Abstract

A novel method is described for sampling images formed with quasimonochromatic light at or near the diffraction limit of the primary imaging system. The high-resolution sampling method uses a binary phase grating placed in the primary image plane. The grating produces multiple images of the entrance pupil that can be spatially filtered to achieve a periodic amplitude modulation in the relayed image. It is shown that the modulation is insensitive to the degree of coherence in the image.

© 1976 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  2. Ron Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Bracewell, Ron

Ron Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Goodman, J. W.

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

Other (2)

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

Ron Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

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Figures (6)

FIG. 1
FIG. 1

Schematic of optical relay system. The entrance pupil P1 of the relay optics coincides with the exit pupil of primary imaging system, such as a telescope or camera objective A phase grating is located in the primary image plane P2 creating multiple images of P1 in P3. The light passes through a second phase filter located in P3 yielding the desired sampled image in P4.

FIG. 2
FIG. 2

Multiple diffracted images of the entrance pupil which are separated in the exit pupil.

FIG. 3
FIG. 3

Grating function for a 25% duty cycle line binary phase grating.

FIG. 4
FIG. 4

Greatly magnified view of a section of a one-dimensional binary phase grating.

FIG. 5
FIG. 5

Fourier transform of the function illustrated in Fig. 3.

FIG. 6
FIG. 6

Greatly magnified view of a section of a two-dimensional binary phase grating.

Equations (22)

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ξ = x / λ f ,
A ( x ; ξ 0 ) = A ( ξ 0 ) e i 2 π ξ 0 x .
I 0 ( x ) = | a ( x ; ξ 0 ) d ξ 0 | 2 time .
g p ( x ) = g ( x ) * comb ( x ) .
a ( x ; ξ 0 ) = A ( ξ 0 ) e i 2 π ξ 0 x [ g ( x ) * comb ( x ) ] .
A ( ξ , ξ 0 ) = A ( ξ 0 ) G ( ξ - ξ 0 ) comb ( ξ - ξ 0 ) .
F ( ξ ) comb ( ξ - ξ 0 ) = F ( ξ - ξ 0 ) comb ( ξ - ξ 0 ) .
G ( ξ ) = G ( ξ ) F ( ξ )
G p ( ξ ) = G p ( ξ ) F ( ξ ) = G ( ξ ) F ( ξ ) comb ( ξ ) .
a ( x ; ξ 0 ) = A ( ξ 0 ) e i 2 π ξ 0 x [ comb ( x ) * g ( x ) ] = A ( ξ 0 ) e i 2 π ξ 0 x [ g p ( x ) ] .
I ( x ) = I 0 ( x ) comb ( x ) * g ( x ) 2 .
d λ ( f - number ) .
g p ( x ) = 2 [ rect ( 4 x ) * comb ( x ) ] - 1 ,
G p ( ξ ) = 1 2 sinc ( ξ / 4 ) comb ( ξ ) - δ ( ξ ) ,
G p ( ξ ) = 1 2 sinc ( ξ / 4 ) comb ( ξ ) .
g p ( x ) = 2 rect ( 4 x ) * comb ( x ) .
M ( x ) = 4 rect ( 4 x ) * comb ( x ) .
g p ( x , y ) = 2 [ rect ( 2 x ) * comb ( x ) ] [ rect ( 2 y ) * comb ( y ) ] - 1 ,
G p ( ξ , η ) = 1 2 sinc ( ξ / 2 ) comb ( ξ ) sinc ( η / 2 ) comb ( η ) - δ ( ξ ) δ ( η )
G p ( ξ , η ) = 1 2 sinc ( ξ / 2 ) comb ( ξ ) sinc ( η / 2 ) comb ( η ) .
g p ( x , y ) = 2 [ rect ( 2 x ) * comb ( x ) ] [ rect ( 2 y ) * comb ( y ) ] .
M ( x , y ) = 4 [ rect ( 2 x ) * comb ( x ) ] [ rect ( 2 y ) * comb ( y ) ] .