Abstract

An achromatic Fourier transforming system is analyzed in a manner which gives new physical insight. A matched spatial filtering experiment is performed comparing the noise performance of a coherently produced matched filter and one made using broad spectrum light in an achromatic Fourier transforming system. The broad spectrum light is obtained by scanning a dye laser through its tuning range, thereby simulating a polychromatic point source. The system is applied to the construction of low noise holographic optical elements.

© 1985 Optical Society of America

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References

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  1. R. H. Katyl, “Compensating Optical Systems, 3: Achromatic Fourier Transformation,” Appl. Opt. 4, 1255 (1972).
    [CrossRef]
  2. G. D. Collins, “Achromatic Fourier Transform Holography,” Appl. Opt. 20, 3109 (1981).
    [CrossRef] [PubMed]
  3. G. M. Morris, “Diffraction Theory for an Achromatic Fourier Transformation,” Appl. Opt. 20, 2017 (1981).
    [CrossRef] [PubMed]
  4. E. N. Leigh, G. J. Swanson, “Achromatic Interferometers for White Light Optical Processing and Holography,” Appl. Opt. 19, 638 (1980).
    [CrossRef]
  5. C. P. Henze, S. K. Case, “Polychromatic Laser Light Source,” Rev. Sci. Instrum. 54, 1334 (1983).
    [CrossRef]

1983 (1)

C. P. Henze, S. K. Case, “Polychromatic Laser Light Source,” Rev. Sci. Instrum. 54, 1334 (1983).
[CrossRef]

1981 (2)

1980 (1)

1972 (1)

R. H. Katyl, “Compensating Optical Systems, 3: Achromatic Fourier Transformation,” Appl. Opt. 4, 1255 (1972).
[CrossRef]

Case, S. K.

C. P. Henze, S. K. Case, “Polychromatic Laser Light Source,” Rev. Sci. Instrum. 54, 1334 (1983).
[CrossRef]

Collins, G. D.

Henze, C. P.

C. P. Henze, S. K. Case, “Polychromatic Laser Light Source,” Rev. Sci. Instrum. 54, 1334 (1983).
[CrossRef]

Katyl, R. H.

R. H. Katyl, “Compensating Optical Systems, 3: Achromatic Fourier Transformation,” Appl. Opt. 4, 1255 (1972).
[CrossRef]

Leigh, E. N.

Morris, G. M.

Swanson, G. J.

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Figures (7)

Fig. 1
Fig. 1

Optical system which compensates for the wavelength dependence of the scale of the Fourier transformation of a grating S(f0) by introducing a zone plate LF as the Fourier transforming element. However, since FF is a function of wavelength, LF introduces a longitudinal dispersion.

Fig. 2
Fig. 2

Spatial filtering system which uses the shift lens concept to compensate for longitudinal dispersion.

Fig. 3
Fig. 3

Final optical system combining Figs. 1 and 2 as described by Collins.2

Fig. 4
Fig. 4

Stereo pair of pictures show separation of signal and noise.

Fig. 5
Fig. 5

Reconstruction of a Fourier transform hologram: (a) coherent case; (b) polychromatic point source case.

Fig. 6
Fig. 6

Autocorrelation function of the letter combination uυ: (a) coherent case; (b) polychromatic point source case.

Fig. 7
Fig. 7

Off-axis zone plates under high magnification (300 lines/mm) recorded under (a) coherent illumination, (b) polychromatic point source illumination.

Equations (7)

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D i = F 2 + F 2 2 / F 1 ( F 2 / F 1 ) 2 D 0 ( F 2 2 / F s 0 ) ( λ / λ 0 )
D 0 = d F F = d F F 0 λ 0 / λ
D i = F 2 + F 2 2 / F 1 d ( F 2 2 / F 1 2 ) + F 2 2 [ ( F F 0 λ 0 / F 1 2 λ ) ( λ / F so λ 0 ) ] .
S = exp [ i π ( x 2 + y 2 ) / λ F I ] ,
u 0 = exp [ i π ( x 2 + y 2 ) / λ F 0 ] ,
exp [ i π ( x 2 + y 2 ) / λ F F 0 ] = exp [ i π ( 1 / F E + 1 / F 1 ) ( x 2 + y 2 ) / λ ] .
F 0 = F 2 ( F 2 / F F 0 F s 0 2 + 1 / F s 0 ) ( F 1 = F 2 = F ) .

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