Abstract

Measurements of very small phase changes in optical measurement techniques are usually performed with interferometric methods that are based on evaluation of interference patterns, which correspond to a phase change of the investigated wave field. If values of the phase change are small, it is difficult to determine accurately the phase values, and one needs very expensive measurement systems. We present a simple method for evaluation of small phase variations that uses the interference of polychromatic light. The phase change affects the color of the interference pattern, and the color of the interference pattern corresponds to a specific phase change that can be evaluated using colorimetric analysis. We describe and analyze our colorimetric phase evaluation method. The proposed method offers accurate results, and it may be suitable for practical utilization in the optical industry.

© 2006 Optical Society of America

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  2. D. Malacara, Optical Shop Testing (Wiley, 1992).
  3. M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).
  4. A. Miks, "Interferometric methods for testing spherical surfaces in optics," Fine Mech. Opt. 46, 29-35 (2001).
  5. A. Miks, Applied Optics 10 (Czech Technical University Publishing, Prague, 2000).
  6. C. Strouhal and V. Novak, Optics (JCMF, Prague, 1919).
  7. J. Fuka and B. Havelka, Optics (SPN, Prague, 1961).
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  10. J. Schwider, "Advanced techniques in interferometry," in Progress in Optics, Vol. XXIX, EWolf, ed. (Elsevier Science, 1990).
  11. J. Novak, "Five-step phase-shifting algorithms with unknown values of phase shift," Optik 114, 63-68 (2003).
  12. J. Novak, "Analysis of phase evaluation algorithms in an interferometric method for static deformation measurement," Acta Polytech. 42, 35-41 (2002).
  13. J. Novak, "New phase shifting algorithms insensitive to linear phase shift errors," Acta Polytech. 42, 51-56 (2002).
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  27. http://www.cvrl.org/.
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  29. P. E. Gill and W. Murrey, Numerical Methods for Constrained Optimization (Academic, 1974).

2004

2003

J. Novak, "Five-step phase-shifting algorithms with unknown values of phase shift," Optik 114, 63-68 (2003).

2002

J. Novak, "Analysis of phase evaluation algorithms in an interferometric method for static deformation measurement," Acta Polytech. 42, 35-41 (2002).

J. Novak, "New phase shifting algorithms insensitive to linear phase shift errors," Acta Polytech. 42, 51-56 (2002).

A. Miks and J. Novak, "Interferometric method for deformation measurement of structures in industry," Proc. SPIE 5036, 20-24 (2002).

K. Barnard and B. Funt, "Camera characterization for color research," Color Res. Appl. 27, 152-163 (2002).

M. Corbalán, M. S. Millán, and M. J. Yzuel, "Color pattern recognition with CIELAB coordinates," Opt. Eng. 41, 130-138 (2002).

2001

G. Hong, M. R. Luo, and P. A. Rhodes, "A study of digital camera colorimetric characterization based on polynomial modeling," Color Res. Appl. 26, 76-84 (2001).

A. Miks, "Interferometric methods for testing spherical surfaces in optics," Fine Mech. Opt. 46, 29-35 (2001).

2000

M. Corbalán, M. S. Millán, and M. J. Yzuel, "Color measurement in standard CIELAB coordinates using a 3CCD camera: correction for the influence of the light source," Opt. Eng. 39, 1470-1476 (2000).

1994

C. S. McCamy, "Simulation of daylight for viewing and measuring color," Color Res. Appl. 19, 434-445 (1994).

1991

Barnard, K.

K. Barnard and B. Funt, "Camera characterization for color research," Color Res. Appl. 27, 152-163 (2002).

Bergmann, L.

L. Bergmann, C. Schaefer, and H. Niedri, Optics of Waves and Particles (CRC Press, 1999).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

Corbalán, M.

M. S. Millán, E. Valencia, and M. Corbalán, "3CCD camera's capability for measuring color differences: experiment in the nearly neutral region," Appl. Opt. 43, 6523-6535 (2004).

M. Corbalán, M. S. Millán, and M. J. Yzuel, "Color pattern recognition with CIELAB coordinates," Opt. Eng. 41, 130-138 (2002).

M. Corbalán, M. S. Millán, and M. J. Yzuel, "Color measurement in standard CIELAB coordinates using a 3CCD camera: correction for the influence of the light source," Opt. Eng. 39, 1470-1476 (2000).

Creath, K.

K. Creath, "Phase-measurement interferometry techniques,", in Progress in Optics, Vol. XXVI, E.Wolf, ed. (Elsevier Science, 1988).

Francon, M.

M. Francon and S. Mallick, Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, 1971).

M. Francon, Optical Interferometry (Academic, 1966).

Fuka, J.

J. Fuka and B. Havelka, Optics (SPN, Prague, 1961).

Funt, B.

K. Barnard and B. Funt, "Camera characterization for color research," Color Res. Appl. 27, 152-163 (2002).

Gill, P. E.

P. E. Gill and W. Murrey, Numerical Methods for Constrained Optimization (Academic, 1974).

Havelka, B.

J. Fuka and B. Havelka, Optics (SPN, Prague, 1961).

Hong, G.

G. Hong, M. R. Luo, and P. A. Rhodes, "A study of digital camera colorimetric characterization based on polynomial modeling," Color Res. Appl. 26, 76-84 (2001).

Jansen, J. F.

Jiracek, M.

M. Jiracek, A. Miks, V. Opocensky, J. Ruzek, P. Scheufter, M. Spevak, P. Styblo, and M. Urban, Technical Fundamentals of Photography (KFZ, Prague, 2002).

Luo, M. R.

G. Hong, M. R. Luo, and P. A. Rhodes, "A study of digital camera colorimetric characterization based on polynomial modeling," Color Res. Appl. 26, 76-84 (2001).

Malacara, D.

D. Malacara, Color Vision and Colorimetry: Theory and Applications (SPIE, 2004).

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

D. Malacara, Optical Shop Testing (Wiley, 1992).

Malacara, Z.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Mallick, S.

M. Francon and S. Mallick, Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, 1971).

McCamy, C. S.

C. S. McCamy, "Simulation of daylight for viewing and measuring color," Color Res. Appl. 19, 434-445 (1994).

Miks, A.

A. Miks and J. Novak, "Interferometric method for deformation measurement of structures in industry," Proc. SPIE 5036, 20-24 (2002).

A. Miks, "Interferometric methods for testing spherical surfaces in optics," Fine Mech. Opt. 46, 29-35 (2001).

M. Jiracek, A. Miks, V. Opocensky, J. Ruzek, P. Scheufter, M. Spevak, P. Styblo, and M. Urban, Technical Fundamentals of Photography (KFZ, Prague, 2002).

A. Miks, Applied Optics 10 (Czech Technical University Publishing, Prague, 2000).

Millán, M. S.

M. S. Millán, E. Valencia, and M. Corbalán, "3CCD camera's capability for measuring color differences: experiment in the nearly neutral region," Appl. Opt. 43, 6523-6535 (2004).

M. Corbalán, M. S. Millán, and M. J. Yzuel, "Color pattern recognition with CIELAB coordinates," Opt. Eng. 41, 130-138 (2002).

M. Corbalán, M. S. Millán, and M. J. Yzuel, "Color measurement in standard CIELAB coordinates using a 3CCD camera: correction for the influence of the light source," Opt. Eng. 39, 1470-1476 (2000).

Murrey, W.

P. E. Gill and W. Murrey, Numerical Methods for Constrained Optimization (Academic, 1974).

Niedri, H.

L. Bergmann, C. Schaefer, and H. Niedri, Optics of Waves and Particles (CRC Press, 1999).

Novak, J.

J. Novak, "Five-step phase-shifting algorithms with unknown values of phase shift," Optik 114, 63-68 (2003).

A. Miks and J. Novak, "Interferometric method for deformation measurement of structures in industry," Proc. SPIE 5036, 20-24 (2002).

J. Novak, "Analysis of phase evaluation algorithms in an interferometric method for static deformation measurement," Acta Polytech. 42, 35-41 (2002).

J. Novak, "New phase shifting algorithms insensitive to linear phase shift errors," Acta Polytech. 42, 51-56 (2002).

Novak, V.

C. Strouhal and V. Novak, Optics (JCMF, Prague, 1919).

Opocensky, V.

M. Jiracek, A. Miks, V. Opocensky, J. Ruzek, P. Scheufter, M. Spevak, P. Styblo, and M. Urban, Technical Fundamentals of Photography (KFZ, Prague, 2002).

Rhodes, P. A.

G. Hong, M. R. Luo, and P. A. Rhodes, "A study of digital camera colorimetric characterization based on polynomial modeling," Color Res. Appl. 26, 76-84 (2001).

Ruzek, J.

M. Jiracek, A. Miks, V. Opocensky, J. Ruzek, P. Scheufter, M. Spevak, P. Styblo, and M. Urban, Technical Fundamentals of Photography (KFZ, Prague, 2002).

Schaefer, C.

L. Bergmann, C. Schaefer, and H. Niedri, Optics of Waves and Particles (CRC Press, 1999).

Scheufter, P.

M. Jiracek, A. Miks, V. Opocensky, J. Ruzek, P. Scheufter, M. Spevak, P. Styblo, and M. Urban, Technical Fundamentals of Photography (KFZ, Prague, 2002).

Schwider, J.

J. Schwider, "Advanced techniques in interferometry," in Progress in Optics, Vol. XXIX, EWolf, ed. (Elsevier Science, 1990).

Servin, M.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Simpson, M. L.

Spevak, M.

M. Jiracek, A. Miks, V. Opocensky, J. Ruzek, P. Scheufter, M. Spevak, P. Styblo, and M. Urban, Technical Fundamentals of Photography (KFZ, Prague, 2002).

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concept and Methods, Quantitative Data and Formulae (Wiley,1982).

Strouhal, C.

C. Strouhal and V. Novak, Optics (JCMF, Prague, 1919).

Styblo, P.

M. Jiracek, A. Miks, V. Opocensky, J. Ruzek, P. Scheufter, M. Spevak, P. Styblo, and M. Urban, Technical Fundamentals of Photography (KFZ, Prague, 2002).

Urban, M.

M. Jiracek, A. Miks, V. Opocensky, J. Ruzek, P. Scheufter, M. Spevak, P. Styblo, and M. Urban, Technical Fundamentals of Photography (KFZ, Prague, 2002).

Valencia, E.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concept and Methods, Quantitative Data and Formulae (Wiley,1982).

Yzuel, M. J.

M. Corbalán, M. S. Millán, and M. J. Yzuel, "Color pattern recognition with CIELAB coordinates," Opt. Eng. 41, 130-138 (2002).

M. Corbalán, M. S. Millán, and M. J. Yzuel, "Color measurement in standard CIELAB coordinates using a 3CCD camera: correction for the influence of the light source," Opt. Eng. 39, 1470-1476 (2000).

Acta Polytech.

J. Novak, "Analysis of phase evaluation algorithms in an interferometric method for static deformation measurement," Acta Polytech. 42, 35-41 (2002).

J. Novak, "New phase shifting algorithms insensitive to linear phase shift errors," Acta Polytech. 42, 51-56 (2002).

Appl. Opt.

Color Res. Appl.

K. Barnard and B. Funt, "Camera characterization for color research," Color Res. Appl. 27, 152-163 (2002).

G. Hong, M. R. Luo, and P. A. Rhodes, "A study of digital camera colorimetric characterization based on polynomial modeling," Color Res. Appl. 26, 76-84 (2001).

C. S. McCamy, "Simulation of daylight for viewing and measuring color," Color Res. Appl. 19, 434-445 (1994).

Fine Mech. Opt.

A. Miks, "Interferometric methods for testing spherical surfaces in optics," Fine Mech. Opt. 46, 29-35 (2001).

Opt. Eng.

M. Corbalán, M. S. Millán, and M. J. Yzuel, "Color pattern recognition with CIELAB coordinates," Opt. Eng. 41, 130-138 (2002).

M. Corbalán, M. S. Millán, and M. J. Yzuel, "Color measurement in standard CIELAB coordinates using a 3CCD camera: correction for the influence of the light source," Opt. Eng. 39, 1470-1476 (2000).

Optik

J. Novak, "Five-step phase-shifting algorithms with unknown values of phase shift," Optik 114, 63-68 (2003).

Proc. SPIE

A. Miks and J. Novak, "Interferometric method for deformation measurement of structures in industry," Proc. SPIE 5036, 20-24 (2002).

Other

L. Bergmann, C. Schaefer, and H. Niedri, Optics of Waves and Particles (CRC Press, 1999).

M. Jiracek, A. Miks, V. Opocensky, J. Ruzek, P. Scheufter, M. Spevak, P. Styblo, and M. Urban, Technical Fundamentals of Photography (KFZ, Prague, 2002).

A. Miks, Applied Optics 10 (Czech Technical University Publishing, Prague, 2000).

C. Strouhal and V. Novak, Optics (JCMF, Prague, 1919).

J. Fuka and B. Havelka, Optics (SPN, Prague, 1961).

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

K. Creath, "Phase-measurement interferometry techniques,", in Progress in Optics, Vol. XXVI, E.Wolf, ed. (Elsevier Science, 1988).

J. Schwider, "Advanced techniques in interferometry," in Progress in Optics, Vol. XXIX, EWolf, ed. (Elsevier Science, 1990).

http://www.cie.co.at/framepublications.html.

http://www.cvrl.org/.

M. Francon and S. Mallick, Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, 1971).

P. E. Gill and W. Murrey, Numerical Methods for Constrained Optimization (Academic, 1974).

D. Malacara, Color Vision and Colorimetry: Theory and Applications (SPIE, 2004).

G. Wyszecki and W. S. Stiles, Color Science: Concept and Methods, Quantitative Data and Formulae (Wiley,1982).

M. Francon, Optical Interferometry (Academic, 1966).

D. Malacara, Optical Shop Testing (Wiley, 1992).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

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