Abstract

The present work is concerned with the development and application of a novel fringe analysis technique based on the principles of the windowed-Fourier-transform (WFT) for the determination of temperature and concentration fields from interferometric images for a range of heat and mass transfer applications. Based on the extent of the noise level associated with the experimental data, the technique has been coupled with two different phase unwrapping methods: the Itoh algorithm and the quality guided phase unwrapping technique for phase extraction. In order to generate the experimental data, a range of experiments have been carried out which include cooling of a vertical flat plate in free convection conditions, combustion of mono-propellant flames, and growth of organic as well as inorganic crystals from their aqueous solutions. The flat plate and combustion experiments are modeled as heat transfer applications wherein the interest is to determine the whole-field temperature distribution. Aqueous-solution-based crystal growth experiments are performed to simulate the mass transfer phenomena and the interest is to determine the two-dimensional solute concentration field around the growing crystal. A Mach–Zehnder interferometer has been employed to record the path-integrated quantity of interest (temperature and/or concentration) in the form of interferometric images in the experiments. The potential of the WFT method has also been demonstrated on numerically simulated phase data for varying noise levels, and the accuracy in phase extraction have been quantified in terms of the root mean square errors. Three levels of noise, i.e., 0%, 10%, and 20% have been considered. Results of the present study show that the WFT technique allows an accurate extraction of phase values that can subsequently be converted into two-dimensional temperature and/or concentration distribution fields. Moreover, since WFT is a local processing technique, speckle patterns and the inherent noise in the interferometric data do not affect the resultant phase values. Brief comparisons of the accuracy of the WFT with other standard techniques such as conventional Fourier-filtering methods are also presented.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. B. Whitte and R. F. Wuerker, “Laser holographic interferometry study of high-speed flow fields,” AIAA J. 8, 581–583 (1970).
    [CrossRef]
  2. D. Mishra, K. Muralidhar, and P. Munshi, “Experimental study of Rayleigh–Bernard convection at intermediate Rayleigh numbers using interferometric tomography,” Fluid Dyn. Res. 25, 231–255 (1999).
    [CrossRef]
  3. E. B. Temple, “Quantitative measurements of gas density by means of light interference in schlieren system,” J. Opt. Soc. Am. 47, 91–100 (1957).
    [CrossRef]
  4. A. A. Chernov, L. N. Rashkovich, and A. A. Mkrtchyan, “Interference-optical investigation of KDP, DKDP, and ADP crystal surface growth processes,” Kristallografiya 32, 737–754 (1987).
  5. R. Goldstein, Fluid Mechanics Measurements, 2nd ed. (Taylor & Francis, 1996).
  6. D. Mishra, K. Muralidhar, and P. Munshi, “Performance evaluation of fringe thinning algorithms for interferometric tomography,” Opt. Lasers Eng. 30, 229–249 (1998).
    [CrossRef]
  7. D. Naylor and N. Duarte, “Direct temperature gradient measurement using interferometry,” Exp. Heat Trans. 12, 219–294 (1999).
  8. M. Mantani, M. Sugiyama, and T. Ogawa, “Electronic measurement of concentration gradient around a crystal growing from a solution by using Mach–Zehnder interferometer,” J. Cryst. Growth 114, 71–76 (1991).
    [CrossRef]
  9. A. Srivastava, P. K. Panigrahi, and K. Muralidhar, “Interferometric study of buoyancy-driven convection in a differentially heated circular fluid layer,” Heat Mass Transfer 41, 353–359 (2005).
    [CrossRef]
  10. A. Srivastava, A. Phukan, P. Panigrahi, and K. Muralidhar, “Imaging of a convective field in a rectangular cavity using interferometry, schlieren and shadowgraph,” Opt. Lasers Eng. 42, 469–485 (2004).
    [CrossRef]
  11. D. Newport, C. B. Sobhan, and J. Garvey, “Digital interferometry: techniques and trends for fluid measurement,” Heat Mass Transfer 44, 535–546 (2008).
    [CrossRef]
  12. K. Okada, E. Yokoyama, and H. Miike, “Interference pattern analysis using inverse cosine function,” Electron. Commun. Jpn. 90, 61–73 (2007).
    [CrossRef]
  13. S. Kostianovski, S. G. Lipson, and E. N. Ribak, “Interference microscopy and Fourier fringe analysis applied to measuring the spatial refractive-index distribution,” Appl. Opt. 32, 4744–4750 (1993).
    [CrossRef]
  14. R. Vander, S. G. Lipson, and I. Leizerson, “Fourier fringe analysis with improved spatial resolution,” Appl. Opt. 42, 6830–6837 (2003).
    [CrossRef]
  15. P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
    [CrossRef]
  16. S. Prasanna and S. P. Venkateshan, “Heat flux and temperature field estimation using differential interferometer,” J. Heat Transfer 132, 094502 (2010).
    [CrossRef]
  17. A. Srivastava, K. Tsukamoto, E. Yokoyama, K. Murayama, and M. Fukuyama, “Fourier analysis based phase shift interferometric tomography for three-dimensional reconstruction of concentration field around a growing crystal,” J. Cryst. Growth 312, 2254–2262 (2010).
    [CrossRef]
  18. A. Ahadi, A. Khoshnevis, and M. Ziad Saghir, “Windowed Fourier transform as an essential digital interferometry tool to study coupled heat and mass transfer,” Opt. Laser Technol. 57, 304–317 (2014).
    [CrossRef]
  19. M. Servin, R. Rodriguez-Vera, J. L. Marraquin, and D. Malacara, “Phase-shifting interferometry using a two dimensional regularized phase tracking technique,” J. Mod. Opt. 45, 1809–1819 (1998).
    [CrossRef]
  20. C. Roddier and F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1653–1660 (1986).
  21. J. J. Snyder, “Algorithm for fast digital analysis of interference fringes,” Appl. Opt. 19, 1223–1225 (1980).
    [CrossRef]
  22. Q. Kemao, “Two dimensional windowed Fourier transform for fringe pattern analysis: principles, application and implementation,” Opt. Lasers Eng. 45, 304–317 (2007).
  23. Q. Kemao, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analysis,” Appl. Opt. 47, 5408–5419 (2008).
    [CrossRef]
  24. Q. Kemao and H. S. Seah, “Two dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. 44, 075601 (2005).
    [CrossRef]
  25. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
    [CrossRef]
  26. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. (Academic, 1999).
  27. Q. Kemao, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42, 2792–2793 (2003).
    [CrossRef]
  28. Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm,” Appl. Opt. 47, 5420–5428 (2008).
    [CrossRef]
  29. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  30. G. Domínguez-Guzmán, J. Castillo-Mixcóatl, G. Beltrán-Pérez, and S. Muñoz-Aguirre, “Itoh algorithm to unwrap 2-D phase,” in Seventh Symposium on Optics in Industry, (International Society for Optics and Photonics, 2009), p. 74990H.
  31. D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping Theory, Algorithm and Software (Wiley, 1998).
  32. QG is a path-following method that requires a quality map for its processing which it utilizes to follow an integration path where pixels of higher quality are unwrapped before pixels of lower quality [20]. In the context of the present work, after WFF, the amplitude of the signal has been used as the quality map since it is seen that the low quality or corrupted pixels in the interferogram also possess low amplitude.
  33. J. A. Qi, W. O. Wong, C. W. Lang, and D. W. Yuen, “Temperature field measurement of a premixed butane flame jet with Mach–Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
    [CrossRef]
  34. Y. Zhang, J. Zhao, J. Di, H. Jiang, Q. Wang, J. Wang, Y. Gao, and D. Yin, “Real-time monitoring of the solution concentration variation during the crystallization process of protein-lysozyme by using digital holographic interferometry,” Opt. Express 20, 18415–18421 (2012).
    [CrossRef]
  35. K. Muralidhar, “Temperature field measurement in buoyancy-driven flows using interferometric tomography,” Annu. Rev. Heat Transfer 12, 265–375 (2002).
    [CrossRef]
  36. S. Ostrach, “An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force,” (1953).
  37. A. Abbott, “The monopropellant isopropyl nitrate: its characteristics and uses, and possible future applications,” in Proceedings of the 16th AIAA/SAE/ASME Joint Propulsion Conference (AIAA, 2001).
  38. D. Bradley and K. J. Matthews, “Measurement of high gas temperatures with fine wire thermocouples,” J. Mech. Eng. Sci. 10, 299–305 (1968).
    [CrossRef]
  39. S. Verma and P. J. Shlichta, “Imaging techniques for mapping solution parameters, growth rate, and surface features during the growth of crystals from solution,” Prog. Cryst. Growth Charact. Mater. 54, 1–120 (2008).
    [CrossRef]
  40. A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Solution growth: developments in optical imaging and three-dimensional reconstruction,” Prog. Cryst. Growth Charact. Mater. 58, 209–278 (2012).
    [CrossRef]
  41. A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Reconstruction of the concentration field around a growing KDP crystal using schlieren tomography,” Appl. Opt. 44, 5381–5393 (2005).
    [CrossRef]
  42. K. Onuma, K. Tsukamoto, and I. Sunagawa, “Role of buoyancy driven convection in aqueous solution growth: a case study of (BaNO3)2 crystal,” J. Cryst. Growth 89, 177–188 (1988).
    [CrossRef]
  43. S. Maruyama, T. Shibata, and K. Tsukamoto, “Measurement of diffusion fields of solutions using real-time phase-shift interferometer and rapid heat-transfer control system,” Exp. Therm. Fluid. Sci. 19, 34–48 (1999).
    [CrossRef]
  44. K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610–622 (1994).
    [CrossRef]
  45. L. Duan and J. Z. Shu, “The convection during NaClO3 crystal growth observed by the phase shift interferometer,” J. Cryst. Growth 223, 181–188 (2001).
    [CrossRef]
  46. W. R. Wilcox, “Influence of convection on the growth of crystals from solution,” J. Cryst. Growth 65, 133–142 (1983).
    [CrossRef]
  47. S. Maki, Y. Oda, and M. Ataka, “High-quality crystallization of lysozyme by magneto-Archimedes levitation in a superconducting magnet,” J. Cryst. Growth 261, 557–565 (2004).
    [CrossRef]
  48. W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
    [CrossRef]

2014

A. Ahadi, A. Khoshnevis, and M. Ziad Saghir, “Windowed Fourier transform as an essential digital interferometry tool to study coupled heat and mass transfer,” Opt. Laser Technol. 57, 304–317 (2014).
[CrossRef]

2013

W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
[CrossRef]

2012

A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Solution growth: developments in optical imaging and three-dimensional reconstruction,” Prog. Cryst. Growth Charact. Mater. 58, 209–278 (2012).
[CrossRef]

Y. Zhang, J. Zhao, J. Di, H. Jiang, Q. Wang, J. Wang, Y. Gao, and D. Yin, “Real-time monitoring of the solution concentration variation during the crystallization process of protein-lysozyme by using digital holographic interferometry,” Opt. Express 20, 18415–18421 (2012).
[CrossRef]

2010

S. Prasanna and S. P. Venkateshan, “Heat flux and temperature field estimation using differential interferometer,” J. Heat Transfer 132, 094502 (2010).
[CrossRef]

A. Srivastava, K. Tsukamoto, E. Yokoyama, K. Murayama, and M. Fukuyama, “Fourier analysis based phase shift interferometric tomography for three-dimensional reconstruction of concentration field around a growing crystal,” J. Cryst. Growth 312, 2254–2262 (2010).
[CrossRef]

2008

S. Verma and P. J. Shlichta, “Imaging techniques for mapping solution parameters, growth rate, and surface features during the growth of crystals from solution,” Prog. Cryst. Growth Charact. Mater. 54, 1–120 (2008).
[CrossRef]

J. A. Qi, W. O. Wong, C. W. Lang, and D. W. Yuen, “Temperature field measurement of a premixed butane flame jet with Mach–Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

D. Newport, C. B. Sobhan, and J. Garvey, “Digital interferometry: techniques and trends for fluid measurement,” Heat Mass Transfer 44, 535–546 (2008).
[CrossRef]

Q. Kemao, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analysis,” Appl. Opt. 47, 5408–5419 (2008).
[CrossRef]

Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm,” Appl. Opt. 47, 5420–5428 (2008).
[CrossRef]

2007

K. Okada, E. Yokoyama, and H. Miike, “Interference pattern analysis using inverse cosine function,” Electron. Commun. Jpn. 90, 61–73 (2007).
[CrossRef]

Q. Kemao, “Two dimensional windowed Fourier transform for fringe pattern analysis: principles, application and implementation,” Opt. Lasers Eng. 45, 304–317 (2007).

2005

Q. Kemao and H. S. Seah, “Two dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. 44, 075601 (2005).
[CrossRef]

A. Srivastava, P. K. Panigrahi, and K. Muralidhar, “Interferometric study of buoyancy-driven convection in a differentially heated circular fluid layer,” Heat Mass Transfer 41, 353–359 (2005).
[CrossRef]

A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Reconstruction of the concentration field around a growing KDP crystal using schlieren tomography,” Appl. Opt. 44, 5381–5393 (2005).
[CrossRef]

2004

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
[CrossRef]

A. Srivastava, A. Phukan, P. Panigrahi, and K. Muralidhar, “Imaging of a convective field in a rectangular cavity using interferometry, schlieren and shadowgraph,” Opt. Lasers Eng. 42, 469–485 (2004).
[CrossRef]

P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

S. Maki, Y. Oda, and M. Ataka, “High-quality crystallization of lysozyme by magneto-Archimedes levitation in a superconducting magnet,” J. Cryst. Growth 261, 557–565 (2004).
[CrossRef]

2003

R. Vander, S. G. Lipson, and I. Leizerson, “Fourier fringe analysis with improved spatial resolution,” Appl. Opt. 42, 6830–6837 (2003).
[CrossRef]

Q. Kemao, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42, 2792–2793 (2003).
[CrossRef]

2002

K. Muralidhar, “Temperature field measurement in buoyancy-driven flows using interferometric tomography,” Annu. Rev. Heat Transfer 12, 265–375 (2002).
[CrossRef]

2001

L. Duan and J. Z. Shu, “The convection during NaClO3 crystal growth observed by the phase shift interferometer,” J. Cryst. Growth 223, 181–188 (2001).
[CrossRef]

1999

D. Mishra, K. Muralidhar, and P. Munshi, “Experimental study of Rayleigh–Bernard convection at intermediate Rayleigh numbers using interferometric tomography,” Fluid Dyn. Res. 25, 231–255 (1999).
[CrossRef]

S. Maruyama, T. Shibata, and K. Tsukamoto, “Measurement of diffusion fields of solutions using real-time phase-shift interferometer and rapid heat-transfer control system,” Exp. Therm. Fluid. Sci. 19, 34–48 (1999).
[CrossRef]

D. Naylor and N. Duarte, “Direct temperature gradient measurement using interferometry,” Exp. Heat Trans. 12, 219–294 (1999).

1998

D. Mishra, K. Muralidhar, and P. Munshi, “Performance evaluation of fringe thinning algorithms for interferometric tomography,” Opt. Lasers Eng. 30, 229–249 (1998).
[CrossRef]

M. Servin, R. Rodriguez-Vera, J. L. Marraquin, and D. Malacara, “Phase-shifting interferometry using a two dimensional regularized phase tracking technique,” J. Mod. Opt. 45, 1809–1819 (1998).
[CrossRef]

1994

K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610–622 (1994).
[CrossRef]

1993

1991

M. Mantani, M. Sugiyama, and T. Ogawa, “Electronic measurement of concentration gradient around a crystal growing from a solution by using Mach–Zehnder interferometer,” J. Cryst. Growth 114, 71–76 (1991).
[CrossRef]

1988

K. Onuma, K. Tsukamoto, and I. Sunagawa, “Role of buoyancy driven convection in aqueous solution growth: a case study of (BaNO3)2 crystal,” J. Cryst. Growth 89, 177–188 (1988).
[CrossRef]

1987

A. A. Chernov, L. N. Rashkovich, and A. A. Mkrtchyan, “Interference-optical investigation of KDP, DKDP, and ADP crystal surface growth processes,” Kristallografiya 32, 737–754 (1987).

1986

C. Roddier and F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1653–1660 (1986).

1983

W. R. Wilcox, “Influence of convection on the growth of crystals from solution,” J. Cryst. Growth 65, 133–142 (1983).
[CrossRef]

1982

1980

1970

A. B. Whitte and R. F. Wuerker, “Laser holographic interferometry study of high-speed flow fields,” AIAA J. 8, 581–583 (1970).
[CrossRef]

1968

D. Bradley and K. J. Matthews, “Measurement of high gas temperatures with fine wire thermocouples,” J. Mech. Eng. Sci. 10, 299–305 (1968).
[CrossRef]

1957

Abbott, A.

A. Abbott, “The monopropellant isopropyl nitrate: its characteristics and uses, and possible future applications,” in Proceedings of the 16th AIAA/SAE/ASME Joint Propulsion Conference (AIAA, 2001).

Ahadi, A.

A. Ahadi, A. Khoshnevis, and M. Ziad Saghir, “Windowed Fourier transform as an essential digital interferometry tool to study coupled heat and mass transfer,” Opt. Laser Technol. 57, 304–317 (2014).
[CrossRef]

Asundi, A.

Q. Kemao, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42, 2792–2793 (2003).
[CrossRef]

Ataka, M.

S. Maki, Y. Oda, and M. Ataka, “High-quality crystallization of lysozyme by magneto-Archimedes levitation in a superconducting magnet,” J. Cryst. Growth 261, 557–565 (2004).
[CrossRef]

Beltrán-Pérez, G.

G. Domínguez-Guzmán, J. Castillo-Mixcóatl, G. Beltrán-Pérez, and S. Muñoz-Aguirre, “Itoh algorithm to unwrap 2-D phase,” in Seventh Symposium on Optics in Industry, (International Society for Optics and Photonics, 2009), p. 74990H.

Bradley, D.

D. Bradley and K. J. Matthews, “Measurement of high gas temperatures with fine wire thermocouples,” J. Mech. Eng. Sci. 10, 299–305 (1968).
[CrossRef]

Castillo-Mixcóatl, J.

G. Domínguez-Guzmán, J. Castillo-Mixcóatl, G. Beltrán-Pérez, and S. Muñoz-Aguirre, “Itoh algorithm to unwrap 2-D phase,” in Seventh Symposium on Optics in Industry, (International Society for Optics and Photonics, 2009), p. 74990H.

Chernov, A. A.

A. A. Chernov, L. N. Rashkovich, and A. A. Mkrtchyan, “Interference-optical investigation of KDP, DKDP, and ADP crystal surface growth processes,” Kristallografiya 32, 737–754 (1987).

Di, J.

Domínguez-Guzmán, G.

G. Domínguez-Guzmán, J. Castillo-Mixcóatl, G. Beltrán-Pérez, and S. Muñoz-Aguirre, “Itoh algorithm to unwrap 2-D phase,” in Seventh Symposium on Optics in Industry, (International Society for Optics and Photonics, 2009), p. 74990H.

Duan, L.

L. Duan and J. Z. Shu, “The convection during NaClO3 crystal growth observed by the phase shift interferometer,” J. Cryst. Growth 223, 181–188 (2001).
[CrossRef]

Duarte, N.

D. Naylor and N. Duarte, “Direct temperature gradient measurement using interferometry,” Exp. Heat Trans. 12, 219–294 (1999).

Faridi, M. S.

P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

Fu, Y.

W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
[CrossRef]

Fukuyama, M.

A. Srivastava, K. Tsukamoto, E. Yokoyama, K. Murayama, and M. Fukuyama, “Fourier analysis based phase shift interferometric tomography for three-dimensional reconstruction of concentration field around a growing crystal,” J. Cryst. Growth 312, 2254–2262 (2010).
[CrossRef]

Gao, W.

Gao, Y.

Garvey, J.

D. Newport, C. B. Sobhan, and J. Garvey, “Digital interferometry: techniques and trends for fluid measurement,” Heat Mass Transfer 44, 535–546 (2008).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping Theory, Algorithm and Software (Wiley, 1998).

Goldstein, R.

R. Goldstein, Fluid Mechanics Measurements, 2nd ed. (Taylor & Francis, 1996).

Ina, H.

Jiang, H.

Kameyama, T.

K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610–622 (1994).
[CrossRef]

Kemao, Q.

Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm,” Appl. Opt. 47, 5420–5428 (2008).
[CrossRef]

Q. Kemao, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analysis,” Appl. Opt. 47, 5408–5419 (2008).
[CrossRef]

Q. Kemao, “Two dimensional windowed Fourier transform for fringe pattern analysis: principles, application and implementation,” Opt. Lasers Eng. 45, 304–317 (2007).

Q. Kemao and H. S. Seah, “Two dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. 44, 075601 (2005).
[CrossRef]

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
[CrossRef]

Q. Kemao, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42, 2792–2793 (2003).
[CrossRef]

Khoshnevis, A.

A. Ahadi, A. Khoshnevis, and M. Ziad Saghir, “Windowed Fourier transform as an essential digital interferometry tool to study coupled heat and mass transfer,” Opt. Laser Technol. 57, 304–317 (2014).
[CrossRef]

Kobayashi, S.

Koizumi, M.

W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
[CrossRef]

Kostianovski, S.

Lang, C. W.

J. A. Qi, W. O. Wong, C. W. Lang, and D. W. Yuen, “Temperature field measurement of a premixed butane flame jet with Mach–Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

Leizerson, I.

Li, A.

W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
[CrossRef]

Lipson, S. G.

Maki, S.

S. Maki, Y. Oda, and M. Ataka, “High-quality crystallization of lysozyme by magneto-Archimedes levitation in a superconducting magnet,” J. Cryst. Growth 261, 557–565 (2004).
[CrossRef]

Malacara, D.

M. Servin, R. Rodriguez-Vera, J. L. Marraquin, and D. Malacara, “Phase-shifting interferometry using a two dimensional regularized phase tracking technique,” J. Mod. Opt. 45, 1809–1819 (1998).
[CrossRef]

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. (Academic, 1999).

Mantani, M.

M. Mantani, M. Sugiyama, and T. Ogawa, “Electronic measurement of concentration gradient around a crystal growing from a solution by using Mach–Zehnder interferometer,” J. Cryst. Growth 114, 71–76 (1991).
[CrossRef]

Marraquin, J. L.

M. Servin, R. Rodriguez-Vera, J. L. Marraquin, and D. Malacara, “Phase-shifting interferometry using a two dimensional regularized phase tracking technique,” J. Mod. Opt. 45, 1809–1819 (1998).
[CrossRef]

Maruyama, S.

S. Maruyama, T. Shibata, and K. Tsukamoto, “Measurement of diffusion fields of solutions using real-time phase-shift interferometer and rapid heat-transfer control system,” Exp. Therm. Fluid. Sci. 19, 34–48 (1999).
[CrossRef]

Matthews, K. J.

D. Bradley and K. J. Matthews, “Measurement of high gas temperatures with fine wire thermocouples,” J. Mech. Eng. Sci. 10, 299–305 (1968).
[CrossRef]

Miike, H.

K. Okada, E. Yokoyama, and H. Miike, “Interference pattern analysis using inverse cosine function,” Electron. Commun. Jpn. 90, 61–73 (2007).
[CrossRef]

Mishra, D.

D. Mishra, K. Muralidhar, and P. Munshi, “Experimental study of Rayleigh–Bernard convection at intermediate Rayleigh numbers using interferometric tomography,” Fluid Dyn. Res. 25, 231–255 (1999).
[CrossRef]

D. Mishra, K. Muralidhar, and P. Munshi, “Performance evaluation of fringe thinning algorithms for interferometric tomography,” Opt. Lasers Eng. 30, 229–249 (1998).
[CrossRef]

Mkrtchyan, A. A.

A. A. Chernov, L. N. Rashkovich, and A. A. Mkrtchyan, “Interference-optical investigation of KDP, DKDP, and ADP crystal surface growth processes,” Kristallografiya 32, 737–754 (1987).

Muñoz-Aguirre, S.

G. Domínguez-Guzmán, J. Castillo-Mixcóatl, G. Beltrán-Pérez, and S. Muñoz-Aguirre, “Itoh algorithm to unwrap 2-D phase,” in Seventh Symposium on Optics in Industry, (International Society for Optics and Photonics, 2009), p. 74990H.

Munshi, P.

D. Mishra, K. Muralidhar, and P. Munshi, “Experimental study of Rayleigh–Bernard convection at intermediate Rayleigh numbers using interferometric tomography,” Fluid Dyn. Res. 25, 231–255 (1999).
[CrossRef]

D. Mishra, K. Muralidhar, and P. Munshi, “Performance evaluation of fringe thinning algorithms for interferometric tomography,” Opt. Lasers Eng. 30, 229–249 (1998).
[CrossRef]

Muralidhar, K.

A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Solution growth: developments in optical imaging and three-dimensional reconstruction,” Prog. Cryst. Growth Charact. Mater. 58, 209–278 (2012).
[CrossRef]

A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Reconstruction of the concentration field around a growing KDP crystal using schlieren tomography,” Appl. Opt. 44, 5381–5393 (2005).
[CrossRef]

A. Srivastava, P. K. Panigrahi, and K. Muralidhar, “Interferometric study of buoyancy-driven convection in a differentially heated circular fluid layer,” Heat Mass Transfer 41, 353–359 (2005).
[CrossRef]

A. Srivastava, A. Phukan, P. Panigrahi, and K. Muralidhar, “Imaging of a convective field in a rectangular cavity using interferometry, schlieren and shadowgraph,” Opt. Lasers Eng. 42, 469–485 (2004).
[CrossRef]

K. Muralidhar, “Temperature field measurement in buoyancy-driven flows using interferometric tomography,” Annu. Rev. Heat Transfer 12, 265–375 (2002).
[CrossRef]

D. Mishra, K. Muralidhar, and P. Munshi, “Experimental study of Rayleigh–Bernard convection at intermediate Rayleigh numbers using interferometric tomography,” Fluid Dyn. Res. 25, 231–255 (1999).
[CrossRef]

D. Mishra, K. Muralidhar, and P. Munshi, “Performance evaluation of fringe thinning algorithms for interferometric tomography,” Opt. Lasers Eng. 30, 229–249 (1998).
[CrossRef]

Murayama, K.

A. Srivastava, K. Tsukamoto, E. Yokoyama, K. Murayama, and M. Fukuyama, “Fourier analysis based phase shift interferometric tomography for three-dimensional reconstruction of concentration field around a growing crystal,” J. Cryst. Growth 312, 2254–2262 (2010).
[CrossRef]

Naylor, D.

D. Naylor and N. Duarte, “Direct temperature gradient measurement using interferometry,” Exp. Heat Trans. 12, 219–294 (1999).

Newport, D.

D. Newport, C. B. Sobhan, and J. Garvey, “Digital interferometry: techniques and trends for fluid measurement,” Heat Mass Transfer 44, 535–546 (2008).
[CrossRef]

Oda, Y.

S. Maki, Y. Oda, and M. Ataka, “High-quality crystallization of lysozyme by magneto-Archimedes levitation in a superconducting magnet,” J. Cryst. Growth 261, 557–565 (2004).
[CrossRef]

Ogawa, T.

M. Mantani, M. Sugiyama, and T. Ogawa, “Electronic measurement of concentration gradient around a crystal growing from a solution by using Mach–Zehnder interferometer,” J. Cryst. Growth 114, 71–76 (1991).
[CrossRef]

Okada, K.

K. Okada, E. Yokoyama, and H. Miike, “Interference pattern analysis using inverse cosine function,” Electron. Commun. Jpn. 90, 61–73 (2007).
[CrossRef]

Onuma, K.

K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610–622 (1994).
[CrossRef]

K. Onuma, K. Tsukamoto, and I. Sunagawa, “Role of buoyancy driven convection in aqueous solution growth: a case study of (BaNO3)2 crystal,” J. Cryst. Growth 89, 177–188 (1988).
[CrossRef]

Ostrach, S.

S. Ostrach, “An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force,” (1953).

Pan, W.

W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
[CrossRef]

Panigrahi, P.

A. Srivastava, A. Phukan, P. Panigrahi, and K. Muralidhar, “Imaging of a convective field in a rectangular cavity using interferometry, schlieren and shadowgraph,” Opt. Lasers Eng. 42, 469–485 (2004).
[CrossRef]

Panigrahi, P. K.

A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Solution growth: developments in optical imaging and three-dimensional reconstruction,” Prog. Cryst. Growth Charact. Mater. 58, 209–278 (2012).
[CrossRef]

A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Reconstruction of the concentration field around a growing KDP crystal using schlieren tomography,” Appl. Opt. 44, 5381–5393 (2005).
[CrossRef]

A. Srivastava, P. K. Panigrahi, and K. Muralidhar, “Interferometric study of buoyancy-driven convection in a differentially heated circular fluid layer,” Heat Mass Transfer 41, 353–359 (2005).
[CrossRef]

Phukan, A.

A. Srivastava, A. Phukan, P. Panigrahi, and K. Muralidhar, “Imaging of a convective field in a rectangular cavity using interferometry, schlieren and shadowgraph,” Opt. Lasers Eng. 42, 469–485 (2004).
[CrossRef]

Prasanna, S.

S. Prasanna and S. P. Venkateshan, “Heat flux and temperature field estimation using differential interferometer,” J. Heat Transfer 132, 094502 (2010).
[CrossRef]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping Theory, Algorithm and Software (Wiley, 1998).

Qi, J. A.

J. A. Qi, W. O. Wong, C. W. Lang, and D. W. Yuen, “Temperature field measurement of a premixed butane flame jet with Mach–Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

Rashkovich, L. N.

A. A. Chernov, L. N. Rashkovich, and A. A. Mkrtchyan, “Interference-optical investigation of KDP, DKDP, and ADP crystal surface growth processes,” Kristallografiya 32, 737–754 (1987).

Ribak, E. N.

Roddier, C.

C. Roddier and F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1653–1660 (1986).

Roddier, F.

C. Roddier and F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1653–1660 (1986).

Rodriguez-Vera, R.

M. Servin, R. Rodriguez-Vera, J. L. Marraquin, and D. Malacara, “Phase-shifting interferometry using a two dimensional regularized phase tracking technique,” J. Mod. Opt. 45, 1809–1819 (1998).
[CrossRef]

Seah, H. S.

Q. Kemao and H. S. Seah, “Two dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. 44, 075601 (2005).
[CrossRef]

Q. Kemao, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42, 2792–2793 (2003).
[CrossRef]

Servin, M.

M. Servin, R. Rodriguez-Vera, J. L. Marraquin, and D. Malacara, “Phase-shifting interferometry using a two dimensional regularized phase tracking technique,” J. Mod. Opt. 45, 1809–1819 (1998).
[CrossRef]

Shakher, C.

P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

Shibata, T.

S. Maruyama, T. Shibata, and K. Tsukamoto, “Measurement of diffusion fields of solutions using real-time phase-shift interferometer and rapid heat-transfer control system,” Exp. Therm. Fluid. Sci. 19, 34–48 (1999).
[CrossRef]

Shlichta, P. J.

S. Verma and P. J. Shlichta, “Imaging techniques for mapping solution parameters, growth rate, and surface features during the growth of crystals from solution,” Prog. Cryst. Growth Charact. Mater. 54, 1–120 (2008).
[CrossRef]

Shu, J. Z.

L. Duan and J. Z. Shu, “The convection during NaClO3 crystal growth observed by the phase shift interferometer,” J. Cryst. Growth 223, 181–188 (2001).
[CrossRef]

Singh, P.

P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

Snyder, J. J.

Sobhan, C. B.

D. Newport, C. B. Sobhan, and J. Garvey, “Digital interferometry: techniques and trends for fluid measurement,” Heat Mass Transfer 44, 535–546 (2008).
[CrossRef]

Srivastava, A.

A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Solution growth: developments in optical imaging and three-dimensional reconstruction,” Prog. Cryst. Growth Charact. Mater. 58, 209–278 (2012).
[CrossRef]

A. Srivastava, K. Tsukamoto, E. Yokoyama, K. Murayama, and M. Fukuyama, “Fourier analysis based phase shift interferometric tomography for three-dimensional reconstruction of concentration field around a growing crystal,” J. Cryst. Growth 312, 2254–2262 (2010).
[CrossRef]

A. Srivastava, P. K. Panigrahi, and K. Muralidhar, “Interferometric study of buoyancy-driven convection in a differentially heated circular fluid layer,” Heat Mass Transfer 41, 353–359 (2005).
[CrossRef]

A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Reconstruction of the concentration field around a growing KDP crystal using schlieren tomography,” Appl. Opt. 44, 5381–5393 (2005).
[CrossRef]

A. Srivastava, A. Phukan, P. Panigrahi, and K. Muralidhar, “Imaging of a convective field in a rectangular cavity using interferometry, schlieren and shadowgraph,” Opt. Lasers Eng. 42, 469–485 (2004).
[CrossRef]

Sugiyama, M.

M. Mantani, M. Sugiyama, and T. Ogawa, “Electronic measurement of concentration gradient around a crystal growing from a solution by using Mach–Zehnder interferometer,” J. Cryst. Growth 114, 71–76 (1991).
[CrossRef]

Sunagawa, I.

K. Onuma, K. Tsukamoto, and I. Sunagawa, “Role of buoyancy driven convection in aqueous solution growth: a case study of (BaNO3)2 crystal,” J. Cryst. Growth 89, 177–188 (1988).
[CrossRef]

Takeda, M.

Temple, E. B.

Tsukamoto, K.

W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
[CrossRef]

A. Srivastava, K. Tsukamoto, E. Yokoyama, K. Murayama, and M. Fukuyama, “Fourier analysis based phase shift interferometric tomography for three-dimensional reconstruction of concentration field around a growing crystal,” J. Cryst. Growth 312, 2254–2262 (2010).
[CrossRef]

S. Maruyama, T. Shibata, and K. Tsukamoto, “Measurement of diffusion fields of solutions using real-time phase-shift interferometer and rapid heat-transfer control system,” Exp. Therm. Fluid. Sci. 19, 34–48 (1999).
[CrossRef]

K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610–622 (1994).
[CrossRef]

K. Onuma, K. Tsukamoto, and I. Sunagawa, “Role of buoyancy driven convection in aqueous solution growth: a case study of (BaNO3)2 crystal,” J. Cryst. Growth 89, 177–188 (1988).
[CrossRef]

Vander, R.

Venkateshan, S. P.

S. Prasanna and S. P. Venkateshan, “Heat flux and temperature field estimation using differential interferometer,” J. Heat Transfer 132, 094502 (2010).
[CrossRef]

Verma, S.

S. Verma and P. J. Shlichta, “Imaging techniques for mapping solution parameters, growth rate, and surface features during the growth of crystals from solution,” Prog. Cryst. Growth Charact. Mater. 54, 1–120 (2008).
[CrossRef]

Wang, H.

Wang, J.

Wang, Q.

Whitte, A. B.

A. B. Whitte and R. F. Wuerker, “Laser holographic interferometry study of high-speed flow fields,” AIAA J. 8, 581–583 (1970).
[CrossRef]

Wilcox, W. R.

W. R. Wilcox, “Influence of convection on the growth of crystals from solution,” J. Cryst. Growth 65, 133–142 (1983).
[CrossRef]

Wong, W. O.

J. A. Qi, W. O. Wong, C. W. Lang, and D. W. Yuen, “Temperature field measurement of a premixed butane flame jet with Mach–Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

Wuerker, R. F.

A. B. Whitte and R. F. Wuerker, “Laser holographic interferometry study of high-speed flow fields,” AIAA J. 8, 581–583 (1970).
[CrossRef]

Xu, J.

W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
[CrossRef]

Yamazaki, T.

W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
[CrossRef]

Yin, D.

Yokoyama, E.

A. Srivastava, K. Tsukamoto, E. Yokoyama, K. Murayama, and M. Fukuyama, “Fourier analysis based phase shift interferometric tomography for three-dimensional reconstruction of concentration field around a growing crystal,” J. Cryst. Growth 312, 2254–2262 (2010).
[CrossRef]

K. Okada, E. Yokoyama, and H. Miike, “Interference pattern analysis using inverse cosine function,” Electron. Commun. Jpn. 90, 61–73 (2007).
[CrossRef]

Yuen, D. W.

J. A. Qi, W. O. Wong, C. W. Lang, and D. W. Yuen, “Temperature field measurement of a premixed butane flame jet with Mach–Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

Zhang, Y.

Zhao, J.

Zhou, R.

W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
[CrossRef]

Ziad Saghir, M.

A. Ahadi, A. Khoshnevis, and M. Ziad Saghir, “Windowed Fourier transform as an essential digital interferometry tool to study coupled heat and mass transfer,” Opt. Laser Technol. 57, 304–317 (2014).
[CrossRef]

AIAA J.

A. B. Whitte and R. F. Wuerker, “Laser holographic interferometry study of high-speed flow fields,” AIAA J. 8, 581–583 (1970).
[CrossRef]

Annu. Rev. Heat Transfer

K. Muralidhar, “Temperature field measurement in buoyancy-driven flows using interferometric tomography,” Annu. Rev. Heat Transfer 12, 265–375 (2002).
[CrossRef]

Appl. Opt.

Appl. Therm. Eng.

J. A. Qi, W. O. Wong, C. W. Lang, and D. W. Yuen, “Temperature field measurement of a premixed butane flame jet with Mach–Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

Electron. Commun. Jpn.

K. Okada, E. Yokoyama, and H. Miike, “Interference pattern analysis using inverse cosine function,” Electron. Commun. Jpn. 90, 61–73 (2007).
[CrossRef]

Exp. Heat Trans.

D. Naylor and N. Duarte, “Direct temperature gradient measurement using interferometry,” Exp. Heat Trans. 12, 219–294 (1999).

Exp. Therm. Fluid. Sci.

S. Maruyama, T. Shibata, and K. Tsukamoto, “Measurement of diffusion fields of solutions using real-time phase-shift interferometer and rapid heat-transfer control system,” Exp. Therm. Fluid. Sci. 19, 34–48 (1999).
[CrossRef]

Fluid Dyn. Res.

D. Mishra, K. Muralidhar, and P. Munshi, “Experimental study of Rayleigh–Bernard convection at intermediate Rayleigh numbers using interferometric tomography,” Fluid Dyn. Res. 25, 231–255 (1999).
[CrossRef]

Heat Mass Transfer

A. Srivastava, P. K. Panigrahi, and K. Muralidhar, “Interferometric study of buoyancy-driven convection in a differentially heated circular fluid layer,” Heat Mass Transfer 41, 353–359 (2005).
[CrossRef]

D. Newport, C. B. Sobhan, and J. Garvey, “Digital interferometry: techniques and trends for fluid measurement,” Heat Mass Transfer 44, 535–546 (2008).
[CrossRef]

J. Cryst. Growth

M. Mantani, M. Sugiyama, and T. Ogawa, “Electronic measurement of concentration gradient around a crystal growing from a solution by using Mach–Zehnder interferometer,” J. Cryst. Growth 114, 71–76 (1991).
[CrossRef]

A. Srivastava, K. Tsukamoto, E. Yokoyama, K. Murayama, and M. Fukuyama, “Fourier analysis based phase shift interferometric tomography for three-dimensional reconstruction of concentration field around a growing crystal,” J. Cryst. Growth 312, 2254–2262 (2010).
[CrossRef]

K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610–622 (1994).
[CrossRef]

L. Duan and J. Z. Shu, “The convection during NaClO3 crystal growth observed by the phase shift interferometer,” J. Cryst. Growth 223, 181–188 (2001).
[CrossRef]

W. R. Wilcox, “Influence of convection on the growth of crystals from solution,” J. Cryst. Growth 65, 133–142 (1983).
[CrossRef]

S. Maki, Y. Oda, and M. Ataka, “High-quality crystallization of lysozyme by magneto-Archimedes levitation in a superconducting magnet,” J. Cryst. Growth 261, 557–565 (2004).
[CrossRef]

W. Pan, J. Xu, K. Tsukamoto, M. Koizumi, T. Yamazaki, R. Zhou, A. Li, and Y. Fu, “Crystal growth of hen egg-white lysozyme (HEWL) under various gravity conditions,” J. Cryst. Growth 377, 43–50 (2013).
[CrossRef]

K. Onuma, K. Tsukamoto, and I. Sunagawa, “Role of buoyancy driven convection in aqueous solution growth: a case study of (BaNO3)2 crystal,” J. Cryst. Growth 89, 177–188 (1988).
[CrossRef]

J. Heat Transfer

S. Prasanna and S. P. Venkateshan, “Heat flux and temperature field estimation using differential interferometer,” J. Heat Transfer 132, 094502 (2010).
[CrossRef]

J. Mech. Eng. Sci.

D. Bradley and K. J. Matthews, “Measurement of high gas temperatures with fine wire thermocouples,” J. Mech. Eng. Sci. 10, 299–305 (1968).
[CrossRef]

J. Mod. Opt.

M. Servin, R. Rodriguez-Vera, J. L. Marraquin, and D. Malacara, “Phase-shifting interferometry using a two dimensional regularized phase tracking technique,” J. Mod. Opt. 45, 1809–1819 (1998).
[CrossRef]

J. Opt. Soc. Am.

Kristallografiya

A. A. Chernov, L. N. Rashkovich, and A. A. Mkrtchyan, “Interference-optical investigation of KDP, DKDP, and ADP crystal surface growth processes,” Kristallografiya 32, 737–754 (1987).

Opt. Eng.

P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

Q. Kemao and H. S. Seah, “Two dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. 44, 075601 (2005).
[CrossRef]

Q. Kemao, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42, 2792–2793 (2003).
[CrossRef]

Opt. Express

Opt. Laser Technol.

A. Ahadi, A. Khoshnevis, and M. Ziad Saghir, “Windowed Fourier transform as an essential digital interferometry tool to study coupled heat and mass transfer,” Opt. Laser Technol. 57, 304–317 (2014).
[CrossRef]

Opt. Lasers Eng.

Q. Kemao, “Two dimensional windowed Fourier transform for fringe pattern analysis: principles, application and implementation,” Opt. Lasers Eng. 45, 304–317 (2007).

D. Mishra, K. Muralidhar, and P. Munshi, “Performance evaluation of fringe thinning algorithms for interferometric tomography,” Opt. Lasers Eng. 30, 229–249 (1998).
[CrossRef]

A. Srivastava, A. Phukan, P. Panigrahi, and K. Muralidhar, “Imaging of a convective field in a rectangular cavity using interferometry, schlieren and shadowgraph,” Opt. Lasers Eng. 42, 469–485 (2004).
[CrossRef]

Prog. Cryst. Growth Charact. Mater.

S. Verma and P. J. Shlichta, “Imaging techniques for mapping solution parameters, growth rate, and surface features during the growth of crystals from solution,” Prog. Cryst. Growth Charact. Mater. 54, 1–120 (2008).
[CrossRef]

A. Srivastava, K. Muralidhar, and P. K. Panigrahi, “Solution growth: developments in optical imaging and three-dimensional reconstruction,” Prog. Cryst. Growth Charact. Mater. 58, 209–278 (2012).
[CrossRef]

Other

S. Ostrach, “An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force,” (1953).

A. Abbott, “The monopropellant isopropyl nitrate: its characteristics and uses, and possible future applications,” in Proceedings of the 16th AIAA/SAE/ASME Joint Propulsion Conference (AIAA, 2001).

G. Domínguez-Guzmán, J. Castillo-Mixcóatl, G. Beltrán-Pérez, and S. Muñoz-Aguirre, “Itoh algorithm to unwrap 2-D phase,” in Seventh Symposium on Optics in Industry, (International Society for Optics and Photonics, 2009), p. 74990H.

D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping Theory, Algorithm and Software (Wiley, 1998).

QG is a path-following method that requires a quality map for its processing which it utilizes to follow an integration path where pixels of higher quality are unwrapped before pixels of lower quality [20]. In the context of the present work, after WFF, the amplitude of the signal has been used as the quality map since it is seen that the low quality or corrupted pixels in the interferogram also possess low amplitude.

S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. (Academic, 1999).

R. Goldstein, Fluid Mechanics Measurements, 2nd ed. (Taylor & Francis, 1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1.

Numerically simulated phase distribution. Interferograms corresponding to the phase distribution shown in (a) with a noise level of (b) 0%, (c) 10%, and (d) 20%.

Fig. 2.
Fig. 2.

Unwrapped phase distribution using the WFF and QC method for (a) 0%, (b) 10%, and (c) 20% noise levels. (d)–(f) Distribution of RMSE values.

Fig. 3.
Fig. 3.

(a) Interferogram of an isothermal flat plate maintained at 122°C and (b) the corresponding infinite fringe pattern. (c) Two-dimensional temperature distribution. (d) Comparison of local values of the heat transfer coefficient as obtained in the present work using the WFF and QG approach with those reported in the literature corresponding to the plate temperature of 122°C.

Fig. 4.
Fig. 4.

Time sequence of the interferometric images during the combustion process of IPN. Image at t=0s shows the initial wedge fringe setting mode of the interferometer. A videographic snapshot of the flame is shown in the inset of the first image.

Fig. 5.
Fig. 5.

Whole-field temperature contours as retrieved from the interferometric images using the developed fringe analysis technique at four different time instances of the combustion process. Quantitative values of temperatures are shown in the figure legends.

Fig. 6.
Fig. 6.

Comparison of the temporal variation of flame temperature as retrieved from the interferometric data with thermocouple measurements.

Fig. 7.
Fig. 7.

(a) Interferogram of a NaClO3 crystal growing from its supersaturated aqueous solution. (b) and (c) Two-dimensional concentration distribution obtained using WFF+QG and Fourier filtering, respectively. (d) Local variation of degree of supersaturation from the surface of the NaClO3 crystal to the bulk solution.

Fig. 8.
Fig. 8.

(a) Interferometric image of the concentration field around a lysozyme crystal growing from its supersaturation solution. (b) Two-dimensional concentration field as determined from the recorded interferogram using the WFF+QG approach. (c) Local variation of the degree of supersaturation from the surface of the lysozyme crystal to the bulk solution.

Tables (1)

Tables Icon

Table 1. Comparison of RMSE Values of Phase Distribution Obtained Using Three Different Fringe Analysis Approaches for 0%, 10%, and 20% Noise Levels

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

Io(x,y)=A(x,y)+B(x,y)cos(2πf⃗or⃗+Δϕ(x,y)).
I0(x)=A+B2(ei[2πfox+Δϕ(x)]+ei[2πfox+Δϕ(x)]).
F[I](f)=F[A]+F[B/2]*(δ(ffo)*F[Δϕ]+δ(f+fo)*F*[Δϕ],
δ(f)={1whenf=0,0whenf0.
F[I](f)=F[A]+F[B/2]*(δ(ffo)*F[Δϕ+θ]+δ(f+fo)*F*[Δϕ+θ].
Iπ/2(x)=A+Bcos(2πfox+Δϕ(x,y)+π/2),
Iπ(x)=A+Bcos(2πfox+Δϕ(x,y)+π),
I3π/2(x)=A+Bcos(2πfox+Δϕ(x,y)+3π/2).
Φ(x)=tan1(I3π/2Iπ/2I0Iπ).
f(x,y)=b(x,y)ej(ΔΦ(x,y)),
Sf(u,v,ξ,η)=f(x,y)gu,v,ξ,η*(x,y)dxdy.
gu,v,ξ,η(x,y)=g(xu,yv)ejξx+jηy.
g(x,y)=e[x22σx2y22σy2].
f¯(x,y)=14π2η1η2ξ1ξ2S¯f(u,v,ξ,η)gu,v,ξ,η(x,y)dudvdξdη,
S¯f(u,v,ξ,η)={Sf(u,v,ξ,η)if|Sf(u,v,ξ,η|thr,0if|Sf(u,v,ξ,η|thr.
f¯(x,y)=b¯(x,y)ejΦ¯(x,y).
n(x,y)=n0(Δϕ(x,y)2π)(λL),
T(x,y)=[n01n(x,y)1]T0.
C(x,y)=C0+λΔϕ(x,y)2πL(nC)T.
ϕ(x,y)=a×e(xx)2+(yy)2b2.
I(x,y)=A(x,y)+B(x,y)cos(2π(ϕ(x,y)Rxk)).
RMSE=1N(ϕtϕt)2,

Metrics