Abstract

Diffraction grating interferometers, under extended source monochromatic illumination and with appropriate spatial filtering, are seen to be essentially imaging systems, linear in amplitude. By broadening the spectrum of the illumination, the system becomes linear in irradiance.

© 1985 Optical Society of America

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References

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  1. E. Lau, “Beugungserscheinungen an Doppelrastern,” Ann. Phys. 6, 417 (1948).
    [CrossRef]
  2. J. Jahns, A. W. Lohmann, “The Lau Effect: A Diffraction Experiment with Incoherent Illumination,” Opt. Commun. 28, 263 (1979).
    [CrossRef]
  3. R. Sudol, B. J. Thompson, “An Explanation of the Lau Effect Based on Coherence Theory,” Opt. Commun. [ 331, 105 (1979).
    [CrossRef]
  4. R. Sudol, B. J. Thompson, “Lau Effect: Theory and Experiment,” Appl. Opt. 20, 1107 (1981).
    [CrossRef] [PubMed]
  5. F. Gori, “Lau Effect and Coherence Theory,” Opt. Commun. 31, 4 (1979).
    [CrossRef]
  6. K. Patorski, Incoherent Superposition of Multiple Self-Imaging Lau Effect and Moiré Fringe Explanation,” Opt. Acta 30, 745 (1983).
    [CrossRef]
  7. K. Patorski, “Heuristic Explanation of Grating Shearing Inter-ferometry Using Incoherent Illumination,” Opt. Acta 31, 33 (1984).
    [CrossRef]
  8. A. Lohmann, J. Ojeda-Casteñeda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 49, 388 (1984).
    [CrossRef]
  9. F. O. Weinberg, N. B. Wood, “Interferometer Based on Four Diffraction Gratings,” J. Sci. Instrum. 36, 227 (1959).
    [CrossRef]
  10. E. N. Leith, G. J. Swanson, “Achromatic Interferometers for White Light Optical Processing and Holography,” Appl. Opt. 19, 638 (1980).
    [CrossRef] [PubMed]
  11. B. J. Chang, “Grating Based Interferometer,” Ph.D. Thesis, U. Michigan, Ann Arbor (University Microfilms, Ann Arbor, order no. 74-25-170, 1974).
  12. G. J. Swanson, “Partially Coherent Imaging and Interferometry Based on Diffraction Gratings,” Ph.D. Thesis, U. Michigan, Ann Arbor (University Microfilms, Ann Arbor, 1983).

1984

K. Patorski, “Heuristic Explanation of Grating Shearing Inter-ferometry Using Incoherent Illumination,” Opt. Acta 31, 33 (1984).
[CrossRef]

A. Lohmann, J. Ojeda-Casteñeda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 49, 388 (1984).
[CrossRef]

1983

K. Patorski, Incoherent Superposition of Multiple Self-Imaging Lau Effect and Moiré Fringe Explanation,” Opt. Acta 30, 745 (1983).
[CrossRef]

1981

1980

1979

J. Jahns, A. W. Lohmann, “The Lau Effect: A Diffraction Experiment with Incoherent Illumination,” Opt. Commun. 28, 263 (1979).
[CrossRef]

R. Sudol, B. J. Thompson, “An Explanation of the Lau Effect Based on Coherence Theory,” Opt. Commun. [ 331, 105 (1979).
[CrossRef]

F. Gori, “Lau Effect and Coherence Theory,” Opt. Commun. 31, 4 (1979).
[CrossRef]

1959

F. O. Weinberg, N. B. Wood, “Interferometer Based on Four Diffraction Gratings,” J. Sci. Instrum. 36, 227 (1959).
[CrossRef]

1948

E. Lau, “Beugungserscheinungen an Doppelrastern,” Ann. Phys. 6, 417 (1948).
[CrossRef]

Chang, B. J.

B. J. Chang, “Grating Based Interferometer,” Ph.D. Thesis, U. Michigan, Ann Arbor (University Microfilms, Ann Arbor, order no. 74-25-170, 1974).

Gori, F.

F. Gori, “Lau Effect and Coherence Theory,” Opt. Commun. 31, 4 (1979).
[CrossRef]

Jahns, J.

J. Jahns, A. W. Lohmann, “The Lau Effect: A Diffraction Experiment with Incoherent Illumination,” Opt. Commun. 28, 263 (1979).
[CrossRef]

Lau, E.

E. Lau, “Beugungserscheinungen an Doppelrastern,” Ann. Phys. 6, 417 (1948).
[CrossRef]

Leith, E. N.

Lohmann, A.

A. Lohmann, J. Ojeda-Casteñeda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 49, 388 (1984).
[CrossRef]

Lohmann, A. W.

J. Jahns, A. W. Lohmann, “The Lau Effect: A Diffraction Experiment with Incoherent Illumination,” Opt. Commun. 28, 263 (1979).
[CrossRef]

Ojeda-Casteñeda, J.

A. Lohmann, J. Ojeda-Casteñeda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 49, 388 (1984).
[CrossRef]

Patorski, K.

K. Patorski, “Heuristic Explanation of Grating Shearing Inter-ferometry Using Incoherent Illumination,” Opt. Acta 31, 33 (1984).
[CrossRef]

K. Patorski, Incoherent Superposition of Multiple Self-Imaging Lau Effect and Moiré Fringe Explanation,” Opt. Acta 30, 745 (1983).
[CrossRef]

Sicre, E. E.

A. Lohmann, J. Ojeda-Casteñeda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 49, 388 (1984).
[CrossRef]

Sudol, R.

R. Sudol, B. J. Thompson, “Lau Effect: Theory and Experiment,” Appl. Opt. 20, 1107 (1981).
[CrossRef] [PubMed]

R. Sudol, B. J. Thompson, “An Explanation of the Lau Effect Based on Coherence Theory,” Opt. Commun. [ 331, 105 (1979).
[CrossRef]

Swanson, G. J.

E. N. Leith, G. J. Swanson, “Achromatic Interferometers for White Light Optical Processing and Holography,” Appl. Opt. 19, 638 (1980).
[CrossRef] [PubMed]

G. J. Swanson, “Partially Coherent Imaging and Interferometry Based on Diffraction Gratings,” Ph.D. Thesis, U. Michigan, Ann Arbor (University Microfilms, Ann Arbor, 1983).

Thompson, B. J.

R. Sudol, B. J. Thompson, “Lau Effect: Theory and Experiment,” Appl. Opt. 20, 1107 (1981).
[CrossRef] [PubMed]

R. Sudol, B. J. Thompson, “An Explanation of the Lau Effect Based on Coherence Theory,” Opt. Commun. [ 331, 105 (1979).
[CrossRef]

Weinberg, F. O.

F. O. Weinberg, N. B. Wood, “Interferometer Based on Four Diffraction Gratings,” J. Sci. Instrum. 36, 227 (1959).
[CrossRef]

Wood, N. B.

F. O. Weinberg, N. B. Wood, “Interferometer Based on Four Diffraction Gratings,” J. Sci. Instrum. 36, 227 (1959).
[CrossRef]

Ann. Phys.

E. Lau, “Beugungserscheinungen an Doppelrastern,” Ann. Phys. 6, 417 (1948).
[CrossRef]

Appl. Opt.

J. Sci. Instrum.

F. O. Weinberg, N. B. Wood, “Interferometer Based on Four Diffraction Gratings,” J. Sci. Instrum. 36, 227 (1959).
[CrossRef]

Opt. Acta

K. Patorski, Incoherent Superposition of Multiple Self-Imaging Lau Effect and Moiré Fringe Explanation,” Opt. Acta 30, 745 (1983).
[CrossRef]

K. Patorski, “Heuristic Explanation of Grating Shearing Inter-ferometry Using Incoherent Illumination,” Opt. Acta 31, 33 (1984).
[CrossRef]

Opt. Commun.

A. Lohmann, J. Ojeda-Casteñeda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 49, 388 (1984).
[CrossRef]

J. Jahns, A. W. Lohmann, “The Lau Effect: A Diffraction Experiment with Incoherent Illumination,” Opt. Commun. 28, 263 (1979).
[CrossRef]

R. Sudol, B. J. Thompson, “An Explanation of the Lau Effect Based on Coherence Theory,” Opt. Commun. [ 331, 105 (1979).
[CrossRef]

F. Gori, “Lau Effect and Coherence Theory,” Opt. Commun. 31, 4 (1979).
[CrossRef]

Other

B. J. Chang, “Grating Based Interferometer,” Ph.D. Thesis, U. Michigan, Ann Arbor (University Microfilms, Ann Arbor, order no. 74-25-170, 1974).

G. J. Swanson, “Partially Coherent Imaging and Interferometry Based on Diffraction Gratings,” Ph.D. Thesis, U. Michigan, Ann Arbor (University Microfilms, Ann Arbor, 1983).

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Figures (2)

Fig. 1
Fig. 1

Basic two-grating interferometer: S is the broad source; G1 and G2 are gratings; P is the observatioin plane.

Fig. 2
Fig. 2

Grating interferometer illuminated with converging wave focusing just to the right of G2.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

t 1 = n a n exp ( i 2 π n f 1 x ) ,
t 2 = m b m exp ( i 2 π m f 2 x ) .
u p = n m a n b m exp [ i 2 π ( f 0 + n f 1 + m f 2 ) x ] exp [ i π λ z 0 ( n f 1 + f 0 ) 2 ] × exp [ i π λ z 1 ( n f 1 + m f 2 + f 0 ) 2 ] ,
I p = n m n m a n b m a n * b m * exp { i 2 π [ ( n n ) f 1 + ( m m ) f 2 ] x } exp { i 2 π λ [ ( n n ) ( z 0 + z 1 ) f 1 + ( m m ) z 1 f 2 ] f 0 } exp { i π λ [ n 2 n 2 ) z 0 f 1 2 + z 1 ( n f 1 + m f 2 ) 2 z 1 ( n f 1 + m f 2 ) 2 ] } ,
z 1 = z 0 / [ 1 + f 2 f 1 ( m m n n ) ] ,
u p = n a n b n exp ( i 2 π n f 1 x ) exp { i 2 π λ [ ( z 0 + z 1 ) n f 1 2 z 1 n f 1 ] f 0 } × exp [ i π λ ( z 0 n 2 f 1 2 + z 1 m 2 f 1 2 ) ] .
u p = n a n b n exp ( i 2 π n f 1 x ) exp ( i 2 π λ z 1 f 1 2 ) .
u p = n a n b n exp ( i 2 π n f 1 x ) ,
I p = a n a n * b n b n * exp [ i 2 π ( n n ) f 1 x ] × exp { i π λ [ z 1 f 1 2 ( n 2 n 2 ) ] } .
I p = a n a n * b n b n * exp ( i 4 π n f 1 x ) ,
I p = a n 2 b n 2 exp ( i 4 n f 1 x ) .
t I = a n 2 exp ( i 4 π n f 1 x ) .
| t a | 2 = | a n exp ( i 2 π f 1 ) | 2 = k A k exp ( i 2 k f 1 x ) ,

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