of plates. A number of methods hasbeen proposed and used for determination ofp and q, each of them involving the weakassumption that the tilt repeats itself fromone plate to another. One of the simplest andmost accurate methods requires a dummy­plate with a small centering telescope. 32

Optical distortion usually can be expressedas

where the constant V is positive or negativedepending on whether the distortion is of a"pin-cushion" or "barrel" type. A method foran independent determination has been de­veloped by Konig and Heckmann33 andmodified by the author. 34 Schlesinger has de­rived formulae for determination of distor­tion from residuals of least squares solution(2') and has shown that most of the distortionis absorbed by the scale coefficient. 35 Schle­singer's conclusions, however, are too op­timistic because of two errors in his deriva­tion: (a) in development of formulae for onecoordinate, the mean of the other coordinatewas taken for all stars; actually distortion isvery sensitive to other coordinate; and (b)integration of a continuous function was used

(5)

to demonstrate the absorption of distortionin the process of least squares solution; ac­tually the least square solution requires asummation of coordinates of discrete points.If these errors are taken into account, the con­clusion is significantly different.

Curvature of plates is usually small ifproper care is exercised in selection of glass. 3u

Schlesinger has shown37 that the effect ofspherical curvature has the form of (4), anda cylindrical one can be expressed as

~X = C, xy2+ C2X2y + C3x3

~y = C,'y3 + C2'xy2 + C3'X2y

The type and the amount of the curvaturecan be measured by laboratory means, butthere still is a degree of uncertainty whetherthe curvature during the exposure is the sameas after the plate has been processed anddried.

Distortion of the photographic emulsion isone of the least known sources of errors, inspite of many investigations, and there is nogeneral rule or formula for corrections. Somerecent investigations indicate on one handthat there are some large-scale distortionsdepending on the particular area of theplate38 ; on the other hand, there is indicationof random shifts as reported by ToulouseObservatory.39 Toulouse statistical resultsshow that 64% of star images are shifted lessthan two microns, 18% of displacements arebetween two and three microns, and 2% ofshifts are larger than eight microns. Large­scale distortion can be partly absorbed byplate constants, particularly if higher orderterms are used in addition to the linear ones,but the effect of the random shifts can beminimized only by repeated coverage of thesame field.

Magnitude error is a function of stellarmagnitude (brightness), i.e. of the size ofphotographic image. If a plate is measuredonly in one position without reversing thefield, the personal error of the measurer entersinto measurements as a magnitude effect. Byreversing the field this error is eliminated, butthere are still other sources of magnitudeeffect.

The most common is the guiding errorduring long exposures, which produces slightdeformation of images, depending on theirsize and distribution of density within theimage. Another source is a coma of the opticalsystem, and instruments with an appreciablecoma have never been considered adequatefor photographic astrometry. Recently, how­ever, Eichhorn has shown that the coma ef­fect may be present even with instruments

(3)

(4)~x = V(x2+ y2)X

~y = V(x2 + y2)y

also to be applied. The first of the mostthorough developments, of formulae for largerfields was carried out by Zurhellen29 ; manydiscussions of measuremen ts on large fieldswere made by Schlesinger and Barney,30 andone of the more recent comprehensive reviewsof reduction on large fields is given by A.Konig.3l

Each new correction introduces additionalplate constants and requires additional ref­erence stars, if the least squares method isused for computation of constants. Thescarcity of reference stars and a rapid increasein labor of computation, if old computingmeans are used for least squares solution, hasled to a conventional procedure of independ­ent determination of additional constants.After they are found and applied to themeasured coordinates, formulae (2') can beused.

Til t of a plate is expressed as

L1x = (px + qy)x

L1y = (px + qy)y

466 PHOTOGRAMMETRIC ENGINEERING

(6)

(7)

considered as free of coma. 40 It is impossibleto give a general formula valid in everycase; one of the simplest ways to express thecombined effect of guiding and coma is

l'ix = (m - mo)(g + hx)

l'iy = (m - mo)(g' + h'x)

where m is the stellar magnitude, mO is anadopted constant, usually close to the meanmagnitude of all stars on the plate, and g, g',h, h' are the plate constants to be determinedfor each plate. A coarse objective grating,mentioned in the previous section, eliminatesthe magni tude error to large exten t.

Color magnification is caused by differentscale values of the objective for differentcolors and it produces a shift of red starsrelatively to blue ones. If k is a value relatedto the color of a star, e.g. the ratio of lightintensities in two selected regions of the spec­trum, then the simplest case of the color ef­fect is

l'ix = s(k - ko)x

l'iy = s(k - ko)y

where s is a plate constant, which usuallydepends on the type of a lens and on color sen­sitivity of the plate emulsion. The maximumcolor effect of the 20-inch Carnegie Astro­graph with Eastman Emulsion 103aO is ofthe order of O~2 at the edges of 17-inchsquare plate. 41

Atmospheric refraction enters into themeasured coordinates only as a difference be­tween the refraction for a star and for theplate center. In spite of this differentialcharacter, the formulae for refraction arerather complicated, and they have been asubject of controversy for several decades,until the differences in various proposals wereexplained and reconciled by C. Vick. 42 Thedifferential effect of refraction is expressed inpower series of coordinates, usually ter­minating with the third power. The latter issignificant only on large fields at low altitudes.

Since refraction is a function of color, thecolor effect of the atmospheric dispersion maybecome significant at lower altitudes. Thiscolor effect is not symmetrical towards theplate center, but it is oriented with respect todirection of zenith.

The differential effect of aberration issmaller than that of refraction, and even theterms of the second order are significant onlyin extreme cases. Precession and nutation donot cause relative displacement of stars toeach other, and their effect is absorbed by thelinear plate constan ts of (2').

The procedure of reduction described above

is used when precise positions of many starson a plate have to be determined. Whencoordinates of a single object, e.g. a cometor an asteroid, have to be measured, simplerreduction methods can be used. Simplifiedreductions can also be made if differences ofcoordinates on two plates have to be deter­mined, as for proper motion programs. Thenthe effects, which are equal on both plates,are eliminated.

Finally, the traditional reduction methods,as reviewed above, can be modified if (a) alarge number of position references is avail­able, and (b) high-speed computers are usedfor computation. Then instead of (2') a seriesof powers up to the third power can be writtenand all the plate constants, including those ofhigher powers, can be found from the leastsquares solution. One may object that in thisway effects cannot be separated because someof them have the same mathematical form,and the solution will lump them together;formal attempts at separation of constants donot lead to reliable results because of inter­correlation in the least squares solution. Thisobjection is not valid, if the aim is to deter­mine the positions of stars, but not the in­stantaneous instrumental errors, which are ofno interest as long as they are small. The lat­ter condition is always achieved by customaryinstrumental adjustments. The least squaressolution with many constants means a math­ematical stretching of the plate so as to havethe best fit with the fixed reference points.

CONCLUSION

In order to show the advantages of thephotographic method, let us compare it withthe visual one for determination of stellarpositions. The comparison is not meant tosuggest that visual observations should beabandoned; at present both methods do notoverlap, but supplement each other.

Since the equatorial coordinates are re­ferred to planes determined by the rotation ofearth and its revolution around the sun, thesecoordinates have to be determined by in­struments referred to the earth. Stars are ob­served individually during their meridiantransit, hence the corresponding instrumentis called a meridian or transit circle. Althoughphotographic and photoelectric methods havebeen tried in these observation, they do notoffer significant advantages because of the in­dividual star observations; one of the im­portant features of photography is to coversimultaneously a large field. Therefore prac­tically all the meridian work is done visually.

The telescope of a meridian circle is kept

LARGE-FIELD PHOTOGRAPHIC ASTROMETRY 467

in meridian by a perpendicular axis placedhorizontally in East-West direction. Inclina­tion and azimuth of the axis, errors of pivots,collimation and flexure of the telescope, fullamount of refraction, aberration, precession,nutation, and many other errors have to betaken into accoun t in order to determine pre­cise equatorial coordinates. In spite of the ex­treme care exercised and the great labor in­volved, probable errors of best modern singleobs~rvationsare of the order of 0~3. Actuallyerrors may be larger because of systematic ef­fects different for different observatories, asbecomes evident if observations of many ob­servatories are combined into so-called funda­mental catalogues. These individual observa­tions, however, are necessary to provide areference frame for much more efficient andaccurate photographic method.

Since each photographic plate has to con­tain a number of reference stars, the error ofthe reference frame is smaller than the in­dividual errors of reference stars. A frame of25 reference stars with individuals errors ofthe order of 0~2 will be accurate to approxi­mately 0~05. The final error of a photographicposition will be a combination of the errors ofthe reference, the measuremen t of the image,and of residual systematic errors described inthe previous section.

As was men tioned before, the error of asingle bisection is of the order of two microns;the customary four bisections will yield theposition with probable error of the order ofone micron, which corresponds to 0~1 for anAG astrograph with scale 100" per mm. Thiserror combined with that of the referencegives O~ 11. Actual probable error of a posi­tion from one plate of the Photographic AGCatalogue is of the order of 0~14. The slightdifference may be explained by sligh tty largererrors mentioned, and by some residual in­strumental errors. These errors are still con­siderably smaller than those of the meridiancircle. It should also be added that in theprocess of reduction the photographic posi­tions of reference stars are com pu ted and im­proved.

Astrographs with a longer focus yield moreprecise positions. Experiments with the 20­inch Carnegie Astrograph at Lick Observa­tory (scale 55" per mm.) show that positionof an image on a plate can be measured witha probable error of the order of 0~07. Long­focus astrometry yields still higher precision,2but this field is outside the scope of this re­vie\v. It should be mentioned, however, thatthe precision is not quite proportional to thescale on an instrument; many effects, like

refraction anomalies, atmospheric dispersion,seeing and others, do not depend on scale.

Finally it should be mentioned that sincethe measurements of photographic plates aredone in the laboratory, photographic methodsare more adaptable to automation and otherimprovements of efficiency and accuracy thanare measurements made directly at the tele­scope.

REFERENCES

1. M-itteil. d. Astron. Gesellsch. 1955,-PP. 38 and40.

2. P. van de Kamp, Popular Astronomy, 59: 65,1951.

3. Congres Astrophotographique Internat. de laCarte du Ciel, Paris, 1887.

4. Reunion de Com-ite Intern. Permanent de laCarte PhotogI'. du Ciel, p. 65, Paris, 1891.

5. Trans. Intern. Astr. Un-ion, 7: 251, Cambridge,1950.

6. Intern. Astr. Union, Moscow Meeting, DraftReports, p. 18.1, Cambridge, 1958.

7. Schlesinger, F., and Hudson, C. J., Publ. Alle­gheny Obs., 3: 59, 1914.

8. Trans. Yale Univ. Observ., 4: 1925.9. Ross, F. E., Journ. Opt. Soc. Amer., 5: 123,

1921.to. Schlesinger, F., and Barney, r., Trans. Yale

Univ. Observ., 9: (3 )ff, 1933.11. Schlesinger, F., and Barney, 1., Trans. Yale

Univ. Obs., 11: (5), 1939.12. VJS d. Astron. Gesellsch., 56: 158, 1921.

"'13. VJS d. Astron. Gesellsch., 62: 242,1927.14. Veroif. A stron. Recheninstitut, 55: 6, 1943.15. Zweiter Katalog d. Astl'. Gesellsch., 1: E3, 1951.16. Wright, W. H., Proc. Amer. Phil. Soc., 94: I,

1950.17. Trans. Intern. Astr. Union, 9: 117, Cambridge,

1957.18. Vasilevskis, S., Astr. Journ., 59: 40, 1954.19. Ambronn, L., H b. d. Astron. Instrumenten­

kunde, 2: 671, Berlin, 1899.20. Schlesinger, F., Publ. Allegheny Obs., 3: 83,

1914.21. Konig, A., Astr. Nachr., 246: 237, 1932.22. Zeitschr. f. Instrumentenkunde, to: 447, 1890.23. Lenz, J., and Bennet, R., Electronics, June

1954, p. 158.2.1. Eckert, 'vV. J., and Jones, R. B., Astr. Journ.,

59: 83, 1954.25. Eichner, L. c., eta!., Astr. Journ., 53: 25,1947.26. Turner, H. H., lllonthly Notices R. A. S., 54:

13, 1893.27. Smart, W. M., Text-Book on Spherical Astr.,

p. 284, Cambridge, 1949.28. Turner, H. H., Monthly Notices R. A. 5., 54: 15,

1893.29. Zurhellell, W., Darlegung u. Kritik d. zur Re­

duktion etc., Frankfurt a.M. 1904.30. Trans. Yale Univ. Observ., 5 and 9: 1926 and

1933.31. Konig, A., Hanb. d. Astrophysik, 1, 1: 502,

1935.33. Konig, A., and Hechmann, 0., VJS d. Astr.

Gesellsch., 63: 279, 1928.33. Lo~. cit., p. 291.34. Vasilevskis, S., Astl'. Jount., 56: t07, 1951.35. Schlesinger, F., et a!., Trans. Yale Univ.

Observ., 5: (13), 1926.

468 PHOTOGRAMMETRIC ENGINEERING

36. Zweiter Katalog d Astron. Gesellschaft, 1: E21,1951.

37. Schlesinger, F., and Barney, 1., Trans. YaleUniv. Obs., 9: (20), 1933.

38. Land, G., Astr. Journ., 55: 141, 1950.

39. Intern. Astr. Union, M~oscow !vIeeting, DraftReports, p. 185, Cambridge, 1958.

40. Eichhorn, H., Astr. Journ., 62: 204, 1957.41. Vasilevskis, S., Astr. Journ., 62: 119, 1957.42. Vick, c., Astron. Nachr., 253: 277, 1934.

About the Character of Errors zn

Spatial Aerotriangulation*

H. M. KARARA,

Asst. Prof. of Civil Engineering,Univ. of Illinois, Urbana, Ill.

"We must take into account the errors as they are, not as one would like them to be."-M. ZELLER

ABSTRACT: This paper deals with the character of errors in spatial aerotri­angulation, and investigates the possibility of separating the d~fferent categoriesof errors. A practical example is worked out in some detail; t't shows how thesystematic, quasi-systematic, accidental and pseudo-accidental errors are re­lated to each other. A proposal is made to classify the errors in aerotriangulationaccording to their effect on the results, without regard to their origin or nature.Thus t~e errors could be classified as errors with systematic e.ffect and errorswith accidental effect, and could be treated accordingly.

F OR about 15 years there has been increas­ing uneasiness and endless debating

among the photogrammetrists dealing withaerotriangulation, because of a big and stillunanswered question, brought up by Profes­sor Bachmann, Lausanne, Switzerland, aboutthe character of errors in spatial aerotriangu­lation. He was soon joined by ProfessorRoelofs, Netherlands, who gave a paper atthe 1948 Congress of the International Soci­ety of Photogrammetry, showing that theerror propagation in an aerotriangulation issuch that the influence of purely accidentalerrors might give the impression that a syste­matic error exists. Some of Roelofs' examplesshow also that the result of accidental errorshas a similar effect, as if breaks (jumps orcassures) are present.

Many photogrammetrists have seemed un­convinced by either the Bachmann's orRoelofs' articles and publications and haveretained the opinion that a considerable partof the discrepancies and irregulari ties thatthey found in their practical work were dueto local influences of the photographs-such

as lack of flatness of film, local distortions,instrumental errors, etc.-or to changingoperators during the triangulation on thestereoplotter.

There still exists a great variety of opinionson this subject. Many photogrammetristsconsider this problem of vital importance be­cause one cannot expect to obtain a fruitfuldevelopment of aerotriangulation if there islacking a deep and correct insight in thecharacter of errors with which one deals.

In aerotriangulation, as in any other meas­urement, one expects to have accidental aswell as systematic errors. The ideal solutionof the problem of the adjustment of aerotri­angulation would therefore be based on aseparate treatment of each of these categories.The whole difficulty is how to separate thesystematic from the accidental errors. Un­fortunately, the theory of errors in photo­grammetry does not give enough informationfor solving this problem.

Nowadays, the adjustment of aerotriangu­lation is made by adopting one of two princi­ples: (1) either one must neglect the acci-

* Paper presented at the Fall Technical Meeting of the Ohio Region of the American Society ofPhotogrammetry, held in Columbus, Ohio, October 10, 1958.