Abstract

A detailed study for measuring the temperature distribution in axisymmetric flames by using a Talbot interferometer with circular gratings is presented. We increased the sensitivity of the interferometer by optimizing the pitch of the grating and the Talbot plane. We compare the experimental results with the values that were measured with a thermocouple to an accuracy of ±0.2% of full scale ±4 digits. Good agreement is seen between the temperatures measured by use of a thermocouple and those measured by use of Talbot interferometry.

© 1994 Optical Society of America

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References

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), pp. 329–344.
  2. E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of the temperature distribution of the flames by moiré deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
    [CrossRef] [PubMed]
  3. M. Giglio, S. Musazzi, U. Perini, “A white light Schlieren technique,” Opt. Commun. 36, 117–120 (1981).
    [CrossRef]
  4. C. Shakher, A. K. Nirala, J. Pramila, S. K. Verma, “Use of speckle technique for temperature measurement in gaseous flames,” J. Opt. (Paris) 23, 35–39 (1992).
    [CrossRef]
  5. P. V. Farrell, D. L. Hofeldt, “Temperature measurement in gases using speckle photography,” Appl. Opt. 23, 1055–1059 (1984).
    [CrossRef] [PubMed]
  6. G. H. Kaufmann, “Numerical processing of speckle photograph data by Fourier transform,” Appl. Opt. 20, 4277–4278 (1981).
    [CrossRef] [PubMed]
  7. C. S. Vikram, “Error in speckle photography of lateral sinusoidal vibrations: a simple analytical solution,” Appl. Opt. 21, 1710–1712 (1982).
    [CrossRef] [PubMed]
  8. S. A. Isacson, G. H. Kaufmann, “Two dimensional digital processing of speckle photography fringes. 2: Diffraction halo influence for the noisy case,” Appl. Opt. 24, 1444–1447 (1985).
    [CrossRef] [PubMed]
  9. C. S. Vikram, K. Vedam, “Processing speckle photography data: circular imaging aperture,” Appl. Opt. 22, 653–654 (1983).
    [CrossRef] [PubMed]
  10. K. Hinsch, “Fringe positions in double exposure speckle photography,” Appl. Opt. 28, 5298–5304 (1989).
    [CrossRef] [PubMed]
  11. C. S. Vikram, “Removing the diffraction halo effect in speckle photography of sinusoidal vibration,” Appl. Opt. 29, 3572–3573(1990).
    [CrossRef] [PubMed]
  12. C. Joenathan, R. S. Sirohi, “Elimination of error in speckle photography,” Appl. Opt. 25, 1791–1794 (1986).
    [CrossRef] [PubMed]
  13. D. J. Chen, F. P. Chiang, “Digital processing of Young's fringes in speckle photography,” Opt. Eng. 29, 1413–1420 (1990).
    [CrossRef]
  14. Y. Nakano, K. Murata, “Measurements of phase objects using the Talbot effect and moiré techniques,” Appl. Opt. 23, 2296–2299 (1984).
    [CrossRef] [PubMed]
  15. A. W. Lohmann, D. E. Silva, “A Talbot with circular gratings,” Opt. Commun. 4, 326–328 (1972).
    [CrossRef]
  16. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Chap. 3, p. 122.
  17. A. W. Lohmann, D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413–415 (1971).
    [CrossRef]
  18. R. Rodriguez Vera, D. Kerr, F. Mendoza-Santoyo, “3-D contouring of diffuse objects by Talbot projected fringes,” J. Mod. Opt. 38, 1935–1945 (1991).
    [CrossRef]
  19. D. E. Silva, “Talbot interferometer for radial and lateral derivatives,” Appl. Opt. 11, 2613–2624 (1972).
    [CrossRef] [PubMed]

1992 (1)

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

1991 (1)

R. Rodriguez Vera, D. Kerr, F. Mendoza-Santoyo, “3-D contouring of diffuse objects by Talbot projected fringes,” J. Mod. Opt. 38, 1935–1945 (1991).
[CrossRef]

1990 (2)

D. J. Chen, F. P. Chiang, “Digital processing of Young's fringes in speckle photography,” Opt. Eng. 29, 1413–1420 (1990).
[CrossRef]

C. S. Vikram, “Removing the diffraction halo effect in speckle photography of sinusoidal vibration,” Appl. Opt. 29, 3572–3573(1990).
[CrossRef] [PubMed]

1989 (1)

1986 (1)

1985 (1)

1984 (2)

1983 (1)

1982 (1)

1981 (3)

1972 (2)

A. W. Lohmann, D. E. Silva, “A Talbot with circular gratings,” Opt. Commun. 4, 326–328 (1972).
[CrossRef]

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

1971 (1)

A. W. Lohmann, D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413–415 (1971).
[CrossRef]

Bar-Ziv, E.

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Chap. 3, p. 122.

Chen, D. J.

D. J. Chen, F. P. Chiang, “Digital processing of Young's fringes in speckle photography,” Opt. Eng. 29, 1413–1420 (1990).
[CrossRef]

Chiang, F. P.

D. J. Chen, F. P. Chiang, “Digital processing of Young's fringes in speckle photography,” Opt. Eng. 29, 1413–1420 (1990).
[CrossRef]

Farrell, P. V.

Giglio, M.

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

Glatt, I.

Hinsch, K.

Hofeldt, D. L.

Isacson, S. A.

Joenathan, C.

Kafri, O.

Kaufmann, G. H.

Keren, E.

Kerr, D.

R. Rodriguez Vera, D. Kerr, F. Mendoza-Santoyo, “3-D contouring of diffuse objects by Talbot projected fringes,” J. Mod. Opt. 38, 1935–1945 (1991).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, D. E. Silva, “A Talbot with circular gratings,” Opt. Commun. 4, 326–328 (1972).
[CrossRef]

A. W. Lohmann, D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413–415 (1971).
[CrossRef]

Mendoza-Santoyo, F.

R. Rodriguez Vera, D. Kerr, F. Mendoza-Santoyo, “3-D contouring of diffuse objects by Talbot projected fringes,” J. Mod. Opt. 38, 1935–1945 (1991).
[CrossRef]

Murata, K.

Musazzi, S.

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

Nakano, Y.

Nirala, A. K.

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

Perini, U.

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

Pramila, J.

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

Rodriguez Vera, R.

R. Rodriguez Vera, D. Kerr, F. Mendoza-Santoyo, “3-D contouring of diffuse objects by Talbot projected fringes,” J. Mod. Opt. 38, 1935–1945 (1991).
[CrossRef]

Shakher, C.

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

Silva, D. E.

A. W. Lohmann, D. E. Silva, “A Talbot with circular gratings,” Opt. Commun. 4, 326–328 (1972).
[CrossRef]

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

A. W. Lohmann, D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413–415 (1971).
[CrossRef]

Sirohi, R. S.

Vedam, K.

Verma, S. K.

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

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), pp. 329–344.

Vikram, C. S.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Chap. 3, p. 122.

Appl. Opt. (11)

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

G. H. Kaufmann, “Numerical processing of speckle photograph data by Fourier transform,” Appl. Opt. 20, 4277–4278 (1981).
[CrossRef] [PubMed]

C. S. Vikram, “Error in speckle photography of lateral sinusoidal vibrations: a simple analytical solution,” Appl. Opt. 21, 1710–1712 (1982).
[CrossRef] [PubMed]

S. A. Isacson, G. H. Kaufmann, “Two dimensional digital processing of speckle photography fringes. 2: Diffraction halo influence for the noisy case,” Appl. Opt. 24, 1444–1447 (1985).
[CrossRef] [PubMed]

C. S. Vikram, K. Vedam, “Processing speckle photography data: circular imaging aperture,” Appl. Opt. 22, 653–654 (1983).
[CrossRef] [PubMed]

K. Hinsch, “Fringe positions in double exposure speckle photography,” Appl. Opt. 28, 5298–5304 (1989).
[CrossRef] [PubMed]

C. S. Vikram, “Removing the diffraction halo effect in speckle photography of sinusoidal vibration,” Appl. Opt. 29, 3572–3573(1990).
[CrossRef] [PubMed]

C. Joenathan, R. S. Sirohi, “Elimination of error in speckle photography,” Appl. Opt. 25, 1791–1794 (1986).
[CrossRef] [PubMed]

E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of the temperature distribution of the flames by moiré deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
[CrossRef] [PubMed]

Y. Nakano, K. Murata, “Measurements of phase objects using the Talbot effect and moiré techniques,” Appl. Opt. 23, 2296–2299 (1984).
[CrossRef] [PubMed]

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

J. Mod. Opt. (1)

R. Rodriguez Vera, D. Kerr, F. Mendoza-Santoyo, “3-D contouring of diffuse objects by Talbot projected fringes,” J. Mod. Opt. 38, 1935–1945 (1991).
[CrossRef]

J. Opt. (Paris) (1)

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

Opt. Commun. (3)

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

A. W. Lohmann, D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413–415 (1971).
[CrossRef]

A. W. Lohmann, D. E. Silva, “A Talbot with circular gratings,” Opt. Commun. 4, 326–328 (1972).
[CrossRef]

Opt. Eng. (1)

D. J. Chen, F. P. Chiang, “Digital processing of Young's fringes in speckle photography,” Opt. Eng. 29, 1413–1420 (1990).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Chap. 3, p. 122.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), pp. 329–344.

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Figures (5)

Fig. 1
Fig. 1

Schematic of a typical experimental setup of a Talbot interferometer with circular gratings for temperature measurement.

Fig. 2
Fig. 2

Horizontal cross section showing the distortion of the lth ring of grating G1 along the y axis that is due to a refractive-index gradient at the burner in a typical plane at a distance Zk from the burner.

Fig. 3
Fig. 3

Variations of the smallest detectable deflection ϕmin with (a) the pitch of the grating and (b) the Talbot plane.

Fig. 4
Fig. 4

Photographs of the fringes formed with (a) a candle flame and (b) a LPG flame.

Fig. 5
Fig. 5

Temperature versus distance curve for a LPG flame.

Equations (26)

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y 2 ( 1 + α ) 2 + z 2 ( 1 + β ) 2 = l 2 p 2
y 2 + z 2 = k 2 p 2 ,
k l = m .
( y 2 + z 2 ) 1 / 2 [ y 2 ( 1 + α ) 2 + z 2 ( 1 + β ) 2 ] 1 / 2 = m p .
r [ r 2 ( 1 + α ) 2 ] 1 / 2 = m p ,
α = m p r m p .
l = r p ( 1 + α ) .
l = r m p p .
l p α = m p ,
ϕ = l p α Z k = m p Z k ,
d d s ( n d r d s ) = n .
d s d x , x ( n y x ) = n y , y x = 1 n n y d x .
r = ( x 2 + y 2 ) 1 / 2 , ϕ = d y d x = 1 n 0 n r y r r d r ( r 2 y 2 ) 1 / 2 , ϕ = 2 y n 0 y n r d r ( r 2 y 2 ) 1 / 2 .
( n n 0 n 0 ) = 1 π γ ϕ d y ( y 2 r 2 ) 1 / 2 .
T = T 0 ( n n 0 n 0 ) ( 3 P A + 2 R T 0 3 P A ) + 1 ,
ϕ min = P 2 Z k ,
ϕ min = p λ 2 k p 2 = λ 2 k p ,
ϕ Z k = m p Z k 2 , ϕ r = 0 .
( n n 0 n 0 ) = x , x = ( n n 0 n 0 ) = 1 π r r max ϕ d y ( y 2 r 2 ) 1 / 2 , x = ϕ π Y ,
Y = log [ r max + ( r max 2 r 2 ) 1 / 2 ] log r .
T = k 1 k 2 x + 1 ,
k 2 = ( 3 P A + 2 R T 0 3 P A ) .
T r = T x x r , T Z k = T x x Z k ,
x r = Y π ϕ r ϕ π Y r , x Z k = Y π ϕ Z k .
T x = k 1 k 2 ( k 2 x + 1 ) 2 .
T r 2357 , T Z k 7 .

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