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References

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  1. R. V. L. Hartley, “A More Symmetrical Fourier Analysis Applied to Transmission Problems,” Proc. IRE, 30, 144 (1942).
    [CrossRef]
  2. R. N. Bracewell, “Discrete Hartley Transform,” J. Opt. Soc. Am. 73, 1832 (1983).
    [CrossRef]
  3. R. N. Bracewell, “The Fast Hartley Transform,” Proc. IEEE 72, 1010 (1984).
    [CrossRef]

1984 (1)

R. N. Bracewell, “The Fast Hartley Transform,” Proc. IEEE 72, 1010 (1984).
[CrossRef]

1983 (1)

1942 (1)

R. V. L. Hartley, “A More Symmetrical Fourier Analysis Applied to Transmission Problems,” Proc. IRE, 30, 144 (1942).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, “The Fast Hartley Transform,” Proc. IEEE 72, 1010 (1984).
[CrossRef]

R. N. Bracewell, “Discrete Hartley Transform,” J. Opt. Soc. Am. 73, 1832 (1983).
[CrossRef]

Hartley, R. V. L.

R. V. L. Hartley, “A More Symmetrical Fourier Analysis Applied to Transmission Problems,” Proc. IRE, 30, 144 (1942).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. IEEE (1)

R. N. Bracewell, “The Fast Hartley Transform,” Proc. IEEE 72, 1010 (1984).
[CrossRef]

Proc. IRE (1)

R. V. L. Hartley, “A More Symmetrical Fourier Analysis Applied to Transmission Problems,” Proc. IRE, 30, 144 (1942).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Michelson-type interferometer in which one beam is rotated half a turn by a cube corner and superimposed on itself. Polarizer P, object plane O, lens L, beam splitter B, plane mirror M with quarterwave plate, image plane I, analyzer A.

Equations (6)

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H ( u , υ ) = f ( x , y ) cas [ 2 π ( u x + υ y ) ] dxdy ,
f ( x , y ) = H ( u , υ ) cas [ 2 π ( u x + υ y ) ] dud υ .
2 cos ( x π 4 ) = cos x + sin x = cas x .
H ( u , υ ) = 2 f ( x , y ) cos [ 2 π ( u x + υ y ) π 4 ] dxdy .
H ( u , υ ) = 2 f ( x , y ) ½ { exp [ 2 π i ( u x + υ y ) i π / 4 ] + exp [ 2 π i ( u x + υ y ) + i π / 4 ] } dxdy = 1 2 exp ( i π / 4 ) F ( u , υ ) + 1 2 exp ( i π / 4 ) F ( u , υ ) = exp ( i π / 4 ) 2 [ F ( u , υ + exp ( i π / 2 ) F ( u , υ ) ] .
I out = I in ( x , y ) dxdy + I in ( x , y ) cos [ 4 π ( u x + υ y ) ϕ ] dxdy .

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