Abstract

In this paper, experimental investigations and analysis is presented to measure the temperature and temperature profile of gaseous flames using lensless Fourier transform digital holographic interferometry. The evaluations of the experimental results give the accuracy, sensitivity, spatial resolution, and range of measurements to be well within the experimental limits. Details of the experimental results and analysis are presented.

© 2012 Optical Society of America

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  1. P. R. N. Childs, J. R. Greenwood, and C. A. Long, “Review of temperature measurement,” Rev. Sci. Instrum. 71, 2959–2978 (2000).
    [CrossRef]
  2. C. Shakher and A. K. Nirala, “Measurement of temperature using speckle shearing interferometry,” Appl. Opt. 33, 2125–2127 (1994).
    [CrossRef]
  3. E. Pungor, Flame Photometry (Van Nostrand, 1967), pp. 147–152.
  4. A. A. Boiarski, R. H. Barnes, and J. F. Kircher, “Flame measurements utilizing Raman scattering,” Combust. Flame 32, 111–114 (1978).
    [CrossRef]
  5. S. Kampmann, A. Leipertz, K. Dobbling, J. Hanumann, and T. Sattelmayer, “Two-dimensional temperature measurement in a technical combustor with laser Rayleigh scattering,” Appl. Opt. 32, 6167–6172 (1993).
    [CrossRef]
  6. M. Giglio, S. Musazzi, and U. Perini, “A white light speckle Schlieren technique,” Opt. Commun. 36, 117–120 (1981).
    [CrossRef]
  7. E. Keren, E. Bar-Ziv, I. Glatt, and O. Kafri, “Measurement of temperature distribution of flame by moire deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
    [CrossRef]
  8. D. L. Reuss, “Temperature measurement in a radially symmetric flame using holographic interferometry,” Combust. Flame 49, 207–219 (1983).
    [CrossRef]
  9. P. V. Farrel, G. S. Springer, and C. M. Vest, “Heterodyne holographic interferometry: concentration and temperature measurement in gas mixtures,” Appl. Opt. 21, 1624–1627 (1982).
    [CrossRef]
  10. R. J. Goldstein, “Optical measurement of temperature,” in Measurement Techniques in Heat Transfer, E. R. G. Eckert and R. J. Goldstein, eds. (Technical, 1970), pp. 177–228.
  11. D. Wilkie and S. A. Fisher, “Measurement of temperature by Mach-Zehnder interferometry,” Proc. Inst. Mech. Eng. 178, 461–472 (1963).
  12. A. Stella, G. Guj, and S. Giammartini, “Measurement of axi-symmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
    [CrossRef]
  13. P. Singh and C. Shakher, “Measurement of the temperature of a gaseous flame using a shearing plate,” Opt. Eng. 42, 80–85 (2003).
    [CrossRef]
  14. 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]
  15. P. V. Farrel and D. L. Hofeldt, “Temperature measurement in gases using speckle photography,” Appl. Opt. 23, 1055–1059 (1984).
    [CrossRef]
  16. C. Shakher, A. K. Nirala, A. J. P. Daniel, and S. K. Verma, “Use of speckle technique for temperature measurement in gaseous flame,” J. Opt. 23, 35–39 (1992).
    [CrossRef]
  17. C. Shakher and R. S. Sirohi, “Flame temperature measurement using speckle techniques,” in New Directions in Holography and Speckle, H. J. Caulfield and C. S. Vikram, eds. (American Scientific, 2008), pp. 376–389.
  18. D. E. Silva, “Talbot interferometry for radial and lateral derivatives,” Appl. Opt. 11, 2613–2624 (1972).
    [CrossRef]
  19. C. Shakher and A. J. P. Daniel, “Talbot interferometry with circular grating for the measurement of temperature in axisymmetric gaseous flames,” Appl. Opt. 33, 6068–6072 (1994).
    [CrossRef]
  20. A. J. P. Daniel, “Diffractive optical element in speckle metrology and temperature measurement,” Ph.D. dissertation (Instrument Design and Development Centre, Indian Institute of Technology, 1994).
  21. C. Shakher, A. J. P. Daniel, and S. K. Angra, “Measurement of temperature profile of atomic absorption spectrophotometer burner (pre-mixed laminar flow slot burner) using Talbot interferometer,” Opt. Eng. 33, 2663–2669 (1994).
    [CrossRef]
  22. Y.-S. Cheng and R.-C. Chang, “Theory of image formation using the Talbot effect,” Appl. Opt. 33, 1863–1874 (1994).
    [CrossRef]
  23. Y.-S. Cheng and R.-C. Chang, “Image formation for two dimensional periodic object using Talbot effect,” Opt. Commun. 120, 335–347 (1995).
    [CrossRef]
  24. M. Thakur, A. L. Vyas, and C. Shakher, “Measurement of temperature and temperature profile of an axisymmetric gaseous flames using Lau phase interferometer with linear gratings,” Opt. Lasers Eng. 36, 373–380 (2001).
    [CrossRef]
  25. X. Xiao and I. K. Puri, “Systematic approach based on holographic interferometry measurements to characterize the flame structure of partially premixed flames,” Appl. Opt. 40, 731–740 (2001).
    [CrossRef]
  26. B. Lu, X. Yang, H. Abendroth, H. Eggers, and E. Ziolkowski, “Measurement of a 3D-temperature field applying ESPI and CT techniques,” Opt. Commun. 69, 6–10 (1988).
    [CrossRef]
  27. U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [CrossRef]
  28. C. Wagner, S. Seebacher, W. Osten, and W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 38, 4812–4820 (1999).
    [CrossRef]
  29. T. Kreis, Handbook of Holographic Interferometry Optical and Digital Methods (Wiley, 2005).
  30. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef]
  31. X. Xiao and I. K. Puri, “Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion,” Appl. Opt. 41, 3890–3899 (2002).
    [CrossRef]
  32. M. M. Hussain and C. Shakher, “Temperature measurement in laminar free connective flow using digital holography,” Appl. Opt. 48, 1869–1877 (2009).
    [CrossRef]
  33. S. Sharma, G. Sheoran, and C. Shakher, “Axi-symmetric flame temperature measurement using lensless Fourier transform digital holography,” in Frontiers in Optics, OSA Technical Digest (Optical Society of America, 2011), paper FThU1.
  34. R. M. Goldstein, H. A. Zebker, and C. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
    [CrossRef]
  35. M. Born and E. F. Wolf, Principles of Optics, 4th ed.(Pergamon, 1978), Chap. 2.

2009

2004

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]

2003

P. Singh and C. Shakher, “Measurement of the temperature of a gaseous flame using a shearing plate,” Opt. Eng. 42, 80–85 (2003).
[CrossRef]

2002

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

X. Xiao and I. K. Puri, “Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion,” Appl. Opt. 41, 3890–3899 (2002).
[CrossRef]

2001

X. Xiao and I. K. Puri, “Systematic approach based on holographic interferometry measurements to characterize the flame structure of partially premixed flames,” Appl. Opt. 40, 731–740 (2001).
[CrossRef]

M. Thakur, A. L. Vyas, and C. Shakher, “Measurement of temperature and temperature profile of an axisymmetric gaseous flames using Lau phase interferometer with linear gratings,” Opt. Lasers Eng. 36, 373–380 (2001).
[CrossRef]

2000

A. Stella, G. Guj, and S. Giammartini, “Measurement of axi-symmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
[CrossRef]

P. R. N. Childs, J. R. Greenwood, and C. A. Long, “Review of temperature measurement,” Rev. Sci. Instrum. 71, 2959–2978 (2000).
[CrossRef]

1999

1997

1995

Y.-S. Cheng and R.-C. Chang, “Image formation for two dimensional periodic object using Talbot effect,” Opt. Commun. 120, 335–347 (1995).
[CrossRef]

1994

1993

1992

C. Shakher, A. K. Nirala, A. J. P. Daniel, and S. K. Verma, “Use of speckle technique for temperature measurement in gaseous flame,” J. Opt. 23, 35–39 (1992).
[CrossRef]

1988

B. Lu, X. Yang, H. Abendroth, H. Eggers, and E. Ziolkowski, “Measurement of a 3D-temperature field applying ESPI and CT techniques,” Opt. Commun. 69, 6–10 (1988).
[CrossRef]

R. M. Goldstein, H. A. Zebker, and C. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

1984

1983

D. L. Reuss, “Temperature measurement in a radially symmetric flame using holographic interferometry,” Combust. Flame 49, 207–219 (1983).
[CrossRef]

1982

1981

E. Keren, E. Bar-Ziv, I. Glatt, and O. Kafri, “Measurement of temperature distribution of flame by moire deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
[CrossRef]

M. Giglio, S. Musazzi, and U. Perini, “A white light speckle Schlieren technique,” Opt. Commun. 36, 117–120 (1981).
[CrossRef]

1978

A. A. Boiarski, R. H. Barnes, and J. F. Kircher, “Flame measurements utilizing Raman scattering,” Combust. Flame 32, 111–114 (1978).
[CrossRef]

1972

1963

D. Wilkie and S. A. Fisher, “Measurement of temperature by Mach-Zehnder interferometry,” Proc. Inst. Mech. Eng. 178, 461–472 (1963).

Abendroth, H.

B. Lu, X. Yang, H. Abendroth, H. Eggers, and E. Ziolkowski, “Measurement of a 3D-temperature field applying ESPI and CT techniques,” Opt. Commun. 69, 6–10 (1988).
[CrossRef]

Angra, S. K.

C. Shakher, A. J. P. Daniel, and S. K. Angra, “Measurement of temperature profile of atomic absorption spectrophotometer burner (pre-mixed laminar flow slot burner) using Talbot interferometer,” Opt. Eng. 33, 2663–2669 (1994).
[CrossRef]

Barnes, R. H.

A. A. Boiarski, R. H. Barnes, and J. F. Kircher, “Flame measurements utilizing Raman scattering,” Combust. Flame 32, 111–114 (1978).
[CrossRef]

Bar-Ziv, E.

Boiarski, A. A.

A. A. Boiarski, R. H. Barnes, and J. F. Kircher, “Flame measurements utilizing Raman scattering,” Combust. Flame 32, 111–114 (1978).
[CrossRef]

Born, M.

M. Born and E. F. Wolf, Principles of Optics, 4th ed.(Pergamon, 1978), Chap. 2.

Chang, R.-C.

Y.-S. Cheng and R.-C. Chang, “Image formation for two dimensional periodic object using Talbot effect,” Opt. Commun. 120, 335–347 (1995).
[CrossRef]

Y.-S. Cheng and R.-C. Chang, “Theory of image formation using the Talbot effect,” Appl. Opt. 33, 1863–1874 (1994).
[CrossRef]

Cheng, Y.-S.

Y.-S. Cheng and R.-C. Chang, “Image formation for two dimensional periodic object using Talbot effect,” Opt. Commun. 120, 335–347 (1995).
[CrossRef]

Y.-S. Cheng and R.-C. Chang, “Theory of image formation using the Talbot effect,” Appl. Opt. 33, 1863–1874 (1994).
[CrossRef]

Childs, P. R. N.

P. R. N. Childs, J. R. Greenwood, and C. A. Long, “Review of temperature measurement,” Rev. Sci. Instrum. 71, 2959–2978 (2000).
[CrossRef]

Daniel, A. J. P.

C. Shakher and A. J. P. Daniel, “Talbot interferometry with circular grating for the measurement of temperature in axisymmetric gaseous flames,” Appl. Opt. 33, 6068–6072 (1994).
[CrossRef]

C. Shakher, A. J. P. Daniel, and S. K. Angra, “Measurement of temperature profile of atomic absorption spectrophotometer burner (pre-mixed laminar flow slot burner) using Talbot interferometer,” Opt. Eng. 33, 2663–2669 (1994).
[CrossRef]

C. Shakher, A. K. Nirala, A. J. P. Daniel, and S. K. Verma, “Use of speckle technique for temperature measurement in gaseous flame,” J. Opt. 23, 35–39 (1992).
[CrossRef]

A. J. P. Daniel, “Diffractive optical element in speckle metrology and temperature measurement,” Ph.D. dissertation (Instrument Design and Development Centre, Indian Institute of Technology, 1994).

Dobbling, K.

Eggers, H.

B. Lu, X. Yang, H. Abendroth, H. Eggers, and E. Ziolkowski, “Measurement of a 3D-temperature field applying ESPI and CT techniques,” Opt. Commun. 69, 6–10 (1988).
[CrossRef]

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]

Farrel, P. V.

Fisher, S. A.

D. Wilkie and S. A. Fisher, “Measurement of temperature by Mach-Zehnder interferometry,” Proc. Inst. Mech. Eng. 178, 461–472 (1963).

Giammartini, S.

A. Stella, G. Guj, and S. Giammartini, “Measurement of axi-symmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
[CrossRef]

Giglio, M.

M. Giglio, S. Musazzi, and U. Perini, “A white light speckle Schlieren technique,” Opt. Commun. 36, 117–120 (1981).
[CrossRef]

Glatt, I.

Goldstein, R. J.

R. J. Goldstein, “Optical measurement of temperature,” in Measurement Techniques in Heat Transfer, E. R. G. Eckert and R. J. Goldstein, eds. (Technical, 1970), pp. 177–228.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Greenwood, J. R.

P. R. N. Childs, J. R. Greenwood, and C. A. Long, “Review of temperature measurement,” Rev. Sci. Instrum. 71, 2959–2978 (2000).
[CrossRef]

Guj, G.

A. Stella, G. Guj, and S. Giammartini, “Measurement of axi-symmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
[CrossRef]

Hanumann, J.

Hofeldt, D. L.

Hussain, M. M.

Juptner, W.

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Kafri, O.

Kampmann, S.

Keren, E.

Kircher, J. F.

A. A. Boiarski, R. H. Barnes, and J. F. Kircher, “Flame measurements utilizing Raman scattering,” Combust. Flame 32, 111–114 (1978).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry Optical and Digital Methods (Wiley, 2005).

Leipertz, A.

Long, C. A.

P. R. N. Childs, J. R. Greenwood, and C. A. Long, “Review of temperature measurement,” Rev. Sci. Instrum. 71, 2959–2978 (2000).
[CrossRef]

Lu, B.

B. Lu, X. Yang, H. Abendroth, H. Eggers, and E. Ziolkowski, “Measurement of a 3D-temperature field applying ESPI and CT techniques,” Opt. Commun. 69, 6–10 (1988).
[CrossRef]

Musazzi, S.

M. Giglio, S. Musazzi, and U. Perini, “A white light speckle Schlieren technique,” Opt. Commun. 36, 117–120 (1981).
[CrossRef]

Nirala, A. K.

C. Shakher and A. K. Nirala, “Measurement of temperature using speckle shearing interferometry,” Appl. Opt. 33, 2125–2127 (1994).
[CrossRef]

C. Shakher, A. K. Nirala, A. J. P. Daniel, and S. K. Verma, “Use of speckle technique for temperature measurement in gaseous flame,” J. Opt. 23, 35–39 (1992).
[CrossRef]

Osten, W.

Perini, U.

M. Giglio, S. Musazzi, and U. Perini, “A white light speckle Schlieren technique,” Opt. Commun. 36, 117–120 (1981).
[CrossRef]

Pungor, E.

E. Pungor, Flame Photometry (Van Nostrand, 1967), pp. 147–152.

Puri, I. K.

Reuss, D. L.

D. L. Reuss, “Temperature measurement in a radially symmetric flame using holographic interferometry,” Combust. Flame 49, 207–219 (1983).
[CrossRef]

Sattelmayer, T.

Schnars, U.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Seebacher, S.

Shakher, C.

M. M. Hussain and C. Shakher, “Temperature measurement in laminar free connective flow using digital holography,” Appl. Opt. 48, 1869–1877 (2009).
[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]

P. Singh and C. Shakher, “Measurement of the temperature of a gaseous flame using a shearing plate,” Opt. Eng. 42, 80–85 (2003).
[CrossRef]

M. Thakur, A. L. Vyas, and C. Shakher, “Measurement of temperature and temperature profile of an axisymmetric gaseous flames using Lau phase interferometer with linear gratings,” Opt. Lasers Eng. 36, 373–380 (2001).
[CrossRef]

C. Shakher and A. K. Nirala, “Measurement of temperature using speckle shearing interferometry,” Appl. Opt. 33, 2125–2127 (1994).
[CrossRef]

C. Shakher, A. J. P. Daniel, and S. K. Angra, “Measurement of temperature profile of atomic absorption spectrophotometer burner (pre-mixed laminar flow slot burner) using Talbot interferometer,” Opt. Eng. 33, 2663–2669 (1994).
[CrossRef]

C. Shakher and A. J. P. Daniel, “Talbot interferometry with circular grating for the measurement of temperature in axisymmetric gaseous flames,” Appl. Opt. 33, 6068–6072 (1994).
[CrossRef]

C. Shakher, A. K. Nirala, A. J. P. Daniel, and S. K. Verma, “Use of speckle technique for temperature measurement in gaseous flame,” J. Opt. 23, 35–39 (1992).
[CrossRef]

S. Sharma, G. Sheoran, and C. Shakher, “Axi-symmetric flame temperature measurement using lensless Fourier transform digital holography,” in Frontiers in Optics, OSA Technical Digest (Optical Society of America, 2011), paper FThU1.

C. Shakher and R. S. Sirohi, “Flame temperature measurement using speckle techniques,” in New Directions in Holography and Speckle, H. J. Caulfield and C. S. Vikram, eds. (American Scientific, 2008), pp. 376–389.

Sharma, S.

S. Sharma, G. Sheoran, and C. Shakher, “Axi-symmetric flame temperature measurement using lensless Fourier transform digital holography,” in Frontiers in Optics, OSA Technical Digest (Optical Society of America, 2011), paper FThU1.

Sheoran, G.

S. Sharma, G. Sheoran, and C. Shakher, “Axi-symmetric flame temperature measurement using lensless Fourier transform digital holography,” in Frontiers in Optics, OSA Technical Digest (Optical Society of America, 2011), paper FThU1.

Silva, D. E.

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]

P. Singh and C. Shakher, “Measurement of the temperature of a gaseous flame using a shearing plate,” Opt. Eng. 42, 80–85 (2003).
[CrossRef]

Sirohi, R. S.

C. Shakher and R. S. Sirohi, “Flame temperature measurement using speckle techniques,” in New Directions in Holography and Speckle, H. J. Caulfield and C. S. Vikram, eds. (American Scientific, 2008), pp. 376–389.

Springer, G. S.

Stella, A.

A. Stella, G. Guj, and S. Giammartini, “Measurement of axi-symmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
[CrossRef]

Thakur, M.

M. Thakur, A. L. Vyas, and C. Shakher, “Measurement of temperature and temperature profile of an axisymmetric gaseous flames using Lau phase interferometer with linear gratings,” Opt. Lasers Eng. 36, 373–380 (2001).
[CrossRef]

Verma, S. K.

C. Shakher, A. K. Nirala, A. J. P. Daniel, and S. K. Verma, “Use of speckle technique for temperature measurement in gaseous flame,” J. Opt. 23, 35–39 (1992).
[CrossRef]

Vest, C. M.

Vyas, A. L.

M. Thakur, A. L. Vyas, and C. Shakher, “Measurement of temperature and temperature profile of an axisymmetric gaseous flames using Lau phase interferometer with linear gratings,” Opt. Lasers Eng. 36, 373–380 (2001).
[CrossRef]

Wagner, C.

Werner, C.

R. M. Goldstein, H. A. Zebker, and C. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Wilkie, D.

D. Wilkie and S. A. Fisher, “Measurement of temperature by Mach-Zehnder interferometry,” Proc. Inst. Mech. Eng. 178, 461–472 (1963).

Wolf, E. F.

M. Born and E. F. Wolf, Principles of Optics, 4th ed.(Pergamon, 1978), Chap. 2.

Xiao, X.

Yamaguchi, I.

Yang, X.

B. Lu, X. Yang, H. Abendroth, H. Eggers, and E. Ziolkowski, “Measurement of a 3D-temperature field applying ESPI and CT techniques,” Opt. Commun. 69, 6–10 (1988).
[CrossRef]

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Zhang, T.

Ziolkowski, E.

B. Lu, X. Yang, H. Abendroth, H. Eggers, and E. Ziolkowski, “Measurement of a 3D-temperature field applying ESPI and CT techniques,” Opt. Commun. 69, 6–10 (1988).
[CrossRef]

Appl. Opt.

C. Shakher and A. K. Nirala, “Measurement of temperature using speckle shearing interferometry,” Appl. Opt. 33, 2125–2127 (1994).
[CrossRef]

Y.-S. Cheng and R.-C. Chang, “Theory of image formation using the Talbot effect,” Appl. Opt. 33, 1863–1874 (1994).
[CrossRef]

C. Shakher and A. J. P. Daniel, “Talbot interferometry with circular grating for the measurement of temperature in axisymmetric gaseous flames,” Appl. Opt. 33, 6068–6072 (1994).
[CrossRef]

C. Wagner, S. Seebacher, W. Osten, and W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 38, 4812–4820 (1999).
[CrossRef]

S. Kampmann, A. Leipertz, K. Dobbling, J. Hanumann, and T. Sattelmayer, “Two-dimensional temperature measurement in a technical combustor with laser Rayleigh scattering,” Appl. Opt. 32, 6167–6172 (1993).
[CrossRef]

X. Xiao and I. K. Puri, “Systematic approach based on holographic interferometry measurements to characterize the flame structure of partially premixed flames,” Appl. Opt. 40, 731–740 (2001).
[CrossRef]

X. Xiao and I. K. Puri, “Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion,” Appl. Opt. 41, 3890–3899 (2002).
[CrossRef]

D. E. Silva, “Talbot interferometry for radial and lateral derivatives,” Appl. Opt. 11, 2613–2624 (1972).
[CrossRef]

M. M. Hussain and C. Shakher, “Temperature measurement in laminar free connective flow using digital holography,” Appl. Opt. 48, 1869–1877 (2009).
[CrossRef]

E. Keren, E. Bar-Ziv, I. Glatt, and O. Kafri, “Measurement of temperature distribution of flame by moire deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
[CrossRef]

P. V. Farrel, G. S. Springer, and C. M. Vest, “Heterodyne holographic interferometry: concentration and temperature measurement in gas mixtures,” Appl. Opt. 21, 1624–1627 (1982).
[CrossRef]

P. V. Farrel and D. L. Hofeldt, “Temperature measurement in gases using speckle photography,” Appl. Opt. 23, 1055–1059 (1984).
[CrossRef]

Combust. Flame

A. A. Boiarski, R. H. Barnes, and J. F. Kircher, “Flame measurements utilizing Raman scattering,” Combust. Flame 32, 111–114 (1978).
[CrossRef]

D. L. Reuss, “Temperature measurement in a radially symmetric flame using holographic interferometry,” Combust. Flame 49, 207–219 (1983).
[CrossRef]

Exp. Fluids

A. Stella, G. Guj, and S. Giammartini, “Measurement of axi-symmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
[CrossRef]

J. Opt.

C. Shakher, A. K. Nirala, A. J. P. Daniel, and S. K. Verma, “Use of speckle technique for temperature measurement in gaseous flame,” J. Opt. 23, 35–39 (1992).
[CrossRef]

Meas. Sci. Technol.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Opt. Commun.

Y.-S. Cheng and R.-C. Chang, “Image formation for two dimensional periodic object using Talbot effect,” Opt. Commun. 120, 335–347 (1995).
[CrossRef]

M. Giglio, S. Musazzi, and U. Perini, “A white light speckle Schlieren technique,” Opt. Commun. 36, 117–120 (1981).
[CrossRef]

B. Lu, X. Yang, H. Abendroth, H. Eggers, and E. Ziolkowski, “Measurement of a 3D-temperature field applying ESPI and CT techniques,” Opt. Commun. 69, 6–10 (1988).
[CrossRef]

Opt. Eng.

P. Singh and C. Shakher, “Measurement of the temperature of a gaseous flame using a shearing plate,” Opt. Eng. 42, 80–85 (2003).
[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]

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[CrossRef]

Opt. Lasers Eng.

M. Thakur, A. L. Vyas, and C. Shakher, “Measurement of temperature and temperature profile of an axisymmetric gaseous flames using Lau phase interferometer with linear gratings,” Opt. Lasers Eng. 36, 373–380 (2001).
[CrossRef]

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[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Coordinate system used in the Fresnel transform reconstruction method.

Fig. 2.
Fig. 2.

Cross section of an axisymmetric flame at a particular height.

Fig. 3.
Fig. 3.

Experimental setup for measurement of temperature and temperature profile using LLFTDH.

Fig. 4.
Fig. 4.

Flow chart of phase map, refractive index, and temperature profile computation.

Fig. 5.
Fig. 5.

(a)–(c) Reconstructed phase difference map of a candle flame at different times.

Fig. 6.
Fig. 6.

(a) Line profile of the phase difference map of a candle flame with assigned fringe number at height of 13 mm, (b) unwrapped phase map profile at height of 13 mm, (c) 3D phase profile of a candle flame.

Fig. 7.
Fig. 7.

Plot of fringe number versus radius of a candle flame at height of 13 mm.

Fig. 8.
Fig. 8.

Plot of refractive index difference distribution with radial distance of a candle flame at height of 13 mm.

Fig. 9.
Fig. 9.

Plot of temperature versus radial distance of a candle flame at height of 13 mm.

Equations (14)

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O(XI,YI)=iλdexp[iπλd(XI2+YI2)]++R(XH,YH)h(XH,YH)exp[iπλd(XH2+YH2)]×exp[i2πλd(XHXI+YHYI)]dXHdYH,
O(XI,YI)=exp[iπλd(m2ΔXI2+p2ΔYI2)]×k=0P1l=0P1R(k,l)h(k,l)exp[iπλd(k2ΔXH2+l2ΔYH2)]×exp[i2πλd(kΔXHmΔXI+lΔYHmΔYI)]m=0,1,M1;p=0,1,P1.
ΔXI=λdMΔXH;ΔYI=λdPΔYH.
O(mΔXI,pΔYI)=exp[iπλd(m2M2ΔXH2+p2P2ΔYH2)]k=0M1l=0P1R(k,l)h(k,l)×exp[iπλd(k2ΔXH2+l2ΔYH2)]×exp[i2π(kmM+lpP)].
O(mΔXI,pΔYI)=iλdexp[iπλd(m2M2ΔXH2+p2P2ΔYH2)]×FFT{R(k,l)h(k,l)exp[iπλd(k2ΔXH2+l2ΔYH2)]}.
R(r,s)=(const.)exp[iπλd(k2ΔXH2+l2ΔYH2)].
O(mΔXI,pΔYI)=iλdexp[iπλd(m2M2ΔXH2+p2P2ΔYH2)]×FFT{h(k,l)}.
I(XI,YI)=|O(XI,YI)|2=Re2|O(XI,YI)|+Im2|O(XI,YI)|,
ϕ(k,l)=arctanIm[O(k,l)]Re[O(k,l)],
ϕ1(k,l)=arctanIm[O1(k,l)]Re[O1(k,l)],
ϕ2(k,l)=arctanIm[O2(k,l)]Re[O2(k,l)].
Δϕ(kΔx,lΔy)=2πλ[n2(kΔx,lΔy)n1]Δs=±(N1)λ/2=FN,
Δϕ(kΔx,lΔy)={ϕ1(kΔx,lΔy)ϕ2(kΔx,lΔy)ifϕ1(kΔx,lΔy)ϕ2(kΔx,lΔy)ϕ1(kΔx,lΔy)ϕ2(kΔx,lΔy)+2πifϕ1(kΔx,lΔy)<ϕ2(kΔx,lΔy).
T=T0(nn0n0)(3PA+2RT03PA)+1,

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