Abstract

An achromatic method of seeing through a phase-distorting medium, such as a turbulent atmosphere, utilizes a grating interferometer. Measurements are made at sample points throughout the region of fringe formation. A set of nonlinear simultaneous equations is generated and then solved by computer.

© 1981 Optical Society of America

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References

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  1. D. H. Rogstad, “A technique for measuring visibility phase with an optical interferometer in the presence of atmospheric seeing,” Appl. Opt. 7, 585 (1968).
    [CrossRef] [PubMed]
  2. R. C. Jennison, “A phase sensitive interferometer technique for the measurement of the Fourier transform of spatial brightness distributions of small angular extent,” Mon. Not. R. Astron. Soc. 118, 276 (1958).
  3. W. T. Rhodes, J. W. Goodman, “Interferometric technique for recording and restoring images degraded by unknown aberrations,” J. Opt. Soc. Am. 63, 647 (1973).
    [CrossRef]
  4. E. N. Leith, B. J. Chang, “Image formation with an achromatic interferometer,” Opt. Commun. 23, 217 (1977).
    [CrossRef]

1977 (1)

E. N. Leith, B. J. Chang, “Image formation with an achromatic interferometer,” Opt. Commun. 23, 217 (1977).
[CrossRef]

1973 (1)

1968 (1)

1958 (1)

R. C. Jennison, “A phase sensitive interferometer technique for the measurement of the Fourier transform of spatial brightness distributions of small angular extent,” Mon. Not. R. Astron. Soc. 118, 276 (1958).

Chang, B. J.

E. N. Leith, B. J. Chang, “Image formation with an achromatic interferometer,” Opt. Commun. 23, 217 (1977).
[CrossRef]

Goodman, J. W.

Jennison, R. C.

R. C. Jennison, “A phase sensitive interferometer technique for the measurement of the Fourier transform of spatial brightness distributions of small angular extent,” Mon. Not. R. Astron. Soc. 118, 276 (1958).

Leith, E. N.

E. N. Leith, B. J. Chang, “Image formation with an achromatic interferometer,” Opt. Commun. 23, 217 (1977).
[CrossRef]

Rhodes, W. T.

Rogstad, D. H.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Mon. Not. R. Astron. Soc. (1)

R. C. Jennison, “A phase sensitive interferometer technique for the measurement of the Fourier transform of spatial brightness distributions of small angular extent,” Mon. Not. R. Astron. Soc. 118, 276 (1958).

Opt. Commun. (1)

E. N. Leith, B. J. Chang, “Image formation with an achromatic interferometer,” Opt. Commun. 23, 217 (1977).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Basic concept, showing atmospheric disturbance A, interferometer I, and observing plane P. Aperture L is the limiting aperture of the system; it could be, for example, the aperture of a telescope placed in front of the interferometer.

Fig. 2
Fig. 2

Grating interferometer. G1 and G2 are gratings.

Equations (19)

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1 = | n + | 2 + | n | 2 + 2 | n + | | n 1 | cos ( 4 π f 1 x ϕ + + ϕ ) ,
n + = n ( x + z α ) = | n + | exp ( j ϕ + ) , n = n ( x z α ) = | n | exp ( j ϕ ) .
2 Re { n [ x + z ( α + θ ) + 2 θ d ] × n * [ x z ( α θ ) + 2 θ d ] exp j 4 π f 1 x ) } ,
e j 4 π f 1 x { s ( x ) * [ n ( x + z α ) n * ( x z α ) ] } .
s = k = 1 K s k δ ( θ k Δ θ ) .
s = k = 1 K s k δ ( x k Δ x ) ,
e j 4 π f 1 x k = 1 K s k δ ( x k Δ x ) * | n | 2 = e j 4 π f 1 x k = 1 K s k | n ( x k Δ x ) | 2 .
s 1 | n ( m Δ x Δ x ) | 2 = s 1 | a m | 2 ,
s k | n ( m Δ x + k Δ x 2 Δ x ) | 2 = s k | a m + k 1 | 2 .
u 1 = s 1 a 1 a 1 * + s 2 a 2 a 2 * + + s k a k a k * + , u 2 = s 1 a 2 a 2 * + s 2 a 3 a 3 * + + s k a k + 1 a k + 1 * + , u m = s 1 a m a m * + s 2 a m + 1 a m + 1 * + + s k a m + k 1 a m + k 1 * + ,
k = 1 , K , m = 1 , M .
u 12 = s 1 a 1 a 2 * + + s k a k a k + 1 * + , u m 2 = s 1 a m a m + 1 * + + s k a k + m 1 a k + m * + ,
P = ( 3 M + 3 K 4 ) / 2 ( M 1 ) .
P = 3 ( 1 + K / M ) / 2 ,
P M = 3 ( M + K ) / 2 .
P M = N = 3 M 2 + 3 K M 4 M 2 ( M 1 ) .
M min = 1 + K 1 3
P = 3 ( 1 + K 1 3 ) / 2 ,
N = 3 ( 1 + K 1 3 ) 2 / 2 .

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