Abstract

A new instrument, the liquid-crystal point-diffraction interferometer (LCPDI), is developed for the measurement of phase objects. This instrument maintains the compact, robust design of Linnik's point-diffraction interferometer and adds to it a phase-stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave fronts with very high data density and with automated data reduction. We describe the theory and design of the LCPDI. Afocus shift was measured with the LCPDI, and the results are compared with theoretical results.

© 1996 Optical Society of America

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  1. V. P. Linnik, “Simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. USSR, 1, 208–210 (1933).
  2. R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (abstract only), (1972).
  3. R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” J. Appl. Phys. 14 (Suppl. 14-1), 351–357 (1975).
  4. R. J. Speer, M. Crisp, D. Turner, S. Mrowka, K. Tregidjo, “Grazing incidence interferometry: the use of the Linnik interferometer for testing image-forming reflection systems,” Appl. Opt. 18, 2003–2012 (1979).
    [Crossref] [PubMed]
  5. J. P. Marioge, B. Bonino, F. Bridou, P. Fournet, M. Mullot, “La fabrication et le controle de surface toriques,” J. Opt. (Paris) 15, 286–292 (1984).
    [Crossref]
  6. C. Koliopoulos, O. Kwon, R. Shagam, J. C. Wyant, C. R. Hayslett, “Infrared point-diffraction interferometer,” Opt. Lett. 3, 118–120 (1978).
    [Crossref] [PubMed]
  7. W. Harris, S. Mrowka, R. J. Speer, “Linnik interferometer: its use at short wavelengths,” Appl. Opt. 21, 1155 (1982).
    [Crossref] [PubMed]
  8. A. K. Aggarwal, S. K. Kaura, “Further applications of point diffraction interferometer,” J. Opt. (Paris) 17, 135–138 (1986).
    [Crossref]
  9. M. Giglio, E. Paganini, U. Perini, “A self-aligning point diffraction interferometer for fluid studies,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.805, 82–86 (1987).
  10. S. Musazzi, U. Perini, F. Trespidi, “Point diffraction interferometer for fluids study in microgravity environment,” Exp. Therm. Fluid Sci. 6, 49–55 (1993).
    [Crossref]
  11. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics XXVI, E. Wolf, ed. (Elsevier, New York, 1988), Chap. 5.
    [Crossref]
  12. K. Underwood, J. C. Wyant, C. L. Koliopoulos, “Self-referencing wavefront sensor,” in Wavefront Sensing, N. Bareket, C. L. Koliopoulos, eds., Proc. Soc. Photo-Opt. Instrum. Eng.351, 108–114 (1982).
  13. O. Y. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9, 59–61 (1984).
    [Crossref] [PubMed]
  14. H. Kadono, N. Takai, T. Asakura, “New common-path phase shifting interferometer using a polarization technique,” Appl. Opt. 26, 898–904 (1987).
    [Crossref] [PubMed]
  15. J. Ojeda-Castaneda, Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), Chap. 8.
  16. H. Kadono, M. Ogusu, S. Toyooka, “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Commun. 110, 391–400 (1994).
    [Crossref]
  17. K. Iwata, T. Nishikawa, “Profile measurement with a phase-shifting common-path polarization interferometer,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a SeriesR. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 389–394 (1990).
  18. E. G. Churin, A. G. Sedukhin, “Diffraction common-path interferometer,” Optoelectron. Instrum. Data Proc. 3, 71–74 (1994).
  19. C. R. Mercer, K. Creath, “Liquid crystal point diffraction interferometer,” Opt. Lett. 19, 916–918 (1994).
    [Crossref] [PubMed]
  20. S.-T. Wu, U. Efron, L. D. Hess, “Rotatory power and optical modulation of liquid crystals,” in Spatial Light Modulators and Applications I, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.465, 66–73 (1984).
  21. J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
    [Crossref] [PubMed]
  22. C. R. Mercer, K. Creath, “Phase measurement using a liquid crystal point diffraction interferometer,” in Industrial Optical Sensors for Metrology and Inspection, K. G. Harding, H. P. Stahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2349, 95–99 (1994).
  23. A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).
  24. G. H. Heilmeier, J. A. Castellano, L. A. Zanoni, “Guest-host interactions in nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 8, 293–304 (1969).
    [Crossref]
  25. C. R. Mercer, “Liquid crystal point diffraction interferometer,” Ph.D. dissertation (University Microfilms, Inc., Tucson Ariz., 1995).
  26. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

1994 (3)

H. Kadono, M. Ogusu, S. Toyooka, “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Commun. 110, 391–400 (1994).
[Crossref]

E. G. Churin, A. G. Sedukhin, “Diffraction common-path interferometer,” Optoelectron. Instrum. Data Proc. 3, 71–74 (1994).

C. R. Mercer, K. Creath, “Liquid crystal point diffraction interferometer,” Opt. Lett. 19, 916–918 (1994).
[Crossref] [PubMed]

1993 (1)

S. Musazzi, U. Perini, F. Trespidi, “Point diffraction interferometer for fluids study in microgravity environment,” Exp. Therm. Fluid Sci. 6, 49–55 (1993).
[Crossref]

1991 (1)

1987 (2)

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

H. Kadono, N. Takai, T. Asakura, “New common-path phase shifting interferometer using a polarization technique,” Appl. Opt. 26, 898–904 (1987).
[Crossref] [PubMed]

1986 (1)

A. K. Aggarwal, S. K. Kaura, “Further applications of point diffraction interferometer,” J. Opt. (Paris) 17, 135–138 (1986).
[Crossref]

1984 (2)

J. P. Marioge, B. Bonino, F. Bridou, P. Fournet, M. Mullot, “La fabrication et le controle de surface toriques,” J. Opt. (Paris) 15, 286–292 (1984).
[Crossref]

O. Y. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9, 59–61 (1984).
[Crossref] [PubMed]

1982 (1)

1979 (1)

1978 (1)

1975 (1)

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” J. Appl. Phys. 14 (Suppl. 14-1), 351–357 (1975).

1972 (1)

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (abstract only), (1972).

1969 (1)

G. H. Heilmeier, J. A. Castellano, L. A. Zanoni, “Guest-host interactions in nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 8, 293–304 (1969).
[Crossref]

1933 (1)

V. P. Linnik, “Simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. USSR, 1, 208–210 (1933).

Aggarwal, A. K.

A. K. Aggarwal, S. K. Kaura, “Further applications of point diffraction interferometer,” J. Opt. (Paris) 17, 135–138 (1986).
[Crossref]

Amako, J.

Asakura, T.

Bonino, B.

J. P. Marioge, B. Bonino, F. Bridou, P. Fournet, M. Mullot, “La fabrication et le controle de surface toriques,” J. Opt. (Paris) 15, 286–292 (1984).
[Crossref]

Bridou, F.

J. P. Marioge, B. Bonino, F. Bridou, P. Fournet, M. Mullot, “La fabrication et le controle de surface toriques,” J. Opt. (Paris) 15, 286–292 (1984).
[Crossref]

Castellano, J. A.

G. H. Heilmeier, J. A. Castellano, L. A. Zanoni, “Guest-host interactions in nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 8, 293–304 (1969).
[Crossref]

Churin, E. G.

E. G. Churin, A. G. Sedukhin, “Diffraction common-path interferometer,” Optoelectron. Instrum. Data Proc. 3, 71–74 (1994).

Creath, K.

C. R. Mercer, K. Creath, “Liquid crystal point diffraction interferometer,” Opt. Lett. 19, 916–918 (1994).
[Crossref] [PubMed]

C. R. Mercer, K. Creath, “Phase measurement using a liquid crystal point diffraction interferometer,” in Industrial Optical Sensors for Metrology and Inspection, K. G. Harding, H. P. Stahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2349, 95–99 (1994).

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics XXVI, E. Wolf, ed. (Elsevier, New York, 1988), Chap. 5.
[Crossref]

Crisp, M.

Efron, U.

S.-T. Wu, U. Efron, L. D. Hess, “Rotatory power and optical modulation of liquid crystals,” in Spatial Light Modulators and Applications I, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.465, 66–73 (1984).

Faucz, E. C.

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

Fournet, P.

J. P. Marioge, B. Bonino, F. Bridou, P. Fournet, M. Mullot, “La fabrication et le controle de surface toriques,” J. Opt. (Paris) 15, 286–292 (1984).
[Crossref]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Giglio, M.

M. Giglio, E. Paganini, U. Perini, “A self-aligning point diffraction interferometer for fluid studies,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.805, 82–86 (1987).

Harris, W.

Hayslett, C. R.

Heilmeier, G. H.

G. H. Heilmeier, J. A. Castellano, L. A. Zanoni, “Guest-host interactions in nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 8, 293–304 (1969).
[Crossref]

Hess, L. D.

S.-T. Wu, U. Efron, L. D. Hess, “Rotatory power and optical modulation of liquid crystals,” in Spatial Light Modulators and Applications I, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.465, 66–73 (1984).

Hudson, R. A.

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

Hull, V. J.

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

Iwata, K.

K. Iwata, T. Nishikawa, “Profile measurement with a phase-shifting common-path polarization interferometer,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a SeriesR. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 389–394 (1990).

Kadono, H.

H. Kadono, M. Ogusu, S. Toyooka, “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Commun. 110, 391–400 (1994).
[Crossref]

H. Kadono, N. Takai, T. Asakura, “New common-path phase shifting interferometer using a polarization technique,” Appl. Opt. 26, 898–904 (1987).
[Crossref] [PubMed]

Kaura, S. K.

A. K. Aggarwal, S. K. Kaura, “Further applications of point diffraction interferometer,” J. Opt. (Paris) 17, 135–138 (1986).
[Crossref]

Koliopoulos, C.

Koliopoulos, C. L.

K. Underwood, J. C. Wyant, C. L. Koliopoulos, “Self-referencing wavefront sensor,” in Wavefront Sensing, N. Bareket, C. L. Koliopoulos, eds., Proc. Soc. Photo-Opt. Instrum. Eng.351, 108–114 (1982).

Kwon, O.

Kwon, O. Y.

LaKatos, A. I.

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

Linnik, V. P.

V. P. Linnik, “Simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. USSR, 1, 208–210 (1933).

Marioge, J. P.

J. P. Marioge, B. Bonino, F. Bridou, P. Fournet, M. Mullot, “La fabrication et le controle de surface toriques,” J. Opt. (Paris) 15, 286–292 (1984).
[Crossref]

Martel, R. A.

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

Mercer, C. R.

C. R. Mercer, K. Creath, “Liquid crystal point diffraction interferometer,” Opt. Lett. 19, 916–918 (1994).
[Crossref] [PubMed]

C. R. Mercer, “Liquid crystal point diffraction interferometer,” Ph.D. dissertation (University Microfilms, Inc., Tucson Ariz., 1995).

C. R. Mercer, K. Creath, “Phase measurement using a liquid crystal point diffraction interferometer,” in Industrial Optical Sensors for Metrology and Inspection, K. G. Harding, H. P. Stahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2349, 95–99 (1994).

Mrowka, S.

Mullot, M.

J. P. Marioge, B. Bonino, F. Bridou, P. Fournet, M. Mullot, “La fabrication et le controle de surface toriques,” J. Opt. (Paris) 15, 286–292 (1984).
[Crossref]

Musazzi, S.

S. Musazzi, U. Perini, F. Trespidi, “Point diffraction interferometer for fluids study in microgravity environment,” Exp. Therm. Fluid Sci. 6, 49–55 (1993).
[Crossref]

Narang, R.

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

Nishikawa, T.

K. Iwata, T. Nishikawa, “Profile measurement with a phase-shifting common-path polarization interferometer,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a SeriesR. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 389–394 (1990).

Ogusu, M.

H. Kadono, M. Ogusu, S. Toyooka, “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Commun. 110, 391–400 (1994).
[Crossref]

Ojeda-Castaneda, J.

J. Ojeda-Castaneda, Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), Chap. 8.

Paganini, E.

M. Giglio, E. Paganini, U. Perini, “A self-aligning point diffraction interferometer for fluid studies,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.805, 82–86 (1987).

Perini, U.

S. Musazzi, U. Perini, F. Trespidi, “Point diffraction interferometer for fluids study in microgravity environment,” Exp. Therm. Fluid Sci. 6, 49–55 (1993).
[Crossref]

M. Giglio, E. Paganini, U. Perini, “A self-aligning point diffraction interferometer for fluid studies,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.805, 82–86 (1987).

Perregaux, A. E.

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

Richter, B.

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

Sedukhin, A. G.

E. G. Churin, A. G. Sedukhin, “Diffraction common-path interferometer,” Optoelectron. Instrum. Data Proc. 3, 71–74 (1994).

Shagam, R.

Smartt, R. N.

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” J. Appl. Phys. 14 (Suppl. 14-1), 351–357 (1975).

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (abstract only), (1972).

Sonehara, T.

Speer, R. J.

Steel, W. H.

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” J. Appl. Phys. 14 (Suppl. 14-1), 351–357 (1975).

Stephany, J. F.

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

Strong, J.

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (abstract only), (1972).

Takai, N.

Toyooka, S.

H. Kadono, M. Ogusu, S. Toyooka, “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Commun. 110, 391–400 (1994).
[Crossref]

Tregidjo, K.

Trespidi, F.

S. Musazzi, U. Perini, F. Trespidi, “Point diffraction interferometer for fluids study in microgravity environment,” Exp. Therm. Fluid Sci. 6, 49–55 (1993).
[Crossref]

Turner, D.

Underwood, K.

K. Underwood, J. C. Wyant, C. L. Koliopoulos, “Self-referencing wavefront sensor,” in Wavefront Sensing, N. Bareket, C. L. Koliopoulos, eds., Proc. Soc. Photo-Opt. Instrum. Eng.351, 108–114 (1982).

Wu, S.-T.

S.-T. Wu, U. Efron, L. D. Hess, “Rotatory power and optical modulation of liquid crystals,” in Spatial Light Modulators and Applications I, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.465, 66–73 (1984).

Wyant, J. C.

C. Koliopoulos, O. Kwon, R. Shagam, J. C. Wyant, C. R. Hayslett, “Infrared point-diffraction interferometer,” Opt. Lett. 3, 118–120 (1978).
[Crossref] [PubMed]

K. Underwood, J. C. Wyant, C. L. Koliopoulos, “Self-referencing wavefront sensor,” in Wavefront Sensing, N. Bareket, C. L. Koliopoulos, eds., Proc. Soc. Photo-Opt. Instrum. Eng.351, 108–114 (1982).

Zanoni, L. A.

G. H. Heilmeier, J. A. Castellano, L. A. Zanoni, “Guest-host interactions in nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 8, 293–304 (1969).
[Crossref]

Appl. Opt. (4)

C. R. Acad. Sci. USSR (1)

V. P. Linnik, “Simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. USSR, 1, 208–210 (1933).

Exp. Therm. Fluid Sci. (1)

S. Musazzi, U. Perini, F. Trespidi, “Point diffraction interferometer for fluids study in microgravity environment,” Exp. Therm. Fluid Sci. 6, 49–55 (1993).
[Crossref]

J. Appl. Phys. (1)

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” J. Appl. Phys. 14 (Suppl. 14-1), 351–357 (1975).

J. Opt. (Paris) (2)

A. K. Aggarwal, S. K. Kaura, “Further applications of point diffraction interferometer,” J. Opt. (Paris) 17, 135–138 (1986).
[Crossref]

J. P. Marioge, B. Bonino, F. Bridou, P. Fournet, M. Mullot, “La fabrication et le controle de surface toriques,” J. Opt. (Paris) 15, 286–292 (1984).
[Crossref]

J. Opt. Soc. Am. (1)

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (abstract only), (1972).

Mol. Cryst. Liq. Cryst. (1)

G. H. Heilmeier, J. A. Castellano, L. A. Zanoni, “Guest-host interactions in nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 8, 293–304 (1969).
[Crossref]

Opt. Commun. (1)

H. Kadono, M. Ogusu, S. Toyooka, “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Commun. 110, 391–400 (1994).
[Crossref]

Opt. Lett. (3)

Optoelectron. Instrum. Data Proc. (1)

E. G. Churin, A. G. Sedukhin, “Diffraction common-path interferometer,” Optoelectron. Instrum. Data Proc. 3, 71–74 (1994).

SID Dig. (1)

A. E. Perregaux, J. F. Stephany, E. C. Faucz, R. A. Hudson, V. J. Hull, A. I. LaKatos, R. A. Martel, R. Narang, B. Richter, “Transient nematic liquid crystal image bar for electrophotographic printers,” SID Dig. 28, 360–362 (1987).

Other (9)

C. R. Mercer, K. Creath, “Phase measurement using a liquid crystal point diffraction interferometer,” in Industrial Optical Sensors for Metrology and Inspection, K. G. Harding, H. P. Stahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2349, 95–99 (1994).

C. R. Mercer, “Liquid crystal point diffraction interferometer,” Ph.D. dissertation (University Microfilms, Inc., Tucson Ariz., 1995).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

M. Giglio, E. Paganini, U. Perini, “A self-aligning point diffraction interferometer for fluid studies,” in Optical Components and Systems, A. Masson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.805, 82–86 (1987).

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics XXVI, E. Wolf, ed. (Elsevier, New York, 1988), Chap. 5.
[Crossref]

K. Underwood, J. C. Wyant, C. L. Koliopoulos, “Self-referencing wavefront sensor,” in Wavefront Sensing, N. Bareket, C. L. Koliopoulos, eds., Proc. Soc. Photo-Opt. Instrum. Eng.351, 108–114 (1982).

J. Ojeda-Castaneda, Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), Chap. 8.

S.-T. Wu, U. Efron, L. D. Hess, “Rotatory power and optical modulation of liquid crystals,” in Spatial Light Modulators and Applications I, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.465, 66–73 (1984).

K. Iwata, T. Nishikawa, “Profile measurement with a phase-shifting common-path polarization interferometer,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a SeriesR. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 389–394 (1990).

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Figures (11)

Fig. 1.
Fig. 1.

Schematic of the LCPDI showing the liquid-crystal layer, glass plates, microsphere, spacing rods, electrodes, and leads. The object wave is shown as a solid curve and the reference wave is shown as a dashed curve.

Fig. 2.
Fig. 2.

Effect of applied electric field on liquid-crystal molecules.

Fig. 3.
Fig. 3.

Liquid-crystal layer intensity calibration curve.

Fig. 4.
Fig. 4.

Ray model of the LCPDI.

Fig. 5.
Fig. 5.

Planes used in Fourier analysis.

Fig. 6.
Fig. 6.

Transmittance and phase delay of the LCPDI filter.

Fig. 7.
Fig. 7.

Effect of pinhole diameter on reference wave.

Fig. 8.
Fig. 8.

Optical configuration for defocus measurement.

Fig. 9.
Fig. 9.

Wave-front difference calculated with a standard five-frame algorithm.

Fig. 10.
Fig. 10.

Wave-front difference calculated with exact compensation algorithm [Eq. (9)].

Fig. 11.
Fig. 11.

Cross sections of wave-front differences computed from (a) two-dimensional polynomial curve fits, (b) standard five-frame algorithm, (c) exact compensation algorithm [Eq. (9)], and (d) approximate compensation algorithm [Eq. (10)]. Offsets are added for clarity.

Equations (11)

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Δϕ ( α ) = ϕ obj ( α ) + ( 2 π/λ ) { t g n g /cos  [ sin   1 ( sinα/ n g ) ] }       + ( 2 π/λ ) { t ( n LC n sphere ) /cos  [ sin   1 ( sinα/ n LC ) ] } ,
Δϕ ( α ) ϕ obj ( α ) + ϕ 0 + ( 2 π/λ ) t ( n LC n sphere ) ,
u 1 ( r 1 ) = cyl ( r 1 / D ) exp [ ( 2 π i ) W ( r 1 ) ]    .
τ ( r 2 ) = [ τ b + ( 1 τ b ) ] cyl ( r 2 / d ) ]     × exp { i [ ϕ b + ( ϕ 0 ϕ b ) cyl( r 2 / d ) ] } ,
u 2 ( r 2 ) = τ ( r 2 ) U 1 ( r 2 ) .
u ( r ) = T ( r ) ** u 1 ( r ) ,
T ( r ) = [ exp ( i ϕ 0 ) τ b   exp ( i ϕ b ) ]    [ ( π d 2 ) / 4 λ f ] somb ( d r f )     + τ b   exp ( i ϕ b ) δ ( r f ) r ,
u ( r ) = τ b   exp ( i ϕ b ) cyl ( r / D ) exp [ ( 2 π i ) W ( r ) ]     + ( 1 f ) [ exp ( i ϕ 0 ) τ b exp ( i ϕ b ) ] ( π d 2 / 4 λ f )     ×  somb ( d r f ) * * cyl ( r / D ) exp [ ( 2 π i ) W ( r ) ] ,
tan ( ϕ ) = ( Δ I 3 Δ I 1 Δ I 0 + Δ I 4 2 Δ I 2 )      × ( I 0 obj + I 4 obj + 2 I 2 obj I 3 obj + I 1 obj ) ,
tan ( ϕ ) = 2 ( I 3 / I 3 obj I 1 / I 1 obj ) ( I 0 / I 0 obj + I 4 / I 4 obj 2 I 2 / I 2 obj ) .
Δ ϕ th ( r , δ z ) = ( 2 π/λ ) ( ( s 2 + r 2 ) 1 / 2       { ( s δ z ) 2 + r 2 ] } 1 / 2 δ z ) ,

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