Abstract

A lensless scanning telescope composed of two circular apertures and having good response with minimum aliasing is described. By analogy with an arrangement of two slits, the modulation transfer function (MTF) of this telescope is derived. The MTF of a lensless telescope scanning the earth’s surface from 500-km orbit is developed for both the scan and cross-scan directions. Response of 48% or better at 100-km wavelength in both directions is shown with aliasing errors due to sampling of 1% or less.

© 1980 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), p. 20.
  2. R. M. Scott, Photogr. Sci. Eng. 3, 201 (1959).
  3. H. B. Edwards, W. P. Chu, Appl. Opt. 18, 262 (1979).
    [CrossRef] [PubMed]

1979 (1)

1959 (1)

R. M. Scott, Photogr. Sci. Eng. 3, 201 (1959).

Chu, W. P.

Edwards, H. B.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 20.

Scott, R. M.

R. M. Scott, Photogr. Sci. Eng. 3, 201 (1959).

Appl. Opt. (1)

Photogr. Sci. Eng. (1)

R. M. Scott, Photogr. Sci. Eng. 3, 201 (1959).

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 20.

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Figures (7)

Fig. 1
Fig. 1

Lensless telescope, showing arrangement of apertures. Aperture function showing area of inner aperture exposed to a distant source as a function of view angle.

Fig. 2
Fig. 2

Two slit apertures in line, showing arrangement and aperture function or area of linear aperture exposed as a function of view angle.

Fig. 3
Fig. 3

TFs of single and double slits. Absolute value of amplitude response plotted against the ratio of dimension a to spatial wavelength of input signal.

Fig. 4
Fig. 4

TFs of single circular field-stop aperture and lensless telescope with two apertures of the same size. Absolute value of amplitude response plotted against spatial frequency of input signal in cycles/radian.

Fig. 5
Fig. 5

Derivation of TF of lensless telescope with apertures having a diameter ratio of 4:3. Absolute value of amplitude response plotted against spatial frequency of input signal in cycles/radian.

Fig. 6
Fig. 6

System TF scanner along scan. Outer-aperture diameter, 10 mm; inner-aperture diameter, 7.5 mm; distance between apertures, 100 mm. Absolute value of amplitude response plotted against spatial frequency of input signal in cycles/radian with corresponding inverse scales of spatial wavelength in kilometers and sampling rate in samples/cycle of spatial wavelength. Dashed line shows foldover from sampling rate.

Fig. 7
Fig. 7

TF of scanner across scan. Telescope dimensions, TF plot, scales, and sampling rate foldover plot are the same as in Fig. 6.

Equations (4)

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TF ( rect ) = sin π a / λ π a / λ ,
TF ( diamond ) = ( sin π a / λ π a / λ ) 2 ,
TF ( circle ) = 2 J 1 ( π a f ) π a f , TF ( telescope ) = ( 2 J 1 ( π a f ) π a f ) 2 ,
TF ( telescope ) = 2 J 1 ( π a 1 f ) π a 1 f × 2 J 1 ( π a 2 f ) π a 2 f ,

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