Abstract

The effect of refractive deviation on interferograms of cylindrical and planar disturbances has been investigated analytically by a ray-tracing method. The results indicate that the effects are additive and consist of three physically separable types: (1) deviation in the disturbance only; (2) deviation caused by misfocusing, or separation of the observation plane from the disturbance; and (3) deviation of rays by passage through optically dense thick plates, such as windows. For most applications, the thick-window effect is negligible, especially when strongly deviated rays are excluded by the optical aperture. Applicable equations for typical experimental arrangements are given so the investigator can anticipate errors likely to be caused by deviation. Finally, careful focusing of the observation plane is recommended, both to decrease the additional path of deviated rays, and to prevent image blurring from a light source of finite size.

© 1965 Optical Society of America

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References

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  1. F. D. Bennett, W. C. Carter, and V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
    [Crossref]
  2. F. J. Weinberg, Optics of Flames (Butterworth, Inc., Washington, D. C., 1963), pp. 209–211.
  3. G. P. Wachtell, Phys. Rev. 78, 333 (1950).
  4. F. D. Bennett, H. S. Burden, and D. D. Shear, Phys. Fluids 6, 752 (1963).
    [Crossref]
  5. G. D. Kahl and E. H. Wedemeyer, Phys. Fluids 7, 596 (1964).
    [Crossref]

1964 (1)

G. D. Kahl and E. H. Wedemeyer, Phys. Fluids 7, 596 (1964).
[Crossref]

1963 (1)

F. D. Bennett, H. S. Burden, and D. D. Shear, Phys. Fluids 6, 752 (1963).
[Crossref]

1952 (1)

F. D. Bennett, W. C. Carter, and V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
[Crossref]

1950 (1)

G. P. Wachtell, Phys. Rev. 78, 333 (1950).

Bennett, F. D.

F. D. Bennett, H. S. Burden, and D. D. Shear, Phys. Fluids 6, 752 (1963).
[Crossref]

F. D. Bennett, W. C. Carter, and V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
[Crossref]

Bergdolt, V. E.

F. D. Bennett, W. C. Carter, and V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
[Crossref]

Burden, H. S.

F. D. Bennett, H. S. Burden, and D. D. Shear, Phys. Fluids 6, 752 (1963).
[Crossref]

Carter, W. C.

F. D. Bennett, W. C. Carter, and V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
[Crossref]

Kahl, G. D.

G. D. Kahl and E. H. Wedemeyer, Phys. Fluids 7, 596 (1964).
[Crossref]

Shear, D. D.

F. D. Bennett, H. S. Burden, and D. D. Shear, Phys. Fluids 6, 752 (1963).
[Crossref]

Wachtell, G. P.

G. P. Wachtell, Phys. Rev. 78, 333 (1950).

Wedemeyer, E. H.

G. D. Kahl and E. H. Wedemeyer, Phys. Fluids 7, 596 (1964).
[Crossref]

Weinberg, F. J.

F. J. Weinberg, Optics of Flames (Butterworth, Inc., Washington, D. C., 1963), pp. 209–211.

J. Appl. Phys. (1)

F. D. Bennett, W. C. Carter, and V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
[Crossref]

Phys. Fluids (2)

F. D. Bennett, H. S. Burden, and D. D. Shear, Phys. Fluids 6, 752 (1963).
[Crossref]

G. D. Kahl and E. H. Wedemeyer, Phys. Fluids 7, 596 (1964).
[Crossref]

Phys. Rev. (1)

G. P. Wachtell, Phys. Rev. 78, 333 (1950).

Other (1)

F. J. Weinberg, Optics of Flames (Butterworth, Inc., Washington, D. C., 1963), pp. 209–211.

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Figures (8)

Fig. 1
Fig. 1

Ray path in cylindrical disturbance.

Fig. 2
Fig. 2

Scaled path differences for various focusing. ψ(degrees): +1.0, ○2.0, △3.0, □4.0, ●5.0; n1/n0=1.004.

Fig. 3
Fig. 3

Ray paths through window.

Fig. 4
Fig. 4

Added optical path caused by window. ng/n0=1.5.

Fig. 5
Fig. 5

Window separating different optical media. n2<n0.

Fig. 6
Fig. 6

Ray diagram for disturbance inside a test cell.

Fig. 7
Fig. 7

Plane disturbance.

Fig. 8
Fig. 8

Window behind camera lens.

Tables (1)

Tables Icon

Table I Values of Aj depending on αj, with j at ψ=5°.

Equations (52)

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Δ 2 = p 0 p 1 n 1 d s - n 0 b ;
Δ 1 = n 0 ( R sin γ + a 0 ) .
b cos ψ + a 0 = R sin ( γ + ψ ) .
D = D 1 + D 2 ,
D 1 = p 0 p 1 n 1 d s - 2 R n 0 sin γ - R n 0 cos γ tan ψ ,
D 2 = n 0 a 0 ( sec ψ - 1 ) .
y = y 1 + y 2 ,
y 1 = R cos γ sec ψ
y 2 = - a 0 tan ψ .
D 1 / ( R n 0 ) = 2 ( n 1 / n 0 ) sin ( γ + ψ / 2 ) - 2 sin γ - cos γ tan ψ .
n 0 cos γ = n 1 cos ( γ + ψ / 2 ) .
Δ 1 = n 0 ( M + d ) - n 0 t sec β cos ( α - β ) + n g t sec β ,
Δ 2 = n 0 ( M + d sec ψ + l tan ψ ) - n 0 t sec β cos ( α - ψ - β ) + n g t sec β .
n 0 sin α = n g sin β ,
n 0 sin ( α - ψ ) = n g sin β .
l = t sec β sin ( α - ψ - β ) .
Δ 2 = n 0 ( M + d sec ψ ) - n 0 t sec β sec ψ cos ( α - β ) + n g t sec β .
Δ 2 - Δ 1 = n 0 d ( sec ψ - 1 ) + n g t ( sec β - sec β ) + n 0 t [ cos ( α - β ) sec β - cos ( α - β ) sec β sec ψ ] .
d = ( t / tan ψ ) [ sin ( α - β ) sec β - sin ( α - ψ - β ) sec β sec ψ ] ,
d 0 = t sec 3 β [ cos β - ( n 0 / n g ) cos α ] [ cos α + ( n 0 / n g ) sin 2 α cos β ] .
d 0 ( α = 0 ) = t ( 1 - n 0 / n g ) ,
d ( α = 0 ) = t [ 1 - ( n 0 / n g ) ( cos ψ / cos β ) ] ,
a = a 0 + j ( d 0 j - d j ) ,
D = ( Δ 2 - Δ 1 ) + ( Δ 2 - Δ 1 )
D = D 1 + D 2 + D 3 ,
D 3 = n 0 j { d 0 j ( sec ψ - 1 ) + t j ( n g / n 0 ) [ sec β j - sec β j ] + t j [ cos ( α j - β j ) sec β j - cos ( α j - β j ) sec β j sec ψ ] } .
y = y 1 + y 2 + y 3 ,
y 3 = j ( d j - d 0 j ) tan ψ .
Q j ψ 3 ( A j + B j ψ ) .
g = T ( 1 - tan ψ / tan r ) + t ( 1 - tan β / tan r ) ,
n 2 sin ψ = n g sin β = n 0 sin r .
g 0 = T ( 1 - n 0 / n 2 ) + t ( 1 - n 0 / n g ) ;
D = D 1 ( n 2 ) + D 2 ( n 2 ) + D 3 ( r ) + D 4 ,
D 3 ( r ) = n 0 t [ ( sec β - 1 ) ( n g / n 0 ) - ( sec r - 1 ) ( n 0 / n g ) ] ,
D 4 = n 0 T [ ( sec ψ - 1 ) ( n 2 / n 0 ) - ( sec r - 1 ) ( n 0 / n 2 ) ] .
D 3 / ( n 0 t ) = 3 8 ( n 0 / n g ) [ ( n 0 / n g ) 2 - 1 ] × 9.28 × 10 - 8 r 4 + = - 1.29 × 10 - 8 r 4 + ,             ( n g / n 0 = 1.5 ) ,
D 4 / ( n 0 T ) = 3 8 ( n 0 / n 2 ) [ ( n 0 / n 2 ) 2 - 1 ] × 9.28 × 10 - 8 r 4 + .
y = y 1 + y 2 + y 3 + y 4 ,
y 3 = t [ ( n 0 / n g ) tan r - tan β ] ,
y 4 = T [ ( n 0 / n 2 ) tan r - tan ψ ] .
n 3 sin ψ = n g sin β = n 0 sin r .
D = D 3 ( r ) + D 5 + D 6 .
D 5 = p 0 p 1 n ( s ) d s - n 2 k .
D 6 = - n 0 T [ ( n 0 / n 2 ) ( sec r - 1 ) ]
y = y 0 + y 3 + y 6 - y 5 ( ψ ) .
y 6 = T ( n 0 / n 2 ) tan r ,
y = y 1 - t ( tan α - tan β ) + s tan α ,
s ( ψ , α ) = t { 1 - [ tan β - tan β ] / [ tan α - tan ( α - ψ ) ] } .
s 0 ( α ) = t [ 1 - n 0 / n g ) ( cos α / cos β ) 3 ] ,
d z = - ( 1 / m 0 2 ) d x ,
Δ y = t ( n 0 / n g ) ( sin α / cos β ) [ 1 - ( cos α / cos β ) 2 ] .
E ( y ) = D 1 + D 2 + D 3 - D c ,