Abstract

A technique for the measurement of inhomogeneity of optical glass, fused silica, etc., using a Sagnac interferometer (SI) has been presented. An SI produces a pair of laterally separated, mutually parallel, collimated beams with orthogonal planes of polarization, i.e., p and s polarizations from an expanded, linearly polarized (45°) collimated He–Ne (632.8 nm) input laser beam. The p and s beams pass through a liquid-filled cell with plane parallel glass windows. The test glass with plane parallel end surfaces is kept in the path of the p beam in the index matching liquid, while the s beam traverses a parallel path through the liquid. Another SI recombines the emergent p and s beams by removing the lateral shear. A quarter-wave plate transforms the state of polarization of the beams to opposite circular polarizations of which the components selected by a linear polarizer interfere to form Fizeau fringes. Polarization phase shifting interferometery has been applied to determine the optical path difference (OPD) variations. The OPD variation without the test glass is subtracted from that with test glass to eliminate the effect of system aberration. The results for a phosphate laser glass sample have been presented.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi, “Separate measurements of surface shapes and refractive index homogeneity of an optical element using tunable source phase shifting interferometry,” Appl. Opt. 29, 3280–3285 (1990).
    [CrossRef]
  8. S. Chatterjee and Y. P. Kumar, “Self referenced technique for the determination of meridional figure errors of a toroidal mirror with a Sagnac interferometer,” Appl. Opt. 51, 7308–7313 (2012).
    [CrossRef]
  9. S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase shifting Fizeau interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (1)

2007 (1)

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase shifting Fizeau interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

1995 (1)

J. M. De Freitas and M. A. Player, “Ultra precision measurements of optical heterogeneity of high quality fused silica,” Appl. Phys. Lett. 66, 3552–3554 (1995).
[CrossRef]

1991 (2)

1990 (1)

1987 (1)

1986 (1)

K. Creath, “Comparisons of phase measurement algorithms,” Proc. SPIE 680, 19–28 (1986).
[CrossRef]

1985 (1)

1972 (1)

1969 (1)

Ai, C.

C. Ai and J. C. Wyant, “Measurement of the inhomogeneity of a window,” Opt. Eng. 30, 1399 (1991).
[CrossRef]

Bhaduri, B.

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase shifting Fizeau interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Burow, R.

Chatterjee, S.

S. Chatterjee and Y. P. Kumar, “Self referenced technique for the determination of meridional figure errors of a toroidal mirror with a Sagnac interferometer,” Appl. Opt. 51, 7308–7313 (2012).
[CrossRef]

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase shifting Fizeau interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Creath, K.

K. Creath, “Comparisons of phase measurement algorithms,” Proc. SPIE 680, 19–28 (1986).
[CrossRef]

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, xxviii. E. Wolf, ed. (North-Holland Amsterdam, 1988), pp. 349–393.

De Freitas, J. M.

J. M. De Freitas and M. A. Player, “Ultra precision measurements of optical heterogeneity of high quality fused silica,” Appl. Phys. Lett. 66, 3552–3554 (1995).
[CrossRef]

Eiju, T.

Elssner, K. E.

Frankena, H. J.

Grzanna, J.

Hariharan, P.

Kumar, Y. P.

S. Chatterjee and Y. P. Kumar, “Self referenced technique for the determination of meridional figure errors of a toroidal mirror with a Sagnac interferometer,” Appl. Opt. 51, 7308–7313 (2012).
[CrossRef]

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase shifting Fizeau interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Langenbeck, P.

Malacara, D.

M. V. Mantravadi and D. Malacara, “Newton, Fizeau, and Haidinger interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 17–32.

D. Malacara, S. Malacara, and Z. Malacara, in Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), pp. 248–255.

Malacara, S.

D. Malacara, S. Malacara, and Z. Malacara, in Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), pp. 248–255.

Malacara, Z.

D. Malacara, S. Malacara, and Z. Malacara, in Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), pp. 248–255.

Mantravadi, M. V.

M. V. Mantravadi and D. Malacara, “Newton, Fizeau, and Haidinger interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 17–32.

Okada, K.

Oreb, B. F.

Ose, T.

Player, M. A.

J. M. De Freitas and M. A. Player, “Ultra precision measurements of optical heterogeneity of high quality fused silica,” Appl. Phys. Lett. 66, 3552–3554 (1995).
[CrossRef]

Reitmayer, F.

Roberts, F. E.

Sakuta, H.

Schuster, E.

Schwider, J.

Smorenburg, C.

Spolaczyk, R.

Tsujiuchi, J.

Wingerden, J. V.

Wyant, J. C.

C. Ai and J. C. Wyant, “Measurement of the inhomogeneity of a window,” Opt. Eng. 30, 1399 (1991).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. Lett. (1)

J. M. De Freitas and M. A. Player, “Ultra precision measurements of optical heterogeneity of high quality fused silica,” Appl. Phys. Lett. 66, 3552–3554 (1995).
[CrossRef]

Opt. Eng. (1)

C. Ai and J. C. Wyant, “Measurement of the inhomogeneity of a window,” Opt. Eng. 30, 1399 (1991).
[CrossRef]

Opt. Laser Technol. (1)

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase shifting Fizeau interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Proc. SPIE (1)

K. Creath, “Comparisons of phase measurement algorithms,” Proc. SPIE 680, 19–28 (1986).
[CrossRef]

Other (3)

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, xxviii. E. Wolf, ed. (North-Holland Amsterdam, 1988), pp. 349–393.

D. Malacara, S. Malacara, and Z. Malacara, in Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), pp. 248–255.

M. V. Mantravadi and D. Malacara, “Newton, Fizeau, and Haidinger interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 17–32.

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Figures (9)

Fig. 1.
Fig. 1.

Optical schematic of the setup for determination of RI inhomogeneity of optical material.

Fig. 2.
Fig. 2.

(a)–(e) Phase shifted Fizeau fringes with the object, applying π/2 phase difference between the successive frames.

Fig. 3.
Fig. 3.

(a)–(e) Phase shifted Fizeau fringes without the object, applying π/2 phase difference between the successive frames.

Fig. 4.
Fig. 4.

Unwrapped two-dimensional OPD (Δ1) map with the object.

Fig. 5.
Fig. 5.

Unwrapped two-dimensional OPD (Δ2) map without the object.

Fig. 6.
Fig. 6.

Variation of the errors in OPD (δΔ1) values with the object, with respect to the fitted plane (FP), in two dimensions.

Fig. 7.
Fig. 7.

Variation of the errors in OPD values (δΔ2) without the object, with respect to the FP, in two dimensions.

Fig. 8.
Fig. 8.

Variation of the OPD values for the object (δΔ) after subtraction of the system errors.

Fig. 9.
Fig. 9.

Variation in RI, (δnd) for the object.

Equations (12)

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Δ2(x,y)=Wp(x,y)Wr(x,y),
Δ1(x,y)=Wp(x,y)+[nd(x,y)nL][WS1(x,y)+d+WS2(x,y)]Wr(x,y),
Δ(x,y)=Δ1(x,y)Δ2(x,y)=[nd(x,y)nL]d+{[WS1(x,y)+WS2(x,y)][nd(x,y)nL]}
[Δ(x,y)d]=nd(x,y)nL+[(WS1+WS2)[nd(x,y)nL]d].
(ndnLd)(λx)=107
x=Δn(λd)107.
Δ(x,y)d=nd(x,y)nL(x,y).
[Δ(x,y)+δΔ(x,y)d]=nd(x,y)+δnd(x,y)nL,
δnd(x,y)=[δΔ(x,y)d]=[δΔ1(x,y)δΔ2(x,y)d].
I(x,y)=I0(x,y){1+V(x,y)cos[β(x,y)+ϕj]},
β=tan1[2(I4I2)I1+I52I3].
Δβ=(ε2/4)sin2β,

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