Abstract

It is shown that both single exposure and double exposure two-wavelength holography provide a good method of using visible light to obtain an interferogram identical to what would be obtained if a longer nonvisible wavelength were used. Both techniques provide for the real-time adjustment of defocus and tilt in the final interferogram. When both hologram exposures are made simultaneously, the sensitivity to air turbulence is essentially the same as if the longer nonvisible wavelength were used. Results are shown for testing both lenses and mirrors at equivalent wavelengths at 6.45 μ, 9.47 μ, 14.20 μ, 20.22 μ, and 28.50 μ obtained by using an argon laser for the visible light source.

© 1971 Optical Society of America

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References

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  1. B. P. Hildebrand, K. A. Haines, J. Opt. Soc. Am. 57, 153 (1967).
    [CrossRef]
  2. J. S. Zelenka, J. R. Varner, Appl. Opt. 7, 2107 (1968).
    [CrossRef] [PubMed]
  3. J. S. Zelenka, J. R. Varner, Appl. Opt. 8, 1431 (1969).
    [CrossRef] [PubMed]
  4. B. G. Moreau, R. E. Hopkins, Appl. Opt. 8, 2150 (1969).
    [CrossRef] [PubMed]
  5. H. M. Smith, Principles of Holography (Wiley-Interscience, New York, 1969), p. 193.
  6. C. R. Munnerlyn, M. Latta, Appl. Opt. 7, 1858 (1968).
    [CrossRef] [PubMed]

1969 (2)

1968 (2)

1967 (1)

B. P. Hildebrand, K. A. Haines, J. Opt. Soc. Am. 57, 153 (1967).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for using TWH for testing lenses, (* image of exit pupil of lens under test; image of hologram).

Fig. 2
Fig. 2

Interferograms of a single lens. (a) λ = 0.4880 μ, (b) λeq = 6.45 μ, (c) λeq = 6.45 μ, (d) λeq 9.47 μ, (e) λeq = 9.47 μ, (f) λeq = 20.22 μ, (g) λeq = 28.5 μ.

Fig. 3
Fig. 3

Interferograms of an aspheric lens. (a) λ = 0.5145 μ, (b) λeq = 6.45 μ, (c) λeq = 9.47 μ, (d) λeq = 14.2 μ.

Fig. 4
Fig. 4

Contour map obtained from interferogram shown in Fig. 3(b) (rms error = 1.00 λ, peak-to-peak error = 4.982 λ, λ = 6.45 μ).

Fig. 5
Fig. 5

Interferogram of waxed ground glass mirror (λeq = 9.47 μ).

Fig. 6
Fig. 6

Double exposure TWH interferogram of a waxed ground glass mirror taken with turbulence present.

Fig. 7
Fig. 7

Double exposure holographic interferogram of forced turbulence present in interferometer (λ = 05145 μ)

Fig. 8
Fig. 8

Interferograms of a portion of a ground glass mirror. (a) λeq = 9.47 μ, (b) λeq = 14.19 μ.

Tables (1)

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Table I Possible Equivalent Wavelengths, λeq, Obtainable Using an Argon and a He–Ne Laser

Equations (10)

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λ e q = λ 1 λ 2 / λ 1 - λ 2 .
exp [ i ( 2 π / λ 1 ) ϕ ( x , y ) ] + exp ( i ( 2 π / λ 1 ) x sin θ 1 ) ,
2 + ( exp { i ( 2 π / λ 1 ) [ ϕ ( x , y ) - x sin θ 1 ] } + C . C . ) ,
2 exp [ 2 π i ϕ ( x , y ) λ 2 ] + exp { 2 π i [ ϕ ( x , y ) λ 1 + x ( sin θ 2 λ 2 - sin θ 1 λ 1 ) ] } .
I ( x , y ) = 5 + 4 cos 2 π { ϕ ( x , y ) [ 1 / λ 1 ) - ( 1 / λ 2 ) + x [ ( sin θ 2 / λ 2 ) - ( sin θ 1 / λ 1 ) ] } .
I ( x , y ) = 2 + cos 2 π [ ϕ ( x , y ) ( 1 λ 1 - 1 λ 2 ) + x ( sin θ 2 λ 2 - sin θ 1 λ 1 ) ] + 2 { cos 2 π λ 1 [ ϕ ( x , y ) - x sin θ 1 ] + cos 2 π λ 2 [ ϕ ( x , y ) - x sin θ 2 ] } + cos 2 π [ ϕ ( x , y ) ( 1 λ 1 + 1 λ 2 ) - x ( sin θ 2 λ 2 + sin θ 1 λ 1 ) ] .
4 + exp { i ( 2 π / λ 1 ) [ ϕ ( x , y ) - x sin θ 1 ] } + exp { i ( 2 π / λ 2 ) [ ϕ ( x , y ) - x sin θ 2 ] } + C . C .
1 + cos 2 π { ϕ ( x , y ) [ ( 1 / λ 1 ) - ( 1 / λ 2 ) ] + x [ ( sin θ 2 / λ 2 ) - ( sin θ 1 / λ 1 ) ] } .
exp { 2 π i [ ϕ ( x , y ) λ 1 + x ( sin θ 3 λ 3 - sin θ 1 λ 1 ) ] } + exp { 2 π i [ ϕ ( x , y ) λ 2 + x ( sin θ 4 λ 3 - sin θ 2 λ 2 ) ] } .
1 + cos 2 π [ ϕ ( x , y ) ( 1 λ 1 - 1 λ 2 ) + x ( sin θ 2 λ 2 - sin θ 1 λ 1 + sin θ 3 - sin θ 4 λ 3 ) ] .

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