Abstract

In diffraction-limited optical systems the number of optical components is rather high. Local changes in the refractive index of the order of 10−6 must be detected to guarantee an adequate performance of the system as a whole. Therefore, the Twyman-Perry method for the evaluation of refractive-index deviations from uniformity—further developed by Roberts and Langenbeck—has been programmed for a digital Twy-man-Green interferometer. If the glass block to be tested is slightly wedge shaped (wedge angle ~10−3 rad), the measurement can be carried out without coating the glass block. With the help of four interferograms the variations of the refractive index apart from a linear slope, as well as the thickness variations of the glass block, can be measured and displayed.

© 1985 Optical Society of America

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References

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  1. F. Twyman, J. W. Perry, “Measuring Small Differences of Refractive Index,” Proc. Phys. Soc. London 34, 151 (1922); C. Candler, Modern Interferometers (Hilger & Watts, London, 1951).
    [CrossRef]
  2. F. E. Roberts, P. Langenbeck, “Homogeneity Evaluation of Very Large Disks,” Appl. Opt. 8, 2311 (1969).
    [CrossRef] [PubMed]
  3. J. Schwider, “Interferometrische Homogenitatsprüfung mit Kompensation,” Opt. Commun. 6, 106 (1972).
    [CrossRef]
  4. J. H. Bruning, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, D. R. Herriott, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  5. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421 (1983); J. Schwider et al., “High Accuracy Phase Measurement in Real Time,” Proc. Soc. Photo-Opt. Instrum. Eng. 473, 156 (1984); J. Schwider et al., “Echtzeitinterferometrie,” Opt. Appl.15, (1985), in press; J. Schwider et al., “Echtzeitinterferometer für die Op-tikprüfung,” Opt. Appl.15, (1985), in press.
    [CrossRef] [PubMed]
  6. R. Dandliker, “Heterodyne Holographic Interferometry,” Prog. Opt. 17, 1 (1980); N. A. Massie, R. D. Nelson, S. Holly, “High-Performance Real-Time Heterodyne Interferometry,” Appl. Opt. 18, 1797 (1979).
    [CrossRef] [PubMed]

1983 (1)

1980 (1)

R. Dandliker, “Heterodyne Holographic Interferometry,” Prog. Opt. 17, 1 (1980); N. A. Massie, R. D. Nelson, S. Holly, “High-Performance Real-Time Heterodyne Interferometry,” Appl. Opt. 18, 1797 (1979).
[CrossRef] [PubMed]

1974 (1)

1972 (1)

J. Schwider, “Interferometrische Homogenitatsprüfung mit Kompensation,” Opt. Commun. 6, 106 (1972).
[CrossRef]

1969 (1)

1922 (1)

F. Twyman, J. W. Perry, “Measuring Small Differences of Refractive Index,” Proc. Phys. Soc. London 34, 151 (1922); C. Candler, Modern Interferometers (Hilger & Watts, London, 1951).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Burow, R.

Dandliker, R.

R. Dandliker, “Heterodyne Holographic Interferometry,” Prog. Opt. 17, 1 (1980); N. A. Massie, R. D. Nelson, S. Holly, “High-Performance Real-Time Heterodyne Interferometry,” Appl. Opt. 18, 1797 (1979).
[CrossRef] [PubMed]

Elssner, K.-E.

Gallagher, J. E.

Grzanna, J.

Herriott, D. R.

Langenbeck, P.

Merkel, K.

Perry, J. W.

F. Twyman, J. W. Perry, “Measuring Small Differences of Refractive Index,” Proc. Phys. Soc. London 34, 151 (1922); C. Candler, Modern Interferometers (Hilger & Watts, London, 1951).
[CrossRef]

Roberts, F. E.

Rosenfeld, D. P.

Schwider, J.

Spolaczyk, R.

Twyman, F.

F. Twyman, J. W. Perry, “Measuring Small Differences of Refractive Index,” Proc. Phys. Soc. London 34, 151 (1922); C. Candler, Modern Interferometers (Hilger & Watts, London, 1951).
[CrossRef]

White, A. D.

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Figures (4)

Fig. 1
Fig. 1

Interferometric setup used for homogeneity testing. The Twyman-Green interferometer is equipped for the phase sampling technique. A polarizing beam splitter (PBS) allows for the balancing of intensities in the single test steps.

Fig. 2
Fig. 2

Four-step procedure for homogeneity evaluations. Only the essential part of the test arm of the interferometer is shown; the optical ray path is schematic.

Fig. 3
Fig. 3

Δn variations of a 65-mm diam fused silica plate: (a) pseudo-3-D plot of t0Δn; (b) contour line plot of t0Δn; λ/16 is equivalent to Δn = 4.04 × 10−6, Δnrma = 1.55 × 10−6, ΔnPV = 1.69 × 10−5; (c) PUA representation of t0Δn; S, slice level; S = 0.01λ is equivalent to 6.5 × 10−7; P, percentage of usable area; values calculated for 0.9 of the diameter of the sample; (d) superimposition of contour line plot on the PUA representation for S = 0.02λ and a contour line distance of 0.02λ corresponding to Δn = 1.3 × 10−6.

Fig. 4
Fig. 4

Thickness variation z1 + z2: (a) pseudo-3-D plot; (b) contour line plot; (c) PUA representation with a slice level of λ/16.

Equations (6)

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t ( x , y ) = t 0 + z 1 ( x , y ) + z 2 ( x , y ) .
n ( x , y ) = n 0 + Δ n ( x , y ) .
W 1 = W I 2 z 1 , W 2 = W I + 2 ( n 0 1 ) z 1 + 2 n 0 z 2 + 2 t 0 Δ n , W 3 = W I + 2 ( n 0 1 ) ( z 1 + z 2 ) + 2 t 0 Δ n 2 z 3 , W 4 = W I 2 z 3 ,
W 2 W 1 = 2 n 0 ( z 1 + z 2 ) + 2 t 0 Δ n , W 3 W 4 = 2 ( n 0 1 ) ( z 1 + z 2 ) + 2 t 0 Δ n .
Δ n = 1 2 t 0 [ n 0 ( W 3 W 4 ) ( n 0 1 ) ( W 2 W 1 ) ] ,
z 1 + z 2 = 1 2 [ ( W 2 W 1 ) ( W 3 W 4 ) ] .

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