Abstract

In this paper a method of large aperture (Φ500 mm) high sensitivity moire deflectometry is used to obtain multidirectional deflectograms of the asymmetric flow field in hypersonic (M = 10.29) shock tunnel. At the same time, a 3-D reconstructive method of the asymmetric flow field is presented which is based on the integration of the moire deflective angle and the double-cubic many-knot interpolating splines; it is used to calculate the 3-D density distribution of the asymmetric flow field.

© 1991 Optical Society of America

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References

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  1. J. Stricker, O. Kafri, “A New Method for Density Gradient Measurements in Compressible Flows,” AIAA J. 20, 820–823 (1982).
    [CrossRef]
  2. J. Stricker, “Analysis of 3-D Phase Objects by Moire Deflectometry,” Appl. Opt. 23, 3657–3659 (1984).
    [CrossRef] [PubMed]
  3. E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of Temperature Distribution of Flames by Moire Deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
    [CrossRef] [PubMed]
  4. C. M. Vest, “Formation of Images from Projections: Radon and Abel Transforms,” J. Opt. Soc. Am. 64, 1215–1218 (1974).
    [CrossRef]
  5. Qi Dong-Xu, “Matrix Representation and Estimation of Remainder Term of Many-Knot Spline Interpolating Curves and Surfaces,” Computat. Math. 00, 244–249 (1982).
  6. G. T. Herman, A. Lent, “A Family of Iterative Quadratic Optimization Algorithms for Pairs of Inequalities, with Application in Diagnostic Radiology,” Math. Prog. Study 9, 15–20 (1978).
    [CrossRef]
  7. R. Goulard, Combustion Measurement (Academic, New York, 1986), pp. 226–244.

1984 (1)

1982 (2)

Qi Dong-Xu, “Matrix Representation and Estimation of Remainder Term of Many-Knot Spline Interpolating Curves and Surfaces,” Computat. Math. 00, 244–249 (1982).

J. Stricker, O. Kafri, “A New Method for Density Gradient Measurements in Compressible Flows,” AIAA J. 20, 820–823 (1982).
[CrossRef]

1981 (1)

1978 (1)

G. T. Herman, A. Lent, “A Family of Iterative Quadratic Optimization Algorithms for Pairs of Inequalities, with Application in Diagnostic Radiology,” Math. Prog. Study 9, 15–20 (1978).
[CrossRef]

1974 (1)

Bar-Ziv, E.

Dong-Xu, Qi

Qi Dong-Xu, “Matrix Representation and Estimation of Remainder Term of Many-Knot Spline Interpolating Curves and Surfaces,” Computat. Math. 00, 244–249 (1982).

Glatt, I.

Goulard, R.

R. Goulard, Combustion Measurement (Academic, New York, 1986), pp. 226–244.

Herman, G. T.

G. T. Herman, A. Lent, “A Family of Iterative Quadratic Optimization Algorithms for Pairs of Inequalities, with Application in Diagnostic Radiology,” Math. Prog. Study 9, 15–20 (1978).
[CrossRef]

Kafri, O.

J. Stricker, O. Kafri, “A New Method for Density Gradient Measurements in Compressible Flows,” AIAA J. 20, 820–823 (1982).
[CrossRef]

E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of Temperature Distribution of Flames by Moire Deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
[CrossRef] [PubMed]

Keren, E.

Lent, A.

G. T. Herman, A. Lent, “A Family of Iterative Quadratic Optimization Algorithms for Pairs of Inequalities, with Application in Diagnostic Radiology,” Math. Prog. Study 9, 15–20 (1978).
[CrossRef]

Stricker, J.

J. Stricker, “Analysis of 3-D Phase Objects by Moire Deflectometry,” Appl. Opt. 23, 3657–3659 (1984).
[CrossRef] [PubMed]

J. Stricker, O. Kafri, “A New Method for Density Gradient Measurements in Compressible Flows,” AIAA J. 20, 820–823 (1982).
[CrossRef]

Vest, C. M.

AIAA J. (1)

J. Stricker, O. Kafri, “A New Method for Density Gradient Measurements in Compressible Flows,” AIAA J. 20, 820–823 (1982).
[CrossRef]

Appl. Opt. (2)

Computat. Math. (1)

Qi Dong-Xu, “Matrix Representation and Estimation of Remainder Term of Many-Knot Spline Interpolating Curves and Surfaces,” Computat. Math. 00, 244–249 (1982).

J. Opt. Soc. Am. (1)

Math. Prog. Study (1)

G. T. Herman, A. Lent, “A Family of Iterative Quadratic Optimization Algorithms for Pairs of Inequalities, with Application in Diagnostic Radiology,” Math. Prog. Study 9, 15–20 (1978).
[CrossRef]

Other (1)

R. Goulard, Combustion Measurement (Academic, New York, 1986), pp. 226–244.

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Figures (9)

Fig. 1
Fig. 1

Optical schematic diagram of the instrument device.

Fig. 2
Fig. 2

Schematic diagram of the increasing deflection angle.

Fig. 3
Fig. 3

Schematic of the ray deflection.

Fig. 4
Fig. 4

Schematic of moire fringe deviation when there is a test model in the flow field.

Fig. 5
Fig. 5

Interferometric reconstruction.

Fig. 6
Fig. 6

Sketch map for the image function.

Fig. 7
Fig. 7

Multidirectional deflectograms of the flow field generated by the convex model in a large aperture, hypersonic shock tunnel (M = 10.27), where θ is the viewing angle.

Fig. 8
Fig. 8

Test model and fine structure of the flow field from a viewing angle of θ = 0°.

Fig. 9
Fig. 9

Density distribution vs r for z = 2.5-cm cross section.

Equations (21)

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p = p 2 sin ( α / 2 ) p / 2 ,
h = φ · Δ 2 sin ( α / 2 ) φ · Δ α ,
M = f 2 / f 1 ,
φ = M φ = f 2 f 1 · φ .
n ( x · y ) = n 0 + n ˆ ( x · y ) ;
φ ( y , θ ) = 1 n 0 + n ˆ ( y , x ) y d x ,
Φ ( y , θ ) = n ˆ ( x , y ) d L = + n ˆ ( x , y ) δ [ y r sin ( φ θ ) ] d x d y .
n ˆ ( r , φ ) = 1 2 π 2 π / 2 π / 2 d θ + ( Φ / y ) r sin ( φ θ ) y d y ,
Φ y = y L n ˆ ( x , y ) d L = + n ˆ ( x , y ) y d x ,
N ˆ ( r , ψ ) = 1 2 π 2 π / 2 π / 2 d θ + φ ( y , θ ) r sin ( ψ θ ) y d y .
[ π 2 , π 2 ]
Φ y = n 0 φ ( y , θ ) .
Φ ( ρ , θ ) = ρ ρ Φ ρ d ρ = n 0 ρ ρ φ ( ρ , θ ) d ρ ;
Φ ( ρ , θ ) = n 0 ρ ρ φ ( ρ , θ ) d ρ .
L n ˆ ( x , y ) d L = Φ ( ρ , θ ) .
Q 3 ( x , y ) = m = 2 M + 2 n = 2 N + M r m , n q 3 ( x m h h ) q 3 ( y n h h ) , 0 < x < M h , 0 < y < N h .
Q 3 ( x , y ) = n = 1 M m = 1 N r m , n q 3 ( x m h h ) q 3 ( y n h h ) , h < x < M h , h < y < N h .
b i ( x , y ) = { q 3 ( x m h h ) q 3 ( y n h h ) if h x , h y N h , 0 otherwise ;
n ˆ ¯ ( x , y ) = Σ x i b i ( x , y )
P = [ P i j ] = [ S ( b j , ρ i , θ i ) ] , X = ( x 1 , x 2 , X L ) T , Y = ( g 1 , g 2 , g K ) T
P X Y .

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