Abstract

Holographic interferometry (HI) has proved to be a useful tool for nonintrusive temperature measurements in flames (and thereafter for inference of the local composition based on the state relationship approach) with high spatial and temporal resolution. Digital holographic interferometry (DHI) is a relatively new imaging and measurement technique that electronically records a hologram (e.g., on a CCD) and reconstructs it by a numerical method. Cumbersome chemical processing of the hologram is avoided in DHI, which thereby provides greater flexibility, speed, and the potential for real-time processing. In conventional holography, fringes that are neither bright nor dark on a hologram cannot be accurately resolved. The DHI technique has not yet to our knowledge been used for combustion applications. Herein we evaluate its efficacy for making temperature measurements in flames and assess its applicability through a simulation. Each part of a double exposure associated with the holographic technique is considered to be recorded by a hypothetical CCD sensor at a separate time from the other part. We applied the principles of Fourier optics to develop two numerical methods for hologram reconstruction, and we show that both methods provide an accurate reconstruction of the phase image associated with a flame. Because of the periodic nature of the wave function, the reconstructed phase values are limited to the interval [-π/2, π/2]. Thus an unwrapping algorithm is provided that produces a continuous phase distribution based on the condition that the reconstructed phase is jumped by a value of -π or π. We have also developed an iterative calculation method to adjust the value of the digital reference wave parameters that determines the phase imaging reconstruction in DHI.

© 2002 Optical Society of America

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References

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  1. X. Xiao, C. W. Choi, I. K. Puri, “Temperature measurement in steady two-dimentional partially premixed flames using laser holographic interferometry,” Combust. Flame 120, 318–332 (2000).
    [CrossRef]
  2. X. Xiao, 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]
  3. D. Shi, X. Xiao, Y. He, P. Qiao, S. Chen, “Measurement of three-dimensional temperature field using phase-shifting holography and CT technique,” in Optical Technology in Fluid, Thermal, and Combustion Flow III, S. S. Cha, M. Kawahashi, J. D. Trolinger, eds., Proc. SPIE3172, 405–410 (1997).
    [CrossRef]
  4. R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, New York, 1989).
  5. U. Schnars, W. Juptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
  6. S. Schedin, G. Pedrini, H. J. Tiziani, F. Mendoza Santoyo, “Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography,” Appl. Opt. 38, 7056–7062 (1999).
    [CrossRef]
  7. E. Cuche, F. Bevilacqua, C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [CrossRef]
  8. K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and x-ray wavelength,” Nat. Med. 2, 939–941 (1996).
    [CrossRef] [PubMed]
  9. R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
    [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).
  11. X. Xiao, I. K. Puri, “Temperature measurements in steady axisymmetric partially premixed flames using rainbow schlieren deflectometry,” Appl. Opt. 41, 1922–1928 (2002).
    [CrossRef] [PubMed]
  12. Z. Shu, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Flame-vortex dynamics in an inverse partially premixed combustor,” Combust. Flame 111, 276–295 (1997).
    [CrossRef]
  13. Z. Shu, C. W. Choi, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Gravity effects on steady two-dimensional partially premixed methane–air flames,” Combust. Flame 118, 91–107 (1999).
    [CrossRef]
  14. R. Azzoni, S. Ratti, S. K. Aggarwal, I. K. Puri, “The structure of triple flames stabilized on a slot burner,” Combust. Flame 119, 23–40 (1999).
    [CrossRef]
  15. X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
    [CrossRef]

2002 (2)

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

X. Xiao, I. K. Puri, “Temperature measurements in steady axisymmetric partially premixed flames using rainbow schlieren deflectometry,” Appl. Opt. 41, 1922–1928 (2002).
[CrossRef] [PubMed]

2001 (1)

2000 (2)

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

X. Xiao, C. W. Choi, I. K. Puri, “Temperature measurement in steady two-dimentional partially premixed flames using laser holographic interferometry,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

1999 (4)

Z. Shu, C. W. Choi, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Gravity effects on steady two-dimensional partially premixed methane–air flames,” Combust. Flame 118, 91–107 (1999).
[CrossRef]

R. Azzoni, S. Ratti, S. K. Aggarwal, I. K. Puri, “The structure of triple flames stabilized on a slot burner,” Combust. Flame 119, 23–40 (1999).
[CrossRef]

E. Cuche, F. Bevilacqua, C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
[CrossRef]

S. Schedin, G. Pedrini, H. J. Tiziani, F. Mendoza Santoyo, “Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography,” Appl. Opt. 38, 7056–7062 (1999).
[CrossRef]

1997 (1)

Z. Shu, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Flame-vortex dynamics in an inverse partially premixed combustor,” Combust. Flame 111, 276–295 (1997).
[CrossRef]

1996 (1)

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and x-ray wavelength,” Nat. Med. 2, 939–941 (1996).
[CrossRef] [PubMed]

1994 (1)

Aggarwal, S. K.

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

Z. Shu, C. W. Choi, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Gravity effects on steady two-dimensional partially premixed methane–air flames,” Combust. Flame 118, 91–107 (1999).
[CrossRef]

R. Azzoni, S. Ratti, S. K. Aggarwal, I. K. Puri, “The structure of triple flames stabilized on a slot burner,” Combust. Flame 119, 23–40 (1999).
[CrossRef]

Z. Shu, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Flame-vortex dynamics in an inverse partially premixed combustor,” Combust. Flame 111, 276–295 (1997).
[CrossRef]

Azzoni, R.

R. Azzoni, S. Ratti, S. K. Aggarwal, I. K. Puri, “The structure of triple flames stabilized on a slot burner,” Combust. Flame 119, 23–40 (1999).
[CrossRef]

Bevilacqua, F.

Borisov, A. B.

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and x-ray wavelength,” Nat. Med. 2, 939–941 (1996).
[CrossRef] [PubMed]

Boyer, K.

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and x-ray wavelength,” Nat. Med. 2, 939–941 (1996).
[CrossRef] [PubMed]

Chen, S.

D. Shi, X. Xiao, Y. He, P. Qiao, S. Chen, “Measurement of three-dimensional temperature field using phase-shifting holography and CT technique,” in Optical Technology in Fluid, Thermal, and Combustion Flow III, S. S. Cha, M. Kawahashi, J. D. Trolinger, eds., Proc. SPIE3172, 405–410 (1997).
[CrossRef]

Choi, C. W.

X. Xiao, C. W. Choi, I. K. Puri, “Temperature measurement in steady two-dimentional partially premixed flames using laser holographic interferometry,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

Z. Shu, C. W. Choi, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Gravity effects on steady two-dimensional partially premixed methane–air flames,” Combust. Flame 118, 91–107 (1999).
[CrossRef]

Cuche, E.

Depeursinge, C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

He, Y.

D. Shi, X. Xiao, Y. He, P. Qiao, S. Chen, “Measurement of three-dimensional temperature field using phase-shifting holography and CT technique,” in Optical Technology in Fluid, Thermal, and Combustion Flow III, S. S. Cha, M. Kawahashi, J. D. Trolinger, eds., Proc. SPIE3172, 405–410 (1997).
[CrossRef]

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, New York, 1989).

Juptner, W.

Katta, V. R.

Z. Shu, C. W. Choi, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Gravity effects on steady two-dimensional partially premixed methane–air flames,” Combust. Flame 118, 91–107 (1999).
[CrossRef]

Z. Shu, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Flame-vortex dynamics in an inverse partially premixed combustor,” Combust. Flame 111, 276–295 (1997).
[CrossRef]

Longworth, J. W.

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and x-ray wavelength,” Nat. Med. 2, 939–941 (1996).
[CrossRef] [PubMed]

Mendoza Santoyo, F.

Owen, R. B.

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

Pedrini, G.

Puri, I. K.

X. Xiao, I. K. Puri, “Temperature measurements in steady axisymmetric partially premixed flames using rainbow schlieren deflectometry,” Appl. Opt. 41, 1922–1928 (2002).
[CrossRef] [PubMed]

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

X. Xiao, 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, C. W. Choi, I. K. Puri, “Temperature measurement in steady two-dimentional partially premixed flames using laser holographic interferometry,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

Z. Shu, C. W. Choi, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Gravity effects on steady two-dimensional partially premixed methane–air flames,” Combust. Flame 118, 91–107 (1999).
[CrossRef]

R. Azzoni, S. Ratti, S. K. Aggarwal, I. K. Puri, “The structure of triple flames stabilized on a slot burner,” Combust. Flame 119, 23–40 (1999).
[CrossRef]

Z. Shu, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Flame-vortex dynamics in an inverse partially premixed combustor,” Combust. Flame 111, 276–295 (1997).
[CrossRef]

Qiao, P.

D. Shi, X. Xiao, Y. He, P. Qiao, S. Chen, “Measurement of three-dimensional temperature field using phase-shifting holography and CT technique,” in Optical Technology in Fluid, Thermal, and Combustion Flow III, S. S. Cha, M. Kawahashi, J. D. Trolinger, eds., Proc. SPIE3172, 405–410 (1997).
[CrossRef]

Qin, X.

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

Ratti, S.

R. Azzoni, S. Ratti, S. K. Aggarwal, I. K. Puri, “The structure of triple flames stabilized on a slot burner,” Combust. Flame 119, 23–40 (1999).
[CrossRef]

Rhodes, C. K.

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and x-ray wavelength,” Nat. Med. 2, 939–941 (1996).
[CrossRef] [PubMed]

Schedin, S.

Schnars, U.

Shi, D.

D. Shi, X. Xiao, Y. He, P. Qiao, S. Chen, “Measurement of three-dimensional temperature field using phase-shifting holography and CT technique,” in Optical Technology in Fluid, Thermal, and Combustion Flow III, S. S. Cha, M. Kawahashi, J. D. Trolinger, eds., Proc. SPIE3172, 405–410 (1997).
[CrossRef]

Shu, Z.

Z. Shu, C. W. Choi, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Gravity effects on steady two-dimensional partially premixed methane–air flames,” Combust. Flame 118, 91–107 (1999).
[CrossRef]

Z. Shu, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Flame-vortex dynamics in an inverse partially premixed combustor,” Combust. Flame 111, 276–295 (1997).
[CrossRef]

Solem, J. C.

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and x-ray wavelength,” Nat. Med. 2, 939–941 (1996).
[CrossRef] [PubMed]

Tiziani, H. J.

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, New York, 1989).

Xiao, X.

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

X. Xiao, I. K. Puri, “Temperature measurements in steady axisymmetric partially premixed flames using rainbow schlieren deflectometry,” Appl. Opt. 41, 1922–1928 (2002).
[CrossRef] [PubMed]

X. Xiao, 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, C. W. Choi, I. K. Puri, “Temperature measurement in steady two-dimentional partially premixed flames using laser holographic interferometry,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

D. Shi, X. Xiao, Y. He, P. Qiao, S. Chen, “Measurement of three-dimensional temperature field using phase-shifting holography and CT technique,” in Optical Technology in Fluid, Thermal, and Combustion Flow III, S. S. Cha, M. Kawahashi, J. D. Trolinger, eds., Proc. SPIE3172, 405–410 (1997).
[CrossRef]

Zozulya, A. A.

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

Appl. Opt. (4)

Combust. Flame (5)

Z. Shu, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Flame-vortex dynamics in an inverse partially premixed combustor,” Combust. Flame 111, 276–295 (1997).
[CrossRef]

Z. Shu, C. W. Choi, S. K. Aggarwal, V. R. Katta, I. K. Puri, “Gravity effects on steady two-dimensional partially premixed methane–air flames,” Combust. Flame 118, 91–107 (1999).
[CrossRef]

R. Azzoni, S. Ratti, S. K. Aggarwal, I. K. Puri, “The structure of triple flames stabilized on a slot burner,” Combust. Flame 119, 23–40 (1999).
[CrossRef]

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

X. Xiao, C. W. Choi, I. K. Puri, “Temperature measurement in steady two-dimentional partially premixed flames using laser holographic interferometry,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

Nat. Med. (1)

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and x-ray wavelength,” Nat. Med. 2, 939–941 (1996).
[CrossRef] [PubMed]

Opt. Eng. (1)

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

Opt. Lett. (1)

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

D. Shi, X. Xiao, Y. He, P. Qiao, S. Chen, “Measurement of three-dimensional temperature field using phase-shifting holography and CT technique,” in Optical Technology in Fluid, Thermal, and Combustion Flow III, S. S. Cha, M. Kawahashi, J. D. Trolinger, eds., Proc. SPIE3172, 405–410 (1997).
[CrossRef]

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, New York, 1989).

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Figures (12)

Fig. 1
Fig. 1

Simple off-axis digital holography system.

Fig. 2
Fig. 2

Schematic diagram of the coannular burner.

Fig. 3
Fig. 3

Left, computed temperature and right, refractive-index profiles for a partially premixed flame.

Fig. 4
Fig. 4

Simulated spatial frequency spectra of two object waves in cross section taken at axial height z = 5 mm for (a) an object wave passing through a flame and (b) an object wave that is not passing through that flame (i.e., is passing through ambient air).

Fig. 5
Fig. 5

Typical spatial frequency spectra of a simulated hologram recorded with an off-axis holographic system.

Fig. 6
Fig. 6

FTs of a numerically reconstructed hologram that is assumed to be recorded with an off-axis holographic system.

Fig. 7
Fig. 7

Spectra of a simulated hologram that eliminates the so-called dc term multiplied by a digitally computed reference wave R d (k, l) for (a) a flame and (b) air.

Fig. 8
Fig. 8

Comparison of the reconstruction of the phase differences obtained by two methods at an axial plane at height z = 5 mm (a) by deletion of the dc term and (b) by retention of the constant terms.

Fig. 9
Fig. 9

Reconstructed phase differences at an axial plane at height z = 27 mm.

Fig. 10
Fig. 10

Comparison of the reconstructed and the real phase differences at two cross sections: (a), (c) at z = 5 mm and (b), (d) at z = 27 mm.

Fig. 11
Fig. 11

Simulated holographic fringe patterns for a flame.

Fig. 12
Fig. 12

FT of the numerical reconstruction of a simulated hologram recorded in the absence of a flame.

Equations (24)

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

O1=A1x, yexpjϕ1x, y,
O2=A2x, yexpjϕ2x, y,
Ix, y=O1+O22=2Ax, y21+cosΔϕx, y.
Δϕx, y=2π/λn1x, y-n2ds=2πN or n1x, y-n2ds=Nλ,
θarcsinλ/2Δx,
IHx, y=|R|2+|O|2+R*O+RO*,
IHk, l=IHx, yrectx/L, y/L×kl δx-kΔx, y-1Δy,
ψx, y=Rx, yI1Hx, y+I2Hx, y,
ψkΔx, lΔy=Rdk, lIHk, l=Rd|R|2+Rd|O|2+RdR*O+RdRO*.
Rk, l=AR expj2π/λsinθkΔx,
ψ12kΔx, lΔy=Rdk, lI1H-I2H=RdR*O1-O2+RdRO1*-O2*.
FTψ12kΔx, lΔy=F0f0+F1f0-2fr,
ψ1kΔx, lΔy=|R|2O1-O2=IFTFTψ12kΔx, lΔyH1,
ψ2kΔx, lΔy=IFTFTRdk, lI2Hk, lH2,
ϕ2kΔx, lΔy=arctanImψ2kΔx, lΔy/Reψ2kΔx, lΔy,
ϕ1kΔx, lΔy=arctan×Imψ1kΔx, lΔy+Imψ2kΔx, lΔyReψ1kΔx, lΔy+Reψ2kΔx, lΔy.
ΔϕkΔx, lΔy=ϕ1kΔx, lΔy-ϕ2kΔx, lΔy.
n1kΔx, lΔy-n2ds=Nλ.
IHx, y=|R|2+|O|2+AR exp-j2π/λsinθxO+AR expj2π/λsinθxO*.
FTI1Hx, y=FT|R|2+|O1|2+FTR*O1+FTRO1*,
IFTFTI1Hx, yH0=R*O1+RO1*,
Rdk, l=Ad expj2π/λkxkΔx,
FTIHk, l=C0f0+C1f0-fr+C-1f0+fr,
FTRdk, lIHk, l=D0f0+fd+D1f0-fr+fd+D-1f0+fr+fd.

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