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Plotting convergent photographs in instruments with orthogonal observation
138
Plotting Convergent Photographs in Instruments with Orthogonal Observation by W. Lbscher, Heerbrugg, Switzerland. I. General The use of convergent photographs for the establishment of maps and plans by photogrammetric means has gained little practical importance. Nevertheless it occasionally happens t h a t convergent photographs have to be plotted in the extremely precise mechanical plotting instruments. In this connection the erroneous opinion is frequently vented t h a t for fundamental reasons this could only be performed in a makeshift way. In the following expos6 we aim to prove t h a t there a r e no technical difficulties worth mentioning which might prevent the adaptation of a mechanical plotting instrument with orthogonal observation for plotting of convergent photographs. Since the mechanical measuring system permits the plotting of oblique views without difficulties, the problem is limited to adapting the scanning system so as to give the observer continually maximum stereoscopic effect. As one knows, there are a few conditions to be fulfilled in order to produce stereoscopic vision when observing two central perspectives of an object. 1. In the f i r s t instance it is necessary t h a t the ratio base to object distance and to the variations in distances be such t h a t under observation the parallaxes incurring in the field of view do not exceed 70'. With the customary dispositions for taking aerial photographs this condition is usually fulfilled. However this 70' condition sets a limit to the increase of the base ratio by convergent photographs, desirable for reasons of accuracy. This is why some of the dispositions recommended for convergent photographs are practicable only with completely flat terrain bare of any vegetation. 2. The two p a r t images must be orientated in such a m a n n e r that the s t r a i g h t lines of an object which are parallel to the flight base appear parallel to the base of observation. Straight lines which are parallel to the base intersect in the ep~polar center of the convergent picture. Therefore, undcr orthogonal observation of the whole picture the stereoscopic effect is greatly reduced or even impossible. This means that convergent photographs are generally useless for interpretation purposes by observation under mirror stereoscopes. Since, however, in the plotting instruments only small p a r t s of the picture appear at high magnification in the field of view, condition 2 can be fulfilled by an image rotation. 3. Under natural stereoscopic vision the scale of the two images formed on the left and right retina is practically the same in the direction normal to the eye-base. In the case of convergent pictures this scale varies in the direction of the projection of the base. The magnification of the scanning system of a plotting i n s t r u m e n t must, therefore, be altered according to the zone under observation in such a way t h a t the two partial images appear of equal size in the direction perpendicular to the base of observation. Since all plotting instruments permit the optical rotation of the image by means of the Dove prisms, the problem boils down to the creation of a scanning system which permits to vary the magnification continually. This can be attained by means of a pancratic lens system to be built into the scanning system a t a suitable place. For practical purposes it is of course necessary to provide automatic control for image rotation and magnification, so as to maintain continually maximum stereoscopic effect. Due to the angular deformations and the above mentioned differences of scale
139 between the two axial directions in the convergent photographs, the optical model will undergo similar inclinations and deformations as occur in instruments based on the Porro-Koppe system.
II.
Functions. For the design of the automatic control the functions to be performed must be known. The variables must be chosen in such a m a n n e r t h a t on the one hand the function is as simple as possible while on the other hand the facilities already existing in the instrument can be utilized. Fig. 1 shows a photograph tilted by the angle ~ and the corresponding vertical view with same principal distance f in vertical and lateral projection.
i
i
i
Fig. 1 I f we assume t h a t the projection center of the second picture of the stereo pair lies in the x-axis, the image conditions of a s t r a i g h t line s on the ground lying in the y direction are to be investigated with respect to the equalization of the magnification. Using the designations of fig. 1, its length in the oblique picture is :~
s' = s . - -f
. [cos~--
sin ( a - -
q~)]
Z
In the corresponding vertical photograph it is 8 rt
8 •
f Z
The magnification necessary for orthogonal observation is thus s" v=7=
1 cos~--sin (a--~)
By simple transformation one obtains [ !
v = cos~ + sin~.tana
I i
140 The equalization of the magnification is thus found to be a linear function of tan a. The function of the image rotation can easily be determined in the following m a n n e r : If a plane is laid through the point under observation and the base, the image plane is intersected by it along a epipolar ray. The angle y between the epipolar ray and thb image of the base corresponds to the required image rotation. If /? is the angle between epipolar plane and y z plane one obtains in the oblique picture the values given by fig. 2.
-®_ g
Fig. 2 The relation is found without difficulty I
tan 7 = sin99 tan/?
!
Thus the t a n g e n t s of the image rotation and of the angle of the epipolar plane are proportional.
III. Accuracy, The accuracy which is required for controlling the two functions is of paramount importance with regard to the design of the automatic control mechanism. A 14% difference in magnification of two partial views is declared as tolerable in the pertaining literature. This can easily be checked by means of a m i r r o r stereoscope (with 8 X binocular attachment in order to have similar conditions as in a plotting instrument) and a stereopair, one of the two pictures having been enlarged in suitable steps. Detailed experiments, carried out with several observers" have shown t h a t in a normal-sized field of view a 10% difference in magnification does not affect the stereoscopic effect. It can thus safely be assumed t h a t a control mechanism working to within a tolerance of 5% will stand up to practical requirements. In order to determine the accuracy required for controlling the image rotation, stereopairs were orientated ir~ a plotting instrument. The zone surrounding the principal point of one camera was then observed. Now the swing of this camera w a s coarsly changed, whereupon several operators had to t r y to re-establish the optimum stereo-effect by means of the swing. F r o m the series of observations obtained by reading the swing scale a mean uncertainty of the image rotation of ± 1.3g was established. The table (page 141) gives three of these series of observations. F r o m the above there results t h a t a control mechanism for the image rotation, working to ± lg is sufficient. IV. Construction. The construction of the automatic controls m u s t be so conceived as to exclude any influence on the measuring accuracy when adding the control mechanism. Due to the relatively low accuracy required for the control mechanism, this requirement is easy to fulfil. F u r t h e r m o r e the wide tolerances permit of substantial simplifications being made, e.g. the neglect of the base components. Thus the assumptions upon which our calculation of the functions has been based prove to be justified.
141 Table Observer I"
Observer l l
103,50g 104,80 106,04 103,32 105,24 108,40 104,33 102,38 104,05 103,68
105,03u 105,00 103,84 104,54 104,09 103,86 103,05 105,57 105,88 105,00
Observer I I I
101,10g 100,90 102,40 98,60 99,20 101,10 99,70 100,60 101,90 99,10
m~ = --+ 1,Tg
m~ = -+ 0,9g
m r : ± 1,3g
The overall design of the control mechanism depends on the type of plotting instrument. In the case of the A7 autograph, the angle a is formed by a rotation of the guide rod sleeve around its p r i m a r y axis, lying in the y direction. The angle fl can be formed for beth cameras simultaneously by means of the measuring spindles on the base plate according to Y tan/? = ~ The rotation a and fl can be t r a n s m i t t e d either mechanically or electrically to computing gears, which in t u r n will form the two functions and control the pancratic system and the Dove prisms. The p a r a m e t e r ~v could be relayed directly to the computing gear by t r a n s m i t t i n g the movements of the cameras. In practice it will however suffice to set the computing gear to the known angle of convergence before s t a r t i n g work. Since we have to do with linear functions of tangents, the computing gears can be designed along similar principles as in the case of rectifiers, where they are needed in order to fulfil the Scheimpflug conditions. Either mechanical (guide rails of curve cams) or electric devices could be used. This is not the place to go into constructional details. S u m m i n g up it can however be said t h a t plotting i n s t r u m e n t s with orthogonal observation can quite easily be adapted for observing convergent photographs by means Of relatively simple known elements and a reasonable expenditure.
10
Plotting Convergent Photographs in Instruments with Orthogonal Observation by W. Lbscher, Heerbrugg, Switzerland. I. General The use of convergent photographs for the establishment of maps and plans by photogrammetric means has gained little practical importance. Nevertheless it occasionally happens t h a t convergent photographs have to be plotted in the extremely precise mechanical plotting instruments. In this connection the erroneous opinion is frequently vented t h a t for fundamental reasons this could only be performed in a makeshift way. In the following expos6 we aim to prove t h a t there a r e no technical difficulties worth mentioning which might prevent the adaptation of a mechanical plotting instrument with orthogonal observation for plotting of convergent photographs. Since the mechanical measuring system permits the plotting of oblique views without difficulties, the problem is limited to adapting the scanning system so as to give the observer continually maximum stereoscopic effect. As one knows, there are a few conditions to be fulfilled in order to produce stereoscopic vision when observing two central perspectives of an object. 1. In the f i r s t instance it is necessary t h a t the ratio base to object distance and to the variations in distances be such t h a t under observation the parallaxes incurring in the field of view do not exceed 70'. With the customary dispositions for taking aerial photographs this condition is usually fulfilled. However this 70' condition sets a limit to the increase of the base ratio by convergent photographs, desirable for reasons of accuracy. This is why some of the dispositions recommended for convergent photographs are practicable only with completely flat terrain bare of any vegetation. 2. The two p a r t images must be orientated in such a m a n n e r that the s t r a i g h t lines of an object which are parallel to the flight base appear parallel to the base of observation. Straight lines which are parallel to the base intersect in the ep~polar center of the convergent picture. Therefore, undcr orthogonal observation of the whole picture the stereoscopic effect is greatly reduced or even impossible. This means that convergent photographs are generally useless for interpretation purposes by observation under mirror stereoscopes. Since, however, in the plotting instruments only small p a r t s of the picture appear at high magnification in the field of view, condition 2 can be fulfilled by an image rotation. 3. Under natural stereoscopic vision the scale of the two images formed on the left and right retina is practically the same in the direction normal to the eye-base. In the case of convergent pictures this scale varies in the direction of the projection of the base. The magnification of the scanning system of a plotting i n s t r u m e n t must, therefore, be altered according to the zone under observation in such a way t h a t the two partial images appear of equal size in the direction perpendicular to the base of observation. Since all plotting instruments permit the optical rotation of the image by means of the Dove prisms, the problem boils down to the creation of a scanning system which permits to vary the magnification continually. This can be attained by means of a pancratic lens system to be built into the scanning system a t a suitable place. For practical purposes it is of course necessary to provide automatic control for image rotation and magnification, so as to maintain continually maximum stereoscopic effect. Due to the angular deformations and the above mentioned differences of scale
139 between the two axial directions in the convergent photographs, the optical model will undergo similar inclinations and deformations as occur in instruments based on the Porro-Koppe system.
II.
Functions. For the design of the automatic control the functions to be performed must be known. The variables must be chosen in such a m a n n e r t h a t on the one hand the function is as simple as possible while on the other hand the facilities already existing in the instrument can be utilized. Fig. 1 shows a photograph tilted by the angle ~ and the corresponding vertical view with same principal distance f in vertical and lateral projection.
i
i
i
Fig. 1 I f we assume t h a t the projection center of the second picture of the stereo pair lies in the x-axis, the image conditions of a s t r a i g h t line s on the ground lying in the y direction are to be investigated with respect to the equalization of the magnification. Using the designations of fig. 1, its length in the oblique picture is :~
s' = s . - -f
. [cos~--
sin ( a - -
q~)]
Z
In the corresponding vertical photograph it is 8 rt
8 •
f Z
The magnification necessary for orthogonal observation is thus s" v=7=
1 cos~--sin (a--~)
By simple transformation one obtains [ !
v = cos~ + sin~.tana
I i
140 The equalization of the magnification is thus found to be a linear function of tan a. The function of the image rotation can easily be determined in the following m a n n e r : If a plane is laid through the point under observation and the base, the image plane is intersected by it along a epipolar ray. The angle y between the epipolar ray and thb image of the base corresponds to the required image rotation. If /? is the angle between epipolar plane and y z plane one obtains in the oblique picture the values given by fig. 2.
-®_ g
Fig. 2 The relation is found without difficulty I
tan 7 = sin99 tan/?
!
Thus the t a n g e n t s of the image rotation and of the angle of the epipolar plane are proportional.
III. Accuracy, The accuracy which is required for controlling the two functions is of paramount importance with regard to the design of the automatic control mechanism. A 14% difference in magnification of two partial views is declared as tolerable in the pertaining literature. This can easily be checked by means of a m i r r o r stereoscope (with 8 X binocular attachment in order to have similar conditions as in a plotting instrument) and a stereopair, one of the two pictures having been enlarged in suitable steps. Detailed experiments, carried out with several observers" have shown t h a t in a normal-sized field of view a 10% difference in magnification does not affect the stereoscopic effect. It can thus safely be assumed t h a t a control mechanism working to within a tolerance of 5% will stand up to practical requirements. In order to determine the accuracy required for controlling the image rotation, stereopairs were orientated ir~ a plotting instrument. The zone surrounding the principal point of one camera was then observed. Now the swing of this camera w a s coarsly changed, whereupon several operators had to t r y to re-establish the optimum stereo-effect by means of the swing. F r o m the series of observations obtained by reading the swing scale a mean uncertainty of the image rotation of ± 1.3g was established. The table (page 141) gives three of these series of observations. F r o m the above there results t h a t a control mechanism for the image rotation, working to ± lg is sufficient. IV. Construction. The construction of the automatic controls m u s t be so conceived as to exclude any influence on the measuring accuracy when adding the control mechanism. Due to the relatively low accuracy required for the control mechanism, this requirement is easy to fulfil. F u r t h e r m o r e the wide tolerances permit of substantial simplifications being made, e.g. the neglect of the base components. Thus the assumptions upon which our calculation of the functions has been based prove to be justified.
141 Table Observer I"
Observer l l
103,50g 104,80 106,04 103,32 105,24 108,40 104,33 102,38 104,05 103,68
105,03u 105,00 103,84 104,54 104,09 103,86 103,05 105,57 105,88 105,00
Observer I I I
101,10g 100,90 102,40 98,60 99,20 101,10 99,70 100,60 101,90 99,10
m~ = --+ 1,Tg
m~ = -+ 0,9g
m r : ± 1,3g
The overall design of the control mechanism depends on the type of plotting instrument. In the case of the A7 autograph, the angle a is formed by a rotation of the guide rod sleeve around its p r i m a r y axis, lying in the y direction. The angle fl can be formed for beth cameras simultaneously by means of the measuring spindles on the base plate according to Y tan/? = ~ The rotation a and fl can be t r a n s m i t t e d either mechanically or electrically to computing gears, which in t u r n will form the two functions and control the pancratic system and the Dove prisms. The p a r a m e t e r ~v could be relayed directly to the computing gear by t r a n s m i t t i n g the movements of the cameras. In practice it will however suffice to set the computing gear to the known angle of convergence before s t a r t i n g work. Since we have to do with linear functions of tangents, the computing gears can be designed along similar principles as in the case of rectifiers, where they are needed in order to fulfil the Scheimpflug conditions. Either mechanical (guide rails of curve cams) or electric devices could be used. This is not the place to go into constructional details. S u m m i n g up it can however be said t h a t plotting i n s t r u m e n t s with orthogonal observation can quite easily be adapted for observing convergent photographs by means Of relatively simple known elements and a reasonable expenditure.
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