Abstract

Testing of coherent optical data processing systems has shown a need for a method which measures resolution at all points in the image format. The use of multifrequency linear gratings as test objects satisfies this need. Quantitative data may be obtained if care is taken to calibrate and linearize the photographic process. However, the method’s principal application seems to be for qualitative testing. A comparison is made between calculated wavefront aberrations and experimental results obtained using linear gratings.

© 1970 Optical Society of America

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References

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  1. H. H. Hopkins, Proc. Roy. Soc., Ser. A 217, 408 (May1953).
    [Crossref]
  2. D. A. Ansley, C. B. Cykowski, Tech. Rept. RADC-TR-68-52, Rome Air Development Center, Griffiss Air Force Base, New York.
  3. M. Levy, Phot. Sci. Eng. 11, 46 (Jan–Feb. 1967).

1967 (1)

M. Levy, Phot. Sci. Eng. 11, 46 (Jan–Feb. 1967).

1953 (1)

H. H. Hopkins, Proc. Roy. Soc., Ser. A 217, 408 (May1953).
[Crossref]

Ansley, D. A.

D. A. Ansley, C. B. Cykowski, Tech. Rept. RADC-TR-68-52, Rome Air Development Center, Griffiss Air Force Base, New York.

Cykowski, C. B.

D. A. Ansley, C. B. Cykowski, Tech. Rept. RADC-TR-68-52, Rome Air Development Center, Griffiss Air Force Base, New York.

Hopkins, H. H.

H. H. Hopkins, Proc. Roy. Soc., Ser. A 217, 408 (May1953).
[Crossref]

Levy, M.

M. Levy, Phot. Sci. Eng. 11, 46 (Jan–Feb. 1967).

Phot. Sci. Eng. (1)

M. Levy, Phot. Sci. Eng. 11, 46 (Jan–Feb. 1967).

Proc. Roy. Soc. (1)

H. H. Hopkins, Proc. Roy. Soc., Ser. A 217, 408 (May1953).
[Crossref]

Other (1)

D. A. Ansley, C. B. Cykowski, Tech. Rept. RADC-TR-68-52, Rome Air Development Center, Griffiss Air Force Base, New York.

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Figures (9)

Fig. 1
Fig. 1

Optical demodulation schematic. Wave aberration: ϕ0 − [(ϕ+k + ϕk)/2], n = 0, 1, 2.

Fig. 2
Fig. 2

Comparison of grating images (59.5 cpm) before and after demodulation.

Fig. 3
Fig. 3

Comparison response patterns (59.5 cpm) spatially coherent imaging vs noncoherent imaging; same lens system, monochromatic light.

Fig. 4
Fig. 4

Wave aberrations for focus position = 0.00500 in hundredths of wavelength 632.8 mμ (image height = 0″).

Fig. 5
Fig. 5

Lens system used in test.

Fig. 6
Fig. 6

Demodulated images.

Fig. 7
Fig. 7

Calculated response vs image radius for several different spatial frequency gratings.

Fig. 8
Fig. 8

Space bandwidth product.

Fig. 9
Fig. 9

Aberrated response pattern produced by misalignment.

Tables (1)

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Table I Radius of Zero Response Calculated and Experimental

Equations (21)

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T i ( x ) = [ a + b cos k x ] 2 .
T a ( x ) = a + b cos k x .
A ( x ) = a + ( b / 2 ) exp ( i k x ) + ( b / 2 ) exp ( - i k x ) .
A ( x ) = a exp ( i ϕ 0 ) + b 2 exp ( i k x + i ϕ + k ) + b 2 × exp ( - i k x + i ϕ - k )
= a exp ( i ϕ 0 ) + b 2 exp ( i ϕ + k + i ϕ - k 2 ) × [ exp ( i k x + i ϕ + k 2 - i ϕ - k 2 ) + exp ( - i k x - i ϕ + k 2 + i ϕ - k 2 ) ]
= a exp ( i ϕ 0 ) + b [ exp ( i ϕ + k + i ϕ - k 2 ) ] × cos ( k x + ϕ + k 2 - ϕ - k 2 ) .
I ( x ) = A ( x ) 2 ,
I ( x ) = a 2 + 2 a b cos [ ϕ 0 - ( ϕ + k + ϕ - k 2 ) ] × cos [ k x + ( ϕ + k - ϕ - k 2 ) ] + b 2 cos 2 { k x + ( ϕ + k - ϕ - k 2 ) } .
cos 2 {             } = 1 2 + 1 2 cos 2 {             } ,
I ( x ) = a 2 + b 2 2 + 2 a b cos [ ϕ 0 - ( ϕ + k + ϕ - k 2 ) ] × cos [ k x + ( ϕ + k - ϕ - k 2 ) ] + b 2 2 cos 2 [ k x + ( ϕ + k - ϕ - k 2 ) ] .
ϕ 0 - ( ϕ + k + ϕ - k 2 ) = ( n + 1 2 ) π ,             n = 0 , 1 , 2 , .
ϕ 0 - ( ϕ + k + ϕ - k 2 ) = n π ,             n = 0 , 1 , 2 , 3 , ,
Percent C = I ( x ) max - I ( x ) min I ( x ) max + I ( x ) min ,
Percent C = 4 a b cos { ϕ 0 - [ ( ϕ + k + ϕ - k ) / 2 ] } 2 a 2 + 2 b 2 .
cos { ϕ 0 - [ ( ϕ + k + ϕ - k ) / 2 ] } .
ρ = ± n λ f ν 0 ,
ρ = λ f ν 0 , θ = θ ,
T a = a + b I ( x ) ,
I ( x ) = | b a b cos [ ϕ 0 - ( ϕ + k + ϕ - k 2 ) ] × exp ( i k x + i ϕ + k - i ϕ - k 2 ) | 2
I ( x ) = b 2 a 2 b 2 cos 2 [ ϕ 0 - ( ϕ + k + ϕ - k 2 ) ] .
SBP = ν · d ,

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