Abstract

A polarization Sagnac interferometer (SI) is used to produce two laterally separated, identical, convergent emergent beams with linear orthogonal polarizations. The emergent p-polarized and s-polarized beams converge toward their respective focal points. The test and reference spherical mirrors are placed at confocal positions with respect to the s and p focal points so as to normally reflect back the test and reference beams through the SI that recombines the test and reference waves. Polarization phase shifting interferometry is applied to obtain the surface form error of the test surface with respect to the reference surface. A two-step measurement procedure eliminates the system aberrations. Results obtained for a concave spherical test surface with respect to a convex spherical reference surface are presented. The optical configuration is relatively less susceptible to external mechanical vibration.

© 2014 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon, 1989), pp. 286–291.
  2. M. V. Mantravadi and D. Malacara, “Newton, Fizeau and Haidinger interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 17–32.
  3. K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, 1988), Vol. 28, pp. 349–393.
  4. J. Schwider, “Advanced evaluation technique in interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, 1990), Vol. 28, pp. 271–359.
  5. J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 547–655.
  6. C. Ai and J. C. Wyant, “Effect of piezo-electric transducer non-linearity on phase shift interferomer,” Appl. Opt. 26, 1112–1116 (1987).
    [CrossRef]
  7. K. Creath and P. Hariharan, “Phase shifting errors in interferometric tests with high numerical aperture reference surfaces,” Appl. Opt. 33, 24–25 (1994).
    [CrossRef]
  8. S. Chatterjee and Y. P. Kumar, “Measurement of the surface form error of a spherical surface with a wedge phase shifting Fizeau interferometer,” J. Opt. 42, 122–127 (2013).
    [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]
  10. D. Malacara, “Newton, Fizeau and Haidinger interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 46–91.
  11. J. C. Wyant, “Computerized interferometric surface measurements,” Appl. Opt. 52, 1–8 (2013).
    [CrossRef]
  12. S. Chatterjee and Y. P. Kumar, “Determination of the index inhomogeneity of transparent isotropic optical material with a dual Sagnac interferometer,” Appl. Opt. 52, 4820–4826 (2013).
    [CrossRef]
  13. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase shifting interferometery: a simple error compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
    [CrossRef]
  14. D. Malacara, S. Malacara, and Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998), pp. 248–255.

2013

2007

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]

1994

1987

Ai, C.

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]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1989), pp. 286–291.

Bruning, J. H.

J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 547–655.

Chatterjee, S.

S. Chatterjee and Y. P. Kumar, “Measurement of the surface form error of a spherical surface with a wedge phase shifting Fizeau interferometer,” J. Opt. 42, 122–127 (2013).
[CrossRef]

S. Chatterjee and Y. P. Kumar, “Determination of the index inhomogeneity of transparent isotropic optical material with a dual Sagnac interferometer,” Appl. Opt. 52, 4820–4826 (2013).
[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 and P. Hariharan, “Phase shifting errors in interferometric tests with high numerical aperture reference surfaces,” Appl. Opt. 33, 24–25 (1994).
[CrossRef]

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, 1988), Vol. 28, pp. 349–393.

Eiju, T.

Greivenkamp, J. E.

J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 547–655.

Hariharan, P.

Kumar, Y. P.

S. Chatterjee and Y. P. Kumar, “Determination of the index inhomogeneity of transparent isotropic optical material with a dual Sagnac interferometer,” Appl. Opt. 52, 4820–4826 (2013).
[CrossRef]

S. Chatterjee and Y. P. Kumar, “Measurement of the surface form error of a spherical surface with a wedge phase shifting Fizeau interferometer,” J. Opt. 42, 122–127 (2013).
[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]

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, “Newton, Fizeau and Haidinger interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 46–91.

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

Malacara, S.

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

Malacara, Z.

D. Malacara, S. Malacara, and Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 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.

Oreb, B. F.

Schwider, J.

J. Schwider, “Advanced evaluation technique in interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, 1990), Vol. 28, pp. 271–359.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1989), pp. 286–291.

Wyant, J. C.

Appl. Opt.

J. Opt.

S. Chatterjee and Y. P. Kumar, “Measurement of the surface form error of a spherical surface with a wedge phase shifting Fizeau interferometer,” J. Opt. 42, 122–127 (2013).
[CrossRef]

Opt. Laser Technol.

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]

Other

D. Malacara, “Newton, Fizeau and Haidinger interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 46–91.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1989), pp. 286–291.

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

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, 1988), Vol. 28, pp. 349–393.

J. Schwider, “Advanced evaluation technique in interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, 1990), Vol. 28, pp. 271–359.

J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 547–655.

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

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Figures (8)

Fig. 1.
Fig. 1.

Optical schematic of the SI-based setup for surface form error measurement of spherical mirror.

Fig. 2.
Fig. 2.

(a)–(e) Phase shifted Fizeau fringes, for phase steps of π/2 between successive frames, obtained with SET1.

Fig. 3.
Fig. 3.

(a)–(e) Phase shifted Fizeau fringes, for phase steps of π/2 between successive frames, obtained with SET2.

Fig. 4.
Fig. 4.

Unwrapped two-dimensional OPD [OPDTS] variations for SET1.

Fig. 5.
Fig. 5.

Unwrapped two-dimensional OPD [OPDMS] variations for SET2.

Fig. 6.
Fig. 6.

Variation of errors in OPD [Δ1] with respect to the fitted plane for SET1.

Fig. 7.
Fig. 7.

Variation of errors in OPD [Δ2] with respect to the fitted plane for SET2.

Fig. 8.
Fig. 8.

Surface form error [Δ] of STM.

Equations (8)

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Δ1=[WSTM(x,y)+WS(x,y)][WSRM(x,y)+WP(x,y)],
Δ2=[WSRM(x,y)+WS(x,y)][WSTM(x,y)+WP(x,y)].
[WSTM(x,y)WSRM(x,y)]=[Δ1Δ22].
ΔSYS=[Δ1+Δ22].
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,
Δ=(λ4π)β.

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