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Analytical multicollimator camera calibration
Photogrammetria, 34 (1978) 179--197 179 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
ANALYTICAL MULTICOLLIMATOR CAMERA CALIBRATION
WILLIAM P. TAYMAN U.S. Geological Survey, Reston, Va. 22092 (U.S.A.) (Received September 5, 1977; accepted January 3, 1978)
ABSTRACT Tayman, W.P.,1978. Analytical multicollim~or~ameracalibration. Photo~ammetria, 34:179--197. Calibration with the U.S. Geological Survey multicollimator determines the calibrated focal length, the point of symmetry, the radial distortion referred to the point of symmetry, and the asymmetric characteristics of the camera lens. For this project, two cameras were calibrated, a Zeiss RMK A 15/23 and a Wild RC 8. Four test exposures were made with each camera. Results are tabulated for each exposure and averaged for each set. Copies of the standard USGS calibration reports are included.
INTRODUCTION A n a l y t i c a l m u l t i c o l l i m a t o r c a l i b r a t i o n was p e r f o r m e d b y t h e U.S. G e o l o g i c a l S u r v e y ( U S G S ) o n t w o aerial m a p p i n g c a m e r a s e q u i p p e d w i t h r6seaus. S t a n d a r d c a l i b r a t i o n p r o c e d u r e , including t w o a d d i t i o n a l t e s t e x p o s u r e s , f o l l o w e d t h e m e t h o d d e s c r i b e d b y Bean ( 1 9 6 2 ) and T a y m a n ( 1 9 7 4 ) . T h e c a m e r a u n d e r t e s t is placed o n t h e c a l i b r a t o r in a m o u n t similar t o t h a t u s e d in a survey aircraft. Its p o s i t i o n is a d j u s t e d t o p u t t h e f r o n t n o d a l p o i n t o f t h e lens at t h e p o i n t o f i n t e r s e c t i o n o f t h e c o l l i m a t o r axes. T h e focal p l a n e f r a m e is m a d e p e r p e n d i c u l a r t o t h e axis o f t h e c e n t r a l c o l l i m a t o r b y use o f an a u t o c o l l i m a t i n g t e l e s c o p e a n d t h e p r e c i s i o n grid (r6seau) p l a t e in f r o n t o f t h e i m a g e plane; n o r m a l l y a plane-parallel p l a t e is p l a c e d o n t h e focal plane. T h e c a m e r a is r o t a t e d in a z i m u t h so t h a t t h e images o f t h e c o l l i m a t o r targets lie along t h e diagonals o f t h e f o c a l p l a n e f r a m e . T w o p h o t o g r a p h i c t e s t plates are e x p o s e d - - t h e first w i t h t h e c a m e r a d a t a strip t o t h e l e f t side o f t h e t e s t s t a n d ( p o s i t i o n A), a n d t h e s e c o n d w i t h t h e c a m e r a r o t a t e d 180 ° f r o m A ( p o s i t i o n B). F o r t h e special t e s t t w o a d d i t i o n a l e x p o s u r e s w e r e m a d e w i t h t h e c a m e r a r o t a t e d - 1 5 ° and +15 ° f r o m p o s i t i o n A. T h e e x p o s e d plates w e r e p r o c e s s e d at 20 ° + 0 . 3 ° C as follows: Develop: 3 m i n , K o d a k D-19 Rinse: 20 s, K o d a k S t o p B a t h Fix: 5 min, Kodak Rapid Fixer
180
Wash: 20 min, running water Rinse: 20 s, K odak Phot o- Fl o 200 Dry: R o o m t em pe r at ur e , horizontal position. All target images on each negative were measured with a Mann m o n o c o m parator t y p e 4 2 2 F calibrated t o 1 pro. The results were averaged and included in this r ep o r t (tests 1 and 2). This m e t h o d is a modification of the one described by T a y m a n (1974). The modification consists primarily of the additional test exposures with the camera r o t a t e d - 1 5 ° and +15 ° . Fig. 1 indicates the positions of the collimator targets as t hey appear in the N
+15
! ° ,
--15
liso!
%
k 30 °
\
/
x
./.. y../
+15
/
/ ~-
4+
--15
~ ', 4--
°
/
/
-F
x/./ \.~x ~ .
4/ V-
°
"7-
20 r ~ S ' '
+
,,.~ \
~/-~,
/
~60
Jr
\
~.
x
N
~c
X
×
,,\
°
\
SS O
I _15
°
/
~
×
×
,-15o
,//"
_is o
-----~_~.
.k \
x
\
x
Fig. 1. I m a g e p o s i t i o n s o f t h e c o l l i m a t o r t a r g e t s w i t h c a m e r a in n o r m a l o r i e n t a t i o n ( N ) and rotated -15 ° and +15 ° .
field when the camera is r o t a t e d - 1 5 ° and +15 ° from the normal location marked N. The USGS calibration includes a least-squares solution t hat determines the calibrated focal length, the poi nt of s y m m e t r y , the radial distortion referred to the p o i n t of s y m m e t r y , and the asymmetric characteristics of the camera lens. A separate solution is obtained for each exposure. The final results are the average o f the i n d e p e n d e n t solutions. C om put at i ons are described by Karren (1968). F o r a co mp lete evaluation of the camera system, the calibration also includes tests o f stereomodel flatness and film resolution for wide-angle and super-wide-
181
angle cameras. After the glass test plates have been exposed, the magazine is loaded with Kodak Double-X Aerographic film, t y p e 2405. At least twelve exposures are made in t w o or m o r e positions, with the camera r o t a t e d 90 ° , 180 ° , or 270 ° on the test stand. T he camera u n d e r test is operated normally for the film exposures. Small defects in the camera, such as variation from planarity of the film platen, irregularity of the film flattening system (vacuum), distortions, centering of the camera lens, and nonparallelism and wedge angle of the filter surfaces all c o n t r i b u t e to the results of the stereomodel flatness evaluation. The collimators are so arranged that a pair of diapositives made from films exposed in the calibrator can be placed in a plotting instrument and model flatness measured by stereoscopic observations at points in the overlap area, as shown in Fig. 2. However, in the current m e t h o d the selected points are
+
+
e
+ 44+
+
÷ +
Fig. 2. Image positions used in stereomodel test.
measured with a m o n o c o m p a r a t o r , and the model is produced analytically. The target images, w he n projected stereoscopically, determine a nearly plane model whose base/height ratio is a f unc t i on o f the effective principal distance o f the negatives. The base/height ratio is approxi m at el y 0.6 for wide-angle (90°-field) and 1.0 for super-wide-angle (120°-field) photographs. From the c o m p a r a t o r measurements t w o sets of stereomodel d e f o r m a t i o n data are c o m p u t e d and averaged for the calibration report. Angular positions of the collimator used for cameras with a 90 ° field are shown in Fig. 3; additional collimators are used for cameras with a 120 ° field. Any lack of stability in the test film can be d e t e c t e d and evaluated by rotating one or b o t h diapositives of a pair 90 °, 180 °, or 270 ° . Because the f o u r quadrants of each negative are symmetrical, m a n y combinations are possible. F o r example, the X-direction can be interchanged for Y, or one pair can be used in the X-direction and one in the Y-direction, or a cont i nuous strip o f stereopairs can be tested.
182
+
+
+ 35 ~
-4-
-I30 °
.+-
+
22 ° 45' 38"
+
+ 15°
+
+
7° 30'
+
+
+
+
0°
4-
+
+
+
+ }6 ° ~-~ 26"
+
4-
+
26°20
+
' 28"
+
-43 0 ° 4~0' 5 4 "
Fig. 3. Target images r e c o r d e d by camera w i t h 90 ° field. S t e r e o m o d e l test p o s i t i o n s are circled.
TEST 1 Zeiss RMK AR 15/23 No. 21197 Cam era: Zeiss Pleogon AR No. 98222 Lens: Test aperture: f/5.6 January 31, 1975 Date o f test exposures: 0.25-in microflat glass Base: Kodak Spectroscopic V-F Emulsion: 109 per set of plates N u m b e r o f target images measured: 152.058 + 0.002 m m Calibrated focal length Tables I--IV give the m e a n distortion for each plate and the standard error based on the plate residuals. These values are useful for comparing the quality o f the plate measurements when m o r e than one plate is made for the same camera. Table V gives the mean values for the f ou r sets. Table VI gives lens-distortion cor r ect i on values at 1-mm intervals.
183
TABLE I C a m e r a in A P o s i t i o n Field angle (deg)
Radial distance (mm)
Mean distortion (tLm)
Standard deviation (tLm)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 1(}6.5 127.6
-12 -7 -5 2 2 4
3 4 2 1 2 1
D i s t o r t i o n range lowest (um)
highest (um)
-15 -11 -7 1 0 2
-9 -3 -4 3 4 5
S t a n d a r d deviation o f t h e x - c o o r d i n a t e = 0 . 0 0 5 0 6 S t a n d a r d deviation o f t h e y - c o o r d i n a t e = 0 . 0 0 5 0 6 S t a n d a r d d e v i a t i o n o f t h e calibrated focal length = 0 . 0 0 1 7 0 S t a n d a r d deviation o f o m e g a ( m i n ) = 0 . 0 9 9 3 8 S t a n d a r d deviation o f phi ( m i n ) = 0 . 0 9 9 3 8 S t a n d a r d deviation o f k a p p a ( m i n ) = 0 . 0 3 8 5 0 S t a n d a r d d e v i a t i o n o f u n i t w e i g h t (based o n plate residuals) = 0 . 0 0 5 3 6 Calibrated focal length = 152.056 m m
T A B L E II C a m e r a in B p o s i t i o n Field angle (deg)
Radial distance (mm)
Mean distortion (ttm)
Standard deviation (t~m)
D i s t o r t i o n range lowest (pm)
highest (pm)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 106.5 127.6
-12 -7 -5 3 2 3
4 2 3 1 2 2
-17 -9 -8 1 -1 0
--8 -6 -3 4 3 6
Standard deviation of the x-coordinate = 0.00500 Standard deviation of the y-coordinate = 0.00500 S t a n d a r d deviation o f t h e calibrated focal length = 0.00168 S t a n d a r d deviation o f o m e g a ( m i n ) = 0.09827 S t a n d a r d d e v i a t i o n o f phi ( m i n ) = 0.09827 S t a n d a r d d e v i a t i o n o f k a p p a (rain) = 0.03807 S t a n d a r d d e v i a t i o n o f u n i t w e i g h t ( b a s e d o n plate residuals) = 0 . 0 0 5 3 0 Calibrated focal l e n g t h = 152.059 m m
184
T A B L E III C a m e r a in A p o s i t i o n - 1 5 ° Field angle (deg)
7.5 15 22.5 30 35 40
Radial distance (mm)
20.0 40.7 63.8 87.8 106.5 127.6
Mean distortion (um)
-11 -6 -4 2 0 4
Standard deviation (um)
4 3 2 3 2 3
D i s t o r t i o n range lowest
highest
(~m)
(~m)
16 -11 -6 -1 -1 1
-8 -3 -3 6 4 7
Standard deviation of the x-coordinate = 0.00459 Standard deviation of the y-coordinate = 0.00459 S t a n d a r d d e v i a t i o n o f t h e c a l i b r a t e d focal l e n g t h = 0 . 0 0 1 5 4 Standard deviation of omega (min) = 0.09013 Standard deviation of phi (min) = 0.09013 S t a n d a r d d e v i a t i o n o f k a p p a (rain) = 0 . 0 3 4 9 2 S t a n d a r d d e v i a t i o n o f u n i t w e i g h t ( b a s e d o n plate r e s i d u a l s ) = 0 . 0 0 4 8 6 C a l i b r a t e d focal l e n g t h = 1 5 2 . 0 5 9 m m
T A B L E IV C a m e r a in A p o s i t i o n +15 ° Field angle (deg)
7.5 15 22.5 30 35 40
Radial distance (mm)
20.0 40.7 63.8 87.8 106.5 127.6
Mean distortion (um)
-11 -8 -5 3 0 4
Standard deviation (urn)
3 3 1 1 1 1
Distortion range lowest
highest
(~m)
(~m)
-15 -11 -6 2 -1 3
-8 -5 -5 4 1 6
Standard deviation of the x-coordinate = 0.00489 Standard deviation of the y-coordinate = 0.00489 S t a n d a r d d e v i a t i o n o f t h e c a l i b r a t e d focal l e n g t h = 0 . 0 0 1 6 4 Standard deviation of omega (min) = 0.09596 Standard deviation of phi (min) = 0.09597 Standard deviation of kappa (min) = 0.03718 Standard deviation of unit weight (based on plate residuals) = 0.00518 C a l i b r a t e d focal l e n g t h = 1 5 2 . 0 5 8 m m
185
TABLE V Mean values for the four sets Field angle (deg)
Radial distance (ram)
Mean distortion (pm)
Standard deviation (~m)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 106.5 127.6
-12 -7 -5 2 1 4
1 1 0 0 1 1
Calibrated focal length = 152.058 mm
TABLE VI M e a n r a d i a l - d i s t o r t i o n c o r r e c t i o n v a l u e s (in pro) at l - r a m intervals f r o m axis t o 1 5 0 m m o f f axis Intervals
(ram) 1--14 15--28 29--42 43--56 57--70 71--84 85--98 99--112 113--126 127--140 141--150
1. 7. 10. 9. 7. 3. O. --3. -4. --3. 2.
1. 7. 10. 9. 7. 3. O. --3. -4. --2. 3.
2. 8. 10. 9. 6. 3. --1. --3. -4. --~. 4.
2. 8. 10. 9. 6. 3. --1. --3. -4. --2. 4.
3. S. 10. 9. 6. 2. --I. --4. -4. --2. 5.
3. S. 10. 8. 6. 2. --I. --4. -4. --I. 5.
4. 9. 10. 8. 5. 2. --2. --4. --4. --i. 6.
4. 9. 10. 8. 5. 2. --2. --4. --4. --i. 7.
5. 9. 10. 8. 5. 1. --2. --4. -4. O. 7.
5. 9. 10. 8. 5. 1. --2. --4. --4. O. 8.
6. 9. 10. S. 4. 1. --2. --4. --3. I.
6. 9. 9. 7. 4. 0. --3. -4. --3. I.
REPORT 1 Camera: Lens: Date of test exposures: Base: Emulsion: N u m b e r of target images measured: Calibrated focal length: F o r f u r t h e r d e t a i l s see t h e s t a n d a r d Calibration.
Zeiss R M K A R 1 5 / 2 3 N o . 2 1 1 9 7 Zeiss P l e o g o n A R N o . 9 8 2 2 2 J a n u a r y 31, 1 9 7 5 0 . 2 5 - i n m i c r o f l a t glass Kodak Spectroscopic V-F 25 p e r p l a t e 152.058 + 0.002 mm U.S. G e o l o g i c a l S u r v e y R e p o r t o f
6. 9. 9. 7. 4. 0. --3, --4, --3. I.
7. 9. 9. 7. 4. 0. --3. --4. --3. 2.
186
Form 9-1780 (rev. C-75)
USGS
United States Department
Report b!o. RT-R/ISP-1
of the Interior
GEOLOGICAL SC-R\'E\' RESTOS,~IRGI~lA 22092
REPORT OF CALIBRATIO~I
October
(
1975
of Aerial Hzpping Camera Zeiss RMK AR 15123 Camera type Zeiss Pleogon AR Lens type 153 ~-mm Nominel focal length
Reference:
Caners serial no. Lens serial no. Maxinu~ zperture Test aperture
21197 90222 f/5.6 f/5.6
Submitted by Conrmiseion I, Image Geometry International So&ty of Photogranrmetry Letter dated July 27, 1973 from Dr. 11. Ziemann
These measurerents wrre nade on Kodak micro flat glass plates, 0.25 inch tl.ick , developer1 iu D-19 at with spectroscopic emulsion type J-F Panchromatic 68°F for 3 minutes with continuo,;s agitation.. These photu;:i-aphicplrtes ixrf exposed on a nulticcllimatcr camer.~ calibrator usir.g a white light 'UUTCI rated et apprOXir,Z,tcIy3500K. I.
Calibrated Tocal Langth:
152.058 mm
This measureraent is considered accurate within II.
0.005 mm
Radial Distortion: D
Field angle (degrees)
ii c
7.5 15 22.5 30
-12 -7 -5 2 2 3
Ym
c
for azimuth axle
0" A-C w
90" A-D iin
-11 -9 -5 1
-13 -9 -3 7
180" B-D -___ !Jm -13 -6 -6 2
270" B-C w -12 -6 -6 7 3 4
The radial distortion is nezsurcd for each ?f 4 radii of the focal plane separated by 90" in azimuth. Tc iainirrizeplotting error due to distortion, a full least-squares solu~ton is ~sstl to determine the calibrated focal length. IJc is the average distortion for a eiven :icld angle. Values of distortion Dc based on the calibrated fecal ier.gtb referred to the calibrated prilxi@ point (point of s)nmetry) are listed for aztmuths O', 90", X0", and 270'. The radial distortion i:: given in i-dcromctrcs ani indicates the radial displocr?ment of the image froa its ideal position for the calibrated Focal l.rn:th. ir positive value indicates a disp1pcener.t aiuy frown the center of the tield. These measurements rre considered accurate within _5 pm.
187
II].
Resolving
F_ield angle: Radial lines Tangential lines
power i~ cycles/mm 0° ii~ 113
Area-weighted
7.5 °
15 °
22.5 =
30 =
113 80
95 57
57 57
28 67
average 35 ° 28 48
resolution
48.9
40 = 34 24
The resolving power is obtained by photographing a series of test bars and examining the resulting image with appropriate magnification to find the spatial frequency of th~ finest pattern in which the bars can be counted with reasonable confidence. The series of patterns has spatial frequencies from 5 to 113 cycles/mm in a geometric series having a ratio of the 4th root ol 2. Radial lines are parallel to a radius from the center of the field, and tangential lines are perpendicular to a radius. IV.
Filter Parallelism
The two surfaces of the B No. 14480, D No. 15497, and KL No. 15438 filters accompanying this camera are within ten seconds of being parallel. The B filter was used for the calibration.
V.
Shutte r Calibration Indicated
(Not Applicable) shutter speed Effective shutter speed
Efficienc~
The effective shutter speeds were determined with the lens at aperture f/ The method is considered accurate ~,ithin 3%. The technique used is Methed described in American National Standard PH3.48-1972. VI.
I
Ma~a zine Platen
The platen mounted in FK 24/120 film magazine No. does not depart from a true plane by mor~ than 13 ~m (0.0005
110026 in).
( ~ a _ o f 4_ )
188
VII.
l’rincipa.1
Indicated Indicated Principal Calibrated
Pajut _.~ _
and-__Fiducial
1,’
c
1 (F”)
8
Coordinates
Positions of all points are referenced to the principal point of autocollimation as origin. The diagram indicates the orientation 01 the reference points when the camera is viewed from the back, or a cqntact positive with the emulsion up. The direction-of-flirht fiducial marker or data strjp is to ;he left.
\
4 (270’)
rrinciral point, corner fiducials principal gUi:lt, r.jdside fiducials poinr nf au: 0~01 limnt ion J,rincipni pQint (point of syweL.ry) Fiducial
-100.028 100.006 -100.020 100.003 -113.026 113.002 -0.005 -0.009
8
Corner Lines Midside J.iues Corner
Distances
Y coordinate -0.026 -0.024 0.0 0.001
Ydrks I. 2 3 4 5 6
VIII.
X coordinate -0.006 mm -0.004 0.0 0.041
--.BetKeen
Fiducial
rmn
-100.044 99.988 99.993 -100.044 -0.020 -0.028 112.993 113.045
!.lnrks
fiducials (diagonals) 282.890 mm 3-4 l-2 joil?ing these markers intersect
282.884 w .~t an angle of
89”
59’
55”
fiducials 5-6 226.028 m joining these narkers
226.038 mm at an angle of
89”
59’
56”
fiducisls ( erimcler) l-3 200. 6 37 mm l-4 200.031 mm
The method
of measuring
these
7-8 intersect 2-3 2-4 distances
200.026 200.032 is
nrm nrm considered
accurate
within
~INU.
mn
189
~TEREOMODEL FLATNESS TEST AND FILM RESOLUTION
Camera No. Focal length
21197
Lens No. 98222
152.058~
Base-helght ratio
Magazine No.
110026
Maximum angle of field tested
0.6
Accuracy of determination
3
40° 5 um
-1_2_
-7
> Ii
-i
18
Direction of flight
1
-i0
-2
Stereomodel Test point array (values in micrometres)
The values show** on the diogr~m are the average departures from flatness (at negative scale) for two computer-simulated stereomodels based on comparator measurements on contact glass (Kodak micro flat) diapositives made from Kodak 2405 film exposures. Resolvin~ Po~;er, in e y c l e ~ / ~ FLIm: Type 2405 F___leld angle: Radial lines Ta___n~ential lines
0° 48 48
Area-weighted average resolution
7.5 °
15 °
22.5 °
30 °
35 °
40 40
40 34
28 28
24 28
24 28
27.7
40 ° 24 20
William P. Tay~an / Branch of Research and Design Topographic Division (~of~)
190
TEST 2 Camera: Wild RC8 R No. 107 Lens: Wild Universal-Aviogon UAg R 1 0 Test aperture: f/5.6 Date of test exposures: F e b r u a r y 3, 1 9 7 5 Base: 0 . 2 5 - i n m i c r o f l a t glass Emulsion: Kodak Spectroscopic V-F Number of target images measured: 109 per set of plates Calibrated focal length: 1 5 2 . 1 4 8 -+ 0 . 0 0 2 m m T a b l e s V I I - - X give t h e m e a n d i s t o r t i o n f o r e a c h p l a t e a n d t h e s t a n d a r d e r r o r b a s e d o n t h e p l a t e r e s i d u a l s . T h e s e v a l u e s are u s e f u l f o r c o m p a r i n g t h e q u a l i t y o f t h e p l a t e m e a s u r e m e n t s w h e n m o r e t h a n o n e p l a t e is m a d e f o r t h e s a m e camera. T a b l e X I gives t h e m e a n v a l u e s f o r t h e f o u r sets. T a b l e X I I gives t h e l e n s - d i s t o r t i o n c o r r e c t i o n v a l u e s a t 1 - m m i n t e r v a l s .
TABLE VII Camera in A position Field angle (deg)
Radial distance (mm)
Mean distortion (t~m)
Standard deviation (um)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 106.5 127.6
4 6 4 -i -5 -4
1 2 1 1 2 2
Distortion range lowest (t~m)
highest (urn)
2 5 2 -2 -7 -6
5 8 5 1 -3 -2
Standard deviation of the x-coordinate = 0.00339 Standard deviation of the y-coordinate = 0.00339 Standard deviation of the calibrated focal length = 0.00114 Standard deviation of omega (min) = 0.06648 Standard deviation of phi (min) = 0.06648 Standard deviation of kappa (min) = 0.02575 Standard deviation of unit weight (based on plate residuals) = 0.00359 Calibrated focal length = 152.150 mm
191
T A B L E VIII C a m e r a in B p o s i t i o n Field angle (deg)
7.5 15 22.5 30 35 40
Radial distance (mm)
2O.O 40.7 63.8 87.8 106.5 127.6
Mean distortion (um)
4 6 4 0 -6 -4
Standard deviation (t~m)
1 1 2 2 2 4
Distortion range lowest
highest
(~m)
(~m)
3 6 2 2 -8 -9
5 7 7 2 4 1
Standard deviation of the x-coordinate = 0.00383 Standard deviation of the y-coordinate = 0.00383 S t a n d a r d d e v i a t i o n o f t h e c a l i b r a t e d focal l e n g t h = 0 . 0 0 1 2 9 Standard deviation of omega (min) = 0.07513 Standard deviation of phi (min) = 0.07513 Standard deviation of kappa (min) = 0.02910 Standard deviation of unit weight (based on plate residuals) = 0.00405 C a l i b r a t e d focal l e n g t h = 1 5 2 . 1 5 0 m m
' F A B L E IX C a m e r a in A p o s i t i o n - 1 5 ° Field angle (deg)
Radial distance (ram)
Mean distortion (pm)
Standard deviation (pm)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 106.5 127.6
3 6 3 1 -6 -4
1 2 1 2 3 4
Distortion range lowest (um)
highest (um)
2 4 3 -4 -8 -7
5 7 4 1 -2 0
Standard deviation of the x-coordinate = 0.00340 Standard deviation of the y-coordinate = 0.00340 S t a n d a r d d e v i a t i o n o f t h e c a l i b r a t e d focal l e n g t h = 0 . 0 0 1 1 4 Standard deviation of omega (min) = 0.06664 Standard deviation of phi (min) = 0.06665 Standard deviation of kappa (min) = 0.02581 Standard deviation of unit weight (based on plate residuals) = 0.00360 C a l i b r a t e d focal l e n g t h = 1 5 2 . 1 4 9 m m
192
TABLE X C a m e r a in A p o s i t i o n +15 ° Field angle (deg)
7.5 15 22.5 30 35 40
Radial distance (ram)
20.0 40.7 63.8 87.8 106.5 127.6
Mean distortion (~m)
4 6 4 -1 -6 -2
Standard deviation (urn)
1 1 1 2 3 4
D i s t o r t i o n range lowest (t~m)
highest
2 4 3 -3 -9 -7
4 8 6 0 -3 2
(~m)
S t a n d a r d d e v i a t i o n o f t h e x - c o o r d i n a t e = 0.00337 S t a n d a r d d e v i a t i o n o f t h e y - c o o r d i n a t e = 0.00337 S t a n d a r d deviation o f the c a l i b r a t e d focal l e n g t h = 0.00113 S t a n d a r d deviation o f o m e g a ( m i n ) = 0 . 0 6 6 1 0 S t a n d a r d deviation o f phi ( m i n ) = 0 . 0 6 6 1 0 S t a n d a r d deviation o f k a p p a (rain) = 0 . 0 2 5 6 0 S t a n d a r d deviation o f u n i t w e i g h t (based on plate residuals) = 0.00357 Calibrated focal length = 1 5 2 . 1 4 4 m m
T A B L E XI Mean values for t h e f o u r sets Field angle (deg)
Radial distance (mm)
Mean distortion (ttm)
Standard deviation (~m)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 106.5 127.6
4 6 4 -1 -6 -3
0 0 0 0 0 1
Calibrated focal l e n g t h = 152.148 m m
193
TABLE XH Mean radial-distortion correction values (in/~m) at l-mm intervals from axis to 150 mm off axis Intervals (mrn)
1--14 15--28 29---42 43--56
O. --4. --6. --6.
--I. --5. --6. --5.
--I. --5. --6. --5.
--I. --5. --6. --5.
--2. --5. -6, --5,
--2. --5. --6. --5.
--2. --5. --6. --5.
--3. --5. --6. --5.
--3. --5. -6. --5.
--3. --6. --6. --5.
--3. --6. --6. -4.
--4. --6. --6. -4.
--4. -6. -6. --4.
--4. -6. --6. --4.
57--70
--4.
--4.
-4.
--3.
--3,
--3.
--3.
--3.
--3.
--2.
--2.
--2.
--2.
--2.
71--84 85--98 99--112 113--126 127--140 141--150
-2 I. 3. 4. 4. 2.
--1. I. 3. 4. 4. 1.
--1. I. 3. 4. 4. 1.
--1. 2. 4. 4. 4. 1.
--1. 2, 4. 5. 4, 1,
--1. 2. 4. 5. 4. 0.
O. 2. 4. 4. 3. 0.
O. 2. 4. 4. 3. 0.
O. 2. 4. 4. 3. --1.
O. 3. 4. 4. 3. --1.
O. 3. 4. 4. 3.
1. 3. 4. 4. 2.
I. 3. 4. 4. 2.
1. 3. 4. 4, 2.
REPORT 2
Camera: Lens: Date of test exposures: Base: Emulsion: Number of target images measured: Calibrated focal length: For further details see the standard Calibration.
Wild RC8 R No. 107 Wild Universal-Aviogon UAg R10 February 3, 1975 0.25-in microflat glass Kodak Spectroscopic V-F 25 per plate 1 5 2 . 1 5 0 mm + 0.002 mm U.S. Geological Survey Report of
Form 9-1780 ( r e v . ~
USGS Report No. RT-R/ISP-2
United States Department of the Interior GE( )L( )GI CAL SURVEY REST()N, V I R G I N I A 22092
REPORT OF CALIBRATION
October
,
1975
o f Aerial Mapping Camera
Camera type Wild HeerbruKg RC8R Lens type Wild Universal Avio~on__ Nominal focal length 152 ~m
Reference:
Camera serial no. 1QT Lens serial no. UA R R10 Maximum aperture f/5.6 Test aperture f/5.6
Submitted by Commission I, Image Geometry International Society of Photogra~mmetry Letter dated July 27, 1973 from Dr. H. Ziemann
These measurements were made on Kodak micro flat glass plates, 0.25 inch thick with spectroscopic enlulsion type V-F Panchromatic , developed in D-19 at 68°F for 3 minutes with continuous agitation. These photographic plates were
194
exposed on a multicollimator at zpproximately 3SOOK. I.
Calibrated
J-ocal Length:
This measurement II.
camera calibrator using a white light source rated
is considered
152.150 nm, accurate within
0.005 mm
Radial Distortion: --_Dc for azimuth angle
Field angle (degrees) 7.5 15 22.5 30 35 40
9 Ilm
O" A-C w
4 6 4 -1 -6 -4
4 5 3 -2 -a -7
90' A-D Urn
180' B-D w
4 6 6 1 -5 -2
270° B-C !Jm
2 7 3 -2 -7 -4
4 8 3 1 -4 -1
The radial distortion is measured for each of 4 radji of the focal plane separated by 90' in azimuth. To mir.inize plotting error due to distortion, a full least-squares solution is used to deternine the calibrated focal ler.gth. Dc is the average distortjon for a given field zn~le. Values of distortion D based cn the calibrated focal lencth referred to the calibrated principal pgint (poiot oi ;yrxetryj arc listed-for azimuths O', 9o", 180°, and 27v: The radial distor:icn is given in microrwtrc~ bnd indicates the radial displacement of the imaye Erorn qts
III.
Resolving pcwer -~-~ in cycles~mm ___
Field angle: Radial lines Tangenriol lines
0” 95 95
7.5'
15" --
95 67
95 57
Area-weighted average resolution 58.2 22.5' 57 57
30' 80 67
35' 67 57
40" 17 40
resolving power is obtained bv photographtng a series of test bars and examining th-_ resnltil,g imngc with approprintc magnification to find the spatial frequency oi the ri;ws~ pattern In which the bars can be counted with reasonabie canfidencc. The series ot patterns has spatial frequencies from 5 to _lA_ cycleslmn~ in a geometric series having a ratio of the 4th root of 2. Radial 1uw.s are pnrnllcl to a radjus from the center of the field, and tsqgdnzial lines are perpendicular to a radius.
The
IV.
Filter Parnllelism
The two surfaces of the 450 Pan No. 1527. and 600 Pan No. 2880 filters accompanying this camera are within ten seconds of being parallel. The 450 filter was used for the calibration.
195
V.
Shutter Calibration (Not Applicable) Indicated shutter speed Effective shutter speed
Efficiency
The effective shutter speeds were determJncd with the lens at aperture f/ The method is considered accurale wlthLn 3%. The technique used is Method I described in American r~atJona] StarLdard P]13.48-1972. Vl.
Magazine Platen
The p l a t e n mou~ted in _ ~ l l l d _ R C 8 . . . . . . .
238
does
in).
not depart
from a t r u e
f t ] m ,n.n~:.,zi~e No. p];m¢, by mort! t h a l l 13 ik,, (O.OOD5
(2
Vll.
of 4 )
Principal Point and Fiducial Coordinates 3 (90 ° )
7 D
(180")
Positions of all points are referenced to the principal point of autocollimatlon as origin. The diagram indicates the orientation of the reference points when the camera is viewed from the back, or a contact positive with the emulsion up. The direction-of-flight fidueial marker or data strip is to the left.
5
1 (0 °)
8
4 (270 =)
Indicated principal point, corner fiducials Indicated principal point, midside fiducials Principal point of autocollimation Calibrated principal point (point of symmetry)
X coordinate 0.008 mm 0.013 0.0 -0.002
Y coordinate 0.022 In 0.021 0.O -0.002
Fiducial Marks -106.108 mm 106.119 -106.108 106.131 -110.107 110.130 0.008 0.017
VIII.
Distances ~etween Fiducial Marks
Corner fiducials (diagonals) 1-2 300.140 mm 3-4 300.146 mm Lines joining these markers intersect at an ang]e of 90 ° 00' 0"
-106.O98 m 106.137 106.135 -106.098 0.019 Q.023 110.137 -110.103
196
Hldside
f ilucIals 5-6 220.237 nm 7-8 220.240 m,,, Lines joining these markers int.crsect nt an angle of 89’ 59’ 55”
Corner fjducinls (pcrjmcter) l-3 212.233 mm 2-3 212.227 ,,,,,, l-4 212.239 mm 2-4 212.235 E,,,, The wcthod of menwring these distancrr; is considcrud
sr~RxMow _-
FLATNESSTEST AND FILM RESOLUTION
Camera No. -~ 107 Focal
Base-height
Lens No.
UAg RlO
152.150 m
length
ratio
nccur~te within --0.005 ,,w,.
Magazine No.
Maximumangle of field
0.6
Accuracy
238
tested
40’
of determination
5 urn
1
8
-
-32
-
9
Direction flight
>
of
5 -12 -
-16
Stereomodel Test point array (values in micrometres)
The values shovm ori the diagram are the average departures from flatness (at negative scale) for two compvlter-simulated stereomodels hased on comparator meacuremeDts on contact S13ss (Sodak micro flat) diapositives made from Kc&k 2405 film exposures. Resolving Power, -.-_ in r&es/mm ----. ‘Type 24L:5 Film: Field
angle:
-_-_-- I)*
Radial l.ines Tallgential lixs
48 48
Area-weighted
average
resolution
7.5O
15O
22.5’
30’
35’
40’
40 40
48 40
40 34
40 34
40 28
17 24
d *;&&. -
33.3
f?zL
William P. Tayman J”““” Branch of Research and Design Topogriphic Divirion
L
197
REFERENCES Bean, R.K., 1962. U.S. Geological Survey camera calibrator. Paper presented at ACSM-ASP Annual Convention, Washington, D.C. Karren, R.J., 1968. Camera calibration by the multicollimator method. Photogramm. Eng., 34 (7): 706--719. Tayman, W.P., 1974. Calibration of lenses and cameras at the USGS. Photogramm. Eng., 40 (11): 1331--1334.
ANALYTICAL MULTICOLLIMATOR CAMERA CALIBRATION
WILLIAM P. TAYMAN U.S. Geological Survey, Reston, Va. 22092 (U.S.A.) (Received September 5, 1977; accepted January 3, 1978)
ABSTRACT Tayman, W.P.,1978. Analytical multicollim~or~ameracalibration. Photo~ammetria, 34:179--197. Calibration with the U.S. Geological Survey multicollimator determines the calibrated focal length, the point of symmetry, the radial distortion referred to the point of symmetry, and the asymmetric characteristics of the camera lens. For this project, two cameras were calibrated, a Zeiss RMK A 15/23 and a Wild RC 8. Four test exposures were made with each camera. Results are tabulated for each exposure and averaged for each set. Copies of the standard USGS calibration reports are included.
INTRODUCTION A n a l y t i c a l m u l t i c o l l i m a t o r c a l i b r a t i o n was p e r f o r m e d b y t h e U.S. G e o l o g i c a l S u r v e y ( U S G S ) o n t w o aerial m a p p i n g c a m e r a s e q u i p p e d w i t h r6seaus. S t a n d a r d c a l i b r a t i o n p r o c e d u r e , including t w o a d d i t i o n a l t e s t e x p o s u r e s , f o l l o w e d t h e m e t h o d d e s c r i b e d b y Bean ( 1 9 6 2 ) and T a y m a n ( 1 9 7 4 ) . T h e c a m e r a u n d e r t e s t is placed o n t h e c a l i b r a t o r in a m o u n t similar t o t h a t u s e d in a survey aircraft. Its p o s i t i o n is a d j u s t e d t o p u t t h e f r o n t n o d a l p o i n t o f t h e lens at t h e p o i n t o f i n t e r s e c t i o n o f t h e c o l l i m a t o r axes. T h e focal p l a n e f r a m e is m a d e p e r p e n d i c u l a r t o t h e axis o f t h e c e n t r a l c o l l i m a t o r b y use o f an a u t o c o l l i m a t i n g t e l e s c o p e a n d t h e p r e c i s i o n grid (r6seau) p l a t e in f r o n t o f t h e i m a g e plane; n o r m a l l y a plane-parallel p l a t e is p l a c e d o n t h e focal plane. T h e c a m e r a is r o t a t e d in a z i m u t h so t h a t t h e images o f t h e c o l l i m a t o r targets lie along t h e diagonals o f t h e f o c a l p l a n e f r a m e . T w o p h o t o g r a p h i c t e s t plates are e x p o s e d - - t h e first w i t h t h e c a m e r a d a t a strip t o t h e l e f t side o f t h e t e s t s t a n d ( p o s i t i o n A), a n d t h e s e c o n d w i t h t h e c a m e r a r o t a t e d 180 ° f r o m A ( p o s i t i o n B). F o r t h e special t e s t t w o a d d i t i o n a l e x p o s u r e s w e r e m a d e w i t h t h e c a m e r a r o t a t e d - 1 5 ° and +15 ° f r o m p o s i t i o n A. T h e e x p o s e d plates w e r e p r o c e s s e d at 20 ° + 0 . 3 ° C as follows: Develop: 3 m i n , K o d a k D-19 Rinse: 20 s, K o d a k S t o p B a t h Fix: 5 min, Kodak Rapid Fixer
180
Wash: 20 min, running water Rinse: 20 s, K odak Phot o- Fl o 200 Dry: R o o m t em pe r at ur e , horizontal position. All target images on each negative were measured with a Mann m o n o c o m parator t y p e 4 2 2 F calibrated t o 1 pro. The results were averaged and included in this r ep o r t (tests 1 and 2). This m e t h o d is a modification of the one described by T a y m a n (1974). The modification consists primarily of the additional test exposures with the camera r o t a t e d - 1 5 ° and +15 ° . Fig. 1 indicates the positions of the collimator targets as t hey appear in the N
+15
! ° ,
--15
liso!
%
k 30 °
\
/
x
./.. y../
+15
/
/ ~-
4+
--15
~ ', 4--
°
/
/
-F
x/./ \.~x ~ .
4/ V-
°
"7-
20 r ~ S ' '
+
,,.~ \
~/-~,
/
~60
Jr
\
~.
x
N
~c
X
×
,,\
°
\
SS O
I _15
°
/
~
×
×
,-15o
,//"
_is o
-----~_~.
.k \
x
\
x
Fig. 1. I m a g e p o s i t i o n s o f t h e c o l l i m a t o r t a r g e t s w i t h c a m e r a in n o r m a l o r i e n t a t i o n ( N ) and rotated -15 ° and +15 ° .
field when the camera is r o t a t e d - 1 5 ° and +15 ° from the normal location marked N. The USGS calibration includes a least-squares solution t hat determines the calibrated focal length, the poi nt of s y m m e t r y , the radial distortion referred to the p o i n t of s y m m e t r y , and the asymmetric characteristics of the camera lens. A separate solution is obtained for each exposure. The final results are the average o f the i n d e p e n d e n t solutions. C om put at i ons are described by Karren (1968). F o r a co mp lete evaluation of the camera system, the calibration also includes tests o f stereomodel flatness and film resolution for wide-angle and super-wide-
181
angle cameras. After the glass test plates have been exposed, the magazine is loaded with Kodak Double-X Aerographic film, t y p e 2405. At least twelve exposures are made in t w o or m o r e positions, with the camera r o t a t e d 90 ° , 180 ° , or 270 ° on the test stand. T he camera u n d e r test is operated normally for the film exposures. Small defects in the camera, such as variation from planarity of the film platen, irregularity of the film flattening system (vacuum), distortions, centering of the camera lens, and nonparallelism and wedge angle of the filter surfaces all c o n t r i b u t e to the results of the stereomodel flatness evaluation. The collimators are so arranged that a pair of diapositives made from films exposed in the calibrator can be placed in a plotting instrument and model flatness measured by stereoscopic observations at points in the overlap area, as shown in Fig. 2. However, in the current m e t h o d the selected points are
+
+
e
+ 44+
+
÷ +
Fig. 2. Image positions used in stereomodel test.
measured with a m o n o c o m p a r a t o r , and the model is produced analytically. The target images, w he n projected stereoscopically, determine a nearly plane model whose base/height ratio is a f unc t i on o f the effective principal distance o f the negatives. The base/height ratio is approxi m at el y 0.6 for wide-angle (90°-field) and 1.0 for super-wide-angle (120°-field) photographs. From the c o m p a r a t o r measurements t w o sets of stereomodel d e f o r m a t i o n data are c o m p u t e d and averaged for the calibration report. Angular positions of the collimator used for cameras with a 90 ° field are shown in Fig. 3; additional collimators are used for cameras with a 120 ° field. Any lack of stability in the test film can be d e t e c t e d and evaluated by rotating one or b o t h diapositives of a pair 90 °, 180 °, or 270 ° . Because the f o u r quadrants of each negative are symmetrical, m a n y combinations are possible. F o r example, the X-direction can be interchanged for Y, or one pair can be used in the X-direction and one in the Y-direction, or a cont i nuous strip o f stereopairs can be tested.
182
+
+
+ 35 ~
-4-
-I30 °
.+-
+
22 ° 45' 38"
+
+ 15°
+
+
7° 30'
+
+
+
+
0°
4-
+
+
+
+ }6 ° ~-~ 26"
+
4-
+
26°20
+
' 28"
+
-43 0 ° 4~0' 5 4 "
Fig. 3. Target images r e c o r d e d by camera w i t h 90 ° field. S t e r e o m o d e l test p o s i t i o n s are circled.
TEST 1 Zeiss RMK AR 15/23 No. 21197 Cam era: Zeiss Pleogon AR No. 98222 Lens: Test aperture: f/5.6 January 31, 1975 Date o f test exposures: 0.25-in microflat glass Base: Kodak Spectroscopic V-F Emulsion: 109 per set of plates N u m b e r o f target images measured: 152.058 + 0.002 m m Calibrated focal length Tables I--IV give the m e a n distortion for each plate and the standard error based on the plate residuals. These values are useful for comparing the quality o f the plate measurements when m o r e than one plate is made for the same camera. Table V gives the mean values for the f ou r sets. Table VI gives lens-distortion cor r ect i on values at 1-mm intervals.
183
TABLE I C a m e r a in A P o s i t i o n Field angle (deg)
Radial distance (mm)
Mean distortion (tLm)
Standard deviation (tLm)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 1(}6.5 127.6
-12 -7 -5 2 2 4
3 4 2 1 2 1
D i s t o r t i o n range lowest (um)
highest (um)
-15 -11 -7 1 0 2
-9 -3 -4 3 4 5
S t a n d a r d deviation o f t h e x - c o o r d i n a t e = 0 . 0 0 5 0 6 S t a n d a r d deviation o f t h e y - c o o r d i n a t e = 0 . 0 0 5 0 6 S t a n d a r d d e v i a t i o n o f t h e calibrated focal length = 0 . 0 0 1 7 0 S t a n d a r d deviation o f o m e g a ( m i n ) = 0 . 0 9 9 3 8 S t a n d a r d deviation o f phi ( m i n ) = 0 . 0 9 9 3 8 S t a n d a r d deviation o f k a p p a ( m i n ) = 0 . 0 3 8 5 0 S t a n d a r d d e v i a t i o n o f u n i t w e i g h t (based o n plate residuals) = 0 . 0 0 5 3 6 Calibrated focal length = 152.056 m m
T A B L E II C a m e r a in B p o s i t i o n Field angle (deg)
Radial distance (mm)
Mean distortion (ttm)
Standard deviation (t~m)
D i s t o r t i o n range lowest (pm)
highest (pm)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 106.5 127.6
-12 -7 -5 3 2 3
4 2 3 1 2 2
-17 -9 -8 1 -1 0
--8 -6 -3 4 3 6
Standard deviation of the x-coordinate = 0.00500 Standard deviation of the y-coordinate = 0.00500 S t a n d a r d deviation o f t h e calibrated focal length = 0.00168 S t a n d a r d deviation o f o m e g a ( m i n ) = 0.09827 S t a n d a r d d e v i a t i o n o f phi ( m i n ) = 0.09827 S t a n d a r d d e v i a t i o n o f k a p p a (rain) = 0.03807 S t a n d a r d d e v i a t i o n o f u n i t w e i g h t ( b a s e d o n plate residuals) = 0 . 0 0 5 3 0 Calibrated focal l e n g t h = 152.059 m m
184
T A B L E III C a m e r a in A p o s i t i o n - 1 5 ° Field angle (deg)
7.5 15 22.5 30 35 40
Radial distance (mm)
20.0 40.7 63.8 87.8 106.5 127.6
Mean distortion (um)
-11 -6 -4 2 0 4
Standard deviation (um)
4 3 2 3 2 3
D i s t o r t i o n range lowest
highest
(~m)
(~m)
16 -11 -6 -1 -1 1
-8 -3 -3 6 4 7
Standard deviation of the x-coordinate = 0.00459 Standard deviation of the y-coordinate = 0.00459 S t a n d a r d d e v i a t i o n o f t h e c a l i b r a t e d focal l e n g t h = 0 . 0 0 1 5 4 Standard deviation of omega (min) = 0.09013 Standard deviation of phi (min) = 0.09013 S t a n d a r d d e v i a t i o n o f k a p p a (rain) = 0 . 0 3 4 9 2 S t a n d a r d d e v i a t i o n o f u n i t w e i g h t ( b a s e d o n plate r e s i d u a l s ) = 0 . 0 0 4 8 6 C a l i b r a t e d focal l e n g t h = 1 5 2 . 0 5 9 m m
T A B L E IV C a m e r a in A p o s i t i o n +15 ° Field angle (deg)
7.5 15 22.5 30 35 40
Radial distance (mm)
20.0 40.7 63.8 87.8 106.5 127.6
Mean distortion (um)
-11 -8 -5 3 0 4
Standard deviation (urn)
3 3 1 1 1 1
Distortion range lowest
highest
(~m)
(~m)
-15 -11 -6 2 -1 3
-8 -5 -5 4 1 6
Standard deviation of the x-coordinate = 0.00489 Standard deviation of the y-coordinate = 0.00489 S t a n d a r d d e v i a t i o n o f t h e c a l i b r a t e d focal l e n g t h = 0 . 0 0 1 6 4 Standard deviation of omega (min) = 0.09596 Standard deviation of phi (min) = 0.09597 Standard deviation of kappa (min) = 0.03718 Standard deviation of unit weight (based on plate residuals) = 0.00518 C a l i b r a t e d focal l e n g t h = 1 5 2 . 0 5 8 m m
185
TABLE V Mean values for the four sets Field angle (deg)
Radial distance (ram)
Mean distortion (pm)
Standard deviation (~m)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 106.5 127.6
-12 -7 -5 2 1 4
1 1 0 0 1 1
Calibrated focal length = 152.058 mm
TABLE VI M e a n r a d i a l - d i s t o r t i o n c o r r e c t i o n v a l u e s (in pro) at l - r a m intervals f r o m axis t o 1 5 0 m m o f f axis Intervals
(ram) 1--14 15--28 29--42 43--56 57--70 71--84 85--98 99--112 113--126 127--140 141--150
1. 7. 10. 9. 7. 3. O. --3. -4. --3. 2.
1. 7. 10. 9. 7. 3. O. --3. -4. --2. 3.
2. 8. 10. 9. 6. 3. --1. --3. -4. --~. 4.
2. 8. 10. 9. 6. 3. --1. --3. -4. --2. 4.
3. S. 10. 9. 6. 2. --I. --4. -4. --2. 5.
3. S. 10. 8. 6. 2. --I. --4. -4. --I. 5.
4. 9. 10. 8. 5. 2. --2. --4. --4. --i. 6.
4. 9. 10. 8. 5. 2. --2. --4. --4. --i. 7.
5. 9. 10. 8. 5. 1. --2. --4. -4. O. 7.
5. 9. 10. 8. 5. 1. --2. --4. --4. O. 8.
6. 9. 10. S. 4. 1. --2. --4. --3. I.
6. 9. 9. 7. 4. 0. --3. -4. --3. I.
REPORT 1 Camera: Lens: Date of test exposures: Base: Emulsion: N u m b e r of target images measured: Calibrated focal length: F o r f u r t h e r d e t a i l s see t h e s t a n d a r d Calibration.
Zeiss R M K A R 1 5 / 2 3 N o . 2 1 1 9 7 Zeiss P l e o g o n A R N o . 9 8 2 2 2 J a n u a r y 31, 1 9 7 5 0 . 2 5 - i n m i c r o f l a t glass Kodak Spectroscopic V-F 25 p e r p l a t e 152.058 + 0.002 mm U.S. G e o l o g i c a l S u r v e y R e p o r t o f
6. 9. 9. 7. 4. 0. --3, --4, --3. I.
7. 9. 9. 7. 4. 0. --3. --4. --3. 2.
186
Form 9-1780 (rev. C-75)
USGS
United States Department
Report b!o. RT-R/ISP-1
of the Interior
GEOLOGICAL SC-R\'E\' RESTOS,~IRGI~lA 22092
REPORT OF CALIBRATIO~I
October
(
1975
of Aerial Hzpping Camera Zeiss RMK AR 15123 Camera type Zeiss Pleogon AR Lens type 153 ~-mm Nominel focal length
Reference:
Caners serial no. Lens serial no. Maxinu~ zperture Test aperture
21197 90222 f/5.6 f/5.6
Submitted by Conrmiseion I, Image Geometry International So&ty of Photogranrmetry Letter dated July 27, 1973 from Dr. 11. Ziemann
These measurerents wrre nade on Kodak micro flat glass plates, 0.25 inch tl.ick , developer1 iu D-19 at with spectroscopic emulsion type J-F Panchromatic 68°F for 3 minutes with continuo,;s agitation.. These photu;:i-aphicplrtes ixrf exposed on a nulticcllimatcr camer.~ calibrator usir.g a white light 'UUTCI rated et apprOXir,Z,tcIy3500K. I.
Calibrated Tocal Langth:
152.058 mm
This measureraent is considered accurate within II.
0.005 mm
Radial Distortion: D
Field angle (degrees)
ii c
7.5 15 22.5 30
-12 -7 -5 2 2 3
Ym
c
for azimuth axle
0" A-C w
90" A-D iin
-11 -9 -5 1
-13 -9 -3 7
180" B-D -___ !Jm -13 -6 -6 2
270" B-C w -12 -6 -6 7 3 4
The radial distortion is nezsurcd for each ?f 4 radii of the focal plane separated by 90" in azimuth. Tc iainirrizeplotting error due to distortion, a full least-squares solu~ton is ~sstl to determine the calibrated focal length. IJc is the average distortion for a eiven :icld angle. Values of distortion Dc based on the calibrated fecal ier.gtb referred to the calibrated prilxi@ point (point of s)nmetry) are listed for aztmuths O', 90", X0", and 270'. The radial distortion i:: given in i-dcromctrcs ani indicates the radial displocr?ment of the image froa its ideal position for the calibrated Focal l.rn:th. ir positive value indicates a disp1pcener.t aiuy frown the center of the tield. These measurements rre considered accurate within _5 pm.
187
II].
Resolving
F_ield angle: Radial lines Tangential lines
power i~ cycles/mm 0° ii~ 113
Area-weighted
7.5 °
15 °
22.5 =
30 =
113 80
95 57
57 57
28 67
average 35 ° 28 48
resolution
48.9
40 = 34 24
The resolving power is obtained by photographing a series of test bars and examining the resulting image with appropriate magnification to find the spatial frequency of th~ finest pattern in which the bars can be counted with reasonable confidence. The series of patterns has spatial frequencies from 5 to 113 cycles/mm in a geometric series having a ratio of the 4th root ol 2. Radial lines are parallel to a radius from the center of the field, and tangential lines are perpendicular to a radius. IV.
Filter Parallelism
The two surfaces of the B No. 14480, D No. 15497, and KL No. 15438 filters accompanying this camera are within ten seconds of being parallel. The B filter was used for the calibration.
V.
Shutte r Calibration Indicated
(Not Applicable) shutter speed Effective shutter speed
Efficienc~
The effective shutter speeds were determined with the lens at aperture f/ The method is considered accurate ~,ithin 3%. The technique used is Methed described in American National Standard PH3.48-1972. VI.
I
Ma~a zine Platen
The platen mounted in FK 24/120 film magazine No. does not depart from a true plane by mor~ than 13 ~m (0.0005
110026 in).
( ~ a _ o f 4_ )
188
VII.
l’rincipa.1
Indicated Indicated Principal Calibrated
Pajut _.~ _
and-__Fiducial
1,’
c
1 (F”)
8
Coordinates
Positions of all points are referenced to the principal point of autocollimation as origin. The diagram indicates the orientation 01 the reference points when the camera is viewed from the back, or a cqntact positive with the emulsion up. The direction-of-flirht fiducial marker or data strjp is to ;he left.
\
4 (270’)
rrinciral point, corner fiducials principal gUi:lt, r.jdside fiducials poinr nf au: 0~01 limnt ion J,rincipni pQint (point of syweL.ry) Fiducial
-100.028 100.006 -100.020 100.003 -113.026 113.002 -0.005 -0.009
8
Corner Lines Midside J.iues Corner
Distances
Y coordinate -0.026 -0.024 0.0 0.001
Ydrks I. 2 3 4 5 6
VIII.
X coordinate -0.006 mm -0.004 0.0 0.041
--.BetKeen
Fiducial
rmn
-100.044 99.988 99.993 -100.044 -0.020 -0.028 112.993 113.045
!.lnrks
fiducials (diagonals) 282.890 mm 3-4 l-2 joil?ing these markers intersect
282.884 w .~t an angle of
89”
59’
55”
fiducials 5-6 226.028 m joining these narkers
226.038 mm at an angle of
89”
59’
56”
fiducisls ( erimcler) l-3 200. 6 37 mm l-4 200.031 mm
The method
of measuring
these
7-8 intersect 2-3 2-4 distances
200.026 200.032 is
nrm nrm considered
accurate
within
~INU.
mn
189
~TEREOMODEL FLATNESS TEST AND FILM RESOLUTION
Camera No. Focal length
21197
Lens No. 98222
152.058~
Base-helght ratio
Magazine No.
110026
Maximum angle of field tested
0.6
Accuracy of determination
3
40° 5 um
-1_2_
-7
> Ii
-i
18
Direction of flight
1
-i0
-2
Stereomodel Test point array (values in micrometres)
The values show** on the diogr~m are the average departures from flatness (at negative scale) for two computer-simulated stereomodels based on comparator measurements on contact glass (Kodak micro flat) diapositives made from Kodak 2405 film exposures. Resolvin~ Po~;er, in e y c l e ~ / ~ FLIm: Type 2405 F___leld angle: Radial lines Ta___n~ential lines
0° 48 48
Area-weighted average resolution
7.5 °
15 °
22.5 °
30 °
35 °
40 40
40 34
28 28
24 28
24 28
27.7
40 ° 24 20
William P. Tay~an / Branch of Research and Design Topographic Division (~of~)
190
TEST 2 Camera: Wild RC8 R No. 107 Lens: Wild Universal-Aviogon UAg R 1 0 Test aperture: f/5.6 Date of test exposures: F e b r u a r y 3, 1 9 7 5 Base: 0 . 2 5 - i n m i c r o f l a t glass Emulsion: Kodak Spectroscopic V-F Number of target images measured: 109 per set of plates Calibrated focal length: 1 5 2 . 1 4 8 -+ 0 . 0 0 2 m m T a b l e s V I I - - X give t h e m e a n d i s t o r t i o n f o r e a c h p l a t e a n d t h e s t a n d a r d e r r o r b a s e d o n t h e p l a t e r e s i d u a l s . T h e s e v a l u e s are u s e f u l f o r c o m p a r i n g t h e q u a l i t y o f t h e p l a t e m e a s u r e m e n t s w h e n m o r e t h a n o n e p l a t e is m a d e f o r t h e s a m e camera. T a b l e X I gives t h e m e a n v a l u e s f o r t h e f o u r sets. T a b l e X I I gives t h e l e n s - d i s t o r t i o n c o r r e c t i o n v a l u e s a t 1 - m m i n t e r v a l s .
TABLE VII Camera in A position Field angle (deg)
Radial distance (mm)
Mean distortion (t~m)
Standard deviation (um)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 106.5 127.6
4 6 4 -i -5 -4
1 2 1 1 2 2
Distortion range lowest (t~m)
highest (urn)
2 5 2 -2 -7 -6
5 8 5 1 -3 -2
Standard deviation of the x-coordinate = 0.00339 Standard deviation of the y-coordinate = 0.00339 Standard deviation of the calibrated focal length = 0.00114 Standard deviation of omega (min) = 0.06648 Standard deviation of phi (min) = 0.06648 Standard deviation of kappa (min) = 0.02575 Standard deviation of unit weight (based on plate residuals) = 0.00359 Calibrated focal length = 152.150 mm
191
T A B L E VIII C a m e r a in B p o s i t i o n Field angle (deg)
7.5 15 22.5 30 35 40
Radial distance (mm)
2O.O 40.7 63.8 87.8 106.5 127.6
Mean distortion (um)
4 6 4 0 -6 -4
Standard deviation (t~m)
1 1 2 2 2 4
Distortion range lowest
highest
(~m)
(~m)
3 6 2 2 -8 -9
5 7 7 2 4 1
Standard deviation of the x-coordinate = 0.00383 Standard deviation of the y-coordinate = 0.00383 S t a n d a r d d e v i a t i o n o f t h e c a l i b r a t e d focal l e n g t h = 0 . 0 0 1 2 9 Standard deviation of omega (min) = 0.07513 Standard deviation of phi (min) = 0.07513 Standard deviation of kappa (min) = 0.02910 Standard deviation of unit weight (based on plate residuals) = 0.00405 C a l i b r a t e d focal l e n g t h = 1 5 2 . 1 5 0 m m
' F A B L E IX C a m e r a in A p o s i t i o n - 1 5 ° Field angle (deg)
Radial distance (ram)
Mean distortion (pm)
Standard deviation (pm)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 106.5 127.6
3 6 3 1 -6 -4
1 2 1 2 3 4
Distortion range lowest (um)
highest (um)
2 4 3 -4 -8 -7
5 7 4 1 -2 0
Standard deviation of the x-coordinate = 0.00340 Standard deviation of the y-coordinate = 0.00340 S t a n d a r d d e v i a t i o n o f t h e c a l i b r a t e d focal l e n g t h = 0 . 0 0 1 1 4 Standard deviation of omega (min) = 0.06664 Standard deviation of phi (min) = 0.06665 Standard deviation of kappa (min) = 0.02581 Standard deviation of unit weight (based on plate residuals) = 0.00360 C a l i b r a t e d focal l e n g t h = 1 5 2 . 1 4 9 m m
192
TABLE X C a m e r a in A p o s i t i o n +15 ° Field angle (deg)
7.5 15 22.5 30 35 40
Radial distance (ram)
20.0 40.7 63.8 87.8 106.5 127.6
Mean distortion (~m)
4 6 4 -1 -6 -2
Standard deviation (urn)
1 1 1 2 3 4
D i s t o r t i o n range lowest (t~m)
highest
2 4 3 -3 -9 -7
4 8 6 0 -3 2
(~m)
S t a n d a r d d e v i a t i o n o f t h e x - c o o r d i n a t e = 0.00337 S t a n d a r d d e v i a t i o n o f t h e y - c o o r d i n a t e = 0.00337 S t a n d a r d deviation o f the c a l i b r a t e d focal l e n g t h = 0.00113 S t a n d a r d deviation o f o m e g a ( m i n ) = 0 . 0 6 6 1 0 S t a n d a r d deviation o f phi ( m i n ) = 0 . 0 6 6 1 0 S t a n d a r d deviation o f k a p p a (rain) = 0 . 0 2 5 6 0 S t a n d a r d deviation o f u n i t w e i g h t (based on plate residuals) = 0.00357 Calibrated focal length = 1 5 2 . 1 4 4 m m
T A B L E XI Mean values for t h e f o u r sets Field angle (deg)
Radial distance (mm)
Mean distortion (ttm)
Standard deviation (~m)
7.5 15 22.5 30 35 40
20.0 40.7 63.8 87.8 106.5 127.6
4 6 4 -1 -6 -3
0 0 0 0 0 1
Calibrated focal l e n g t h = 152.148 m m
193
TABLE XH Mean radial-distortion correction values (in/~m) at l-mm intervals from axis to 150 mm off axis Intervals (mrn)
1--14 15--28 29---42 43--56
O. --4. --6. --6.
--I. --5. --6. --5.
--I. --5. --6. --5.
--I. --5. --6. --5.
--2. --5. -6, --5,
--2. --5. --6. --5.
--2. --5. --6. --5.
--3. --5. --6. --5.
--3. --5. -6. --5.
--3. --6. --6. --5.
--3. --6. --6. -4.
--4. --6. --6. -4.
--4. -6. -6. --4.
--4. -6. --6. --4.
57--70
--4.
--4.
-4.
--3.
--3,
--3.
--3.
--3.
--3.
--2.
--2.
--2.
--2.
--2.
71--84 85--98 99--112 113--126 127--140 141--150
-2 I. 3. 4. 4. 2.
--1. I. 3. 4. 4. 1.
--1. I. 3. 4. 4. 1.
--1. 2. 4. 4. 4. 1.
--1. 2, 4. 5. 4, 1,
--1. 2. 4. 5. 4. 0.
O. 2. 4. 4. 3. 0.
O. 2. 4. 4. 3. 0.
O. 2. 4. 4. 3. --1.
O. 3. 4. 4. 3. --1.
O. 3. 4. 4. 3.
1. 3. 4. 4. 2.
I. 3. 4. 4. 2.
1. 3. 4. 4, 2.
REPORT 2
Camera: Lens: Date of test exposures: Base: Emulsion: Number of target images measured: Calibrated focal length: For further details see the standard Calibration.
Wild RC8 R No. 107 Wild Universal-Aviogon UAg R10 February 3, 1975 0.25-in microflat glass Kodak Spectroscopic V-F 25 per plate 1 5 2 . 1 5 0 mm + 0.002 mm U.S. Geological Survey Report of
Form 9-1780 ( r e v . ~
USGS Report No. RT-R/ISP-2
United States Department of the Interior GE( )L( )GI CAL SURVEY REST()N, V I R G I N I A 22092
REPORT OF CALIBRATION
October
,
1975
o f Aerial Mapping Camera
Camera type Wild HeerbruKg RC8R Lens type Wild Universal Avio~on__ Nominal focal length 152 ~m
Reference:
Camera serial no. 1QT Lens serial no. UA R R10 Maximum aperture f/5.6 Test aperture f/5.6
Submitted by Commission I, Image Geometry International Society of Photogra~mmetry Letter dated July 27, 1973 from Dr. H. Ziemann
These measurements were made on Kodak micro flat glass plates, 0.25 inch thick with spectroscopic enlulsion type V-F Panchromatic , developed in D-19 at 68°F for 3 minutes with continuous agitation. These photographic plates were
194
exposed on a multicollimator at zpproximately 3SOOK. I.
Calibrated
J-ocal Length:
This measurement II.
camera calibrator using a white light source rated
is considered
152.150 nm, accurate within
0.005 mm
Radial Distortion: --_Dc for azimuth angle
Field angle (degrees) 7.5 15 22.5 30 35 40
9 Ilm
O" A-C w
4 6 4 -1 -6 -4
4 5 3 -2 -a -7
90' A-D Urn
180' B-D w
4 6 6 1 -5 -2
270° B-C !Jm
2 7 3 -2 -7 -4
4 8 3 1 -4 -1
The radial distortion is measured for each of 4 radji of the focal plane separated by 90' in azimuth. To mir.inize plotting error due to distortion, a full least-squares solution is used to deternine the calibrated focal ler.gth. Dc is the average distortjon for a given field zn~le. Values of distortion D based cn the calibrated focal lencth referred to the calibrated principal pgint (poiot oi ;yrxetryj arc listed-for azimuths O', 9o", 180°, and 27v: The radial distor:icn is given in microrwtrc~ bnd indicates the radial displacement of the imaye Erorn qts
III.
Resolving pcwer -~-~ in cycles~mm ___
Field angle: Radial lines Tangenriol lines
0” 95 95
7.5'
15" --
95 67
95 57
Area-weighted average resolution 58.2 22.5' 57 57
30' 80 67
35' 67 57
40" 17 40
resolving power is obtained bv photographtng a series of test bars and examining th-_ resnltil,g imngc with approprintc magnification to find the spatial frequency oi the ri;ws~ pattern In which the bars can be counted with reasonabie canfidencc. The series ot patterns has spatial frequencies from 5 to _lA_ cycleslmn~ in a geometric series having a ratio of the 4th root of 2. Radial 1uw.s are pnrnllcl to a radjus from the center of the field, and tsqgdnzial lines are perpendicular to a radius.
The
IV.
Filter Parnllelism
The two surfaces of the 450 Pan No. 1527. and 600 Pan No. 2880 filters accompanying this camera are within ten seconds of being parallel. The 450 filter was used for the calibration.
195
V.
Shutter Calibration (Not Applicable) Indicated shutter speed Effective shutter speed
Efficiency
The effective shutter speeds were determJncd with the lens at aperture f/ The method is considered accurale wlthLn 3%. The technique used is Method I described in American r~atJona] StarLdard P]13.48-1972. Vl.
Magazine Platen
The p l a t e n mou~ted in _ ~ l l l d _ R C 8 . . . . . . .
238
does
in).
not depart
from a t r u e
f t ] m ,n.n~:.,zi~e No. p];m¢, by mort! t h a l l 13 ik,, (O.OOD5
(2
Vll.
of 4 )
Principal Point and Fiducial Coordinates 3 (90 ° )
7 D
(180")
Positions of all points are referenced to the principal point of autocollimatlon as origin. The diagram indicates the orientation of the reference points when the camera is viewed from the back, or a contact positive with the emulsion up. The direction-of-flight fidueial marker or data strip is to the left.
5
1 (0 °)
8
4 (270 =)
Indicated principal point, corner fiducials Indicated principal point, midside fiducials Principal point of autocollimation Calibrated principal point (point of symmetry)
X coordinate 0.008 mm 0.013 0.0 -0.002
Y coordinate 0.022 In 0.021 0.O -0.002
Fiducial Marks -106.108 mm 106.119 -106.108 106.131 -110.107 110.130 0.008 0.017
VIII.
Distances ~etween Fiducial Marks
Corner fiducials (diagonals) 1-2 300.140 mm 3-4 300.146 mm Lines joining these markers intersect at an ang]e of 90 ° 00' 0"
-106.O98 m 106.137 106.135 -106.098 0.019 Q.023 110.137 -110.103
196
Hldside
f ilucIals 5-6 220.237 nm 7-8 220.240 m,,, Lines joining these markers int.crsect nt an angle of 89’ 59’ 55”
Corner fjducinls (pcrjmcter) l-3 212.233 mm 2-3 212.227 ,,,,,, l-4 212.239 mm 2-4 212.235 E,,,, The wcthod of menwring these distancrr; is considcrud
sr~RxMow _-
FLATNESSTEST AND FILM RESOLUTION
Camera No. -~ 107 Focal
Base-height
Lens No.
UAg RlO
152.150 m
length
ratio
nccur~te within --0.005 ,,w,.
Magazine No.
Maximumangle of field
0.6
Accuracy
238
tested
40’
of determination
5 urn
1
8
-
-32
-
9
Direction flight
>
of
5 -12 -
-16
Stereomodel Test point array (values in micrometres)
The values shovm ori the diagram are the average departures from flatness (at negative scale) for two compvlter-simulated stereomodels hased on comparator meacuremeDts on contact S13ss (Sodak micro flat) diapositives made from Kc&k 2405 film exposures. Resolving Power, -.-_ in r&es/mm ----. ‘Type 24L:5 Film: Field
angle:
-_-_-- I)*
Radial l.ines Tallgential lixs
48 48
Area-weighted
average
resolution
7.5O
15O
22.5’
30’
35’
40’
40 40
48 40
40 34
40 34
40 28
17 24
d *;&&. -
33.3
f?zL
William P. Tayman J”““” Branch of Research and Design Topogriphic Divirion
L
197
REFERENCES Bean, R.K., 1962. U.S. Geological Survey camera calibrator. Paper presented at ACSM-ASP Annual Convention, Washington, D.C. Karren, R.J., 1968. Camera calibration by the multicollimator method. Photogramm. Eng., 34 (7): 706--719. Tayman, W.P., 1974. Calibration of lenses and cameras at the USGS. Photogramm. Eng., 40 (11): 1331--1334.