Abstract

An interferometry system is presented that is useful in large-scale measurements such as those of topographic maps. The envelope of a propagating wave is used to create the desired fringe patterns, representing range contours, through the interference of a light modulation function and an image modulation function. A number of variations are shown that either provide altitude contours or place the contour information on a spatial frequency carrier. This latter system offers the flexibility of electronic processing when the image is scanned. The comparison of contour patterns taken at different times provides an accurate indication of subtle surface deformations.

© 1974 Optical Society of America

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References

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  1. K. A. Stetson, R. L. Powell, J. Opt. Soc. Am. 55, 1964 (1965).
    [CrossRef]
  2. M. M. Thomson, Ed., Manual of Photogrammetry (American Society of Photogrammetry, 1966).
  3. G. Fiocco, L. D. Smullin, Nature 199, 275 (1963).
    [CrossRef]
  4. K. E. Golden, D. E. Kind, S. L. Leonard, R. C. Ward, Appl. Opt. 12, 1447 (1973).
    [CrossRef] [PubMed]
  5. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
    [CrossRef]

1973 (1)

1965 (1)

K. A. Stetson, R. L. Powell, J. Opt. Soc. Am. 55, 1964 (1965).
[CrossRef]

1963 (1)

G. Fiocco, L. D. Smullin, Nature 199, 275 (1963).
[CrossRef]

1962 (1)

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
[CrossRef]

K. A. Stetson, R. L. Powell, J. Opt. Soc. Am. 55, 1964 (1965).
[CrossRef]

Nature (1)

G. Fiocco, L. D. Smullin, Nature 199, 275 (1963).
[CrossRef]

Other (1)

M. M. Thomson, Ed., Manual of Photogrammetry (American Society of Photogrammetry, 1966).

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Figures (3)

Fig. 1
Fig. 1

Basic interferometry system showing modulated light source and modulated imaging device, which are effectively at the same point.

Fig. 2
Fig. 2

Image modulation system at an intermediate imaging plane for creating altitude contours.

Fig. 3
Fig. 3

Imaging system for obtaining the effect of a moving grating pattern superimposed on the image.

Equations (16)

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I s = f l ( t r / c ) ,
I i = K a [ ( x / M ) ( y / M ) ] f l [ t ( 2 r / c ) ] f i ( t ) ,
I ¯ i = I i d t = K a [ ( x / M ) , ( y / M ) ] f i ( t ) f l ( t 2 r / c ) d t = K a [ ( x / M ) , ( y / M ) ] [ f i ( 2 r / c ) f l ( 2 r / c ) ] ,
I ¯ i = K a [ ( x / M ) , ( y / M ) ] [ 1 + cos 2 k r ] ,
r = ( z 2 + x 2 + y 2 ) 1 / 2 z + [ ( x 2 + y 2 ) / 2 z ] for z 2 ( x 2 + y 2 ) max .
r = z + x 2 + y 2 2 z ¯ ,
I ¯ i = K a [ ( x / M ) , ( y / M ) ] f i ( t ) f l { t 2 z c [ ( x 2 + y 2 ) / z ¯ c ] } d t .
f i ( x , y , t ) = f i [ t ( x 2 + y 2 ) / z ¯ c ] .
I ¯ i = K a [ ( x / M ) , ( y / M ) ] [ f i ( 2 z / c ) f l ( 2 z / c ) ] .
τ 1 τ 2 = K a 2 [ 1 + cos 2 k r 1 + cos 2 k r 2 + 1 / 2 cos 2 k ( r 1 + r 2 ) + 1 / 2 cos 2 k ( r 1 r 2 ) ] ,
( τ 1 τ 2 ) * h ( x , y ) K a 2 [ 1 + 1 / 2 cos 2 k ( r 1 r 2 ) ] ,
f i ( x , y , t ) = 1 + cos ω [ t ( x / υ ) ] ,
I ¯ i = K a [ ( x / M ) , ( y / M ) ] { 1 + cos [ ( ω x / υ ) 2 k r ] } .
I total = K a [ ( x / M ) , ( y / M ) { 2 + cos [ ( ω 1 x / υ ) 2 k r 1 ] + cos [ ( ω 2 x / υ ) 2 k r 2 ] } .
e f = cos { [ ( ω 1 ω 2 ) υ s / υ ] t 2 k ( r 1 r 2 ) } .
cos n [ ( ω υ s / υ ) t 2 k r ] · cos n [ ( ω υ s / υ ) t ] = cos 2 n k r + high frequency term .

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