Abstract

Previous methods of two-wavelength variable-sensitivity interferometry are reviewed and a simplified two-wavelength technique for interferometric testing under static conditions is discussed. An extension of the static technique to real-time dynamic testing is proposed and an operational variable-sensitivity interferometer utilizing the real-time technique is described.

© 1973 Optical Society of America

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References

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  1. J. C. Wyant, Appl. Opt. 10, 2113 (1971).
    [CrossRef] [PubMed]
  2. C. Polhemus, C. Chocol, Appl. Opt. 10, 441 (1971).
    [CrossRef] [PubMed]
  3. S. Yokozeki, T. Suzuki, Appl. Opt. 11, 446 (1972).
    [CrossRef] [PubMed]
  4. G. Yanow, “CIDRS: Computerized Interferogram Data Reduction Systems,” paper presented at the 1972 spring meeting of the Optical Society of America, April 1972.

1972 (1)

1971 (2)

Chocol, C.

Polhemus, C.

Suzuki, T.

Wyant, J. C.

Yanow, G.

G. Yanow, “CIDRS: Computerized Interferogram Data Reduction Systems,” paper presented at the 1972 spring meeting of the Optical Society of America, April 1972.

Yokozeki, S.

Appl. Opt. (3)

Other (1)

G. Yanow, “CIDRS: Computerized Interferogram Data Reduction Systems,” paper presented at the 1972 spring meeting of the Optical Society of America, April 1972.

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Figures (6)

Fig. 1
Fig. 1

Signal-processing circuitry.

Fig. 2
Fig. 2

Flow diagram of operational two-wavelength interferometer system.

Fig. 3
Fig. 3

Oscilloscope photograph of electrical signal before and after processing.

Fig. 4
Fig. 4

Interferometer data reduction sequence.

Fig. 5
Fig. 5

Digitized interferometer output with 64 grey levels.

Fig. 6
Fig. 6

Contrast-modulated output of dynamic two-wavelength interferometer.

Equations (11)

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exp [ i ( 2 π / λ 1 ) ϕ ( x , y ) ] + exp [ i ( 2 π / λ 1 ) x sin θ 1 ] .
I λ 1 = 2 + exp { - i 2 π / λ 1 [ ϕ 1 ( x , y ) - x sin θ 1 ] } . + exp { + i 2 π / λ 1 [ ϕ 1 ( x , y ) - x sin θ 1 ] } . = 2 + 2 cos { 2 π / λ 1 [ ϕ 1 ( x , y ) - x sin θ 1 ] } .
( I λ 1 ) ( I λ 2 ) = 4 + 4 cos { 2 π / λ 1 [ ϕ 1 ( x , y ) - x sin θ 1 ] } + 4 cos { 2 π / λ 2 [ ϕ 2 ( x , y ) - x sin θ 2 ] } + 4 cos { 2 π / λ 1 [ ϕ 1 ( x , y ) - x sin θ 1 ] } × · cos { 2 π / λ 2 [ ϕ 2 ( x , y ) - x sin θ 2 ] } .
( I λ 1 ) ( I λ 2 ) = 4 + 4 cos { 2 π / λ 1 [ ϕ 1 ( x , y ) - x sin θ 1 ] } + 4 cos { 2 π / λ 2 [ ϕ 2 ( x , y ) - x sin θ 2 ] } + 2 cos { 2 π / λ 1 [ ϕ 1 ( x , y ) - x sin θ 1 ] + 2 π / λ 2 [ ϕ 2 ( x , y ) - x sin θ 2 ] } + 2 cos { 2 π / λ 1 [ ϕ 1 ( x , y ) - x sin θ 1 ] - 2 π / λ 2 [ ϕ 2 ( x , y ) - x sin θ 2 ] } .
I λ eq = 4 + 2 cos { 2 π / λ 1 [ ϕ 1 ( x , y ) - x sin θ 1 ] - 2 π / λ 2 [ ϕ 2 ( x , y ) - x sin θ 2 ] } .
ϕ 1 ( x , y ) - x sin θ 1 = ϕ 2 ( x , y ) - x sin θ 2 .
I λ eq = 4 + 2 cos { [ ϕ ( x , y ) - x sin θ ] ( 2 π / λ 1 - 2 π / λ 2 ) } = 4 + 2 cos { [ ϕ ( x , y ) - x sin θ ] 2 π ( λ 2 - λ 1 / λ 1 λ 2 ) } ,
I λ 1 + I λ 2 = 4 + 2 cos { 2 π / λ 1 [ ϕ 1 ( x , y ) - x sin θ 1 ] } + 2 cos { 2 π / λ 2 [ ϕ 2 ( x , y ) - x sin θ 2 ] } ,
I λ 1 + I λ 2 = 4 + 4 cos ½ { [ ϕ ( x , y ) - x sin θ ] ( 2 π ( 1 / λ 1 + 1 / λ 2 ) } · cos ½ { [ ϕ ( x , y ) - x sin θ ] ( 2 π ( 1 / λ 1 - 1 / λ 2 ) } = 4 ( 1 + cos { [ ϕ ( x , y ) - x sin θ ] × [ 2 π ( λ 1 + λ 2 ) / ( 2 λ 1 λ 2 ) ] } · cos { [ ϕ ( x , y ) - x sin θ ] [ 2 π ( λ 2 - λ 1 ) / ( 2 λ 1 λ 2 ) ] } ) = 4 ( 1 + ½ cos { [ ϕ ( x , y ) - x sin θ ] ( π / λ 2 ) } + ½ cos { [ ϕ ( x , y ) - x sin θ ] ( π / λ 1 ) } ) .
( 2 cos { [ ϕ ( x , y ) - x sin θ ] 2 π / λ 2 } + 2 cos { [ ϕ ( x , y ) - x sin θ ] 2 π / λ 1 } ) 2 = 4 cos 2 { [ ϕ ( x , y ) - x sin θ ] 2 π / λ 1 } + 4 cos 2 { [ ϕ ( x , y ) - x sin θ ] 2 π / λ 2 } + 8 cos { [ ϕ ( x , y ) - x sin θ ] 2 π / λ 2 } × cos { [ ϕ ( x , y ) - x sin θ ] 2 π / λ 1 } = 4 + 2 cos { 4 / λ 1 [ ϕ ( x , y ) - x sin θ ] } + 2 cos { 4 π / λ 2 [ ϕ ( x , y ) - x sin θ ] } + 4 cos { [ 2 π ( λ 1 + λ 2 ) / λ 1 λ 2 ] [ ϕ ( x , y ) - x sin θ ] } + 4 cos { [ 2 π ( λ 1 + λ 2 ) / λ 1 λ 2 ] [ ϕ ( x , y ) - x sin θ ] } .
I λ eq = 4 cos { [ 2 π ( λ 1 - λ 2 ) / λ 1 λ 2 ] [ ϕ ( x , y ) - x sin θ ] } + dc

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