TARGET RESEARCH: COMPUTER PROGRAM DOCUMENTATION

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Document Number (FOIA) /ESDN (CREST): 
CIA-RDP03-00121R000100010006-9
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RIPPUB
Original Classification: 
K
Document Page Count: 
13
Document Creation Date: 
December 28, 2016
Document Release Date: 
April 18, 2012
Sequence Number: 
6
Case Number: 
Publication Date: 
August 1, 1969
Content Type: 
REPORT
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PDF icon CIA-RDP03-00121R000100010006-9.pdf365.86 KB
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Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 DTN-69-5 COO 14 e- 7 TECHNICAL NOTE TARGET RESEARCH: COMPUTER PROGRAM DOCUMENTATION Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 DTN-69-5 TECHNICAL NOTE TARGET RESEARCH: COMPUTER PROGRAM DOCUMENTATION by ? a - August 1969 Prepared By Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 1 1 1 1 1 1 1 1 SECTION I INTRODUCTION This technical note is divided into two main parts,. each pertaining to target re- search through computer programs. The first part is devoted to the theory and appli- cation of a solution to background error present, in the STFC (system transfer function calculations) program. The program-COMBGEN (Modified Dirac Comb generator) is documented in the second main part of the report. COMBGEN facilitates the genera- tion, of realistic modifigd Dirac Comb traces for a system having a known modulation transfer function (MTF). Results of COMBGEN are input to the STFC program. j 1 1 1 1 I Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 at frequencies of interest. Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 A. THEORY SECTION II SOLUTION TO BACKGROUND ERROR Conceptually, the optical transfer function of a photographic system is given by relating a known ground target, i (x) , to its corresponding image on film, h (x). This relationship is given by where F denofes the Fourier transform operator and f is spatial frequency. Since neither y nor h is available as a continuous function, we estimate T by A T , given by volves a background exposure EB "in order to use Equation (2), we must set I 1x) exp ( -277 ifI Ax ) For convenience, the -functiol~--I (x ).h4s background zero.' Let usedenote, by h' (x) , the image in effective exposure as it is actually measured. Since h'-(x) in- Let us now suppose that an error has been made in the calculation of EB n pose we have estimated E. by EB and A where E is the error which has been made. Let us denote by T the new value of T which is due to this background error. We will show that it is possible to cause Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 1 If we denote by h (x) the image function involving the background error, then T(f) Now, h(lAx )exp(-2nifl-Ax) of y (I Ax) exp (-277 ifl Ax ) J = - M h(x) h'(x)-ER h(..x) - (EU - ~) = h'(x) - ER + E = h'( x + 4( Hence, we may rewrite Equatior (6) as N _ Sf h (I Ax) exp (-277 ifl Ax) + e exp (-277 if! Ax (f) 1 1 1 1 I If we let of y (l Ax) exp (-2 rr ifl x )' C(f) _ y(IAx)exp(-2 we may rewrite Equation (7) as M ~. (h(l 1x)+fI exp(-277' fl Ax) T (f) _ / ` - M ( I Ax) exp (-2n ifl Ax ) V 7) T (f) = A (r)+ (f) if1 A x) , M exp (-277 ifl Ax ). . Moreover, if we let a - 277 f Ax, we may write T(f) = T(f)+((1'li(f)]E' exp(-ila)'~ J M 2M = T (f) + [f;`C (f )]e.xp (- iM a) exp (ila ) J O = T(f)+[c exp(-iMa)/G(f)] 1-exp. [i(2M+1Ia] 1 - exp (i) a Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 T (f)+ [E G(f)] exp(--iM)a - exp[i(M+1)al 1 - exp (Oa T. (f) + [f~'G(f )] Pxp [ -1 (M + % )a 1 -exp [ i. (M + exp (-i a )/2 -, exp (W/2 )a] = T (f) +-[(,' (f)] sin (M + .',2 )a sin '2a 1 1 = T(J)[E-`G(J)] sin[(2M+1)rrfAx] sin (nf Ax) Finally, observe that when f is a multiple of 1 /(2M +.1) Ax , L e , - k (2M+1)Ax we may rewrite Equation (8) as in Ir7r T (f) T (J) + [f'G(J)] 477 (2M+1) (f) . T (f) = A Notice in Equation (9) that 'k is a function of the record length L Where L is given by 1 1 1 1 1 1 I B. APPLICATION Since the error introduced in the Fourier transform of the image due to, an error in calculating the background is a function of the record length, we may virtually elimi- nate this error in the following way. L-- (2M +1)Ax . In the STFC program, Fourier transforms are calculated at multiples of the fun- damental frequency of the target on the ground. This fundamental frequency is 0. 05 lines/ft.. Further, the distance between the Tirst and last bars in the target is 120 feet. Utilizing these facts in Equation (9), we obtain . 0.05 k ft. J ft. where L is the desired record length. Solving Equation (10) for L , eve obtain L k . 0.05 Since it is required that L > 120 , the proper choice for L is L = 140 feet 4 (10) Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 1 Since this value of L represents a one-sixth inerease in the target length, the STFC prografn adjusts the record length of the target, trace by estimating the centers of the first.and last bars (x, , h) . Then the record length is adjusted by defining the left-hand endpoint of the trace, WY , to be M Y = r r - _ ______ ) 12 1 1 1 1 1 I 1 1 I and the right-hand endpoint, L Y , to be It is possible that ,MYC 0 or that LY exceeds the number of points in the trace. Such traces are'rejected by the STFC program. As a final check on the background correction outlined above, the STFC program was run with an iteration on various values for the background exposure. The MTF 'varied significantly with the change in background exposure. A plot of the MTF asso- ciated with each background level is given in Figure 1. Next, the record length cor- rection was inserted and the program rerun. The calculated MTF was almost pre- cisely the same, regardless of the background exposure, demonstrating that the back- ground problem was virtually eriininated. Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 1 I 11 10 20 30 40 50 60 Background Exposure Figure 1. Theoretical MTF and Results of Looping on Background Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 1 SECTION III 1 1 I C OM BGE N PROGRAM DOCUMENTATION The modified Dirac Comb target can be considered as the sum of 31 rectangular unit pulses of the .form w.) ( (1, it', x) , where If we denote the target by T (x) , we may write I 7' (x) _ ~., (a u'1, x) . : = 1 (12) If we denote the impulse response (spread function) of the system by S (x) , then the ' 1 0 image of 7',(x ) , denoted by y (,r), is given by ~~ (x) T (x) * S (x) (14) where the asterisk denotes the convolution operation. The particular spread function selected was S (x) 0.l sech (.177 x) Hence, the MTF of the system, denotedby F (/) , is given by where F (/) IF IS (x)- (/) F IS(x)f (0) F(/), sech(1077 /), is spatial frequency in lines/micron, We may now rewrite Equation (14) as %, I is the center of the pulse and uv is the width. Hence, 5d rt', .r) = 1 for ~~.'2 0 others isE. 9 (x) T (x) * 0.1 sech (0.177 x) .? 1 *0.1 sech(.177x) Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 304800,1 S, foot Further, the Micro-Analyzer sampling rate is simulated in y (.,)by generating: this function at sample spacing of 1x microns: The various values of zr~, ~) .1 sech 1.177 (x-?) du - arctan I exp (- .0577 W,) exp I .177 (a, r) J a and u' for the target on the ground are given 11 (1() ) in Table.I. function y (x) is translated to the actual image of T (x) on film by correcting each and u-, for the scale factor S, :304ti0U fc Ss foot g (n Ax) = 2-'n {arctanIep ( .0577 a , ) exp I .177 '( a, n .'1x) J - - arctan exp (= .05n w,) exp (.1 n (a, - n Ax J 1 } (17 ) Recall that the function 7' (and hence t 'e function y ) was normalized to range from zero to one; i. e. , the background of the target has a value of zero and a bar of the- target has a value of one. Once the function g has been constructed by Equation (17.), the actual exposure levels can be set by redefining g by ..where a is the background exposure and (/3 - a) is the exposure level of a bar of the ? target. In order to convert g from exposure to density, the COMBGEN program uses the film response function Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 1 1 1 1 1 1 1 1 1 1 1 1 I 1 TABLE I. FIELD TARGET SPECIFICATIONS POSITION RELATIVE TO. CENTER -60 ft. . - 57 ft. (; in. -52 ft. 8 in. -47 ft. 6 in. -42 ft. 8 in. -40 ft. -37 ft. 6 in. -32 ft. 8 in. -27 ft. 6 in. - 22 ft. 8 in. -20 ft. -17 ft. 6 in. -12 ft. 8 in. - 7 ft. 6 in. 2 ft. 8 i n. Oft. ? 2 ft. 6 in. .7 ft. 4 i n. 12 ft. 6 in. 17 ft. 4 in. 20 ft. 22 ft. 6 in. 27 ft. 4 ,i n. 32 ft. 6 in., 37 ft. 4 i1a. 40 ft. 42 ft. (i in. 47 ft. 4 in. 52 ft. 6 in. 57 ft. 4 in. 60 ft. 9 WIDTH OF BAR 8 in. 2 in. f; in. 2 in. in. in. 2 in. (; i n. 2 in. 6 i n. 8 in. 2in. 6 i n. 2 in. 6 in. 8 in. 2 in. (; i n. 2 in. f; i n. 8 i n. .~. 2 in. jr). in. 2 in. 6, i n. 8 i n. 2 in. 6 in. 2 in. 6 in. 8 in. Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 ? where h = 0. 29 and x is given in.relative log exposure units., Once y has been converted to density through Equation (19), realistic rain noise ? 1 is added to 9 in the same way as in the general DATGEN program. Finally, the function y is punched on cards. for use with the STFC program. Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9 Declassified in Part - Sanitized Copy Approved for Release 2012/04/18: CIA-RDP03-00121 R000100010006-9