Abstract

An experimental method for determining the transfer function and accompanying cutoff frequency of a Fabry-Perot interferometer (FPI) is described and a set of experimental results is presented. It is shown that upon passage through the FPI, the level of image distortion decreases with a decrease in cavity length (resulting in an increase in Fresnel number) when the FPI finesse is held constant. This phenomenon is in agreement with the theoretical prediction.

© 1981 Optical Society of America

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References

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  1. A. Riazi, D. A. Christensen, O. P. Gandhi, J. Opt. Soc. Amer. 69, 348 (1979).
    [CrossRef]
  2. L. A. Vainstein, Sov. Phys. JETP, 17, 709 (1963).
  3. S. D. Cone, C. D. deBoor, Elementary Numerical Analysis: An Algorithmic Approach (McGraw-Hill, New York, 1972).
  4. A. Riazi, Ph.D. Dissertation, Department of Electrical Engineering, U. Utah, 1978.
  5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).

1979 (1)

A. Riazi, D. A. Christensen, O. P. Gandhi, J. Opt. Soc. Amer. 69, 348 (1979).
[CrossRef]

1963 (1)

L. A. Vainstein, Sov. Phys. JETP, 17, 709 (1963).

Christensen, D. A.

A. Riazi, D. A. Christensen, O. P. Gandhi, J. Opt. Soc. Amer. 69, 348 (1979).
[CrossRef]

Cone, S. D.

S. D. Cone, C. D. deBoor, Elementary Numerical Analysis: An Algorithmic Approach (McGraw-Hill, New York, 1972).

deBoor, C. D.

S. D. Cone, C. D. deBoor, Elementary Numerical Analysis: An Algorithmic Approach (McGraw-Hill, New York, 1972).

Gandhi, O. P.

A. Riazi, D. A. Christensen, O. P. Gandhi, J. Opt. Soc. Amer. 69, 348 (1979).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).

Riazi, A.

A. Riazi, D. A. Christensen, O. P. Gandhi, J. Opt. Soc. Amer. 69, 348 (1979).
[CrossRef]

A. Riazi, Ph.D. Dissertation, Department of Electrical Engineering, U. Utah, 1978.

Vainstein, L. A.

L. A. Vainstein, Sov. Phys. JETP, 17, 709 (1963).

J. Opt. Soc. Amer. (1)

A. Riazi, D. A. Christensen, O. P. Gandhi, J. Opt. Soc. Amer. 69, 348 (1979).
[CrossRef]

Sov. Phys. JETP (1)

L. A. Vainstein, Sov. Phys. JETP, 17, 709 (1963).

Other (3)

S. D. Cone, C. D. deBoor, Elementary Numerical Analysis: An Algorithmic Approach (McGraw-Hill, New York, 1972).

A. Riazi, Ph.D. Dissertation, Department of Electrical Engineering, U. Utah, 1978.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).

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Figures (4)

Fig. 1
Fig. 1

Diagram of the experimental setup for transferring an image through an FPI.

Fig. 2
Fig. 2

Experimental results of passing an image through an FPI of finesse F = 97.5: (a) input image; (b) output image when FPI mirror separation was set at L = 0.0368 cm; (c) output image for L = 0.132 cm; (d) output image for L = 1.021 cm.

Fig. 3
Fig. 3

Frequency spectra of images of Fig. 2: (a) the spectrum of input image of Fig. 2(a); (b) the spectrum of output image of Fig. 2(b); (c) the spectrum of output image of Fig. 2(c); (d) the spectrum of output image of Fig. 2(d).

Fig. 4
Fig. 4

Experimental transfer function obtained for an FPI of finesse F = 97.5, (a) for mirror spacing L = 0.0368; (b) for L = 0.132 cm; and (c) for L = 1.021 cm.

Tables (1)

Tables Icon

Table I Theoretical and Experimental Cutoff Frequencies for Different FPI Parameters

Equations (4)

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n c = ( N 0.196 ) 1 / 2 K ( F R ) 1 / 4 ,
K ( F R ) = [ 1 16 r 8 - 8 r 4 t 4 { - 4 t 4 r 2 + t 8 + 8 r 2 t 6 + 4 r 4 t 4 + [ ( 4 t 4 r 2 - t 8 - 8 r 2 t 6 - 4 r 4 t 4 ) 2 + 2 t 8 ( 8 r 8 - 4 r 4 t 4 ) ] 1 / 2 } ] ,
ν c = 1 4 a n c .
ν c = 1 1.77 L λ [ K ( F R ) ] 1 / 4 .

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