Abstract

A two-channel incoherent spatial filtering system is generalized by considering two object transparencies, one in each of the two channels. Various special cases result, including two that have previously been described and others not previously given. The system can be either linear in irradiance (the basic incoherent case) or linear in field (the basic coherent case) even though the illumination is incoherent in either case. In particular, we show spatial filtering with the object in one channel and the spatial filter in the other channel.

© 1986 Optical Society of America

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References

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  1. D. Gorlitz, F. Lanzl, “Methods of Zero-Order Noncoherent Filtering,” Opt. Commun. 20, 68 (1977).
    [CrossRef]
  2. A. W. Lohmann, “Incoherent Optical Processing of Complex Data,” Appl. Opt. 16, 261 (1977).
    [CrossRef] [PubMed]
  3. W. T. Rhodes, “Bipolar Pointspread Function Synthesis by Phase Switching,” Appl. Opt. 16, 265 (1977).
    [CrossRef] [PubMed]
  4. A. W. Lohmann, W. T. Rhodes, “Two-Pupil Synthesis of Optical Transfer Functions,” Appl. Opt. 17, 1141 (1978).
    [CrossRef] [PubMed]
  5. W. Stoner, “Edge Enhancement with Incoherent Optics,” Appl. Opt. 16, 1451 (1977).
    [CrossRef] [PubMed]
  6. W. Stoner, “Incoherent Optical Processing via Spatially Offset Pupil Masks,” Appl. Opt. 17, 2454 (1978).
    [CrossRef] [PubMed]
  7. D. Angell, “Incoherent Spatial Filtering with Grating Interferometers,” Appl. Opt. 24, 2903 (1985).
    [CrossRef] [PubMed]
  8. G. D. Collins, “Temporally and Spatially Incoherent Methods for Fourier Transform Holography and Optical Information Processing,” Ph.D. Dissertation, U. Michigan, Ann Arbor (1983); available from University Microfilms, Ann Arbor.
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3, p. 53.

1985

1978

1977

Angell, D.

Collins, G. D.

G. D. Collins, “Temporally and Spatially Incoherent Methods for Fourier Transform Holography and Optical Information Processing,” Ph.D. Dissertation, U. Michigan, Ann Arbor (1983); available from University Microfilms, Ann Arbor.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3, p. 53.

Gorlitz, D.

D. Gorlitz, F. Lanzl, “Methods of Zero-Order Noncoherent Filtering,” Opt. Commun. 20, 68 (1977).
[CrossRef]

Lanzl, F.

D. Gorlitz, F. Lanzl, “Methods of Zero-Order Noncoherent Filtering,” Opt. Commun. 20, 68 (1977).
[CrossRef]

Lohmann, A. W.

Rhodes, W. T.

Stoner, W.

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Figures (4)

Fig. 1
Fig. 1

Interferometer for generalized spatial filtering: S, source; G1, G2, gratings; s1, s2, objects; H1, H2, spatial filters; O, output plane.

Fig. 2
Fig. 2

Edge sharpening with incoherent source.

Fig. 3
Fig. 3

Image of straightedge formed with pinhole spatial filter in conventional one-channel imaging system.

Fig. 4
Fig. 4

Image of straightedge formed with pinhole spatial filter in object beam and no restrictive aperture in other beam.

Equations (13)

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H 1 ( f x ) s 1 ( x ) exp [ j 2 π ( f 0 + f x ) x ] d x ,
u 1 = H 1 ( f x ) { s 1 ( x ) exp [ j 2 π ( f 0 + f x ) x ] d x } × exp ( j 2 π f x x ) d f x .
u 2 = H 2 ( f x ) { s 2 ( x ) exp [ j 2 π ( f 0 + f x ) ] d x } × exp ( j 2 π f x x ) d f x .
u = u 1 exp ( j 2 π f 1 x ) + u 2 exp ( j 2 π f 1 x )
I = | u | 2 d f 0 = | u 1 | 2 d f 0 + | u 2 | 2 d f 0 + exp ( j 4 π f 1 x ) × u 1 u 2 * d f 0 + exp ( j 4 π f 1 x ) u 1 * u 2 d f 0 .
u 1 u 2 * d f 0 = { H 1 ( f x ) { s 1 ( x ) × exp [ j 2 π ( f 0 + f x ) x ] d x } exp ( j 2 π f x x ) d f x } { H 2 * ( f x ) { s 2 * ( x ) × exp [ j 2 π ( f 0 + f x ) x ] d x } exp ( j 2 π f x x ) d f x } d f 0 .
u 1 u 2 * d f 0 = [ H 1 ( f x ) S 1 ( f x + f 0 ) exp ( j 2 π f x x ) d f x ] × [ H 2 * ( f x ) S 2 * ( f x f 0 ) exp ( j 2 π f x x ) d f x ] d f 0 ,
u 1 u 2 * d f 0 = h 1 ( α x ) h 2 * ( β x ) s 1 ( α ) × s 2 * ( β ) exp [ j 2 π f 0 ( α β ) ] d α d β d f .
u 1 u 2 * d f 0 = h 1 ( α x ) h 2 * ( α x ) s 1 ( α ) s 2 * ( α ) d α .
I = u 1 u 2 * d f 0 = h 1 ( α x ) h 2 * ( β x ) | s | 2 d α ,
{ I } = S ( H 1 H 2 ) ,
I = s 1 h 1 .
I = s 1 h 2 * .

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