XIII Congress of theInternational Society for Photogrammetry

Helsinki, 1976Commission V

Working Group V/2Invited Paper

OTTO R. KOLBLSwiss Forest Research InstitutBirmensdorf (ZH), Switzerland

Metric or Non-Metric CamerasNon-metric cameras may be sufficiently accurate if narrowcone angles, and analytical methodsare employed.

(Abstracts on next page)

INTRODUCTION

VARIOUS PROBLEMS in engineering requirehigh precision measurements. In many

cases photogrammetric methods haveproved to be extremely useful. Special ad­vantages of this measuring technique are itshigh precision and great versatility; further­more, the object itself is not touched by themeasuring tool.

Special cameras (mono- and stereo­cameras) and measuring devices (Wild A-40,Zeiss Terragraph, and others) have beendeveloped to take and restitute the photo­graphs. These instruments are conceived forthe production of plans, profiles, or contourmaps and demand very few numerical com­putations. The restitution instruments can beconsidered as analog computers and are con­structed for specific camera arrangements.These limitations simplify considerably thehandling of the equipment and permit anefficient operation. In general only photo­graphs with parallel camera axes can be used(e.g., Zeiss Terragraph) and consequentlythe base-to-height ratio and the accuracy indepth is very limited.

The standard outputs of analog restitutioninstruments are in a graphical form. Besidesthe graphical representation of the measure­ments, digital methods are increasingly usedfor the description of an object. The data arevery flexible and suitable for further process­ing with electronic computers. Although au­tomatic coordinate registration devices canbe connected to analog plotters, it is advisa-

ble to use mono- or stereocomparators for themeasurements. Comparators offer a highermeasuring accuracy than the analog plotters,and furthermore there are practically no limi­tations for the camera arrangement. Devia­tions from the normal case of photogram­metry do not cause any time delay in therestitution phase, as the orientation of thestereo model is achieved analytically by thecomputer. Consequently, convergent photo­graphs can be used without restrictions, andsystematic errors of the picture coordinatescaused by lens distortion, film shrinkage, etc.can be taken into account.

Under these conditions photogrammetricmeasurements are no longer restricted topictures taken with metric cameras. This is ofgreat importance because for many applica­tions appropriate cameras are not available,such as in close-range photogrammetry fordistances of less than 2 meters. The opticalindustry has also developed several highlyspecialized cameras for various applicationswhich can be used for metric applications aswell. Then photogrammetric measuringtechniques are not bound to specific survey­ing instruments, which might give impetusto a wider application of these methods.! .

In this paper the accuracy limitationswhich are caused by the properties of non­metric cameras are discussed and the differ­ences in application ofmetric and non-metriccameras are pointed out. In the beginning adefinition is given for the term "metriccameras", and accuracy tolerances for the

PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSING,

Vol. 42, No.1, January 1976, pp. 103-113.103

104 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976

ABSTRACT: For a comparison of metric and non"metric cameras thereproducibility of the principal distance and the principal point areof primary interest. Such a comparison should take into account theprecision requirements for these parameters. Tolerances for theparameters ofthe elements ofinner orientation can be derived from afictitious camera calibration. The estimations show that the com­puted values depend only on the opening angle ofthe camera and theextension of the test field, whereas the size of the camera format isimmaterial. Because the tolerances are much larger for normal-anglecameras than for wide-angle or super-wide-angle cameras, it issuggested that,for precision measurements, cameras with long focallengths be applied. A comparison ofthe computed tolerances with thereproducibility of the principal distance and the principal pointindicate that non-metric cameras do fulfill the requirements withincertain limits, Problems may arise under certain conditions for theprincipal point. An accuracy discussion also should include theparameters of exterior orientation. For example, an unfavourablebase-to-height ratio or vibrations of the stereocamera might reducethe final measuring precision considerably. Under these conditionssmall errors of the inner orientation are of minor importance. Ingeneral, about the same measuring precision can be reached withmetric and non-metric cameras. The data processing for photographstaken with non-metric cameras is practically bound to analyticalmethods, and sophisticated computer programs are needed. Picturestaken by metric cameras can be restituted with analog plotters.Therefore it is more a question of the restitution method than amatter of precision whether metric or non-metric cameras should beused.

RESUME: C'est Ie degre de reproductibilite du point principal et de ladistance principale qui constitue Ie critere essentiel d'une com­paraison entre chambres metriques et non-metriques. Les exigences deprecision importent alors. On calcule donc des tolerances ap­propriees a l'aide d'une calibration fictive de la chambre. Lesresultats dependent du champ angulaire de la chambre, de lagrandeur du terrain d'essai, de la precision des mesures sur lescliches, mais non du format ou de l'echelle photographique. A egalitede champ angulaire, on a donc les memes tolerances pourun appareilde petit format que pour une cham ':'re aerienne metrique.' Il estconseillable d'employer, pour les Wn,es photogrammetriques, deschambres non-metriques de champ angulaire aussi faible que pos­sible. Les exigences de precision sont alors plus facilement remplies.La comparaison des tolerances calculees avec leur reproductibilitemontre que les chambres non-metriques repondent elles aussi assezbien aux exigences. La reproductibilite du point principal demeureimparfaite, mais elle n'est pas meilleure dans les chambres metriques.Il convieut, dans ces considerations sur la precision, de tenir compteaussi des elements de l'orientation externe. L'article montre sur labase d'exemples pratiques que la precision finale depend beaucoupplus d'une bonne disposition de la chambre, et de l'absence devibrations, que d'une orientation interne raffinee. On arriv.: engeneral iJ atteindre avec des chambres non-metriques la memeprecision qu'avec des chambres metriques. La restitution de clichesnon-metriques presuppose iJ vrai dire l'emploi exclusif de procedesanalytiques, alors que les cliches metriques se pretent iJ la stereoresti­tution. Le choix entre chambre metrique et non-metrique ne dependdone pas tant de la precision desiree que du materiel restituteurdisponible ou preferable.

METRIC OR NON-METRIC CAMERAS

ZUSAMMENFASSUNG: Beim Vergleich von Messkammern und Nicht­Messkammern interessieren primiir die Reproduzierbarkeit vonBildhauptpunkt und Kammerkonstante; dabei sollten die Genauig­keitsanforderungen an diese Parameter mitberucksichtigt werden.Mit Hilfe einer fiktiven Kammerkalibrierung werden daher Tole­ranzen fur die Kammerkonstante und den Bildhauptpunkt berechnet.Massgebend fur die berechneten Werte sind der Oeffnungswinkel derAufnahmekammer, die Ausdehnung des Testfeldes und die Koor­dinatenmessgenauigkeit im Bild. Dagegen kommen dem Bildformatder Kammer und den Abbildungsmassstab keine Bedeutung zu. Esgelten somit zahlenmiissig die gleichen Toleranzwerte fur eineKleinbildkammer als auch fur eine Luftbild-Messkammet, voraus­gesetzt dass der Oeffnungswinkel fur beide Kammern gleich gross ist.Wegen der erheblich geringeren Genauigkeitsanforderungen bei Kam­mern mit kleinem Oeffnungswinkel empfiehlt es sich moglichst lang­brennweitige Nicht-Messkammern fur metrische Aufgaben zu verwen­den. Ein Vergleich der berechneten Toleranzen mit der Reproduzierbar­keit dieser Werte zeigt, dass auch Nicht-Messkammern den Anforde­rungen grosstenteils genugen. Einige Diskrepanzen ergeben sich beiNicht-Messkammern als auch bei Messkammern bei der Re­produzierbarkeit des Bildhauptpunktes. Bei derartigen Genauig­keitsuberlegungen sollten die Elemente der iiusseren Orientierungnicht ausser acht bleiben. An Hand einiger praktischer Beispiele wirdaufgezeigt, dass die Messgenauigkeit am Objekt viel empfindlicherdurch eine ungunstige Kammeranordnung oder durch Vibrationender Stereokammer beeinflusst werden kann als durch eine ungenaueinnere Orientierung. 1m allgemeinen gelingt es mit Nicht-Messkam­mern die gleiche Genauigkeit zu erreichen wie mit Messkammern.Die Auswertung von Bildern, die mit Nicht-Messkammern aufgenom­men wurden, setzt allerdings die Verwendung analytischerMethoden voraus. Dagegen konnen Aufnahmen von Messkammernan Stereokartiergeriiten ausgewertet werden. Entscheidend fur dieVerwendung einer Messkammer oder einer Nicht-Messkammer istdaher nicht so sehr die angestrebte Messgenauigkeit als die Wahl desAuswerteverfahrens.

105

inner orientation are computed. These esti­mates are based on fictitious camera calibra­tions. The next part deals with the reproduci­bility of the elements of inner orientation forvarious cameras, and finally the influence ofthe elements of the exterior orientation ispointed out.

CHARACTERISTIC OF METRIC CAMERAS

For precision measurements some highlyspecialized cameras are on the market (Wild

,P 31, Zeiss-Oberkochen TMK, Zeiss-JenaUMK, Galileo-Santoni, etc.). Their construc­tion differs conSiderably from amateur cam­eras, but the differences become less distinctif e.g., the Hasselblad MK 70 is comparedwith the Hasselblad 500 EI, especiallyshould glass plates be used.

By definition a metric camera has a knowninner orientation and a calibrated radial dis-

tortion.2 This definition could be mislead­ing, because every camera calibrated bya test field could consequently be consid­ered a "metric camera." Also, the specifi­cations that a metric camera has certainfacilities to define the elements of innerorientation does not help very much. Ingeneral, the edge of the picture can be usedto determine the position of the principalpoint, and the position of the image planemust be fairly constant, otherwise the picturewould get out offocus. Ofcourse the require­ments for proper image quality do not copecompletely with the requirements for preci­sion measurements. Additionally, with met­ric cameras one may dispense with facilitiesto determine the orientation of the cameraaxis in space or to fix the relative orientationof two conjugate pictures.

Consequently, it should be stated that

106 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976

photographs taken with metric cameras canbe used for precision measurements or forrestitution in analog plotters without addi­tional control of the elements of inner andrelative orientation. The measuring preci­sion should be limited only by unavoidableerrors of the photographic material. Further­more the lens distortion should be smallenough so that it can be neglected for plot­ting on analog restitution instmments.

TOLERANCES FOR THE PRINCIPAL POINT AND

THE PRINCIPAL DISTANCE

The tolerances for the inner orientationdepend on a number of factors such as theopening angle of the camera, the size of theobject, or the type ofphotographic material tobe used (roll film, plane film, or glass plates).Therefore it is not possible to give figureswhich are applicable under all circum­stances. These tolerances will also help tojudge under which conditions non-metriccameras can be used for precision measure­ments without any loss of accuracy.

Such an accuracy evaluation can be per­formed by a simulated camera calibration. Ifone assumes that the object to be measuredincludes control points, then the principaldistance, the coordinates of the principalpoint, and eventually the distortion can becomputed. The precision of the calculatedparameters is obtained from the system ofinverted normal equations. In case the con­trol points are unfavorably distributed, theunknowns are fairly inaccurate. This doesnot effect the precision of the points to bemeasured within the area defined by thecontrol points, provided that the camera cali­bration is restricted to the principal distanceand the coordinates of the principal point.

The simulated camera calibration has beenbased on the projection equations ofHallert,3 extended for the elements of theinner orientation.

x' = x'o + I1r'.r + c

ordinates of the projection center. The rota­tion elements are the swing K, the tip cf>, andthe tilt w. The lens distortion is taken intoaccount by I1r'.r and I1r'y.

The form of the projection equations andthe sequence of the axes of the rotationelements is immaterial; it is of importanceonly that the physical imaging process isapproximated sufficiently. The inclusion ofthe radial distortion or the principal point ofsymmetry as unknowns would degrade theprecision of the estimated parameters con­siderably. The increase of the variances isthen combined with a strong correlationbetween the unknowns. The high correlationbetween the orientation elements means thatan error of one of these parameters can becompensated by a proper choice of the othervariables. This compensation is possibleonly if at least one of two highly correlatedvalues can be chosen freely.

For the study of the reproducibility of theelements of inner orientation it is assumedthat these parameters are considered con­stant and only the elements of the exteriororientation are variable. Therefore the accu­racy estimations should be performed foreach orientation element separately. Be­cause the correlation between the princip~lpoint and the principal distance is small, thisprecaution is not necessary for these threeparameters, but it would not be correct tointroduce more parameters of the inner ori­entation as stochastic variables.

The size of an object or the size of the testfield for a calibration is physically limitedby the characteristics of the camera. Its lat­eral extension is restricted by the openingangle of the camera, and the depth extensionin general by the depth of focus. Especiallyfor short imaging distances the depth offocuscan be very narrow. Figure 1 gives a survey ofthe depth of focus for cameras with differentfocal lengths. It has been assumed for the

(x-xo) (coscf> COSK - sincf> sinw sinK)-(Y-Yo) coswsinK+(H-ho)'(sincf> COSK + coscf> sinw sinK)(x-xo) sincf> cosw - (Y-iJo) sinw -(H-ho) coscf> cosw (1)

y' = y'o + I1r'JJ + c

(x-xo) (coscf> sinK + sincf> sin w COSK)+(Y-Yo)cosw cosK+(H-ho) (sincf> sinK-coscf> sinw COSK)(x -xo) sincf> cosw - (y -Yo) sinw - (H -hoY coscf> cosw (2)

In the formulae x' and Y' are the picture co­ordinates (measured in the comparator); x, Y,and H the corresponding coordinates of thepoints in the test field; c the principal dis­tance; x'o and y'o the coordinates of theprincipal point; and xO, Yo> and ho the co-

computation that the circle of confusionshould not be larger than 30ILm and thesmallest admittable aperture stop has beenfixed at 1 : 16. These limitations might appearrather narrow but less severe restrictionswould cause a serious degradation of the

METRIC OR NON-METRIC CAMERAS 107

\\\\\\\\\

FIG. 2. For the determination oftolerances for the principal dis­tance and the principal point, asimulated camera calibration isused. The figure shows the distri­bution of the control points andthe dimensions of the fictitioustest field. Normally the test fieldhas the shape of a cube. For close­range photographs the depth-of­focus can get very narrow. Thenthe depth extension t1Z of the testfield has to be adapted to thedepth-of-focus (ex is the angle un­der which the test field is photo­graphed, Z the maximum distanceof the object points).

the principal point are independent of thefocal length and depend only on the openingangle of the camera and the extension of thetestfield. This means that the numericalvalues for the tolerances of the in~er orienta­tion would be the same for a small-sizecamera as for an aerial camera with a pictureformat of 23 x 23 cm as long as the openingangle of the lenses are the same.

The computed variances are presented inFigures 3 and 4. The graphs show that a highprecision for the parameters of the innerorientation is necessary only for objects withconsiderable depth extension. Ifthe object isfairly flat, then the tolerances for these pa­rameters are obviously less severe. In theextreme case, for a completely flat object andvertical photographs, the values for the prin­cipal distance and the principal point can bearbitrary. Deviations from the nominal val­ues are completely compensated by a proper

~ 0

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FIG. 1. Ratio between the depth-of-focus andthe maximum object distance IXIJZ. This valuecan be used to enter in the graphs of Figure 3 andFigure 4. (admitted circle of confusion, 30 ILm;aperture 1: 16; D, focusing distance)

image quality, which is intolerable for pre­cision measurements. Nevertheless the dia­gram can be used for other values; the result­ing depth of focus has only to be multipliedby the factor to the initial values of theapelture stop or the diameter of the circle ofconfusion.

The accuracy estimation has been per­formed with a fictitious test field of eightcontrol points. These points were located inthe corners of a quadratic prism (see Figure2). The side length of the prism should bechosen so that it might fill four fifths of thepicture format. The height of the prism isvariable and is expressed as a fraction of theimaging distance. The computation wasstopped when the depth of the fictitious testfield was equal to its lateral extension.

Finally a figure for the mean square errorof unit weight (To must be assumed in order tocompute the variances for the principal pointand the principal distance. This term (To

indicates the measuring precision in thepicture and can be determined from theresidual errors of a camera calibration. Ac­cording to various experiments4 •5 •6 a measur­ing accuracy of (To = ± 3 /1-m can be achievedwith glass plates or plane film, and for rollfilm a (To = ± 10 to 12 /1-m must be expected.

The simulated camera calibration was per­formed on an electronic computer (CDC6400). The program was run for various focallengths and opening angles of the camera.The computation showed that the accuracyrequirements for the principal distance and

108 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976

FIG. 3. Tolerances for the mean square coor­dinate error of the principal point according to asimulated camera calibration. The measuringprecision in the picture has been assumed to be0"0 = ± 10 /Lm. a is the angle under which the testfield is seen from the camera.

choice of the projection distance. As thedepth of the test field increases, the correla­tion between the principal distance and theprojection distance diminishes and the pre­cision requirements become more severe.

This is of importance for close-range pho­togrammetry because the depth of focus isvery narrow for imaging distances of 2-1 mor less (see Figure 1). Consequently, thedepth extension of an object is severelyrestricted and the accuracy requirements onthe parameters of inner orientation need notbe so high. Therefore it seems unrealistic todemand special metric cameras for suchshort imaging distances.

The computed tolerances are surprisinglylarge for narrow-angle cameras whereas theybecome very strict for wide-angle and super­wide-angle cameras. The precision of theprincipal distance should be on the order of± 0.1 mm for the Hasselblad camera withPlanar 1:3.5/100 (c = 100 mm, S = 27 x 27mm) whereas the tolerance for a wide-anglecamera like the Zeiss TMK (c = 60 mm, S = 8x 10 cm) gets reduced to ± 25/Lm for film (<To± 10 /Lm). The corresponding values for glassplates (<To ± 3 /Lm) are smaller by a factor of 3and would be ± 30 /Lm for the Hasselblad and± 8 /Lm for the TMK. Therefore, it shouldbe recommended that non-metric camerasare mainly applied with narrow openingangles and, consequently, long focal lengths.The precision requirements for wide-angle

~ t.c

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LENS DISTORTION

The principal distance and the location ofthe principal point are liable to certainchanges from photograph to photograph.These variations are caused by erroneouspositioning of the plate or film during expo­sure. The lens distortion should not be influ­enced by this effect. Nevertheless the lensdistortion determined by a camera calibra­tion might show considerable differenceswhen the calibration procedure is repeated.This is due mainly to a superposition of thelens distortion with various other imagingerrors such as atmospheric refraction, filmshrinkage, or lack of flatness of the imageplane. In general the symmetrical lens dis­tortion can be separated by a study of thereproducibility. The precision of the distor­tion curve should be at least ofthe same orderas the measuring precision.

An extension of the mathematical modelfor affinity or for the tangential and asym­metric lens distortion should not be neces­sary for small- or medium-format cameras!,7.The only exception would be for the princi­pal point of symmetry, and it is advisable tocontrol its location in a camera calibration.This point is defined only for lenses with anoticeable distortion (more than ± 5 to ± 20/Lm). The precision of this point determinedby a camera calibration varies from ± 1 mm

20

30

[-urn500

300

50

200

70

150

FIG. 4. Tolerances for the principal distance.

cameras are on the order of ± 10 to ± 30 /Lmfor film and ± 3 to ± 10 /Lm for plates. Thesetolerances are very narrow and it seemsdoubtful whether these values are alwaysmet by metric cameras.

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METRIC OR NON-METRIC CAMERAS 109

The distance between the two contactpoints is s and should coincide with thediagonal of the plate format. For the compu­tation of the variances the differential valuestld( and tld" have to be replaced by theirstandard deviation md' According to the lawof error propagation one gets the followingrelations:

for a nearly distortion-free lens (Topogonwith ancillary lens and a maximum distortionof about 5 J.Lm) to ± 0.2 mm for the Planar 1 :2.8/80 mm lens (maximum distortion about0.4 mm). The definition and the reproduci­bility of the principal point of symmetryshould not cause any problems in a pre­calibrated camera as the tolerances are con­sequently rather large.

; illi = f (tid., - Ild[) (3)

FIG. 5. Falsification of the principal point andthe principal distance by an erroneous position­ing of the photo plate (tJI, l:1c errors of theprincipal point and the principal distance; l:1d",lid( displacement of the edge of the plate fromthe camera frame, and a tilt of the plate).

The computation becomes more complexif it is taken into account that the film or platein the camera does not form a plane but hasthe shape ofa cylinder or an arbitrary, higher­order surface. Therefore the formula can giveonly a rough approximation and indicates acertain ratio between the reproducibility ofthe principal point and the principal dis­tance. For the Hasselblad camera equippedwith the Planar 1:2.8/80 lens one would ex­pect an accuracy ofthe principal point of ± 60to ± 80 J.Lm according to the assumed vari­ance of the principal distance of ± 30 to ± 40J.Lm. This computation coincides fairly wellwith the practical experiences in camera cali­bration4•6 (see Table 1, Columns 5,8). The

(5)

(4)v2' cs

Thus

REPRODUCIBILITY OF THE ELEMENTS OF

INNER ORIENTATION

The investigations have shown that thetolerances for the parameters of inner orien­tation are not uniform and that they dependon various factors. Especially for long focallengths the tolerances are very large and itseems possible that these values could bemet even by non-metric cameras. In a photo­graphic camera the position of the imageplane is defined by optical conditions. If thephotographic material deviates from its pre­scribed position, then the image qualitymight deteriorate. For the estimation of tol­erances again the circle of confusion cansimilarly be used as for determination of thedepth of focus. For this computation thelargest possible aperture stop should betaken into account. For the Hasselblad cam­era with the Planar 1 : 2.8/80 mm lens a circleof confusion of 30 J.Lm is already reached bya displacement of the image plane of 84 J.Lmfor the aperture of 1:2.8. In this case anobject point at the nominal focusing distancewould be out of focus. From a statistical pointof view this deviation should not be reachedin 95 per cent or even 99 per cent ofthe cases.The calculated tolerances for the principaldistance have been standard errors (with asignificance level of 68 per cent). Conse­quently, the standard error for the position­ing of the picture plane should be only one­half or even one-third of the computed tol­erance: that means ± 30 to ± 40 J.Lm.

A positioning error of the image plane ingeneral also will affect the location of theprincipal point (see Figure 5). With somesimplifications the displacement of the prin­cipal point can be computed. For the deriva­tion of a mathematical relation it is assumedthat the photographic material is completelyflat and pressed with its edge against theframe of the camera. Due to imperfections ofthe contact surface the plate has a varyingdistance (M"tid[) to the upper and loweredge of the camera. From these differentialvalues the error of the principal point and theprincipal distance can be computed.

110 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976

same estimations should be valid for thelarger format cameras such as the Linhof­Technika and the Phototheodolite. The vari­ation of the principal point also should beapproximately twice the value for the princi­pal distance. The reproducibility of the prin­cipal distance seems slightly less accurateaccording to the figures in Table 1, whichmight be due to deformations of the imageplate.

A comparison of these figures with thetolerances discussed earlier shows that thereproducibility of the principal distance israther satisfying whereas the precision of theprincipal point is adequate only for an as­sumed measuring accuracy of (To = ± 10 !-tm.This is valid for non-metric cameras and tosome extent also for the tested metric cam­eras. Again, the tendency can be seen thatnarrow-angle cameras are better fi tted forprecision measurements than wide-anglecameras. Although the reproducibility of theprincipal point becomes less accurate forcameras with long focal lengths, the toler­ance for this parameter increases even morerapidly.

MODEL ACCURACY

The accuracy discussion has assumed thatthe measuring precision should be limitedonly by uncontrollable components, such asfilm shrinkage or lack of flatness of thephotographic plate, whereas errors of theorientation elements should be small enoughto be neglected. Up to now the discussion hasconcentrated on the elements of inner orien­tation, but would be incomplete without theinclusion of elements of exterior orientation.In the following, an example is given inwhich the overall precision was decisivelylimited by vibrations of the stereocamera

whereas the use of metric cameras would nothave contributed to any increase of themeasuring precision.

At the Swiss Forest Research Institute aninvestigation has been undertaken to per­form a forest inventory with extremely large­scale photographs taken from helicopters.The task was to measure tree height, stemdiameter, and a few other parameters indeciduous woods with the help of stereo­photographs. The required precision was ± 1 mfor the tree height and ± 1 to ± 2 cm for thestem diameter. The base length chosen couldbe relatively small because the precisionrequirements in depth were not very severeand the use of a stereocamera became fea­sible.

After a few experiments, a base of 4.5 mwas adopted, and two Hasselblad 500 ELcameras with Planar 1:2.8/80 mm lensesequipped with film were used; the flyingheight chosen was 100m (see Figure 6). Itwas of great importance that the model scalebe kept constant within about ± 1 per centbecause a signalization of control pointsseemed unreasonable. The observation ofthis tolerance proved to be very difficult.Theoretically, scale errors can be caused by avarying base length, an inferior definition ofthe principal point (for the indicated meas­urements, the principal point used for thereconstruction of the pencil of rays must notexactly coincide with the principal point ofautocollimation), and by a variation of theangle of convergency of the two camerasduring flight (see Figure 7). To avoid scaleerrors in the model of more then 1 per cent,the tolerance for the base length would be± 5 cm, Ot ± 30 to 40 !-tm for the definition ofthe assumed principal point (picturescale1:1200) and ± 3c for the angle of convergency.The observation of the convergency proved

TABLE 1. COMPARISON OF THE TOLERANCES FOR THE PRINCIPAL POINT AND THE PRINCIPAL DISTANCEWITH THE REPRODUCIBILITY OF THESE PARAMETERS FOR PLATE CAMERAS4 •6 • (A: NON-METRIC CAMERAS,

M: METRIC CAMERA, ex OPENING ANGLE COMPUTED FOR A REDUCED P·LATE FORMAT OF 80%, THETOLERANCES IN BRACKETS ARE VALID FOR ADEPTH OF FIELD OF dvz = 1110).

Principal Point Principal Distance

Camera ex Tolerances Reprod. Tolerances Reprod.

CTo= ± 10 JLm CTo = ± 3 JLm CTo=±10JLm CT o = ± 3 JLm

Hasselblad 500 C (A) 34- 65 20 70 85 25 31f = 80 mm, 5.5 x 5.5 cm (100) (30) (290) (87)Linhof Technika (A) 36- 60 18 70 80 24 50f = 135 mm, 9 x 12 em (95) (28) (270) (81)Photo-Theo (M) 37- 55 17 46 75 22 32f = 190 mm, 13 x 18 cm (90) (27) (260) (78)SMK(M) 69- 15 5 10 27 8 10f = 60 mm, 9 x 12 em (75) (22) (U5) (34)

METRIC OR NON-METRIC CAMERAS 111

FIG. 6. Stereocamera in a helicopter takingphotographs for a forest inventory. (A: Basebeam, length 4.5 m; B, C: Hasselblad cameras500 EL)

to be most difficult due to the vibrations ofthe base beam of the stereocamera. Thesevibrations were caused by the movements ofthe rotor of the helicopter and air turbulence.The camera suspension vibrates like a beamsupported in its central part. The movementsare extremely critical if the vibrations of thehelicopter match the self-frequencies of thecamera suspension. A great stiffness is neces­sary so that the bending of the axis of thebeam does not exceed the given tolerance,which means that the deflection in the cen­tral part should remain within 0.3 mm.Laboratory tests on a vibrating table haveshown that a framework in combination withshock absorbers is necessary for the camera'suspension whereas a tube would render lessfavorable results. This effect is due to thebetter damping property of a framework.

The example shows that it is not useful todiscuss the metric behavior of non-metric ormetric cameras alone, but the whole cameraset-up has to be taken into consideration. In

this special case, the application of metriccameras would not have contributed to anyincrease of the measuring precision becausethe accuracy limitations originate from acompletely different source. The require­ments for the depth precision were ex­tremely low in this case, but this is not therule for photogrammetric measurements andvery often this is the limiting factor for thechoice of the photoscale.

In several investigations the advantage ofconvergent photographs compared with pho­tographs taken by stereocameras has beenpointed out (see Table 2)1.6.9. The increase ofprecision is considerable and it should benoted that erroneous elements of inner orien­tation degrade the overall precision less thanan unfavourable base-to-height ratio. Earlier,tolerances for the elements of inner orienta­tion were computed. It has been pointed outthat the test field should include the wholeobject so that the determination of the objectcoordinates can be considered as a sort ofinterpolation. The point determination getsmore critical if the measurements are ex­tended outside the area defined by the con­trol points. The deterioration of the pointaccuracy can be estimated with the help ofthe law of error-propagation. The coordi­nates of an object point are a function of theimage coordinates and the orientation ele­ments. The variances of these point coordi­nates are computed from the linearized de­termination equation and the variance andcovariance matrix of the orientation ele­ments. With the covariance matrix taken froma camera calibration, these variances havebeen computed for several points within andoutside the test field (see Figure 8). Accord­ing to this estimation the measurements canbe extended up to a factor ofthree outside the

FIG. 7. Factors affecting the measuring precision of distances, in pictures taken by astereocamera. A convergency ofthe two cameras (b) or an erroneous definition ofthe principalpoint (c) will cause systematic scale errors. For a stereocamera mounted in a helicopter itproved more difficult to get the camera suspension sufficiently stable and to avoid vibrationsof the base beam than to reconstruct the principal point in a non-metric camera with sufficientaccuracy (see Figure 6).

I

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112 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976

TABLE 2. MODEL ACCURACY FOR METRIC CAMERAS (PHOTO-THEO, SMK-40) AND NON-METRICCAMERAS FROM PRACTICAL :rESTS.

Camera Arrangement Convergent PhotographsVerticalPhotos

CalibrationReference

Selfcalibration(6)

Test Field(4) (9) (10)

0.10

SMK 401: 45

601 : 6.5

4.2x 4.2 m16

Hasselblad SMK 401 : 36 1 : 43

82 601 : 1.5 1 : 1.5

2.0 x 2.0m 2 x 2 m120 64

Linhof Hasselblad Contarex1 : 25 1 : 44 1 : 45141 82 53

1 : 1.5 1 : 1.5 1 : 12.0 x2.5 m 2.4 x 2.4 m 1.1 X1.6m

27 22 230.10 0.14 0.130.10 0.20 0.15 0.19 0.16

Co-ordinate Errors Reduced to a Picture Scale of 1 : 20

Camera Photo-TheoPicture scale 1 : 22Principal distance 204Base to height ratio 1 : 1.5Object size 2.7 x 3.9 mNumber ofcontrol points 30Residual parallaxes (mm) 0.08Co-ordinate errors (mm) 0.11

m. (mm)m.r(mm)my (mm)mz (mm)

0.100.080.060.15

0.080.060.050.12

0.090.080.060.12

0.070.060.060.11

0.100.060.060.16

0.080.050.070.10

0.490.390.390.65

area of the control points until the coordi nateerrors exceed the influence of the unavoid­able measuring errors by a factor of two.These reflections point out that the questionof metrij: or non-metric cameras is even

mr In [mm]

",,.ll 1---+--+--+--+----,;'+----1>"'-----1

Z in [mm]

700 SH>O 1100 1300 1500 1700 1900

FIG. 8. Estimated planimetric errors in radialdirection for photogrammetric point determina­tion. It is assumed that the camera is calibratedby a test field located within the marked area (Z= 900 to 1100 mm). As the depth of the test field isvery narrow the precision of the parameters ofthe inner orientation is relatively low. Neverthe­less the influence of these errors is completelycompensated within the area ofthe test field. Themeasuring precision decreases for points closerto or further from the cam'era (camera: Hassel­blad with Planar 1 : 2.8/80; the calibration wasperformed with 74 control points and includedthe radial distortion and the principal point ofsymmetry; u. = '± 4.4/Lm, Il1c = ± 53 !Lm, mH= ± 37 !Lm, maximum correlation coefficient 0.95, rr indicates the distance ofthe image point from theprincipal point, m. the effect of the measuringprecision).

inferior to the problem of using a favorablecamera arrangement.

CONCLUSIONS

The aim of this paper was to show toler­ances for the parameters of inner orientationand to compare these figures with the poten­tials of various cameras. The differences inprecision between metric and non-metriccameras are smaller than one would expect.To a great extent the model accuracy de­pends on factors other than the use of metricor non-metric cameras. Nevertheless, theapplication of non-metric cameras is coupledwith a number of problems which are notexpressed by such figures. The user of non­metric cameras has to calibrate the camera byhimself and should investigate the repro­ducibility of the principal point and theprincipal distance. Sophisticated computerprograms are needed for the calibration ofthe cameras and for the data reduction of thephotographs, whereas for metric cameras themanufacturer delivers the calibration report.Photographs taken with metric cameras canbe restituted on analog plotters due to thesmaller lens distortion and the controlledrelative orientation. Consequently it is morea question of comfort than a matter of preci­sion whether metric or non-metric camerasshould be used. But this comfort requires aconsiderable capital investment.

REFERENCES

1. Karara, H. M. and Abdel-Aziz, Y. I., "AccuracyAspects of Non-Metric Imageries", Photo­grammetric Engineering 40,1107-1117,1974

2. Jordan-Eggert-Kneissel (Editor), Handbuch

METRIC OR NON-METRIC CAMERAS 113

der Vennessungskunde, Bd. UIa/l (p. 199),Stuttgart, 1972

3. HaBert, B., Photogrammetry, New York, 1960.4. Dohler, M., "Nahbildmessung mit Nicht­

Messkammern", Bildmessung und Luftbild­wesen, 39, 67-76, 1971

5. Kenefick, J. F., "Ultra-Precise Analytics",Photogrammetric Engineering, 37,1167-1187,1971

6. Kolbl, 0., "Selbstkalibrierung von Aufnahme­kammern", Bildmessung und Luftbildwesen,40, 31-37, 1972

7. Kolbl, 0., "Tangential and Asymmetrical Lens

Distortion", Bildmessung und Luftbildwesen,43,35-42, 1975

8. Aicher, W., Eberle, K., Kirschstein, M., "DieNahbere'ichs-Photogrammetrie als Verfor­mungsmessverfahren in der Luft- und Raum­fahrttechnik", Bildmessung und Luftbild­wesen, 42, 166-170, 1974

9. Karara, H. M., "On the Precision of Stereo­metric Systems," Int. Archive, Lausanne, 1968

10. Berling, D., Beitriige zur terrestrischen Pho­togrammetrie im Nahbereich fiir Material­prufung und Rontgendiagnostik. Diss., T. H.Aachen, 1970

(Continued from page 80)the entire Birdseye Family which feels sogreatly honored by the gallant action of thephotogrammetric community.

In her place we have the pleasure towelcome one of Lt. Col. and Mrs. BertSweigart's eight children, namely Col.Birdseye's grandson, Karl Sweigart, whocame to bring us the message of the BirdseyeFamily.

Postscript:Following the dedication ceremony at

Hopi Pont, an enterprising group consistingof Heinz Gruner, Fred Doyle, and KarlSweigart, accompanied by a pilot and pho­tographer, took off in a helicopter from theGrand Canyon airfield. They flew down thecanyon to Birdseye Point north of the riverand circled the point several times, witheverybody taking pictures.

-M. M. Thompson

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