Abstract

We describe here a grating interferometer with extremely high stability and which can be used as a differential refractometer. The instrument uses heterodyne techniques to achieve high sensitivity. We present an analysis of the operation of the system and results which show that it has a long term stability of the order of 1/1500 wavelength over 2 h.

© 1991 Optical Society of America

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References

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  1. P. Debye, “Light Scattering in Solutions,” J. Appl. Phys. 15, 338–342 (1944).
    [CrossRef]
  2. R. Kocholaty, “Microbiological Oxidation of Ethanol in Volatile Fruit Concentrates,” Food Res. 15, 347–354 (1950).
    [CrossRef] [PubMed]
  3. A. Weissberger, Ed., Physical Methods of Organic Chemistry (Interscience, New York, 1949), Chap. 20.
  4. B. A. Brice, M. Halwer “A Differential Refractometer,” J. Opt. Soc. Am. 41, 1033–1037 (1951).
    [CrossRef]
  5. E. S. Watson “Differential Refractometry,” U.S. Patent3,386,332 (4June1968).
  6. W. Kinder “Ein Interferenz-Refraktometer fur Gase und Flussigkeiten,” Optik Stuttgart 24, 323–334 (1966).
  7. L. J. Edwards, B. D. Hopkins, D. D. Rice “Apparatus for Measuring Changes in the Optical Refractive Index of Fluids,” U.S. Patent3,680,963 (1Aug.1972).
  8. N. Konforti, E. Marom, S. T. Wu “Phase-Only Modulation With Twisted Nematic Liquid-Crystal Spatial Light Modulators,” Opt. Lett. 13, 251–253 (1988).
    [CrossRef] [PubMed]
  9. T. H. Barnes “Heterodyne Fizeau Interferometer for Testing Flat Surfaces,” Appl. Opt. 26, 2804–2809 (1987).
    [CrossRef] [PubMed]

1988 (1)

1987 (1)

1966 (1)

W. Kinder “Ein Interferenz-Refraktometer fur Gase und Flussigkeiten,” Optik Stuttgart 24, 323–334 (1966).

1951 (1)

1950 (1)

R. Kocholaty, “Microbiological Oxidation of Ethanol in Volatile Fruit Concentrates,” Food Res. 15, 347–354 (1950).
[CrossRef] [PubMed]

1944 (1)

P. Debye, “Light Scattering in Solutions,” J. Appl. Phys. 15, 338–342 (1944).
[CrossRef]

Barnes, T. H.

Brice, B. A.

Debye, P.

P. Debye, “Light Scattering in Solutions,” J. Appl. Phys. 15, 338–342 (1944).
[CrossRef]

Edwards, L. J.

L. J. Edwards, B. D. Hopkins, D. D. Rice “Apparatus for Measuring Changes in the Optical Refractive Index of Fluids,” U.S. Patent3,680,963 (1Aug.1972).

Halwer, M.

Hopkins, B. D.

L. J. Edwards, B. D. Hopkins, D. D. Rice “Apparatus for Measuring Changes in the Optical Refractive Index of Fluids,” U.S. Patent3,680,963 (1Aug.1972).

Kinder, W.

W. Kinder “Ein Interferenz-Refraktometer fur Gase und Flussigkeiten,” Optik Stuttgart 24, 323–334 (1966).

Kocholaty, R.

R. Kocholaty, “Microbiological Oxidation of Ethanol in Volatile Fruit Concentrates,” Food Res. 15, 347–354 (1950).
[CrossRef] [PubMed]

Konforti, N.

Marom, E.

Rice, D. D.

L. J. Edwards, B. D. Hopkins, D. D. Rice “Apparatus for Measuring Changes in the Optical Refractive Index of Fluids,” U.S. Patent3,680,963 (1Aug.1972).

Watson, E. S.

E. S. Watson “Differential Refractometry,” U.S. Patent3,386,332 (4June1968).

Wu, S. T.

Appl. Opt. (1)

Food Res. (1)

R. Kocholaty, “Microbiological Oxidation of Ethanol in Volatile Fruit Concentrates,” Food Res. 15, 347–354 (1950).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

P. Debye, “Light Scattering in Solutions,” J. Appl. Phys. 15, 338–342 (1944).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Optik Stuttgart (1)

W. Kinder “Ein Interferenz-Refraktometer fur Gase und Flussigkeiten,” Optik Stuttgart 24, 323–334 (1966).

Other (3)

L. J. Edwards, B. D. Hopkins, D. D. Rice “Apparatus for Measuring Changes in the Optical Refractive Index of Fluids,” U.S. Patent3,680,963 (1Aug.1972).

A. Weissberger, Ed., Physical Methods of Organic Chemistry (Interscience, New York, 1949), Chap. 20.

E. S. Watson “Differential Refractometry,” U.S. Patent3,386,332 (4June1968).

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Figures (9)

Fig. 1
Fig. 1

Optical system of the instrument.

Fig. 2
Fig. 2

Optical system of the interferometer with important phase delays marked.

Fig. 3
Fig. 3

Interferometer output phase error introduced by second-order diffraction effects. Relative intensity of the second order was 0.01.

Fig. 4
Fig. 4

Optical system of the interferometer unwrapped about mirror M1 (see text).

Fig. 5
Fig. 5

Block diagram of the data logging and analysis system of the interferometer.

Fig. 6
Fig. 6

Drift characteristic of the interferometer. (no sample, wavelength = 632.8 nm).

Fig. 7
Fig. 7

Variation of path difference caused by rotation of a glass plate; interferometer measurements are compared with theoretical result. All path differences in wavelength 632.8 nm.

Fig. 8
Fig. 8

Modulated and unmodulated areas of the liquid crystal panel.

Fig. 9
Fig. 9

Phase modulation characteristic of the liquid crystal.

Equations (10)

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A 1 A 2 cos ( w t + 3 ϕ D + 2 S + 2 P 1 ) + A 1 cos ( w t + ϕ D + 2 P 0 ) + A 1 cos ( w t ϕ D + 2 P 1 ) ,
A 1 cos ( w t + ϕ D + 2 S + 2 P 1 ) + A 1 cos ( w t ϕ D + 2 P 0 ) + A 1 A 2 cos ( w t 3 ϕ D + 2 P 1 ) .
I + 1 = A 1 2 { 2 + A 2 2 + 2 cos [ 2 ϕ D + 2 ( P 0 P 1 ) ] + 2 A 2 cos [ 2 ϕ D + 2 S + 2 ( P 1 P 0 ) ] + 2 A 2 cos [ 4 ϕ D + 2 S + 2 ( P 1 P 1 ) ] } ,
I 1 = A 1 2 { 2 + A 2 2 + 2 cos [ 2 ϕ D + 2 ( P 1 P 0 ) ] + 2 A 2 cos [ 2 ϕ D + 2 ( P 0 P 1 ) ] + 2 A 2 cos [ 4 ϕ D + 2 S + 2 ( P 1 P 1 ) ] } .
2 S 2 tan 1 [ A 2 sin 2 S / ( 1 + A 2 cos 2 S ) ] .
x = f 2 Δ / ( 2 Δ 2 f 2 ) ,
x Δ
s = 2 Δ λ / d ,
path difference = 2 Δ λ 2 / d 2 .
8 π Δ λ / d 2 .

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