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Considerations in the design of an electronic computer for a photogrammetric plotting instrument
97 Considerations in the design of an electronic computer for a photogrammetric plotting instrument by William J. M. MOORE Radio and Electrical Engineering Division National Research Council Ottawa, Canada.
Introduction. In photogrammetric plotting i n s t r u m e n t s the dimensions of the photographed object are obtained by performing measurements on a stereomodel of the object. In the past the stereomodel has been created by using an optical or mechanical projection of two photographs. This has resulted in a r a t h e r inflexible construction and in mechanical arrangements which require a very high degree of precision and care in manufacture. In the new instrument, which has been described in a companion paper [1], it is proposed to use elecv*' tronic computing circuits and electromechanical positioning of the two photographs to achieve the same results t h a t were accomplished by the older type instruments. The introduction of electronic methods is expected to produce an instrument which is /7: more flexible and versatile than its mechanica] counterpart and to make possible the correction of errors which heretofore were considered to be very difficult, if not impossible. The general scheme of the new i n s t r u m e n t is shown in figure 1. It consists of a main carriage upon which is mounted two photo-carriages. An optical system is constructed so as to view corresponding points on the two photo-carriages, and as a consequence, corresponding points on the two photographs mounted thereon. Movement of the main carriage changes the area being viewed, and the relative position of the two photocarriages must be adjusted to provide correct viewing.
Mathematical relationships. The mathematics relating the motions of the photo-carriages to t h a t of the main carriages are given in the following equations. These have been developed in the com~ panion paper [1] and are reproduced here for reference purposes.
AZ+B AX=AX~--f~AZ__B AY=AY
1-
z
q) + z X +- x + 2f tan
AZ + B z f__AZ__B z(Y-Bv)
co +2f tan~ +Bu
where
X 1= 7~
X±
+-/__.AZ__Bz
X±
--f
tan
2
98 Yt = (Y--Bu)
LJ Z + B z + f__AZ__B z (Y--Bu)--f
oo tan~
and A=
Y1 tan o~ - - X 1 tan f ~/1 + tan2~ + tan2eo + Y1 tan eo - - X 1 tan
The quantities X, Y, and Z are the input variables, AZ being the elevation parameter. The quantity f represents the camera focal length, which is constant for any set of photographs. B.~, By, Bz, 7~ and oJ are constants which relate to the attitude and position of the camera a t the time a particular photograph was taken. The quantity Bw is positive for the left hand photo-carriage, and negative for the right hand photo-carriage.
Computing methods. The computer is required to solve the above equations, producing outputs /IX and ~Y for each photo-carriage as continuous functions of the input variables X, Y, and zJZ. The method proposed for this calculation is known as the electronic operational analog method. The name arises from the f a c t t h a t electronic circuits are used in which electrical voltages behave in a m a n n e r analogous to mathematical operations. Electronic computers based on this principle have seen tremendous development in the past ten years, and there are now available, as s t a n d a r d components, operational units of very high quality. The advantage of the a n a l o g approach over the digital is t h a t the solution of the equations is continuous, and thus continuous input functions, such as contour following, can be easily handled. Digital solutions on the other hand are essentially step-by-step, and to obtain the appearance of continuous motion with digital computations would require several complete solutions per second. While such solution times can probably be achieved digitally, computing units t h a t can do so are not as generally available as those required for the analog solution. Rather than discussing how the complete equation is solved by analog means in detail, it is more convenient to show how the individual mathematical operations are achieved. Since the equations are algebraic, these include only addition, subtraction, multiplication and' division: To arrive at the complete solution, it is only necessary to connect the various operational units together in the apRo propriate manner. INPUT OUTPUT The method by which addition and el R ~ e ° subtraction is achieved is shown in e2 R2 figure 2. The circuit consists of a high gain, phase inverting amplifier around which is connected a feedback e I - eg + e z -eg = eg - e o ond eo = -/~eg F! I R2 RO resistor R0, and to which is connected Ro Ro RO ] a number of input resistors, R 1 and , .... h,ch eo -L I+~ I Ro+Ro R 2. If it is assumed t h a t no current is drawn into the i n p u t of the ampliFig. 2 fier (and this is nearly so since in Addition and subtraction the modern amplifier this current is of the order of 10- l o amperes) then by writing the equation for t h e voltage drop in the resistors, a relation for the output voltage in terms of the input voltage can be obtained. F o r large values of amplifier gain - - 100 million is a common figure for this quantity - - the equation resolves into one of s t r a i g h t summation, with some variation due to the values of the input resistors relative to the feedback resistor. Subtraction differs from addition only in t h a t the sign of the input voltage is changed before connecting it to the input resistor, an operation
99 easily accomplished with another circuit of the same type, since in each, a sign changing operation or phase inversion is inherent. The process of multiplication has been realized in many ways, but from the point of view of general purpose computing, two methods have turned out to be most popular. These are the servo multiplier and the electronic time division multiplier. In the servo multiplier, fig. 3 a position servomechanism is used to accurately position the arm of the potentiometer proportional to one of the variables, and, by applying the other variable to the potentiometer winding itself, a voltage proportional to the product is realized at the potentiometer arm. In the time division multiplier, electronic switching circuits are used in such a way that a rectangular alternating waveform is produced in which the amplitude is proportional to one variable and the time a . for one complete cycle is divided between t h e positive -FIOOV
-Y
Y Y>O
~
MULTIPLIER
-p(x
A=
+AY)
-p-X I "I-FY
X
= A
°X
y
I00 -IOOV
+Y
-X Y
Fig. 3 Multiplication
Fig. 4 Divison
and negative half cycles in proportion to the second variable. The average value of this waveform then is proportional to the product. Of the two methods the servo multiplier was for a long time the most popular, and, in fact, the only type in use. However, the preference is now shifting to the time division type, mainly on account of its better accuracy and higher speed. Division is achieved not through any specialized unit but r a t h e r by a combination of a multiplier and amplifier. One such combination, known as the "implicit" method, is shown in figure 4. Feedback which is made proportional to the divisor by the multiplier, is applied around a high gain amplifier. It is evident from the equations that, provided the gain is large and the divisor not too small, a good approximation to division is obtained. An additional type of computing unit is the function generator, which, although not required for the equations as presented, has potential use as a means of introducing improvements in the instrument. Function generators t a k e many forms, as non-linear potentiometers driven by a servo, as diode-switched devices which provide s t r a i g h t line approximations to the function, or as photographic masks scanned by an electron beam on the face of a cathode ray tube. Each will produce a quantity which is a function of a second quantity and in each, the function can be changed with little or no trouble. The complete computer for one of the photo-carriages is shown schematically in figure 5. A similar a r r a n g e m e n t would be required for the other photo-carriage.
Computer requirements. The overriding requirement of the computer for the photogrammetric application is very high accuracy. It has been estimated that for the instrument to be competitive, the photo-carriage s must be positioned with a mean square error of not more t h a n 0.01 millimeters. Since the overall range of the output is about 40 millimeters, this means that extreme care must be taken to minimize errors in not only the computer itself, but also the input and output equipment.
>-
~ -X
s~ecL~
..
WORM D~VIL
$[RVO
HIGH GAW4 O P ( R A T ~ N ~ AMPI~IFII~
@
®
Fig. 5
~/.
~T[~M(T[~
A R [ TO B ( ~ N G [ O ,
o o
101 In the modern computer, g r e a t e f f o r t is made to minimize errors. I n p u t and feedback resistors, wound f r o m resistance wire which is relatively insensitive to t e m p e r a t u r e , are selected to m a t c h closer t h a n 0.01%, and are kept in ovens m a i n t a i n e d a t c o n s t a n t temperature. Stabilizing circuits a r e used w h e r e v e r possible to minimize drift, rates of 0.01% per d a y or less being realized. One of the more serious sources of error arises in the potentiometers which supply input data to the computer. The a c c u r a t e conversion of the X and Y motions of the m a i n c a r r i a g e into voltages are required as continuous linear functions. U n f o r t u n a t e l y , such a function is not realized with linear potentiometers except in the ease where load impedance a s seen f r o m the poten0.15 tiometer a r m is infinite. The f o r m of the o error obtained when the potentiometer is loaded, and the i n p u t resistor of an R RL o.to amplifier in essence constitutes such a ,~ ._~_ =,oo load, is shown in f i g u r e 6. T h i s t y p e of 0.05 error can be g r e a t l y reduced however by purposely non-linearizing the potentiometer or by m a k i n g use of special cir0.2 0.4 0.6 0.8 I.O cuits which in effect p r e s e n t an infinite POTENTIOMETER SETTING impedance to the input. Fig. 6 The o u t p u t positioning servo also Potentiometer loading error p r e s e n t s a source of difficulty in meeting accuracy r e q u i r e m e n t s u n d e r all conditions of use. While it is probably f a i r l y easy to realize a static positioning accuracy which is s u f f i c i e n t for the purpose here, to m a i n t a i n this a c c u r a c y u n d e r t r a c k i n g conditions, such as in contour plotting, is a m u c h more difficult problem. As t r a c k i n g speed is increased, it is n e c e s s a r y to increase servo-amplifier g a i n in proportion if the specified accuracy is to be m a i n t a i n e d and special circuits will be required in the servo-amplifier to a t t a i n s a t i s f a c t o r y stability.
~
m
/
Rt
o/
Present s t a t u s and f u t u r e development. P r e s e n t work on the development is directed toward the problems involved in the i n p u t and o u t p u t equipment. The solution of the equations themselves h a s a l r e a d y been set up on a general purpose computer p r e s e n t l y available in Ottawa, and it would a p p e a r t h a t the accuracy available with p r e s e n t day c o m p u t i n g e q u i p m e n t is of the r i g h t order. L a t e r it is hoped to combine experimental models of the i n p u t and o u t p u t e q u i p m e n t with the general purpose computer to t e s t the accuracy of the complete system. Following construction of a successful prototype i n s t r u m e n t , it is expected t h a t several i m p r o v e m e n t s over p r e s e n t day i n s t r u m e n t s can be made. A p a r t f r o m the ease of m a k i n g a d j u s t m e n t s in focal length and orientation elements it should be possible, by m e a n s of function g e n e r a t o r s , to introduce corrections for such f a c t o r s as lens distortion, atmospheric refraction, e a r t h c u r v a t u r e a n d film shrinkage. Also if a suitable m e a n s of detection other t h a n visual can be found, a u t o m a t i c contouring can be introduced. T h u s the introduction of electronic c o m p u t e r s will, it is hoped, open up a considerable a r e a for f u r t h e r development of p h o t o g r a m m e t r i c plotting i n s t r u m e n t s . References. [1] U. V. Helava, New Principle for P h o t o g r a m m e t r i c Plotters - - companion paper. [2] G. A. Koran and T. M. Korn, Electronic A n a l o g C o m p u t e r s (Book), McGraw-Hill Book C o m p a n y (Second Ed.), 1956. [3] C.L. Johnson, Anolog C o m p u t e r Techniques (Book), McGraw-Hill Book Company, '56. [4] J. Gilbert, Use of T a p s to Conpensate P o t e n t i o m e t e r Loading Errors, Control Eng i n e e r i n g V3 N8, p. 78-82, A u g u s t , 1956.
Introduction. In photogrammetric plotting i n s t r u m e n t s the dimensions of the photographed object are obtained by performing measurements on a stereomodel of the object. In the past the stereomodel has been created by using an optical or mechanical projection of two photographs. This has resulted in a r a t h e r inflexible construction and in mechanical arrangements which require a very high degree of precision and care in manufacture. In the new instrument, which has been described in a companion paper [1], it is proposed to use elecv*' tronic computing circuits and electromechanical positioning of the two photographs to achieve the same results t h a t were accomplished by the older type instruments. The introduction of electronic methods is expected to produce an instrument which is /7: more flexible and versatile than its mechanica] counterpart and to make possible the correction of errors which heretofore were considered to be very difficult, if not impossible. The general scheme of the new i n s t r u m e n t is shown in figure 1. It consists of a main carriage upon which is mounted two photo-carriages. An optical system is constructed so as to view corresponding points on the two photo-carriages, and as a consequence, corresponding points on the two photographs mounted thereon. Movement of the main carriage changes the area being viewed, and the relative position of the two photocarriages must be adjusted to provide correct viewing.
Mathematical relationships. The mathematics relating the motions of the photo-carriages to t h a t of the main carriages are given in the following equations. These have been developed in the com~ panion paper [1] and are reproduced here for reference purposes.
AZ+B AX=AX~--f~AZ__B AY=AY
1-
z
q) + z X +- x + 2f tan
AZ + B z f__AZ__B z(Y-Bv)
co +2f tan~ +Bu
where
X 1= 7~
X±
+-/__.AZ__Bz
X±
--f
tan
2
98 Yt = (Y--Bu)
LJ Z + B z + f__AZ__B z (Y--Bu)--f
oo tan~
and A=
Y1 tan o~ - - X 1 tan f ~/1 + tan2~ + tan2eo + Y1 tan eo - - X 1 tan
The quantities X, Y, and Z are the input variables, AZ being the elevation parameter. The quantity f represents the camera focal length, which is constant for any set of photographs. B.~, By, Bz, 7~ and oJ are constants which relate to the attitude and position of the camera a t the time a particular photograph was taken. The quantity Bw is positive for the left hand photo-carriage, and negative for the right hand photo-carriage.
Computing methods. The computer is required to solve the above equations, producing outputs /IX and ~Y for each photo-carriage as continuous functions of the input variables X, Y, and zJZ. The method proposed for this calculation is known as the electronic operational analog method. The name arises from the f a c t t h a t electronic circuits are used in which electrical voltages behave in a m a n n e r analogous to mathematical operations. Electronic computers based on this principle have seen tremendous development in the past ten years, and there are now available, as s t a n d a r d components, operational units of very high quality. The advantage of the a n a l o g approach over the digital is t h a t the solution of the equations is continuous, and thus continuous input functions, such as contour following, can be easily handled. Digital solutions on the other hand are essentially step-by-step, and to obtain the appearance of continuous motion with digital computations would require several complete solutions per second. While such solution times can probably be achieved digitally, computing units t h a t can do so are not as generally available as those required for the analog solution. Rather than discussing how the complete equation is solved by analog means in detail, it is more convenient to show how the individual mathematical operations are achieved. Since the equations are algebraic, these include only addition, subtraction, multiplication and' division: To arrive at the complete solution, it is only necessary to connect the various operational units together in the apRo propriate manner. INPUT OUTPUT The method by which addition and el R ~ e ° subtraction is achieved is shown in e2 R2 figure 2. The circuit consists of a high gain, phase inverting amplifier around which is connected a feedback e I - eg + e z -eg = eg - e o ond eo = -/~eg F! I R2 RO resistor R0, and to which is connected Ro Ro RO ] a number of input resistors, R 1 and , .... h,ch eo -L I+~ I Ro+Ro R 2. If it is assumed t h a t no current is drawn into the i n p u t of the ampliFig. 2 fier (and this is nearly so since in Addition and subtraction the modern amplifier this current is of the order of 10- l o amperes) then by writing the equation for t h e voltage drop in the resistors, a relation for the output voltage in terms of the input voltage can be obtained. F o r large values of amplifier gain - - 100 million is a common figure for this quantity - - the equation resolves into one of s t r a i g h t summation, with some variation due to the values of the input resistors relative to the feedback resistor. Subtraction differs from addition only in t h a t the sign of the input voltage is changed before connecting it to the input resistor, an operation
99 easily accomplished with another circuit of the same type, since in each, a sign changing operation or phase inversion is inherent. The process of multiplication has been realized in many ways, but from the point of view of general purpose computing, two methods have turned out to be most popular. These are the servo multiplier and the electronic time division multiplier. In the servo multiplier, fig. 3 a position servomechanism is used to accurately position the arm of the potentiometer proportional to one of the variables, and, by applying the other variable to the potentiometer winding itself, a voltage proportional to the product is realized at the potentiometer arm. In the time division multiplier, electronic switching circuits are used in such a way that a rectangular alternating waveform is produced in which the amplitude is proportional to one variable and the time a . for one complete cycle is divided between t h e positive -FIOOV
-Y
Y Y>O
~
MULTIPLIER
-p(x
A=
+AY)
-p-X I "I-FY
X
= A
°X
y
I00 -IOOV
+Y
-X Y
Fig. 3 Multiplication
Fig. 4 Divison
and negative half cycles in proportion to the second variable. The average value of this waveform then is proportional to the product. Of the two methods the servo multiplier was for a long time the most popular, and, in fact, the only type in use. However, the preference is now shifting to the time division type, mainly on account of its better accuracy and higher speed. Division is achieved not through any specialized unit but r a t h e r by a combination of a multiplier and amplifier. One such combination, known as the "implicit" method, is shown in figure 4. Feedback which is made proportional to the divisor by the multiplier, is applied around a high gain amplifier. It is evident from the equations that, provided the gain is large and the divisor not too small, a good approximation to division is obtained. An additional type of computing unit is the function generator, which, although not required for the equations as presented, has potential use as a means of introducing improvements in the instrument. Function generators t a k e many forms, as non-linear potentiometers driven by a servo, as diode-switched devices which provide s t r a i g h t line approximations to the function, or as photographic masks scanned by an electron beam on the face of a cathode ray tube. Each will produce a quantity which is a function of a second quantity and in each, the function can be changed with little or no trouble. The complete computer for one of the photo-carriages is shown schematically in figure 5. A similar a r r a n g e m e n t would be required for the other photo-carriage.
Computer requirements. The overriding requirement of the computer for the photogrammetric application is very high accuracy. It has been estimated that for the instrument to be competitive, the photo-carriage s must be positioned with a mean square error of not more t h a n 0.01 millimeters. Since the overall range of the output is about 40 millimeters, this means that extreme care must be taken to minimize errors in not only the computer itself, but also the input and output equipment.
>-
~ -X
s~ecL~
..
WORM D~VIL
$[RVO
HIGH GAW4 O P ( R A T ~ N ~ AMPI~IFII~
@
®
Fig. 5
~/.
~T[~M(T[~
A R [ TO B ( ~ N G [ O ,
o o
101 In the modern computer, g r e a t e f f o r t is made to minimize errors. I n p u t and feedback resistors, wound f r o m resistance wire which is relatively insensitive to t e m p e r a t u r e , are selected to m a t c h closer t h a n 0.01%, and are kept in ovens m a i n t a i n e d a t c o n s t a n t temperature. Stabilizing circuits a r e used w h e r e v e r possible to minimize drift, rates of 0.01% per d a y or less being realized. One of the more serious sources of error arises in the potentiometers which supply input data to the computer. The a c c u r a t e conversion of the X and Y motions of the m a i n c a r r i a g e into voltages are required as continuous linear functions. U n f o r t u n a t e l y , such a function is not realized with linear potentiometers except in the ease where load impedance a s seen f r o m the poten0.15 tiometer a r m is infinite. The f o r m of the o error obtained when the potentiometer is loaded, and the i n p u t resistor of an R RL o.to amplifier in essence constitutes such a ,~ ._~_ =,oo load, is shown in f i g u r e 6. T h i s t y p e of 0.05 error can be g r e a t l y reduced however by purposely non-linearizing the potentiometer or by m a k i n g use of special cir0.2 0.4 0.6 0.8 I.O cuits which in effect p r e s e n t an infinite POTENTIOMETER SETTING impedance to the input. Fig. 6 The o u t p u t positioning servo also Potentiometer loading error p r e s e n t s a source of difficulty in meeting accuracy r e q u i r e m e n t s u n d e r all conditions of use. While it is probably f a i r l y easy to realize a static positioning accuracy which is s u f f i c i e n t for the purpose here, to m a i n t a i n this a c c u r a c y u n d e r t r a c k i n g conditions, such as in contour plotting, is a m u c h more difficult problem. As t r a c k i n g speed is increased, it is n e c e s s a r y to increase servo-amplifier g a i n in proportion if the specified accuracy is to be m a i n t a i n e d and special circuits will be required in the servo-amplifier to a t t a i n s a t i s f a c t o r y stability.
~
m
/
Rt
o/
Present s t a t u s and f u t u r e development. P r e s e n t work on the development is directed toward the problems involved in the i n p u t and o u t p u t equipment. The solution of the equations themselves h a s a l r e a d y been set up on a general purpose computer p r e s e n t l y available in Ottawa, and it would a p p e a r t h a t the accuracy available with p r e s e n t day c o m p u t i n g e q u i p m e n t is of the r i g h t order. L a t e r it is hoped to combine experimental models of the i n p u t and o u t p u t e q u i p m e n t with the general purpose computer to t e s t the accuracy of the complete system. Following construction of a successful prototype i n s t r u m e n t , it is expected t h a t several i m p r o v e m e n t s over p r e s e n t day i n s t r u m e n t s can be made. A p a r t f r o m the ease of m a k i n g a d j u s t m e n t s in focal length and orientation elements it should be possible, by m e a n s of function g e n e r a t o r s , to introduce corrections for such f a c t o r s as lens distortion, atmospheric refraction, e a r t h c u r v a t u r e a n d film shrinkage. Also if a suitable m e a n s of detection other t h a n visual can be found, a u t o m a t i c contouring can be introduced. T h u s the introduction of electronic c o m p u t e r s will, it is hoped, open up a considerable a r e a for f u r t h e r development of p h o t o g r a m m e t r i c plotting i n s t r u m e n t s . References. [1] U. V. Helava, New Principle for P h o t o g r a m m e t r i c Plotters - - companion paper. [2] G. A. Koran and T. M. Korn, Electronic A n a l o g C o m p u t e r s (Book), McGraw-Hill Book C o m p a n y (Second Ed.), 1956. [3] C.L. Johnson, Anolog C o m p u t e r Techniques (Book), McGraw-Hill Book Company, '56. [4] J. Gilbert, Use of T a p s to Conpensate P o t e n t i o m e t e r Loading Errors, Control Eng i n e e r i n g V3 N8, p. 78-82, A u g u s t , 1956.