Abstract

By using the projection slice theorem, a lensless interferometric imaging process of a two-dimensional object can be achieved by rotating the achromatic grating interferometer about its own optical axis.

© 1987 Optical Society of America

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References

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  1. F. J. Weinberg, N. R. Wood, J. Sci. Instrum. 36, 227 (1959).
    [CrossRef]
  2. E. N. Leith, B. J. Chang, Appl. Opt. 12, 1957 (1973).
    [CrossRef] [PubMed]
  3. B. J. Chang, Opt. Commun. 9, 357 (1973).
    [CrossRef]
  4. B. J. Chang, Ph.D. dissertation, University Microfilms No. 74-25-170 (University of Michigan, Ann Arbor, Mich., 1974).
  5. B. J. Chang, R. Alferness, E. N. Leith, Appl. Opt. 14, 1592 (1975).
    [CrossRef] [PubMed]
  6. Y. S. Cheng, Appl. Opt. 23, 3057 (1984).
    [CrossRef] [PubMed]
  7. E. N. Leith, B. J. Chang, Opt. Commun. 23, 217 (1977).
    [CrossRef]
  8. Y. S. Cheng, E. N. Leith, Appl. Opt. 23, 4029 (1984).
    [CrossRef] [PubMed]
  9. B. J. Chang, J. S. Chang, E. N. Leith, Opt. Lett. 4, 118 (1979).
    [CrossRef] [PubMed]
  10. A. M. Tai, Appl. Opt. 25, 3179 (1986).
    [CrossRef] [PubMed]
  11. Y. S. Cheng, Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1984), p. 183.
  12. A. M. Tai, C. C. Aleksoff, Appl. Opt. 23, 2282 (1984).
    [CrossRef] [PubMed]
  13. M. Hart, U. Bonse, Phys. Today 26(8), 26 (1970).
    [CrossRef]
  14. See, for example, A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), p. 365.

1986 (1)

1984 (3)

1979 (1)

1977 (1)

E. N. Leith, B. J. Chang, Opt. Commun. 23, 217 (1977).
[CrossRef]

1975 (1)

1973 (2)

1970 (1)

M. Hart, U. Bonse, Phys. Today 26(8), 26 (1970).
[CrossRef]

1959 (1)

F. J. Weinberg, N. R. Wood, J. Sci. Instrum. 36, 227 (1959).
[CrossRef]

Aleksoff, C. C.

Alferness, R.

Bonse, U.

M. Hart, U. Bonse, Phys. Today 26(8), 26 (1970).
[CrossRef]

Chang, B. J.

B. J. Chang, J. S. Chang, E. N. Leith, Opt. Lett. 4, 118 (1979).
[CrossRef] [PubMed]

E. N. Leith, B. J. Chang, Opt. Commun. 23, 217 (1977).
[CrossRef]

B. J. Chang, R. Alferness, E. N. Leith, Appl. Opt. 14, 1592 (1975).
[CrossRef] [PubMed]

E. N. Leith, B. J. Chang, Appl. Opt. 12, 1957 (1973).
[CrossRef] [PubMed]

B. J. Chang, Opt. Commun. 9, 357 (1973).
[CrossRef]

B. J. Chang, Ph.D. dissertation, University Microfilms No. 74-25-170 (University of Michigan, Ann Arbor, Mich., 1974).

Chang, J. S.

Cheng, Y. S.

Y. S. Cheng, Appl. Opt. 23, 3057 (1984).
[CrossRef] [PubMed]

Y. S. Cheng, E. N. Leith, Appl. Opt. 23, 4029 (1984).
[CrossRef] [PubMed]

Y. S. Cheng, Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1984), p. 183.

Hart, M.

M. Hart, U. Bonse, Phys. Today 26(8), 26 (1970).
[CrossRef]

Kak, A. C.

See, for example, A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), p. 365.

Leith, E. N.

Rosenfeld, A.

See, for example, A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), p. 365.

Tai, A. M.

Weinberg, F. J.

F. J. Weinberg, N. R. Wood, J. Sci. Instrum. 36, 227 (1959).
[CrossRef]

Wood, N. R.

F. J. Weinberg, N. R. Wood, J. Sci. Instrum. 36, 227 (1959).
[CrossRef]

Appl. Opt. (6)

J. Sci. Instrum. (1)

F. J. Weinberg, N. R. Wood, J. Sci. Instrum. 36, 227 (1959).
[CrossRef]

Opt. Commun. (2)

E. N. Leith, B. J. Chang, Opt. Commun. 23, 217 (1977).
[CrossRef]

B. J. Chang, Opt. Commun. 9, 357 (1973).
[CrossRef]

Opt. Lett. (1)

Phys. Today (1)

M. Hart, U. Bonse, Phys. Today 26(8), 26 (1970).
[CrossRef]

Other (3)

See, for example, A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), p. 365.

B. J. Chang, Ph.D. dissertation, University Microfilms No. 74-25-170 (University of Michigan, Ann Arbor, Mich., 1974).

Y. S. Cheng, Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1984), p. 183.

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Figures (5)

Fig. 1
Fig. 1

Achromatic grating interferometer.

Fig. 2
Fig. 2

Geometry showing the relationship between the xy coordinates and the ξη coordinates. The z axis is in the direction perpendicular to the paper.

Fig. 3
Fig. 3

Four-grating interferometer.

Fig. 4
Fig. 4

Frequency domain.

Fig. 5
Fig. 5

Filling the frequency domain by taking measurements at different angles σ1, σ2, σ3, ….

Equations (11)

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u = exp { - j 2 π [ x sin θ cos ( ϕ - σ ) + y sin θ sin ( ϕ - σ ) ] / λ } ,
I ( x , y ) = 1 + cos { 4 π f 1 [ x - z θ cos ( ϕ - σ ) ] } ,
I ( x , y ) = s ( θ x , θ y ) { 1 + cos [ 4 π f 1 ( x - z θ x ) ] } d θ x d θ y ,
I ( x , y ) = I { 1 + [ S ˜ c ( 2 f 1 z ) 2 + S ˜ s ( 2 f 1 z ) 2 ] 1 / 2 / I cos [ 4 π f 1 x - ψ ( z ) ] } ,
I = s ( θ x ˜ , θ y ) d θ x d θ y , S ˜ c ( 2 f 1 z ) = s ( θ x , θ y ) cos ( 4 π f 1 z θ x ) d θ x d θ y , S ˜ s ( 2 f 1 z ) = s ( θ x , θ y ) sin ( 4 π f 1 z θ x ) d θ x d θ y , ψ ( z ) = S ˜ s ( 2 f 1 z ) / S ˜ c ( 2 f 1 z ) .
I ( x , y ) = s ( θ x , θ y ) [ 1 + cos ( 4 π f 1 z θ x ) ] d θ x d θ y .
I ( x , y ) = s ( θ x , θ y ) [ 1 + sin ( 4 π f 1 z θ x ) ] d θ x d θ y .
S ˜ σ ( w ) = s ( θ x , θ y ) exp ( - j 2 π w θ x ) d θ x d θ y = S ˜ c ( w ) - j S ˜ s ( w ) ,
S ^ ( u , v ) = s ( θ ξ , θ η ) exp [ - j 2 π ( u θ ξ + v θ η ) ] d θ ξ d θ η .
S ^ ( w , σ ) = S ˜ σ ( w ) .
s ( θ ξ , θ η ) = S ^ ( u , v ) exp [ j 2 π ( θ ξ u + θ η v ) ] d u d v .

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