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The NRC camera calibrator
Photogrammetria, 34 (1978) 147--165 147 © Elsevier Scientific Publishing Company, Amsterdam --Printed in The Netherlands
THE NRC CAMERA CALIBRATOR
P.D. CARMAN and H. BROWN Division of Physics, National Research Council, Ottawa, Ont. (Canada) (Received September 5, 1977 ; accepted January 3, 1978)
ABSTRACT Carman, P.D. and Brown, H., 1978. The NRC camera calibrator. Photogrammetria, 34: 147--165. Equipment and techniques for the calibration of aerial survey cameras have been developed progressively at the National Research Council of Canada with the goals of providing a high level of real accuracy, versatility to accomodate a variety of camera, filters, and emulsions, and an economy of operation which permits recalibration at yearly intervals. Present apparatus and methods are described, and reasons for their construction and choice are explained. Results of three calibrations, made at different times, of two test cameras are given. They illustrate the degree to which cameras change with time and use.
INTRODUCTION C a m e r a c a l i b r a t i o n p r o c e d u r e s at the N a t i o n a l R e s e a r c h C o u n c i l o f Canada have been described several times at various stages in their e v o l u t i o n (Field, 1 9 4 6 , 1 9 4 9 ; C a r m a n a n d B r o w n , 1 9 6 1 ; C a r m a n , 1 9 6 9 ) . T h e p r e s e n t p u r p o s e s are to p r o v i d e an u p - t o - d a t e d e s c r i p t i o n o f the c a m e r a c a l i b r a t o r p r o p e r and its o p e r a t i o n , to discuss the reasons for t h e choices m a d e in its design and o p e r a t i o n , and t o explain their a d v a n t a g e s and disadvantages. R o u t i n e results will also be given o f the calibrations carried o u t o n the t w o c a m e r a s used for i n t e r c o m p a r i s o n s b y t h e ISP W o r k i n g G r o u p o n I m a g e G e o m e t r y . R e l a t e d o p t i c a l tests p e r f o r m e d o n survey c a m e r a s will n o t be discussed here. APPARATUS AND METHODS T h e N R C c a l i b r a t o r is a p h o t o g r a p h i c i n s t r u m e n t w i t h o n e f a n o f 43 collimators covering 1 1 8 . 1 2 5 ° . Calibration along various c a m e r a a z i m u t h s is p r o v i d e d b y m e a s u r e d r o t a t i o n o f the c a m e r a . A p h o t o g r a p h i c s y s t e m is used because it provides a direct l a b o r a t o r y s i m u l a t i o n o f c o n d i t i o n s o f use and h e n c e gives results w h i c h are c o r r e c t in practical terms. D i f f e r e n c e s b e t w e e n visual and p h o t o g r a p h i c calibrations were i d e n t i f i e d a n d e x p l a i n e d by C a r m a n and B r o w n ( 1 9 5 6 ) . T h e differences can be m i n i m i z e d o r allowed
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for in various ways, but only a photographic calibration with a " d a y l i g h t " light source, the intended camera filter, and an emulsion with the intended spectral sensitivity provides a straightforward means of obtaining a correct calibration. The fan is in a vertical plane, with its center collimator vertical so that the camera looks vertically downward. This avoids any possibility of spurious changes in the camera d u e to an abnormal mounting position. The calibrator as illustrated in Fig. 1 consists of three main parts: a main
AUTOCOLUMATORS;
Fig. 1. N . R . C . c a m e r a c a l i b r a t o r - - g e n e r a l a r r a n g e m e n t .
casting holding the 43 collimators, a lower bridge holding the camera under test, and an upper bridge supporting three autocollimators used in positioning the camera. A single fan of collimators was chosen to avoid excessive size, complexity, and cost. The simple form may also be inherently more stable than a two-fan system. Overall operating cost is also lower. Rotation of the camera to make exposures along the second diagonal requires less than five minutes. At the present work load of about 75 calibrations per year, this totals only one-twentieth of the time t h a t would be needed for annual recalibration of a second bank of collimators. The collimators are reflecting systems with off-axis parabolic mirrors. They are positioned around the outer arc of the main casting and the reticles around the inner arc. Mirror collimators have the advantage of no chromatic aberration, so that calibrations can be made with equal accuracy at any wavelength, including the infrared. They also have no zonal spherical aberration, so t h a t the position of the camera entrance pupil is n o t critical. Furthermore, the mirror " f o l d i n g " reduces instrument size very substantially. The mirrors of 63 mm clear aperture and 70 mm outside diameter with
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an 83 m m m o u n t width are spaced on 90 mm centers to leave 7 m m clearance. These dimensions combined with the 2.8125 ° angular spacing established the 186 cm radius of the outer arc and hence the size of the whole instrument. An equivalent refracting system would have the collimator focal lengths outside the 186 cm radius. The only significant disadvantage of reflecting collimators is t h a t angular stability is very dependent on the mirrors not tilting on their small mounting bases. The present mirrors are of fused quartz. They were manufactured at the National Research Council and installed in September 1973 replacing the previous partial set of pyrex mirrors which were showing some tendency to warp. The mirrors were polished spherical and then parabolized by vacuum evaporation to give a shape accuracy of 1/40th wavelength of visible light. Consequently the emergent wave front is plane to 1/20th wavelength. In each collimator, a reticle provides a clear white cross on a neutral grey background. The background has a tranmission of 10% rather than being black. The purpose of this is to permit both the cross and its background to be exposed on the approximately straight line portion of the emulsion's characteristic curve. This avoids the possibility of variation of apparent image position with exposure which can occur with a high contrast target. The present reticles are accurate to their nominal dimensions to within 1 ~m and are neutral t h r o u g h o u t the visible and infrared photographic regions with the background transmission lying entirely between 10 and 11.5%. They were obtained from Applied Physics Specialties in T o r o n t o to NRC specifications and were installed in September 1973 replacing earlier reticles from another source which did n o t meet these tolerances either on dimensions or neutrality. The reticles are oriented angularly so t h a t the cross arms lie in the camera's radial and tangential directions to within 1 pm (at reticle scale). This is done primarily to ensure that when the plate is being measured the images of the reticle crosses have their arms parallel to the measuring machine's cross-hairs. Consequently, in making settings, the effects of grain are averaged over the length of the cross and random image irregularities are minimized. The precise orientation also facilitates measurement of the angles between collimators. Reticles are positioned initially to make collimator angles within about 10 sec of the nominal values, but no effort is spent trying to make them exact because actual measured values of the angles can be readily used in computation. Fig. 2 is a photograph of a lower part of the calibrator. Around the outer arc of the main meehanite (heat-treated iron) casting are the meehanite trivets each holding an off-axis parabolic mirror. Around the inner arc are seen 43 microscopes which both illuminate the reticles and permit viewing of them for initial set-up and for measurement of the collimator angles. Illumination is from the white spherical source at the top. It is imaged by a small lens on the side of each microscope just in front of the eye piece through a beam-splitter onto the microscope objective. The apparent white source is actually an integrating sphere made from a " w h i t e " lamp bulb by
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Fig. 2. Collimator array.
removal of the base and filament structure. It is illuminated via a condenser system from a tungsten projection lamp in the lamp house to its right. Between the condensers is a blue glass filter for correcting the spectral energy distribution to approximate that of daylight. This arrangement permits the spectral energy distribution provided to all collimators to be controlled by one filter and to be changed simultaneously when desired. It also has the minor advantage t h a t an exposure cannot be rendered useless by the unnoticed failure of one bulb. The entire calibrator is supported on h y d r o p n e u m a t i c antivibration m o u n t s which can be seen at the top of the corner posts. The suspension has a natural frequency of about 0.5 Hz vertically and horizontally, whereas the supported parts all have natural frequencies of over 100 Hz. Thus the instrument is very well isolated from any vibrations of the ground. This ensures that no relative motions occur during a photographic exposure. It also protects the calibrator from shocks which might tend to affect its stability. Temperature control of the calibrator is aided by polystyrene foam and reflective insulation on the pit walls, by a false floor and by insulating sections in the stands. Temperature is maintained by a high level of forced ventilation from the upper room which is temperature controlled. Strong
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drafts are excluded f r o m the optical paths by covers over the casting openings and by curtains f r o m the ceiling to the inner arc. Without these, air current instabilities were f o u n d to cause significant changes in the directions of the collimated beams. The t e m p e r a t u r e is controllled to 20°C + I° C year after year. On a shorter t er m basis t e m p e r a t u r e is const ant to within 0.1°C over any 24-hour period. This ensures t hat the calibrator and the camera are bot h in t e m p e r a t u r e equilibrium at the time an exposure is made, and also t hat the results o f annual recalibrations of an particular camera can be reliably i n t e r c o m p a r e d to reveal the characteristics of any changes taking place in the camera. Both gradual drifts and r a n d o m wanderings of calibration values have been noted. CALIBRATION PROCEDURE The p r o ced u r e for calibrating the calibrator has been described in detail previously (Carman and Brown, 1961). Briefly the 90 ° nominal angle between the 16th collimators on each side of cent er is c o m p a r e d by autocollimation with a 90 ° optical cube which is accurate to 0.1 sec. This angle is t h e n successively bisected to give all the intervening angles. It is because of this t h a t the angle between collimators is 90 o/32 = 2.8125 ° . Angles of the o u ter collimators needed f or super wide-angle cameras are obtained by a related procedure. T he optical m i c r o m e t e r used for measuring the departures of each collimator f r om its nominal angle is easily kept free of any significant systematic errors and the bisection procedure inherently minimizes cumulative errors. T he latest i m p r o v e m e n t in the system has been the r e p l a c e m e n t o f t he observer at the microscope by closed-circuit T.V. camera to reduce errors due to the observers b o d y heat and incidentally to improve convenience. With this system it has been f o u n d t hat the r o o t mean square error o f a single observation by one observer is 0.23 sec. Usually three sets of five observations are taken by each of two observers. The rms disagreement b etwe e n the means for the two observers is 0.13 sec. As previously stated absolute accuracy is believed to be within 0.5 sec. Data on long-term stability is somewhat limited. It was of the order of 1 sec per year with the first mirrors and reticles. After installation of the new mirrors and reticles, a partial calibration was c o m p l e t e d in D e c e m b e r 1973, and full calibrations in N ove m ber 1974, O c t o b e r 1975, and S e p t e m b e r 1976. Most angles were f o u n d to change 1 sec per year or less. However, two collimators were f o u n d to be changing initially at a b o u t 4 sec per year and subsequently at decreasing rates in the original directions. These two collimators are being m o n i t o r e d . No extensive e f f o r t has y e t been made to stop the drifts. Two possible sources, inherent in the design, are under consideration. As m e n t i o n e d , the mirror m ounti ng base is unavoidably small. T o minimize the problem, the mirror back is polished and it rests on three polished pads on the meehanite trivet. The pad spacing is a b o u t 50 mm. Consequently if a 1/2 p m piece of dust were on one of the pads during
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assembly, and later crumbled or dissolved, a mirror tilt of 2 sec would occur, causing a 4 sec change in beam direction. A similar possibility for motion occurs where the trivets seat on the main casting, but is less likely because the pad spacing is about 250 mm. Tentatively the anomalous instabilities are being attributed to some such initial effect. Fig. 3 shows a general view of the upper part of the calibrator. A camera
Fig. 3. Upper part of calibrator. is in position on the lower bridge. A plane-parallel mirror on the fiducial frame is being used with an autocollimating telescope in the upper bridge to control levelling of the camera. The autocollimator has previously been aimed at the center collimator in the lower array. In the background is the counter-balancing device for the plate flattener {Carman, 1955). This c o u n t e r balance is used to ensure that the load placed on the camera's fiducial frame during calibration is close to that placed on it by the vacuum back during actual photography. The counter-balance also greatly facilitates handling the flattener gently in total darkness. Figs. 4--8 illustrate operations normally carried out in complete darkness. In Fig. 4 the photographic plate is in position on a sensitometer being given a sensitometric exposure for routine control of processing. The plate-flattening device has been placed on the plate. The photographic plates are
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Fig. 4. S e n s i t o m e t r i c c o n t r o l e x p o s u r e being m a d e o n plate o n flattener.
K o d ak 6.3 mm thick microflat plate glass, flat originally to 10 pm. The usual emulsion is Kodak aerial Panatomic X. For infrared calibrations, K o d ak t y p e IV N is used. The flattener f ur t her improves the emulsion flatness by bending the plate. Fig. 5 shows the b o t t o m of the flattener holding, for illustration purposes, an e xpos ed and processed plate. The 25 rubber suction cups c o n n e c t e d to a vacuum pum p hold the plate against metal pads which are on the end of differential screws giving a b o u t 30 pm m o t i o n for a full turn. Fig. 6 shows the flattener with a plate in position for flattening on an infrared interferometer. This is a Fizeau t y p e interferom eter folded for convenience and using infrared radiation at 1014 nm to avoid fogging of even IR emulsions. With it the shape of the emulsion surface can be observed interferometrically by comparison with the reference flat just below it using an infrared image converter telescope. Also part of the system is an auxilliary autocollimating telescope of which the objective can be seen centered over the flattener. This permits the t op face of the reference optical cube on t op of the flattener to be set parallel to the reference flat and hence to the emulsion surface. Fig. 7 shows typical fringe patterns seen in the i n t e r f e r o m e t e r , f r om left to right, at the beginning, at a b o u t half way t hr ough the flattening sequence, and when satisfactory flatness is attained. Final flatness achieved is always within two fringes cor-
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Fig. 5. Method of holding photographic plate on flattener. responding to 1 pm total or + 1/2 pm from a mean plane over the used part of the plate. This plate flattening procedure was developed to provide an optimized combination of accuracy and economy. It ensures that the largest image position errors due to lack of emulsion flatness are less than 1/~m. (It is, of course, implied that the intended emulsion position is a flat surface resting on the camera's fiducial frame, and that photographic film held by a vacuum back approximates such a surface on the average.) Only one flattened plate needs to be used for a calibration. A duplicate may be taken in exceptional circumstances. The flattening can almost always be completed in less than 10 minutes of a skilled operator's time. After the flattening is complete, the flattener with plate is moved to the camera (Fig. 8), levelling is checked by autocollimation on the top of the cube and readjusted if necessary. This relevelling ensures that the emulsion surface is truly perpendicular to the central collimator thus avoiding fictitious contributions to asymmetry of radial measured distortion. A relevelling corresponds to a change in the position of the principal point of autocollimation. Consequently, the three possible causes need to be examined. (1) The camera m a y have tilted between being levelled with the plane parallel mirror and having the flattener placed on it. In this case the relevelling corrects the tilt and eliminates any error.
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Fig. 6. Flattening a photographic plate on infrared interferometer.
Fig. 7. Interference patterns seen during flattening process.
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Fig. 8. Placing f l a t t e n e d plate o n camera.
(2) T h e e m u l s i o n surface m a y rest o n t h e fiducial f r a m e at a slightly diff e r e n t angle t h a n t h e m i r r o r b e c a u s e o f a small piece o f d u s t or a l u m p in the e m u l s i o n . (3) T h e fiducial f r a m e is n e v e r p e r f e c t l y flat. A t o l e r a n c e o f + 8 p m is p e r m i t t e d , f o r e x a m p l e , b y C a n a d i a n " C a t e g o r y A " . T h u s t w o high p o i n t s c o u l d o c c u r o n a line passing t h r o u g h t h e c e n t e r of gravity o f t h e m i r r o r or t h e f l a t t e n e r p e r m i t t i n g it to r o c k b y , t h e o r e t i c a l l y , as m u c h as 14 sec corr e s p o n d i n g t o an u n c e r t a i n t y in p o s i t i o n o f t h e p r i n c i p a l p o i n t o f a u t o c o l l i m a t i o n o f + 10 p m . Such r o c k i n g indicates a real u n c e r t a i n t y in defining the p r i n c i p a l p o i n t o f a u t o c o l l i m a t i o n . H o w e v e r , such an e f f e c t has b e e n n o t e d o n l y on o n e c a m e r a . W h a t e v e r the case, if t h e n e e d e d relevelling exceeds 2 sec, t h e source o f t h e t r o u b l e is e s t a b l i s h e d and it is e i t h e r e l i m i n a t e d or r e p o r t e d . C o n s e q u e n t l y , e r r o r in t h e p o s i t i o n o f t h e p r i n c i p a l p o i n t o f a u t o c o l l i m a t i o n f r o m this cause c a n n o t e x c e e d 1.5 p m . I n c o n j u n c t i o n w i t h levelling, t h e c a m e r a is r o t a t e d so t h a t images will fall along o n e diagonal, a n d p o s i t i o n e d b y a u t o c o l l i m a t i o n o n o n e c u b e face using t h e n e a r e r o f t h e t w o h o r i z o n t a l a u t o c o l l i m a t o r s . A f t e r t h e first e x p o s u r e is m a d e , t h e c a m e r a is r o t a t e d to t h e o t h e r diagonal c o n t r o l l e d b y a u t o c o l l i m a t i o n o n t h e o t h e r c u b e face b y t h e s a m e a u t o c o l l i m a t o r and relevelled. O n l y t h o s e t w o e x p o s u r e s are r o u t i n e l y m a d e b u t , if desired, t h e
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f u r t h e r o f the two autocollimators can also be used t o provide exposures at 45 ° and 135 ° azimuth f r o m the original position. After exposure the flattener and its plate are r e t ur ned to the i n t e r f e r o m e t e r to check that the emulsion surface is still fiat and parallel to the t op of the optical cube. After the plate has been processed, dried, and allowed to come to the t e m p e r a t u r e and h u m i d i t y equilibrium, it is measured on the measuring machine shown in Fig. 9. This machine was built by Askania to NRC speci-
Fig. 9. Measuring images on processed plate. fications. A few modifications have been made primarily to minimize heating problems. Removal o f light sources f r om the machine and a fan to blow away the observer's b o d y heat were f o u n d necessary. The instrument reads on glass scales which were calibrated by the PTB*. Calibrations are q u o t e d to 0.1/~m and stated to be accurate to + 0.5 pm . In the routine calibration procedure, in which only two diagonals are read, data is recorded on paper tape by a telety p e for subsequent c o m p u t e r processing. The c o m p u t e r program first applies the k now n corrections for the scales o f the measuring machine. N e xt it c o m p u t e s the calibrated focal length *Physikalisch-Technische Bundesanstalt (Physical-Technical Federal Institute) in Braunschweig, Germany.
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which best fits the radial distortion of the camera to the " r e f e r e n c e " data f o r th at camera. The best fit is defined as one that minimizes the e x t r e m e departures taking a c c o u n t by weighting of the relaxation of tolerances at larger field angles outside 42.5 ° . Nex t the principal p o i n t of best s y m m e t r y is d e t e r m i n e d again on the basis o f minimizing the m a x i m u m departures from s y m m e t r y . T hen tangential distortions are determined after a similar minimization procedure govern. ing angular choice of reference frame. The c o m p u t e r p r i n t o u t gives results for each o f the two observers who normally read each plate, results for the averages o f their readings, and a comparison of their readings showing their differences and their rms differences. A final c o m p u t e r page gives a simplified s u mmar y f or use in preparation of the routine report. To the capability of measuring distortions along the camera diagonals or at intervals of 45 ° in azimuth there has recently been added a capability of measuring every 9 ° in azimuth. This is achieved as illustrated in Fig. 10. The reference cube controlling camera r o t a t i o n has been replaced by a reference " s a n d w i c h " or " l ayer c a k e " having five layers. Each layer has two faces at 90 ° to one anot her and each layer is r o t a t e d nominally 9 ° from the layer below it with actual angles k n o w n accurately to within 0.5 sec. This
Fig. 10. F l a t t e n e r w i t h 5-layer reference reflector, for c o n t r o l l i n g a z i m u t h in 9 ° intervals.
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makes possible a total of 557 measurement points for a camera with 153 m m focal l e n g t h or 793 m e a s u r e m e n t p o i n t s for a c a m e r a of 85 m m focal l e n g t h . N e e d l e s s t o say t h e r e is n o i n t e n t i o n o f u s i n g t h i s m a n y p o i n t s f o r routine annual recalibrations. However, they prove useful for research p r o j e c t s s u c h as t h e p r e s e n t ISP W o r k i n g G r o u p i n v e s t i g a t i o n a n d it s e e m s l i k e l y t h a t s e l e c t e d p o i n t s f r o m a m o n g t h e s e n u m b e r s will b e u s e f u l f o r a special p u r p o s e at other times. RESULTS Results of the three routine calibrations of each of the two cameras s t u d i e d b y t h e W o r k i n g G r o u p are g i v e n i n T a b l e s I - - V I b e l o w . T e r m i n o l o g y a n d sign c o n v e n t i o n s are i n a c c o r d w i t h t h e ISP R e c o m m e n d e d P r o c e d u r e s for Calibrating P h o t o g r a m m e t r i c Cameras and for Related Optical Tests. L o c a t i o n s o f t h e f o u r s e m i d i a g o n a l s d e s c r i b e d as b a n k 1 t o b a n k 4 are as TABLE I Wild RC5/RC8 15UAg R10 Calibration date: 4 March 1974 Calibrated focal length: 152.149 mm Angle( ° ) 5.63 11.25 16.88 22.50 28.12 Distance (ram) 15.0 30.3 46.1 63.0 81.3 Radial measured Bank 1 Bank 2 Bank 3 Bank 4 Mean Reference
distortion (um) 4 9 9 2 4 7 0 3 5 5 9 9 3 6 8 2 4 6
-2 -8 -6 2 -4 -4
42.19 137.9
1 -7 -4 5 -1 2
Radial asymmetry about principal point o f best symmetry (urn) Bank 1 1 3 1 2 0 -1 -3 Bank 2 -1 -1 0 0 0 -1 2 Bank 3 -2 -3 -2 -1 -1 0 1 Bank 4 2 2 1 0 1 1 0
-2 2 2 -2
2 0 -2 0
5 2 1 8 4 2
39.38 124.8
-6 -11 -9 -1 -7 -6
Tangential measured distortion (urn) Bank 1 1 2 2 Bank 2 0 -1 -1 Bank 3 -1 0 -1 Bank 4 1 0 1
10 7 6 9 8 5
33.75 101.6
3 -1 -1 0
2 -3 -2 1
x 9 6
y -11 -1
Positions relative to fiducial centre (~m)
Principal point of autocollimation Principal point of best symmetry
3 0 -2 1
3 1 0 2
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TABLE II Wild RC5/RC8 15UAg R10 Calibration date: 15 September 1974 Calibrated focal length: 152.140 mm Angle( ° ) 5.63 Distance (mm) 15.0 Radial measured Bank 1 Bank 2 Bank 3
11.25 30.3
16.88 46.1
22.50 63.0
distortion (urn) 2 5 7
28.12 81.3
4
5 5 5 5
8 7 9 8
6 8 9 8
1 4 3 3
2
4
6
5
2
39.38 124.8
42.19 137.9
-4 -8
-6 -9
1 -4
-5 -1 -5
-7 -5 -7
-1 2 -1
-4
-6
2
Radial asymmetry about principal point o f best symmetry (urn) Bank 1 -1 0 -1 -1 1 0 1 Bank 2 -1 0 0 -1 -1 -1 1 Bank 3 1 0 -1 0 1 0 0 Bank 4 1 0 1 1 -1 1 -1
1 0 0 -1
Tangential measured distortion (urn) Bank 1 2 1 0 'Bank 2 0 -1 -1 Bank 3 0 -1 -2 Bank 4 0 -1 0
4 0 -2 2
Bank 4 Mean Reference
7
2 4 4 3
33.75 101.6
0 -2 -3 1
3 -2 -2 2
0 -4 -3 1
-2 0 -2 -1
Positions relative to fiducial centre (urn)
Principal point of autocollimation Principal point of best symmetry
x 7 4
y 0 3
illustrated in Fig. 11. The "reference" distortion values quoted were taken f r o m m a n u f a c t u r e r s d a t a f o r t h e s e r ~ s e a u c a m e r a s as a b a s i s f o r t h e b e s t f i t c a l c u l a t i o n i n v o l v e d in d e t e r m i n i n g c a l i b r a t e d f o c a l l e n g t h . S e v e r a l s m a l l p e c u l i a r i t i e s o f t h e t e s t s s h o u l d b e m e n t i o n e d b e f o r e discussing the results. The first and second sets of routine two-diagonal measurements were made on t h e s a m e p l a t e s u s e d b y Z i e m a n n ( 1 9 7 8 , see p p . 1 6 7 - 1 7 8 , t h i s i s s u e ) f o r s t u d y o f a much larger number of format points. Each plate received a series of 20 sequential exposures with a measured rotation between each exposure. Some difficulty was encountered with plate motions during this long operation. Simple mathematical corrections have been applied where needed to eliminate the clearly spurious effect of the plate motion. For the third test the "routine" two-diagonal calibration exposures were on plates separate from those with 20 azimuths. L e v e l l i n g o f t h e c a m e r a w a s in all c a s e s c o n t r o l l e d b y a u t o c o l l i m a t i o n o n the r~seau plate rather than by the usual technique of autocollimation on an optical plane-parallel placed on the fiducial frame.
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TABLE III Wild RC5/RC8 15UAg R10 Calibration date: 28 October 1976 Calibrated focal length: 152.147 mm Angle( ° ) Distance (ram)
5.63 15.0
11.25 30.3
16.88 46.1
22.50 63.0
28.12 81.3
33.75 101.6
39.38 124.8
42.19 137.9
Radial measured distortion (urn) Bank 1 Bank 2 Bank 3 Bank 4 Mean Reference
3 2 4 3 3 2
6 3 6 6 5 4
8 6 8 8 8 6
6 7 8 9 8 5
0 1 4 4 2 2
-6 -8 -3 -1 -4 -4
-8 -10 -4 0 -6 -6
-3 -5 1 5 -1 2
Radial asymmetry about principal point of best symmetry (urn) Bank Bank Bank Bank
1 2 3 4
0 -1 1 0
1 -2 1 0
1 -1 0 0
-1 1 0 0
-1 1 1 0
0 0 0 0
0 0 -1 0
0 2 -1 -1
0 -1 -1 0
-1 -1 0 -1
0 -1 -2 0
2 0 -1 -2
2 1 -1 0
Tangential measured distortion (urn) Bank Bank Bank Bank
1 2 3 4
0 1 1 0
-1 0 1 -1
-2 0 1 -2
Positions relative to fiducial centre (urn) Principal point of autocollimation Principal point of best symmetry
x 14 6
y -3 0
A s m e n t i o n e d a b o v e , t w o c o l l i m a t o r s w e r e d r i f t i n g a t a b o u t 4 sec p e r y e a r at t h e t i m e s o f t h e first t w o sets o f tests. T h e c o l l i m a t o r s were t h o s e a f f e c t i n g 2 8 . 1 2 ° o n b a n k s 1 a n d 4 a n d 3 3 . 7 5 ° o n b a n k s 3 a n d 2. C o m p u t a t i o n s i n c l u d e d an i n t e r p o l a t i o n a s s u m i n g the d r i f t to be linear w i t h t i m e , and n o residual a n o m a l i e s are a p p a r e n t . DISCUSSION I n c o n s i d e r i n g t h e t a b l e s , it s h o u l d b e b o r n e in m i n d t h a t t h e a c c u r a c y c l a i m e d f o r r o u t i n e c a l i b r a t i o n s is + 3 p m a b s o l u t e a c c u r a c y o n i n d i v i d u a l v a l u e s w i t h a h i g h c o n f i d e n c e l e v e l ( ~ 9 9 % ) . R . M . S . e r r o r s ar e a b o u t _+ 1 t o 1.5 p m .
Wild camera ( 1 5 U A g R 1 O) C a l i b r a t e d f o c a l l e n g t h v a r i e s , w i t h a t o t a l v a r i a t i o n o f 9 p m . T h i s is w i t h in t h e v a r i a t i o n r a n g e t y p i c a l l y f o u n d h e r e .
162
TABLE IV Zeiss RMK AR 15/23 21197 Pleogon AR 98222 Calibration date: 4 March 1974 Calibrated focal length : 152.057 mm Angle( ° ) 5.63 11.25 16.88 22.50 28.12 33.75 Distance (ram) 15.0 30.3 46.1 63.0 81.3 101.6
39.38 124.8
42.19 137.9
45.00 152.1
30 2 -18 5 5 1
27 -6 -31 2 -2 2
48 8 -25 11 10 4
Radial measured distortion (# m) Bank I Bank 2 Bank 3 Bank 4 Mean Reference
-4 -7 -6 -6 -6 -4
-5 -10 -12 -7 -9 -6
0 -6 -10 -7 -6 -5
6 -6 -10 -2 -3 0
15 -3 -9 0 1 4
25 -3 -13 4 3 4
Radial asymmetry about principal point of best symmetry (~m) Bank Bank Bank Bank
1 2 3 4
1 -1 0 0
2 -1 -2 1
2 0 0 -1
2 -2 -1 0
3 -2 1 -2
4 - 4 2 - 2
0 - 5 - 1 2
-3 -8 -1 7
- 2 -11 0 7
- 1 1 4 - 4
-3 0 3 0
-2 3 4 5
0 -14 3 14
-4 -17 -2 12
Tangential measured distortion (urn) Bank 1 Bank2 Bank 3 Bank 4
-1 1 1 1
-1 -2 1 1
-2 -2 -1 0
-2 -13 1 9
Positions relative to fiducial centre (urn) Principal point of autocollimation Principal point of best symmetry
x -2 23
y 2 33
A v e r a g e r a d i a l m e a s u r e d d i s t o r t i o n r e m a i n e d c o n s t a n t t o +- 1 p m . Both radial asymmetry about the principal point of best symmetry and tangential distortion changed (improved) very slightly, to the point where both were within + 2 pm. Individual changes do not exceed the measuring a c c u r a c y claimed above b u t i n s p e c t i o n of the general p a t t e r n suggests t h a t t h e a p p a r e n t c h a n g e s are r e a l , a t l e a s t i n p a r t , r a t h e r t h a n b e i n g m e a s u r i n g errors. T h e p r i n c i p a l p o i n t o f a u t o c o l l i m a t i o n m o v e d b y a t o t a l o f 11 p m a n d t h e principal point of best symmetry by 6 pm, relative to the fiducial centre. The changes in asymmetry, tangential distortion, and principal points suggest t h a t some small b u t definite changes have t a k e n place, p r o b a b l y in the centering of lens components.
Zeiss camera (Pleogon A R 9 8 2 2 2 ) C a l i b r a t e d f o c a l l e n g t h v a r i e d , w i t h a t o t a l r a n g e o f 5 p m . T h i s is w i t h i n the variation range typically found here.
163
TABLE V Zeiss RMK AR 15/23 21197 Pleogon AR 98222 Calibration date: 15 September 1974 Calibrated focal length: 152.059 mm Angle (°) 5.63 Distance (ram) 15.0
11.25 30.3
33.75 101.6
39.38 124.8
42.19 137.9
45.0 152.1
24 0 -15 4 3 4
29 3 -22 3 3 1
31 -1 -28 -3 0 2
48 9 -23 11 11 4
Radial asymmetry about principal p o i n t o f best s y m m e t r y (~m) Bank 1 2 2 3 2 2 3 Bank 2 0 1 0 -1 0 -3 Bank 3 0 -3 -2 -1 -2 -1 Bank 4 -1 0 -1 0 0 1
0 0 0 -1
0 -1 3 -3
-2 -2 3 0
Tangentml measured d ~ r t m n ( u m ) Bank 1 2 2 1 Bank 2 1 -1 -2 Bank 3 0 -2 -3 Bank 4 0 -1 0
-2 -10 -1 7
2 -11 -2 11
2 -12 -3 13
Radial measured distortion (urn) Bank 1 -3 -5 Bank 2 -5 -7 Bank 3 -6 -13 Bank 4 -6 -9 Mean -5 -8 Reference -4 -6
16.88 46.1
-1 -7 -13 -9 -7 -5
22.50 63.0
6 -4 -10 -3 -3 0
28.12 81.3
13 1 -12 0 0 4
2
2
-3 -3 2
-4 -1 7
-1 -7 -3 6
Positions relative to fiducial centre (urn) Principal point of autocollimation Principal point of best symmetry
x -7 20
y 3 30
Average radial m e a s u r e d d i s t o r t i o n r e m a i n e d c o n s t a n t to + 1.5 p m . Both radial asymmetry about the principal point of autocollimation and t a n g e n t i a l d i s t o r t i o n are v e r y m u c h l a r g e r f o r t h i s i n d i v i d u a l c a m e r a t h a n is u s u a l f o r t h i s t y p e o f c a m e r a . E r r o r s o f t h i s size are m o s t u s u a l l y d u e t o t h e camera having received a violent mechanical shock. Significant changes in asymmetry and tangential distortion appear to have occurred. The principal point of autocollimation moved by 43 ~m and the principal point of best symmetry moved 42 pm relative to the fiducial c e n t r e , all s u g g e s t i n g t h a t s o m e d e f i n i t e m e c h a n i c a l c h a n g e s h a v e t a k e n p l a c e in the time period under consideration, mainly between the second and third calibrations. ACKNOWLEDGEMENTS T h e a u t h o r s w i s h t o t h a n k Mr. J. P l u m m e r w h o m a n a g e s t h e r o u t i n e o p e r a t i o n s o f c a m e r a c a l i b r a t i o n , a n d also h a s t a k e n p a r t i n m a n y o f t h e
164
TABLE VI Zeiss RMK A R 15/23 21197 Pleogon AR 9 8 2 2 2 Calibration date: 28 October 1976 Calibrated focal length: 152.054 m m Angle (°) 5.63 Distance ( m m ) 15.0
11.25 30.3
16.88 46.1
22.50 63.0
28.12 81.3
33.75 101.6
39.38 124.8
42.19 137.9
45.0 152.1
24 0 -19 6 3 4
33 4 -21 9 6 1
31 -1 -31 7 1 2
53 3 -33 20 11 4
Radial measured distortion (urn) Bank 1 Bank 2 Bank 3 Bank 4 Mean Reference
-6 -6 -7 -7 -6 -4
-7 -10 -14 -9 -10 -6
-1 -6 -14 -6 -7 -5
6 -3 -13 -3 -3 0
12 -2 -16 0 -1 4
Radial asymmetry about principal point of best symmetry (~m) Bank Bank Bank Bank
1 2 3 4
0 1 -1 0
2 0 -3 1
2 2 -4 0
3 1 -3 0
2 1 -3 0
3 0 -4 1
t0 2 0 -1
-4 2 1 1
2 -2 -3 4
1 -3 -3 2
-2 -5 1 5
1 -8 1 5
1 -12 1 8
1 -11 1 12
2 -11 3 15
x -30 -6
y -30 3
Tangential measured distortion (urn) Bank Bank Bank Bank
1 2 3 4
1 0 -1 0
2 0 0 -1
1 0 -1 - 1
Positions relative to fiducial centre (urn) Principal p o i n t of a u t o c o l l i m a t i o n Principal p o i n t of best s y m m e t r y
Panel
Y __~,._-____ x
I
Fig. 11. Semi-diagonal identification and co-ordinate system, as if looking at emulsion side of negative, i.e., at film plane f r o m lens.
developments of techniques and equipment and in the calibration and adj u s t m e n t o f t h e c a l i b r a t o r . M r . 1%. F i n k is t h e u s u a l s e c o n d r e a d e r o f e v e r y photographic plate and has assisted with maintenance and development of some equipment.
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REFERENCES Carman, P.D., 1955. Control and interferometric measurement of plate flatness. J. Opt. Soc. Am., 45 (12) 1009--1010. Carman, P.D., 1969. Camera calibration laboratory at N.R.C. Photogramm. Eng., 35 (4): 372--376. Carman, P.D. and Brown, H., 1956. Differences between visual and photographic calibrations of air survey cameras. Photogramm. Eng., 22 (4): 623--626. Carman, P.D. and Brown, H., 1961. Camera calibration in Canada. Can. Surv., 15 (8): 425--439. Field, R.H., 1946. The calibration of air cameras in Canada. Photogramm. Eng., 12 (2): 142--146. Field, R.H., 1949. A device for locating the principal point markers of air cameras. Can. Surv., 10 (1): 17--21. Ziemann, H., 1978. Repeated photographic laboratory calibrations of two rdseau cameras. Photogrammetria, 34:167~-178 (this issue).
THE NRC CAMERA CALIBRATOR
P.D. CARMAN and H. BROWN Division of Physics, National Research Council, Ottawa, Ont. (Canada) (Received September 5, 1977 ; accepted January 3, 1978)
ABSTRACT Carman, P.D. and Brown, H., 1978. The NRC camera calibrator. Photogrammetria, 34: 147--165. Equipment and techniques for the calibration of aerial survey cameras have been developed progressively at the National Research Council of Canada with the goals of providing a high level of real accuracy, versatility to accomodate a variety of camera, filters, and emulsions, and an economy of operation which permits recalibration at yearly intervals. Present apparatus and methods are described, and reasons for their construction and choice are explained. Results of three calibrations, made at different times, of two test cameras are given. They illustrate the degree to which cameras change with time and use.
INTRODUCTION C a m e r a c a l i b r a t i o n p r o c e d u r e s at the N a t i o n a l R e s e a r c h C o u n c i l o f Canada have been described several times at various stages in their e v o l u t i o n (Field, 1 9 4 6 , 1 9 4 9 ; C a r m a n a n d B r o w n , 1 9 6 1 ; C a r m a n , 1 9 6 9 ) . T h e p r e s e n t p u r p o s e s are to p r o v i d e an u p - t o - d a t e d e s c r i p t i o n o f the c a m e r a c a l i b r a t o r p r o p e r and its o p e r a t i o n , to discuss the reasons for t h e choices m a d e in its design and o p e r a t i o n , and t o explain their a d v a n t a g e s and disadvantages. R o u t i n e results will also be given o f the calibrations carried o u t o n the t w o c a m e r a s used for i n t e r c o m p a r i s o n s b y t h e ISP W o r k i n g G r o u p o n I m a g e G e o m e t r y . R e l a t e d o p t i c a l tests p e r f o r m e d o n survey c a m e r a s will n o t be discussed here. APPARATUS AND METHODS T h e N R C c a l i b r a t o r is a p h o t o g r a p h i c i n s t r u m e n t w i t h o n e f a n o f 43 collimators covering 1 1 8 . 1 2 5 ° . Calibration along various c a m e r a a z i m u t h s is p r o v i d e d b y m e a s u r e d r o t a t i o n o f the c a m e r a . A p h o t o g r a p h i c s y s t e m is used because it provides a direct l a b o r a t o r y s i m u l a t i o n o f c o n d i t i o n s o f use and h e n c e gives results w h i c h are c o r r e c t in practical terms. D i f f e r e n c e s b e t w e e n visual and p h o t o g r a p h i c calibrations were i d e n t i f i e d a n d e x p l a i n e d by C a r m a n and B r o w n ( 1 9 5 6 ) . T h e differences can be m i n i m i z e d o r allowed
148
for in various ways, but only a photographic calibration with a " d a y l i g h t " light source, the intended camera filter, and an emulsion with the intended spectral sensitivity provides a straightforward means of obtaining a correct calibration. The fan is in a vertical plane, with its center collimator vertical so that the camera looks vertically downward. This avoids any possibility of spurious changes in the camera d u e to an abnormal mounting position. The calibrator as illustrated in Fig. 1 consists of three main parts: a main
AUTOCOLUMATORS;
Fig. 1. N . R . C . c a m e r a c a l i b r a t o r - - g e n e r a l a r r a n g e m e n t .
casting holding the 43 collimators, a lower bridge holding the camera under test, and an upper bridge supporting three autocollimators used in positioning the camera. A single fan of collimators was chosen to avoid excessive size, complexity, and cost. The simple form may also be inherently more stable than a two-fan system. Overall operating cost is also lower. Rotation of the camera to make exposures along the second diagonal requires less than five minutes. At the present work load of about 75 calibrations per year, this totals only one-twentieth of the time t h a t would be needed for annual recalibration of a second bank of collimators. The collimators are reflecting systems with off-axis parabolic mirrors. They are positioned around the outer arc of the main casting and the reticles around the inner arc. Mirror collimators have the advantage of no chromatic aberration, so that calibrations can be made with equal accuracy at any wavelength, including the infrared. They also have no zonal spherical aberration, so t h a t the position of the camera entrance pupil is n o t critical. Furthermore, the mirror " f o l d i n g " reduces instrument size very substantially. The mirrors of 63 mm clear aperture and 70 mm outside diameter with
149
an 83 m m m o u n t width are spaced on 90 mm centers to leave 7 m m clearance. These dimensions combined with the 2.8125 ° angular spacing established the 186 cm radius of the outer arc and hence the size of the whole instrument. An equivalent refracting system would have the collimator focal lengths outside the 186 cm radius. The only significant disadvantage of reflecting collimators is t h a t angular stability is very dependent on the mirrors not tilting on their small mounting bases. The present mirrors are of fused quartz. They were manufactured at the National Research Council and installed in September 1973 replacing the previous partial set of pyrex mirrors which were showing some tendency to warp. The mirrors were polished spherical and then parabolized by vacuum evaporation to give a shape accuracy of 1/40th wavelength of visible light. Consequently the emergent wave front is plane to 1/20th wavelength. In each collimator, a reticle provides a clear white cross on a neutral grey background. The background has a tranmission of 10% rather than being black. The purpose of this is to permit both the cross and its background to be exposed on the approximately straight line portion of the emulsion's characteristic curve. This avoids the possibility of variation of apparent image position with exposure which can occur with a high contrast target. The present reticles are accurate to their nominal dimensions to within 1 ~m and are neutral t h r o u g h o u t the visible and infrared photographic regions with the background transmission lying entirely between 10 and 11.5%. They were obtained from Applied Physics Specialties in T o r o n t o to NRC specifications and were installed in September 1973 replacing earlier reticles from another source which did n o t meet these tolerances either on dimensions or neutrality. The reticles are oriented angularly so t h a t the cross arms lie in the camera's radial and tangential directions to within 1 pm (at reticle scale). This is done primarily to ensure that when the plate is being measured the images of the reticle crosses have their arms parallel to the measuring machine's cross-hairs. Consequently, in making settings, the effects of grain are averaged over the length of the cross and random image irregularities are minimized. The precise orientation also facilitates measurement of the angles between collimators. Reticles are positioned initially to make collimator angles within about 10 sec of the nominal values, but no effort is spent trying to make them exact because actual measured values of the angles can be readily used in computation. Fig. 2 is a photograph of a lower part of the calibrator. Around the outer arc of the main meehanite (heat-treated iron) casting are the meehanite trivets each holding an off-axis parabolic mirror. Around the inner arc are seen 43 microscopes which both illuminate the reticles and permit viewing of them for initial set-up and for measurement of the collimator angles. Illumination is from the white spherical source at the top. It is imaged by a small lens on the side of each microscope just in front of the eye piece through a beam-splitter onto the microscope objective. The apparent white source is actually an integrating sphere made from a " w h i t e " lamp bulb by
150
Fig. 2. Collimator array.
removal of the base and filament structure. It is illuminated via a condenser system from a tungsten projection lamp in the lamp house to its right. Between the condensers is a blue glass filter for correcting the spectral energy distribution to approximate that of daylight. This arrangement permits the spectral energy distribution provided to all collimators to be controlled by one filter and to be changed simultaneously when desired. It also has the minor advantage t h a t an exposure cannot be rendered useless by the unnoticed failure of one bulb. The entire calibrator is supported on h y d r o p n e u m a t i c antivibration m o u n t s which can be seen at the top of the corner posts. The suspension has a natural frequency of about 0.5 Hz vertically and horizontally, whereas the supported parts all have natural frequencies of over 100 Hz. Thus the instrument is very well isolated from any vibrations of the ground. This ensures that no relative motions occur during a photographic exposure. It also protects the calibrator from shocks which might tend to affect its stability. Temperature control of the calibrator is aided by polystyrene foam and reflective insulation on the pit walls, by a false floor and by insulating sections in the stands. Temperature is maintained by a high level of forced ventilation from the upper room which is temperature controlled. Strong
151
drafts are excluded f r o m the optical paths by covers over the casting openings and by curtains f r o m the ceiling to the inner arc. Without these, air current instabilities were f o u n d to cause significant changes in the directions of the collimated beams. The t e m p e r a t u r e is controllled to 20°C + I° C year after year. On a shorter t er m basis t e m p e r a t u r e is const ant to within 0.1°C over any 24-hour period. This ensures t hat the calibrator and the camera are bot h in t e m p e r a t u r e equilibrium at the time an exposure is made, and also t hat the results o f annual recalibrations of an particular camera can be reliably i n t e r c o m p a r e d to reveal the characteristics of any changes taking place in the camera. Both gradual drifts and r a n d o m wanderings of calibration values have been noted. CALIBRATION PROCEDURE The p r o ced u r e for calibrating the calibrator has been described in detail previously (Carman and Brown, 1961). Briefly the 90 ° nominal angle between the 16th collimators on each side of cent er is c o m p a r e d by autocollimation with a 90 ° optical cube which is accurate to 0.1 sec. This angle is t h e n successively bisected to give all the intervening angles. It is because of this t h a t the angle between collimators is 90 o/32 = 2.8125 ° . Angles of the o u ter collimators needed f or super wide-angle cameras are obtained by a related procedure. T he optical m i c r o m e t e r used for measuring the departures of each collimator f r om its nominal angle is easily kept free of any significant systematic errors and the bisection procedure inherently minimizes cumulative errors. T he latest i m p r o v e m e n t in the system has been the r e p l a c e m e n t o f t he observer at the microscope by closed-circuit T.V. camera to reduce errors due to the observers b o d y heat and incidentally to improve convenience. With this system it has been f o u n d t hat the r o o t mean square error o f a single observation by one observer is 0.23 sec. Usually three sets of five observations are taken by each of two observers. The rms disagreement b etwe e n the means for the two observers is 0.13 sec. As previously stated absolute accuracy is believed to be within 0.5 sec. Data on long-term stability is somewhat limited. It was of the order of 1 sec per year with the first mirrors and reticles. After installation of the new mirrors and reticles, a partial calibration was c o m p l e t e d in D e c e m b e r 1973, and full calibrations in N ove m ber 1974, O c t o b e r 1975, and S e p t e m b e r 1976. Most angles were f o u n d to change 1 sec per year or less. However, two collimators were f o u n d to be changing initially at a b o u t 4 sec per year and subsequently at decreasing rates in the original directions. These two collimators are being m o n i t o r e d . No extensive e f f o r t has y e t been made to stop the drifts. Two possible sources, inherent in the design, are under consideration. As m e n t i o n e d , the mirror m ounti ng base is unavoidably small. T o minimize the problem, the mirror back is polished and it rests on three polished pads on the meehanite trivet. The pad spacing is a b o u t 50 mm. Consequently if a 1/2 p m piece of dust were on one of the pads during
152
assembly, and later crumbled or dissolved, a mirror tilt of 2 sec would occur, causing a 4 sec change in beam direction. A similar possibility for motion occurs where the trivets seat on the main casting, but is less likely because the pad spacing is about 250 mm. Tentatively the anomalous instabilities are being attributed to some such initial effect. Fig. 3 shows a general view of the upper part of the calibrator. A camera
Fig. 3. Upper part of calibrator. is in position on the lower bridge. A plane-parallel mirror on the fiducial frame is being used with an autocollimating telescope in the upper bridge to control levelling of the camera. The autocollimator has previously been aimed at the center collimator in the lower array. In the background is the counter-balancing device for the plate flattener {Carman, 1955). This c o u n t e r balance is used to ensure that the load placed on the camera's fiducial frame during calibration is close to that placed on it by the vacuum back during actual photography. The counter-balance also greatly facilitates handling the flattener gently in total darkness. Figs. 4--8 illustrate operations normally carried out in complete darkness. In Fig. 4 the photographic plate is in position on a sensitometer being given a sensitometric exposure for routine control of processing. The plate-flattening device has been placed on the plate. The photographic plates are
153
Fig. 4. S e n s i t o m e t r i c c o n t r o l e x p o s u r e being m a d e o n plate o n flattener.
K o d ak 6.3 mm thick microflat plate glass, flat originally to 10 pm. The usual emulsion is Kodak aerial Panatomic X. For infrared calibrations, K o d ak t y p e IV N is used. The flattener f ur t her improves the emulsion flatness by bending the plate. Fig. 5 shows the b o t t o m of the flattener holding, for illustration purposes, an e xpos ed and processed plate. The 25 rubber suction cups c o n n e c t e d to a vacuum pum p hold the plate against metal pads which are on the end of differential screws giving a b o u t 30 pm m o t i o n for a full turn. Fig. 6 shows the flattener with a plate in position for flattening on an infrared interferometer. This is a Fizeau t y p e interferom eter folded for convenience and using infrared radiation at 1014 nm to avoid fogging of even IR emulsions. With it the shape of the emulsion surface can be observed interferometrically by comparison with the reference flat just below it using an infrared image converter telescope. Also part of the system is an auxilliary autocollimating telescope of which the objective can be seen centered over the flattener. This permits the t op face of the reference optical cube on t op of the flattener to be set parallel to the reference flat and hence to the emulsion surface. Fig. 7 shows typical fringe patterns seen in the i n t e r f e r o m e t e r , f r om left to right, at the beginning, at a b o u t half way t hr ough the flattening sequence, and when satisfactory flatness is attained. Final flatness achieved is always within two fringes cor-
154
Fig. 5. Method of holding photographic plate on flattener. responding to 1 pm total or + 1/2 pm from a mean plane over the used part of the plate. This plate flattening procedure was developed to provide an optimized combination of accuracy and economy. It ensures that the largest image position errors due to lack of emulsion flatness are less than 1/~m. (It is, of course, implied that the intended emulsion position is a flat surface resting on the camera's fiducial frame, and that photographic film held by a vacuum back approximates such a surface on the average.) Only one flattened plate needs to be used for a calibration. A duplicate may be taken in exceptional circumstances. The flattening can almost always be completed in less than 10 minutes of a skilled operator's time. After the flattening is complete, the flattener with plate is moved to the camera (Fig. 8), levelling is checked by autocollimation on the top of the cube and readjusted if necessary. This relevelling ensures that the emulsion surface is truly perpendicular to the central collimator thus avoiding fictitious contributions to asymmetry of radial measured distortion. A relevelling corresponds to a change in the position of the principal point of autocollimation. Consequently, the three possible causes need to be examined. (1) The camera m a y have tilted between being levelled with the plane parallel mirror and having the flattener placed on it. In this case the relevelling corrects the tilt and eliminates any error.
155
Fig. 6. Flattening a photographic plate on infrared interferometer.
Fig. 7. Interference patterns seen during flattening process.
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Fig. 8. Placing f l a t t e n e d plate o n camera.
(2) T h e e m u l s i o n surface m a y rest o n t h e fiducial f r a m e at a slightly diff e r e n t angle t h a n t h e m i r r o r b e c a u s e o f a small piece o f d u s t or a l u m p in the e m u l s i o n . (3) T h e fiducial f r a m e is n e v e r p e r f e c t l y flat. A t o l e r a n c e o f + 8 p m is p e r m i t t e d , f o r e x a m p l e , b y C a n a d i a n " C a t e g o r y A " . T h u s t w o high p o i n t s c o u l d o c c u r o n a line passing t h r o u g h t h e c e n t e r of gravity o f t h e m i r r o r or t h e f l a t t e n e r p e r m i t t i n g it to r o c k b y , t h e o r e t i c a l l y , as m u c h as 14 sec corr e s p o n d i n g t o an u n c e r t a i n t y in p o s i t i o n o f t h e p r i n c i p a l p o i n t o f a u t o c o l l i m a t i o n o f + 10 p m . Such r o c k i n g indicates a real u n c e r t a i n t y in defining the p r i n c i p a l p o i n t o f a u t o c o l l i m a t i o n . H o w e v e r , such an e f f e c t has b e e n n o t e d o n l y on o n e c a m e r a . W h a t e v e r the case, if t h e n e e d e d relevelling exceeds 2 sec, t h e source o f t h e t r o u b l e is e s t a b l i s h e d and it is e i t h e r e l i m i n a t e d or r e p o r t e d . C o n s e q u e n t l y , e r r o r in t h e p o s i t i o n o f t h e p r i n c i p a l p o i n t o f a u t o c o l l i m a t i o n f r o m this cause c a n n o t e x c e e d 1.5 p m . I n c o n j u n c t i o n w i t h levelling, t h e c a m e r a is r o t a t e d so t h a t images will fall along o n e diagonal, a n d p o s i t i o n e d b y a u t o c o l l i m a t i o n o n o n e c u b e face using t h e n e a r e r o f t h e t w o h o r i z o n t a l a u t o c o l l i m a t o r s . A f t e r t h e first e x p o s u r e is m a d e , t h e c a m e r a is r o t a t e d to t h e o t h e r diagonal c o n t r o l l e d b y a u t o c o l l i m a t i o n o n t h e o t h e r c u b e face b y t h e s a m e a u t o c o l l i m a t o r and relevelled. O n l y t h o s e t w o e x p o s u r e s are r o u t i n e l y m a d e b u t , if desired, t h e
157
f u r t h e r o f the two autocollimators can also be used t o provide exposures at 45 ° and 135 ° azimuth f r o m the original position. After exposure the flattener and its plate are r e t ur ned to the i n t e r f e r o m e t e r to check that the emulsion surface is still fiat and parallel to the t op of the optical cube. After the plate has been processed, dried, and allowed to come to the t e m p e r a t u r e and h u m i d i t y equilibrium, it is measured on the measuring machine shown in Fig. 9. This machine was built by Askania to NRC speci-
Fig. 9. Measuring images on processed plate. fications. A few modifications have been made primarily to minimize heating problems. Removal o f light sources f r om the machine and a fan to blow away the observer's b o d y heat were f o u n d necessary. The instrument reads on glass scales which were calibrated by the PTB*. Calibrations are q u o t e d to 0.1/~m and stated to be accurate to + 0.5 pm . In the routine calibration procedure, in which only two diagonals are read, data is recorded on paper tape by a telety p e for subsequent c o m p u t e r processing. The c o m p u t e r program first applies the k now n corrections for the scales o f the measuring machine. N e xt it c o m p u t e s the calibrated focal length *Physikalisch-Technische Bundesanstalt (Physical-Technical Federal Institute) in Braunschweig, Germany.
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which best fits the radial distortion of the camera to the " r e f e r e n c e " data f o r th at camera. The best fit is defined as one that minimizes the e x t r e m e departures taking a c c o u n t by weighting of the relaxation of tolerances at larger field angles outside 42.5 ° . Nex t the principal p o i n t of best s y m m e t r y is d e t e r m i n e d again on the basis o f minimizing the m a x i m u m departures from s y m m e t r y . T hen tangential distortions are determined after a similar minimization procedure govern. ing angular choice of reference frame. The c o m p u t e r p r i n t o u t gives results for each o f the two observers who normally read each plate, results for the averages o f their readings, and a comparison of their readings showing their differences and their rms differences. A final c o m p u t e r page gives a simplified s u mmar y f or use in preparation of the routine report. To the capability of measuring distortions along the camera diagonals or at intervals of 45 ° in azimuth there has recently been added a capability of measuring every 9 ° in azimuth. This is achieved as illustrated in Fig. 10. The reference cube controlling camera r o t a t i o n has been replaced by a reference " s a n d w i c h " or " l ayer c a k e " having five layers. Each layer has two faces at 90 ° to one anot her and each layer is r o t a t e d nominally 9 ° from the layer below it with actual angles k n o w n accurately to within 0.5 sec. This
Fig. 10. F l a t t e n e r w i t h 5-layer reference reflector, for c o n t r o l l i n g a z i m u t h in 9 ° intervals.
159
makes possible a total of 557 measurement points for a camera with 153 m m focal l e n g t h or 793 m e a s u r e m e n t p o i n t s for a c a m e r a of 85 m m focal l e n g t h . N e e d l e s s t o say t h e r e is n o i n t e n t i o n o f u s i n g t h i s m a n y p o i n t s f o r routine annual recalibrations. However, they prove useful for research p r o j e c t s s u c h as t h e p r e s e n t ISP W o r k i n g G r o u p i n v e s t i g a t i o n a n d it s e e m s l i k e l y t h a t s e l e c t e d p o i n t s f r o m a m o n g t h e s e n u m b e r s will b e u s e f u l f o r a special p u r p o s e at other times. RESULTS Results of the three routine calibrations of each of the two cameras s t u d i e d b y t h e W o r k i n g G r o u p are g i v e n i n T a b l e s I - - V I b e l o w . T e r m i n o l o g y a n d sign c o n v e n t i o n s are i n a c c o r d w i t h t h e ISP R e c o m m e n d e d P r o c e d u r e s for Calibrating P h o t o g r a m m e t r i c Cameras and for Related Optical Tests. L o c a t i o n s o f t h e f o u r s e m i d i a g o n a l s d e s c r i b e d as b a n k 1 t o b a n k 4 are as TABLE I Wild RC5/RC8 15UAg R10 Calibration date: 4 March 1974 Calibrated focal length: 152.149 mm Angle( ° ) 5.63 11.25 16.88 22.50 28.12 Distance (ram) 15.0 30.3 46.1 63.0 81.3 Radial measured Bank 1 Bank 2 Bank 3 Bank 4 Mean Reference
distortion (um) 4 9 9 2 4 7 0 3 5 5 9 9 3 6 8 2 4 6
-2 -8 -6 2 -4 -4
42.19 137.9
1 -7 -4 5 -1 2
Radial asymmetry about principal point o f best symmetry (urn) Bank 1 1 3 1 2 0 -1 -3 Bank 2 -1 -1 0 0 0 -1 2 Bank 3 -2 -3 -2 -1 -1 0 1 Bank 4 2 2 1 0 1 1 0
-2 2 2 -2
2 0 -2 0
5 2 1 8 4 2
39.38 124.8
-6 -11 -9 -1 -7 -6
Tangential measured distortion (urn) Bank 1 1 2 2 Bank 2 0 -1 -1 Bank 3 -1 0 -1 Bank 4 1 0 1
10 7 6 9 8 5
33.75 101.6
3 -1 -1 0
2 -3 -2 1
x 9 6
y -11 -1
Positions relative to fiducial centre (~m)
Principal point of autocollimation Principal point of best symmetry
3 0 -2 1
3 1 0 2
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TABLE II Wild RC5/RC8 15UAg R10 Calibration date: 15 September 1974 Calibrated focal length: 152.140 mm Angle( ° ) 5.63 Distance (mm) 15.0 Radial measured Bank 1 Bank 2 Bank 3
11.25 30.3
16.88 46.1
22.50 63.0
distortion (urn) 2 5 7
28.12 81.3
4
5 5 5 5
8 7 9 8
6 8 9 8
1 4 3 3
2
4
6
5
2
39.38 124.8
42.19 137.9
-4 -8
-6 -9
1 -4
-5 -1 -5
-7 -5 -7
-1 2 -1
-4
-6
2
Radial asymmetry about principal point o f best symmetry (urn) Bank 1 -1 0 -1 -1 1 0 1 Bank 2 -1 0 0 -1 -1 -1 1 Bank 3 1 0 -1 0 1 0 0 Bank 4 1 0 1 1 -1 1 -1
1 0 0 -1
Tangential measured distortion (urn) Bank 1 2 1 0 'Bank 2 0 -1 -1 Bank 3 0 -1 -2 Bank 4 0 -1 0
4 0 -2 2
Bank 4 Mean Reference
7
2 4 4 3
33.75 101.6
0 -2 -3 1
3 -2 -2 2
0 -4 -3 1
-2 0 -2 -1
Positions relative to fiducial centre (urn)
Principal point of autocollimation Principal point of best symmetry
x 7 4
y 0 3
illustrated in Fig. 11. The "reference" distortion values quoted were taken f r o m m a n u f a c t u r e r s d a t a f o r t h e s e r ~ s e a u c a m e r a s as a b a s i s f o r t h e b e s t f i t c a l c u l a t i o n i n v o l v e d in d e t e r m i n i n g c a l i b r a t e d f o c a l l e n g t h . S e v e r a l s m a l l p e c u l i a r i t i e s o f t h e t e s t s s h o u l d b e m e n t i o n e d b e f o r e discussing the results. The first and second sets of routine two-diagonal measurements were made on t h e s a m e p l a t e s u s e d b y Z i e m a n n ( 1 9 7 8 , see p p . 1 6 7 - 1 7 8 , t h i s i s s u e ) f o r s t u d y o f a much larger number of format points. Each plate received a series of 20 sequential exposures with a measured rotation between each exposure. Some difficulty was encountered with plate motions during this long operation. Simple mathematical corrections have been applied where needed to eliminate the clearly spurious effect of the plate motion. For the third test the "routine" two-diagonal calibration exposures were on plates separate from those with 20 azimuths. L e v e l l i n g o f t h e c a m e r a w a s in all c a s e s c o n t r o l l e d b y a u t o c o l l i m a t i o n o n the r~seau plate rather than by the usual technique of autocollimation on an optical plane-parallel placed on the fiducial frame.
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TABLE III Wild RC5/RC8 15UAg R10 Calibration date: 28 October 1976 Calibrated focal length: 152.147 mm Angle( ° ) Distance (ram)
5.63 15.0
11.25 30.3
16.88 46.1
22.50 63.0
28.12 81.3
33.75 101.6
39.38 124.8
42.19 137.9
Radial measured distortion (urn) Bank 1 Bank 2 Bank 3 Bank 4 Mean Reference
3 2 4 3 3 2
6 3 6 6 5 4
8 6 8 8 8 6
6 7 8 9 8 5
0 1 4 4 2 2
-6 -8 -3 -1 -4 -4
-8 -10 -4 0 -6 -6
-3 -5 1 5 -1 2
Radial asymmetry about principal point of best symmetry (urn) Bank Bank Bank Bank
1 2 3 4
0 -1 1 0
1 -2 1 0
1 -1 0 0
-1 1 0 0
-1 1 1 0
0 0 0 0
0 0 -1 0
0 2 -1 -1
0 -1 -1 0
-1 -1 0 -1
0 -1 -2 0
2 0 -1 -2
2 1 -1 0
Tangential measured distortion (urn) Bank Bank Bank Bank
1 2 3 4
0 1 1 0
-1 0 1 -1
-2 0 1 -2
Positions relative to fiducial centre (urn) Principal point of autocollimation Principal point of best symmetry
x 14 6
y -3 0
A s m e n t i o n e d a b o v e , t w o c o l l i m a t o r s w e r e d r i f t i n g a t a b o u t 4 sec p e r y e a r at t h e t i m e s o f t h e first t w o sets o f tests. T h e c o l l i m a t o r s were t h o s e a f f e c t i n g 2 8 . 1 2 ° o n b a n k s 1 a n d 4 a n d 3 3 . 7 5 ° o n b a n k s 3 a n d 2. C o m p u t a t i o n s i n c l u d e d an i n t e r p o l a t i o n a s s u m i n g the d r i f t to be linear w i t h t i m e , and n o residual a n o m a l i e s are a p p a r e n t . DISCUSSION I n c o n s i d e r i n g t h e t a b l e s , it s h o u l d b e b o r n e in m i n d t h a t t h e a c c u r a c y c l a i m e d f o r r o u t i n e c a l i b r a t i o n s is + 3 p m a b s o l u t e a c c u r a c y o n i n d i v i d u a l v a l u e s w i t h a h i g h c o n f i d e n c e l e v e l ( ~ 9 9 % ) . R . M . S . e r r o r s ar e a b o u t _+ 1 t o 1.5 p m .
Wild camera ( 1 5 U A g R 1 O) C a l i b r a t e d f o c a l l e n g t h v a r i e s , w i t h a t o t a l v a r i a t i o n o f 9 p m . T h i s is w i t h in t h e v a r i a t i o n r a n g e t y p i c a l l y f o u n d h e r e .
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TABLE IV Zeiss RMK AR 15/23 21197 Pleogon AR 98222 Calibration date: 4 March 1974 Calibrated focal length : 152.057 mm Angle( ° ) 5.63 11.25 16.88 22.50 28.12 33.75 Distance (ram) 15.0 30.3 46.1 63.0 81.3 101.6
39.38 124.8
42.19 137.9
45.00 152.1
30 2 -18 5 5 1
27 -6 -31 2 -2 2
48 8 -25 11 10 4
Radial measured distortion (# m) Bank I Bank 2 Bank 3 Bank 4 Mean Reference
-4 -7 -6 -6 -6 -4
-5 -10 -12 -7 -9 -6
0 -6 -10 -7 -6 -5
6 -6 -10 -2 -3 0
15 -3 -9 0 1 4
25 -3 -13 4 3 4
Radial asymmetry about principal point of best symmetry (~m) Bank Bank Bank Bank
1 2 3 4
1 -1 0 0
2 -1 -2 1
2 0 0 -1
2 -2 -1 0
3 -2 1 -2
4 - 4 2 - 2
0 - 5 - 1 2
-3 -8 -1 7
- 2 -11 0 7
- 1 1 4 - 4
-3 0 3 0
-2 3 4 5
0 -14 3 14
-4 -17 -2 12
Tangential measured distortion (urn) Bank 1 Bank2 Bank 3 Bank 4
-1 1 1 1
-1 -2 1 1
-2 -2 -1 0
-2 -13 1 9
Positions relative to fiducial centre (urn) Principal point of autocollimation Principal point of best symmetry
x -2 23
y 2 33
A v e r a g e r a d i a l m e a s u r e d d i s t o r t i o n r e m a i n e d c o n s t a n t t o +- 1 p m . Both radial asymmetry about the principal point of best symmetry and tangential distortion changed (improved) very slightly, to the point where both were within + 2 pm. Individual changes do not exceed the measuring a c c u r a c y claimed above b u t i n s p e c t i o n of the general p a t t e r n suggests t h a t t h e a p p a r e n t c h a n g e s are r e a l , a t l e a s t i n p a r t , r a t h e r t h a n b e i n g m e a s u r i n g errors. T h e p r i n c i p a l p o i n t o f a u t o c o l l i m a t i o n m o v e d b y a t o t a l o f 11 p m a n d t h e principal point of best symmetry by 6 pm, relative to the fiducial centre. The changes in asymmetry, tangential distortion, and principal points suggest t h a t some small b u t definite changes have t a k e n place, p r o b a b l y in the centering of lens components.
Zeiss camera (Pleogon A R 9 8 2 2 2 ) C a l i b r a t e d f o c a l l e n g t h v a r i e d , w i t h a t o t a l r a n g e o f 5 p m . T h i s is w i t h i n the variation range typically found here.
163
TABLE V Zeiss RMK AR 15/23 21197 Pleogon AR 98222 Calibration date: 15 September 1974 Calibrated focal length: 152.059 mm Angle (°) 5.63 Distance (ram) 15.0
11.25 30.3
33.75 101.6
39.38 124.8
42.19 137.9
45.0 152.1
24 0 -15 4 3 4
29 3 -22 3 3 1
31 -1 -28 -3 0 2
48 9 -23 11 11 4
Radial asymmetry about principal p o i n t o f best s y m m e t r y (~m) Bank 1 2 2 3 2 2 3 Bank 2 0 1 0 -1 0 -3 Bank 3 0 -3 -2 -1 -2 -1 Bank 4 -1 0 -1 0 0 1
0 0 0 -1
0 -1 3 -3
-2 -2 3 0
Tangentml measured d ~ r t m n ( u m ) Bank 1 2 2 1 Bank 2 1 -1 -2 Bank 3 0 -2 -3 Bank 4 0 -1 0
-2 -10 -1 7
2 -11 -2 11
2 -12 -3 13
Radial measured distortion (urn) Bank 1 -3 -5 Bank 2 -5 -7 Bank 3 -6 -13 Bank 4 -6 -9 Mean -5 -8 Reference -4 -6
16.88 46.1
-1 -7 -13 -9 -7 -5
22.50 63.0
6 -4 -10 -3 -3 0
28.12 81.3
13 1 -12 0 0 4
2
2
-3 -3 2
-4 -1 7
-1 -7 -3 6
Positions relative to fiducial centre (urn) Principal point of autocollimation Principal point of best symmetry
x -7 20
y 3 30
Average radial m e a s u r e d d i s t o r t i o n r e m a i n e d c o n s t a n t to + 1.5 p m . Both radial asymmetry about the principal point of autocollimation and t a n g e n t i a l d i s t o r t i o n are v e r y m u c h l a r g e r f o r t h i s i n d i v i d u a l c a m e r a t h a n is u s u a l f o r t h i s t y p e o f c a m e r a . E r r o r s o f t h i s size are m o s t u s u a l l y d u e t o t h e camera having received a violent mechanical shock. Significant changes in asymmetry and tangential distortion appear to have occurred. The principal point of autocollimation moved by 43 ~m and the principal point of best symmetry moved 42 pm relative to the fiducial c e n t r e , all s u g g e s t i n g t h a t s o m e d e f i n i t e m e c h a n i c a l c h a n g e s h a v e t a k e n p l a c e in the time period under consideration, mainly between the second and third calibrations. ACKNOWLEDGEMENTS T h e a u t h o r s w i s h t o t h a n k Mr. J. P l u m m e r w h o m a n a g e s t h e r o u t i n e o p e r a t i o n s o f c a m e r a c a l i b r a t i o n , a n d also h a s t a k e n p a r t i n m a n y o f t h e
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TABLE VI Zeiss RMK A R 15/23 21197 Pleogon AR 9 8 2 2 2 Calibration date: 28 October 1976 Calibrated focal length: 152.054 m m Angle (°) 5.63 Distance ( m m ) 15.0
11.25 30.3
16.88 46.1
22.50 63.0
28.12 81.3
33.75 101.6
39.38 124.8
42.19 137.9
45.0 152.1
24 0 -19 6 3 4
33 4 -21 9 6 1
31 -1 -31 7 1 2
53 3 -33 20 11 4
Radial measured distortion (urn) Bank 1 Bank 2 Bank 3 Bank 4 Mean Reference
-6 -6 -7 -7 -6 -4
-7 -10 -14 -9 -10 -6
-1 -6 -14 -6 -7 -5
6 -3 -13 -3 -3 0
12 -2 -16 0 -1 4
Radial asymmetry about principal point of best symmetry (~m) Bank Bank Bank Bank
1 2 3 4
0 1 -1 0
2 0 -3 1
2 2 -4 0
3 1 -3 0
2 1 -3 0
3 0 -4 1
t0 2 0 -1
-4 2 1 1
2 -2 -3 4
1 -3 -3 2
-2 -5 1 5
1 -8 1 5
1 -12 1 8
1 -11 1 12
2 -11 3 15
x -30 -6
y -30 3
Tangential measured distortion (urn) Bank Bank Bank Bank
1 2 3 4
1 0 -1 0
2 0 0 -1
1 0 -1 - 1
Positions relative to fiducial centre (urn) Principal p o i n t of a u t o c o l l i m a t i o n Principal p o i n t of best s y m m e t r y
Panel
Y __~,._-____ x
I
Fig. 11. Semi-diagonal identification and co-ordinate system, as if looking at emulsion side of negative, i.e., at film plane f r o m lens.
developments of techniques and equipment and in the calibration and adj u s t m e n t o f t h e c a l i b r a t o r . M r . 1%. F i n k is t h e u s u a l s e c o n d r e a d e r o f e v e r y photographic plate and has assisted with maintenance and development of some equipment.
165
REFERENCES Carman, P.D., 1955. Control and interferometric measurement of plate flatness. J. Opt. Soc. Am., 45 (12) 1009--1010. Carman, P.D., 1969. Camera calibration laboratory at N.R.C. Photogramm. Eng., 35 (4): 372--376. Carman, P.D. and Brown, H., 1956. Differences between visual and photographic calibrations of air survey cameras. Photogramm. Eng., 22 (4): 623--626. Carman, P.D. and Brown, H., 1961. Camera calibration in Canada. Can. Surv., 15 (8): 425--439. Field, R.H., 1946. The calibration of air cameras in Canada. Photogramm. Eng., 12 (2): 142--146. Field, R.H., 1949. A device for locating the principal point markers of air cameras. Can. Surv., 10 (1): 17--21. Ziemann, H., 1978. Repeated photographic laboratory calibrations of two rdseau cameras. Photogrammetria, 34:167~-178 (this issue).