Abstract

A novel system for real-time heterodyne interferometry of extended objects is demonstrated. Featured in this system is the direct measurement of the optical path difference, eliminating the sometimes troublesome interpretation of the fringe patterns of traditional interferometry. High spatial and temporal resolutions are available in real time for a properly instrumented system. The concept, its performance, and applications are presented along with results from a breadboard system, where phase accuracy of better than λ/100 is demonstrated.

© 1979 Optical Society of America

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References

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  1. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  2. G. E. Sommargren, Appl. Opt. 16, 1736 (1977); see also R. Danliker, E. Marom, F. M. Mottier, J. Opt. Soc. Am. 66, 23 (1976).
    [CrossRef] [PubMed]
  3. J. N. Dukes, G. B. Gordon, Hewlett Packard J. (Aug.1970).
  4. G. W. Johnson, D. C. Leiner, D. T. Moore, Opt. Eng. 18, 1, (Jan/Feb1979).
    [CrossRef]
  5. A. H. Guenther, D. H. Liebenberg, Eds., “Optical Interferograms—Reduction and Interpretation,” ASTM STP 666, (American Society for Testing and Materials, Philadelphia, Jan.1978).
  6. T. Forrester, D. Gudmundson, P. Johnson, Phys. Rev. 99, 1691 (1955).
    [CrossRef]
  7. N. A. Massie, R. D. Nelson, Opt. Lett. 3, 46 (1978).
    [CrossRef] [PubMed]
  8. N. A. Massie, “Heterodyne Interferometry,” see Ref. 5.
  9. N. A. Massie, S. Holly, Proc. Soc. Photo-Opt. Instrum. Eng. 141, 82 (March1978).
  10. N. A. Massie, Proc. Soc. Photo-Opt. Instrum. Eng. 153, 126 (Aug.1978).
  11. F. Mottier, Proc. Soc. Photo-Opt. Instrum. Eng. 153, 133 (Aug.1978).

1979 (1)

G. W. Johnson, D. C. Leiner, D. T. Moore, Opt. Eng. 18, 1, (Jan/Feb1979).
[CrossRef]

1978 (4)

N. A. Massie, R. D. Nelson, Opt. Lett. 3, 46 (1978).
[CrossRef] [PubMed]

N. A. Massie, S. Holly, Proc. Soc. Photo-Opt. Instrum. Eng. 141, 82 (March1978).

N. A. Massie, Proc. Soc. Photo-Opt. Instrum. Eng. 153, 126 (Aug.1978).

F. Mottier, Proc. Soc. Photo-Opt. Instrum. Eng. 153, 133 (Aug.1978).

1977 (1)

1974 (1)

1970 (1)

J. N. Dukes, G. B. Gordon, Hewlett Packard J. (Aug.1970).

1955 (1)

T. Forrester, D. Gudmundson, P. Johnson, Phys. Rev. 99, 1691 (1955).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Dukes, J. N.

J. N. Dukes, G. B. Gordon, Hewlett Packard J. (Aug.1970).

Forrester, T.

T. Forrester, D. Gudmundson, P. Johnson, Phys. Rev. 99, 1691 (1955).
[CrossRef]

Gallagher, J. E.

Gordon, G. B.

J. N. Dukes, G. B. Gordon, Hewlett Packard J. (Aug.1970).

Gudmundson, D.

T. Forrester, D. Gudmundson, P. Johnson, Phys. Rev. 99, 1691 (1955).
[CrossRef]

Herriott, D. R.

Holly, S.

N. A. Massie, S. Holly, Proc. Soc. Photo-Opt. Instrum. Eng. 141, 82 (March1978).

Johnson, G. W.

G. W. Johnson, D. C. Leiner, D. T. Moore, Opt. Eng. 18, 1, (Jan/Feb1979).
[CrossRef]

Johnson, P.

T. Forrester, D. Gudmundson, P. Johnson, Phys. Rev. 99, 1691 (1955).
[CrossRef]

Leiner, D. C.

G. W. Johnson, D. C. Leiner, D. T. Moore, Opt. Eng. 18, 1, (Jan/Feb1979).
[CrossRef]

Massie, N. A.

N. A. Massie, R. D. Nelson, Opt. Lett. 3, 46 (1978).
[CrossRef] [PubMed]

N. A. Massie, S. Holly, Proc. Soc. Photo-Opt. Instrum. Eng. 141, 82 (March1978).

N. A. Massie, Proc. Soc. Photo-Opt. Instrum. Eng. 153, 126 (Aug.1978).

N. A. Massie, “Heterodyne Interferometry,” see Ref. 5.

Moore, D. T.

G. W. Johnson, D. C. Leiner, D. T. Moore, Opt. Eng. 18, 1, (Jan/Feb1979).
[CrossRef]

Mottier, F.

F. Mottier, Proc. Soc. Photo-Opt. Instrum. Eng. 153, 133 (Aug.1978).

Nelson, R. D.

Rosenfeld, D. P.

Sommargren, G. E.

White, A. D.

Appl. Opt. (2)

Hewlett Packard J. (1)

J. N. Dukes, G. B. Gordon, Hewlett Packard J. (Aug.1970).

Opt. Eng. (1)

G. W. Johnson, D. C. Leiner, D. T. Moore, Opt. Eng. 18, 1, (Jan/Feb1979).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

T. Forrester, D. Gudmundson, P. Johnson, Phys. Rev. 99, 1691 (1955).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

N. A. Massie, S. Holly, Proc. Soc. Photo-Opt. Instrum. Eng. 141, 82 (March1978).

N. A. Massie, Proc. Soc. Photo-Opt. Instrum. Eng. 153, 126 (Aug.1978).

F. Mottier, Proc. Soc. Photo-Opt. Instrum. Eng. 153, 133 (Aug.1978).

Other (2)

N. A. Massie, “Heterodyne Interferometry,” see Ref. 5.

A. H. Guenther, D. H. Liebenberg, Eds., “Optical Interferograms—Reduction and Interpretation,” ASTM STP 666, (American Society for Testing and Materials, Philadelphia, Jan.1978).

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Figures (11)

Fig. 1
Fig. 1

Interferogram of silicon wafer.

Fig. 2
Fig. 2

Phase determination from accurate time measurements.

Fig. 3
Fig. 3

Optical heterodyne interferometer configuration.

Fig. 4
Fig. 4

Moving-fringe model of broad-beam heterodyne interferometry.

Fig. 5
Fig. 5

Error in time (phase) measurement from white noise.

Fig. 6
Fig. 6

Difference between OPD measurements of same object at two different orientations; rms is λ/100 (tip, tilt, and piston removed in plot; 0.1 wave/tic).

Fig. 7
Fig. 7

Fringe interferogram of ZnSe flat with mount distortion.

Fig. 8
Fig. 8

OPD map of ZnSe flat (0.5 wave/tic).

Fig. 9
Fig. 9

OPD map of ZnSe flat with system errors subtracted (0.5 wave/tic).

Fig. 10
Fig. 10

OPD map of deformable mirror with no actuator force (1 wave/tic).

Fig. 11
Fig. 11

OPD map of deformable mirror with single actuator pressure (1 wave/tic).

Equations (18)

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i = [ 0 cos ( ω 0 t ) + 1 cos ( ( ω 0 + ω 1 ) t + ϕ ] 2 ,
i = 0 2 2 + 1 2 2 + 0 1 cos ( ω 1 t + ϕ ) .
SNR = ½ V 0 2 v ¯ 2 ,
v ¯ = V 0 ( 2 SNR ) ½ .
Δ t ¯ T = 1 2 π ( 2 SNR ) 1 / 2 ,
ξ 1 = ξ 0 { cos [ ω 1 t + ϕ 1 ( x , y ) ] + ( β 1 ) 1 / 2 cos ( ω 2 t + ϕ 1 ) } x ^ ξ 2 = ξ 0 { cos [ ω 2 t + ϕ 2 ( x , y ) ] + ( β 2 ) 1 / 2 cos ( ω 1 t + ϕ 2 ) } y ^ } .
i c = 1 2 ξ 0 2 { cos [ δ ω t + δ ϕ ( x , y ) ] + ( β ) 1 / 2 A cos [ δ ω t + δ ϕ 0 ( x , y ) ] } ,
cos [ δ ω t + ( ϕ 1 - ϕ 1 ) ] + cos [ δ ω t + ( ϕ 2 - ϕ 2 ) ] A cos [ δ ω t + δ ϕ 0 ( x , y ) ]
i p = ( β ) 1 / 2 ξ 0 2 cos ( δ ω t + δ ϕ ) ,
i r = cos [ δ ω t + ϕ 0 ( t ) + ϕ ( x r , y r ) ] ,
i t = cos [ δ ω t + ϕ 0 ( t ) + ϕ ( x , y ) ] .
T 1 = ϕ ( B ) b
T 2 = ϕ ( C ) - ϕ ( B ) c .
Δ ϕ = - T 1 ( d x ) - T 2 ( d y ) .
V ( ϕ ) = s [ ϕ 0 + a x + b y + ϕ ( x , y ) ] + F [ ϕ 0 + a x + b y + ϕ ( x , y ) ] ,
V ( ϕ ) = s ( ϕ 0 + ϕ ( x , y ) + a x + b y ) + F ( ϕ 0 + ϕ ( x , y ) + a x + b y ) .
L ( I , J ) = V ( I , J ) - D ( I , J ) - s ( δ ϕ 0 + δ a I + δ b J ) = F [ ϕ ( I , J ) ] - F [ ϕ ( I , J ) ] .
σ = [ L 2 ( I , J ) N ] 1 / 2 ,

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