Abstract

A computer simulation was used to perform a sensitivity analysis on the deflection mapping technique based on the moire effect. The refractive index and the temperature of a hot gas mixture were calculated. The accuracy of the method is shown to have strong dependence on the experimental accuracy. The best mode of experimental operation was found to be the construction of the moire image by using a physical grid and a computer simulated grid.

© 1984 Optical Society of America

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References

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  1. F. J. Weinberg, Optics of Flames (Butterworth, London, 1963).
  2. A. K. Oppenheim, M. M. Kamel, Laser Cinematography of Explosions (Springer, Berlin, 1971), Chap. 2.
  3. J. H. Burgoyne, F. J. Weinberg, “Determination of the Distribution of Some Parameters Across the Combustion Zone of a Flat Flame,” Proc. R. Soc. London Ser. A 224, 286 (1954).
    [CrossRef]
  4. F. J. Weinberg, “Location of the ‘Schlieren Image’ in a Flame,” Fuel London 34, S84 (1955).
  5. F. J. Weinberg, “The Shadow of a Flat Flame,” Proc. R. Soc. London Ser. A 235, 510 (1956).
    [CrossRef]
  6. J. Reck, K. Sumi, F. J. Weinberg, “An Optical Method of Flame Temperature Measurement II—Sensitivity and Application,” Fuel London 35, 364 (1956).
  7. G. Dixon-Lewis, G. L. Isles, Eighth Symposium (International) on Combustion (Butterworth, London, 1962), p. 448.
  8. E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of Temperature Distribution of Flames by Moire Deflectometry,” Appl. Opt. 20, 4263 (1981).
    [CrossRef] [PubMed]
  9. E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, Nineteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, 1982), p. 303.
    [CrossRef]
  10. E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, “Temperature Mapping in Flames by Moire Deflectometry,” Appl. Opt. 22, 698 (1983).
    [CrossRef] [PubMed]
  11. E. Bar-Ziv, G. S. Rau, in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1983), paper WI6.
  12. G. S. Rau S.B. Thesis, Massachusetts Institute of Technology (1983).
  13. For partial explanation of the effect of diffraction on deflection mapping based on the moire phenomenon, see Refs. 9 and 10, also a systematic study of the role of diffraction on the moire effect in the process of publication.

1983 (1)

1981 (1)

1956 (2)

F. J. Weinberg, “The Shadow of a Flat Flame,” Proc. R. Soc. London Ser. A 235, 510 (1956).
[CrossRef]

J. Reck, K. Sumi, F. J. Weinberg, “An Optical Method of Flame Temperature Measurement II—Sensitivity and Application,” Fuel London 35, 364 (1956).

1955 (1)

F. J. Weinberg, “Location of the ‘Schlieren Image’ in a Flame,” Fuel London 34, S84 (1955).

1954 (1)

J. H. Burgoyne, F. J. Weinberg, “Determination of the Distribution of Some Parameters Across the Combustion Zone of a Flat Flame,” Proc. R. Soc. London Ser. A 224, 286 (1954).
[CrossRef]

Bar-Ziv, E.

E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, “Temperature Mapping in Flames by Moire Deflectometry,” Appl. Opt. 22, 698 (1983).
[CrossRef] [PubMed]

E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of Temperature Distribution of Flames by Moire Deflectometry,” Appl. Opt. 20, 4263 (1981).
[CrossRef] [PubMed]

E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, Nineteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, 1982), p. 303.
[CrossRef]

E. Bar-Ziv, G. S. Rau, in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1983), paper WI6.

Burgoyne, J. H.

J. H. Burgoyne, F. J. Weinberg, “Determination of the Distribution of Some Parameters Across the Combustion Zone of a Flat Flame,” Proc. R. Soc. London Ser. A 224, 286 (1954).
[CrossRef]

Dixon-Lewis, G.

G. Dixon-Lewis, G. L. Isles, Eighth Symposium (International) on Combustion (Butterworth, London, 1962), p. 448.

Glatt, I.

Isles, G. L.

G. Dixon-Lewis, G. L. Isles, Eighth Symposium (International) on Combustion (Butterworth, London, 1962), p. 448.

Kafri, O.

Kamel, M. M.

A. K. Oppenheim, M. M. Kamel, Laser Cinematography of Explosions (Springer, Berlin, 1971), Chap. 2.

Keren, E.

Oppenheim, A. K.

A. K. Oppenheim, M. M. Kamel, Laser Cinematography of Explosions (Springer, Berlin, 1971), Chap. 2.

Rau, G. S.

E. Bar-Ziv, G. S. Rau, in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1983), paper WI6.

G. S. Rau S.B. Thesis, Massachusetts Institute of Technology (1983).

Reck, J.

J. Reck, K. Sumi, F. J. Weinberg, “An Optical Method of Flame Temperature Measurement II—Sensitivity and Application,” Fuel London 35, 364 (1956).

Sgulim, S.

E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, “Temperature Mapping in Flames by Moire Deflectometry,” Appl. Opt. 22, 698 (1983).
[CrossRef] [PubMed]

E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, Nineteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, 1982), p. 303.
[CrossRef]

Sumi, K.

J. Reck, K. Sumi, F. J. Weinberg, “An Optical Method of Flame Temperature Measurement II—Sensitivity and Application,” Fuel London 35, 364 (1956).

Weinberg, F. J.

J. Reck, K. Sumi, F. J. Weinberg, “An Optical Method of Flame Temperature Measurement II—Sensitivity and Application,” Fuel London 35, 364 (1956).

F. J. Weinberg, “The Shadow of a Flat Flame,” Proc. R. Soc. London Ser. A 235, 510 (1956).
[CrossRef]

F. J. Weinberg, “Location of the ‘Schlieren Image’ in a Flame,” Fuel London 34, S84 (1955).

J. H. Burgoyne, F. J. Weinberg, “Determination of the Distribution of Some Parameters Across the Combustion Zone of a Flat Flame,” Proc. R. Soc. London Ser. A 224, 286 (1954).
[CrossRef]

F. J. Weinberg, Optics of Flames (Butterworth, London, 1963).

Appl. Opt. (2)

Fuel London (2)

F. J. Weinberg, “Location of the ‘Schlieren Image’ in a Flame,” Fuel London 34, S84 (1955).

J. Reck, K. Sumi, F. J. Weinberg, “An Optical Method of Flame Temperature Measurement II—Sensitivity and Application,” Fuel London 35, 364 (1956).

Proc. R. Soc. London Ser. A (2)

F. J. Weinberg, “The Shadow of a Flat Flame,” Proc. R. Soc. London Ser. A 235, 510 (1956).
[CrossRef]

J. H. Burgoyne, F. J. Weinberg, “Determination of the Distribution of Some Parameters Across the Combustion Zone of a Flat Flame,” Proc. R. Soc. London Ser. A 224, 286 (1954).
[CrossRef]

Other (7)

F. J. Weinberg, Optics of Flames (Butterworth, London, 1963).

A. K. Oppenheim, M. M. Kamel, Laser Cinematography of Explosions (Springer, Berlin, 1971), Chap. 2.

G. Dixon-Lewis, G. L. Isles, Eighth Symposium (International) on Combustion (Butterworth, London, 1962), p. 448.

E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, Nineteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, 1982), p. 303.
[CrossRef]

E. Bar-Ziv, G. S. Rau, in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1983), paper WI6.

G. S. Rau S.B. Thesis, Massachusetts Institute of Technology (1983).

For partial explanation of the effect of diffraction on deflection mapping based on the moire phenomenon, see Refs. 9 and 10, also a systematic study of the role of diffraction on the moire effect in the process of publication.

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Figures (11)

Fig. 1
Fig. 1

Light ray traversing an axially symmetric flat flame and two Ronchi grids.

Fig. 2
Fig. 2

Close-up view of the shifted intensity square wave. G 1 is the transmission pattern of the grid with the flame; G2 is the transmission pattern of the second grid.

Fig. 3
Fig. 3

Digital filtering of the intensity data: bottom, noisy raw data; middle, filtered data; top, square wave.

Fig. 4
Fig. 4

(a) Moire intensity of the flame as a function of the position; (b) enlargement.

Fig. 5
Fig. 5

(a) Unsmoothed deflection angle vs the position; (b) smoothed curve.

Fig. 6
Fig. 6

Standard deviation of T vs temperature for a combination of a real grid and a computer simulated one. The accuracy in intensity is 95%, and the error in position is 0.2 μm. Δ, unfiltered data; □, filtered transmission pattern.

Fig. 7
Fig. 7

Standard deviation of T vs temperature for the two real grid case. The accuracy in the light intensity is 99.8%, and the error in the position is 0.04 μm.

Fig. 8
Fig. 8

Relative error in temperature vs error in the light intensity at different temperatures: (a) T = 1000 K; (b) T = 1500 K; (c) T = 2000 K.

Fig. 9
Fig. 9

Relative error in temperature vs error in position at different temperatures: (a) T = 1000 K; (b) T = 1500 K; (c) T = 2000 K.

Fig. 10
Fig. 10

Base line error in temperature vs temperature due to the finite resolution.

Fig. 11
Fig. 11

Actual error in temperature vs temperature.

Equations (15)

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ϕ ( x ) = 2 [ sin - 1 ( x r · n s n f ) - sin - 1 ( x r ) ] ,
n - 1 = k av N ,
T f = T s n s - 1 n f - 1 ,
I ( x ) = 1 - 2 Δ p ϕ ( x ) .
I ( x ) = 1 p x x + p G 1 ( x ) G 2 ( x ) d x ,
G 1 ( x ) = ½ + 2 π i = 0 sin [ 2 ( 2 i + 1 ) x p ] 2 i + 1 .
G 1 ( x ) = ½ + 2 π i = 0 sin [ 2 π ( 2 i + 1 ) ( x p ) ( 1 - Δ ϕ x ) ] 2 i + 1 .
Δ ϕ 2 ( x ) = [ ϕ E ( x ) - ϕ T ( x ) ] 2 ,
I = F ( T ) ,
d T d T = d F ( T ) d T .
d T 2 = d I 2 [ d F ( T ) d T ] 2 .
Δ T 2 = Δ I 2 [ d F ( T ) d T ] 2 ,
Δ I 2 = ( I E - I T ) 2 .
Δ T = { 1 m - 1 Δ I 2 [ d F ( T ) d T ] 2 } 1 / 2 .
Δ T = [ 1 m - 1 i ( I E - I T ) 2 [ 1 - ( x r 1 + k T s - 1 1 + k T f - 1 ) 2 ] 1 / 2 p r ( 1 + k T f - 1 ) 2 4 × ( k T f - 2 ) ( 1 + k T s - 1 ) ] 1 / 2 .

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