Abstract

An IR Twyman-Green interferometer is described. It uses a cw CO2 laser as a light source operating at a 10.6-μm wavelength. Theoretical analysis and experimental measurements of the relationship between the contrast of the interference fringes and the rms roughness of test surfaces are discussed. Interferometric testing results and special alignment methods are shown for rough surface optics.

© 1980 Optical Society of America

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References

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  1. O. Kwon et al., J. Opt. Soc. Am. 67, 1305 (1977).
  2. O. Kwon et al., Opt. Lett. 3, 118 (1978).
    [CrossRef] [PubMed]
  3. C. R. Munnerlyn, M. Latta, Appl. Opt. 7, 1858 (1968).
    [CrossRef] [PubMed]
  4. W. L. Wolfe, G. J. Zissis, Eds., Infrared Handbook (Office of Naval Research, Department of the Navy, Washington, D.C., 1979), pp. 7–40.
  5. T. Conklin, E. H. Stupp, Opt. Eng. 15, 510 (1976).
    [CrossRef]
  6. J. M. Bennett, Appl. Opt. 15, 2705 (1976).
    [CrossRef] [PubMed]
  7. P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963), Chap. 5.
  8. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap. 11.
  9. B. Kazan, Ed., Advances in Image Pickup and Display, Vol. 3 (Academic, New York, 1977), Chap. 1.

1978

1977

O. Kwon et al., J. Opt. Soc. Am. 67, 1305 (1977).

1976

T. Conklin, E. H. Stupp, Opt. Eng. 15, 510 (1976).
[CrossRef]

J. M. Bennett, Appl. Opt. 15, 2705 (1976).
[CrossRef] [PubMed]

1968

Beckmann, P.

P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963), Chap. 5.

Bennett, J. M.

Conklin, T.

T. Conklin, E. H. Stupp, Opt. Eng. 15, 510 (1976).
[CrossRef]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap. 11.

Kwon, O.

O. Kwon et al., Opt. Lett. 3, 118 (1978).
[CrossRef] [PubMed]

O. Kwon et al., J. Opt. Soc. Am. 67, 1305 (1977).

Latta, M.

Munnerlyn, C. R.

Spizzichino, A.

P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963), Chap. 5.

Stupp, E. H.

T. Conklin, E. H. Stupp, Opt. Eng. 15, 510 (1976).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

O. Kwon et al., J. Opt. Soc. Am. 67, 1305 (1977).

Opt. Eng.

T. Conklin, E. H. Stupp, Opt. Eng. 15, 510 (1976).
[CrossRef]

Opt. Lett.

Other

P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963), Chap. 5.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap. 11.

B. Kazan, Ed., Advances in Image Pickup and Display, Vol. 3 (Academic, New York, 1977), Chap. 1.

W. L. Wolfe, G. J. Zissis, Eds., Infrared Handbook (Office of Naval Research, Department of the Navy, Washington, D.C., 1979), pp. 7–40.

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Figures (9)

Fig. 1
Fig. 1

Infrared Twyman-Green interferometer: (a) schematic; (b) photograph.

Fig. 2
Fig. 2

Interferograms of (a) germanium lens of 2.54-cm (1-in.) diam and 12.5-cm (5-in.) focal length and (b) elliptical mirror of 5-cm (2-in.) diam and 7.5-cm (3-in.) focal length with conic constant of −0.5418.

Fig. 3
Fig. 3

Rough surface interferometry: (a) Twyman-Green interferometer with two image-forming lenses; (b) random surface profile of test object.

Fig. 4
Fig. 4

(a) Talystep readings of glass samples; (b) oscilloscope readings of interferometric fringes; (c) photographic pictures of fringes taken through a TV monitor.

Fig. 5
Fig. 5

Comparison of scaled rms roughness and values of contrast obtained from Talystep readings and interferometric measurements.

Fig. 6
Fig. 6

Interferograms of diamond-turned spherical metal mirrors coated with aluminum (a), (b) and copper (c), (d) at 0.6328 μm. (a), (c) and at 10.6 μm (b), (d).

Fig. 7
Fig. 7

Off-axis parabola: (a) segment from a large on-axis parabola. a = 1.73 m, a′ = 0.71 m, h = 0, and g = 1m. (b) Departure from best-fit sphere. R = 12.8 m.

Fig. 8
Fig. 8

Layout of testing of off-axis parabola.

Fig. 9
Fig. 9

Infrared interferograms of unpolished off-axis parabola in chronological order.

Tables (1)

Tables Icon

Table I Results of Fringe Contrasts vs Standard Deviations

Equations (11)

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U o + = ρ 0 U 0 exp { i [ 2 k h ( x , y ) + α x ] } .
U r + = ρ r U r .
U o = τ q ( x , y ; 1 λ l ) exp ( i k z o ) ρ 0 exp { i [ 2 k h ( x , y ) + α x ] } U o ,
U r = τ q ( x , y ; 1 λ l ) exp ( i k z r ) ρ r U r ,
q ( x , y ; 1 λ l ) exp [ i π ( x 2 + y 2 ) / λ l ]
I = | U o + U r | 2 .
p ( h ) = 1 ( 2 π ) 1 / 2 σ exp ( h 2 2 σ 2 ) .
I = A p ( h ) I ( h ) d h = κ [ 1 + ( ρ o ρ r ) 2 ( U o U r ) + 2 ( ρ o ρ r ) ( U o U r ) cos ( α x ) × exp ( 2 k 2 σ 2 ) ] ,
C I max I min I max + I min = 2 ( ρ o / ρ r ) ( U o / U r ) 1 + ( ρ o / ρ r ) 2 ( U o / U r ) 2 exp ( 8 π 2 σ 2 / λ 2 ) = C o C σ ,
C o = 2 ( ρ o / ρ r ) ( U o / U r ) 1 + ( ρ o / ρ r ) 2 ( U o / U r ) 2 , C σ = exp ( 8 π 2 σ 2 / λ 2 ) .
C = C σ = exp ( 8 π 2 σ 2 / λ 2 ) .

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