Abstract

The basic relations for the rotating mirror smear camera are reviewed and expressions are obtained for the maximum time resolution obtainable in systems uncorrected for the elastic distortion of the mirror surface. Instrumentation for the measurement of the surface distortion at high speed is described and data are reported for rotating rectangular parallelepipeds as a function of size and width-to-thickness ratio. The central sections of the mirrors deform cylindrically, the power varying nearly with the square of the peripheral speed. The distortion effects can be almost completely compensated by the introduction of negative astigmatism into the system. An auxiliary optical system is described which aids in the adjustment of the corrector lens to obtain optimum resolution. A corrected system in current use has a time resolution of 10−8 sec with relative aperture f6.

© 1958 Optical Society of America

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References

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  1. W. E. Buck, Rev. Sci. Instr. 25, 115 (1954).
    [Crossref]
  2. Mueller, Best, Jackson, and Singletary, Nucleonics 10, 53 (1952); Cladis, Jones, and Wickersheim, Rev. Sci. Instr. 27, 83 (1956).
    [Crossref]
  3. B. Brixner, J. Opt. Soc. Am. 45, 876 (1955).
    [Crossref]
  4. B. Brixner, Proceedings of the Third International Congress on High Speed Photography, edited by R. B. Collins, (Butterworth Scientific Publications, London, 1957), p. 289 ff; H. Edels and D. Whittaker, J. Sci. Instr. 32, 103 (1955).
    [Crossref]
  5. J. D. Owen and R. M. Davies, Nature 164, 752 (1949).
    [Crossref]
  6. J. Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., Englewood Cliffs, 1938), p. 69; T. E. Holland, J. Opt. Soc. Am. 46, 1090 (1956).
    [Crossref]
  7. W. C. Davis, Rev. Sci. Instr. 28, 577 (1957).
    [Crossref]
  8. Reference 4, p. 319 ff.

1957 (1)

W. C. Davis, Rev. Sci. Instr. 28, 577 (1957).
[Crossref]

1955 (1)

1954 (1)

W. E. Buck, Rev. Sci. Instr. 25, 115 (1954).
[Crossref]

1952 (1)

Mueller, Best, Jackson, and Singletary, Nucleonics 10, 53 (1952); Cladis, Jones, and Wickersheim, Rev. Sci. Instr. 27, 83 (1956).
[Crossref]

1949 (1)

J. D. Owen and R. M. Davies, Nature 164, 752 (1949).
[Crossref]

Best,

Mueller, Best, Jackson, and Singletary, Nucleonics 10, 53 (1952); Cladis, Jones, and Wickersheim, Rev. Sci. Instr. 27, 83 (1956).
[Crossref]

Brixner, B.

B. Brixner, J. Opt. Soc. Am. 45, 876 (1955).
[Crossref]

B. Brixner, Proceedings of the Third International Congress on High Speed Photography, edited by R. B. Collins, (Butterworth Scientific Publications, London, 1957), p. 289 ff; H. Edels and D. Whittaker, J. Sci. Instr. 32, 103 (1955).
[Crossref]

Buck, W. E.

W. E. Buck, Rev. Sci. Instr. 25, 115 (1954).
[Crossref]

Davies, R. M.

J. D. Owen and R. M. Davies, Nature 164, 752 (1949).
[Crossref]

Davis, W. C.

W. C. Davis, Rev. Sci. Instr. 28, 577 (1957).
[Crossref]

Jackson,

Mueller, Best, Jackson, and Singletary, Nucleonics 10, 53 (1952); Cladis, Jones, and Wickersheim, Rev. Sci. Instr. 27, 83 (1956).
[Crossref]

Mueller,

Mueller, Best, Jackson, and Singletary, Nucleonics 10, 53 (1952); Cladis, Jones, and Wickersheim, Rev. Sci. Instr. 27, 83 (1956).
[Crossref]

Owen, J. D.

J. D. Owen and R. M. Davies, Nature 164, 752 (1949).
[Crossref]

Singletary,

Mueller, Best, Jackson, and Singletary, Nucleonics 10, 53 (1952); Cladis, Jones, and Wickersheim, Rev. Sci. Instr. 27, 83 (1956).
[Crossref]

Strong, J.

J. Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., Englewood Cliffs, 1938), p. 69; T. E. Holland, J. Opt. Soc. Am. 46, 1090 (1956).
[Crossref]

J. Opt. Soc. Am. (1)

Nature (1)

J. D. Owen and R. M. Davies, Nature 164, 752 (1949).
[Crossref]

Nucleonics (1)

Mueller, Best, Jackson, and Singletary, Nucleonics 10, 53 (1952); Cladis, Jones, and Wickersheim, Rev. Sci. Instr. 27, 83 (1956).
[Crossref]

Rev. Sci. Instr. (2)

W. E. Buck, Rev. Sci. Instr. 25, 115 (1954).
[Crossref]

W. C. Davis, Rev. Sci. Instr. 28, 577 (1957).
[Crossref]

Other (3)

Reference 4, p. 319 ff.

J. Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., Englewood Cliffs, 1938), p. 69; T. E. Holland, J. Opt. Soc. Am. 46, 1090 (1956).
[Crossref]

B. Brixner, Proceedings of the Third International Congress on High Speed Photography, edited by R. B. Collins, (Butterworth Scientific Publications, London, 1957), p. 289 ff; H. Edels and D. Whittaker, J. Sci. Instr. 32, 103 (1955).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of a smear camera.

Fig. 2
Fig. 2

Dimensionless plot of angular velocity vs the reciprocal focal length of the cylindrical surface.

Fig. 3
Fig. 3

Schematic diagram of Foucault knife-edge test apparatus. The lenses are achromats with the following focal lengths: L1, L2, 15 in.; L3, L4, L5, L6, 35 in.; L7, 24 in.

Fig. 4
Fig. 4

Shadowgraph of the surface of a mirror rotating at 5000 rps made with the apparatus shown in Fig. 2 with the knife edge placed close to the displaced slit image. Mirror height 1.25 in., width 0.92 in.

Fig. 5
Fig. 5

Schematic diagram of reticle-projecting system.

Fig. 6
Fig. 6

Plot of data taken with the reticle-projecting system, where the points ▲ are for projected lines perpendicular to the rotation axis and points ● for lines parallel to the axis. The upper curve is a plot of data taken with a compensating lens in place, and the lower curve a plot of data taken without a compensating lens.

Equations (26)

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ρ ω L 2 b 2 / 2 E = constant ,
I = const · B · 2 b h / R 2 ,
= const × ( 2 B b h / R 2 ) ( S / 2 ω R ) .
b 2 / ( f a ) = 1.98 σ ρ ω 2 b 2 / E + 340 ( σ ρ ω 2 b 2 / E ) 2 ,
0.25 a / b 0.425 ,             0.95 b 2.5 cm .
Δ R = ( R 2 / f ) sin 2 i sec i ,             Δ R R ,
Δ R = ( R 2 / f ) sec i ,             Δ R R .
S = S + 2 b cos i R · R 2 sec i f .
S = S + 2 R ( a / b ) [ 1.98 σ ρ ω 2 b 2 / E + 340 ( σ ρ ω 2 b 2 / E ) 2 ] .
I = 1 2 I m ( 1 + cos 2 π t / T ) ,
t = 1 2 I m t t + Δ t ( 1 + cos 2 π t / T ) d t ,
Δ t = S / ( 2 ω R ) .
t = I m Δ t 2 + I m T 4 π [ ( cos 2 π Δ t T - 1 ) sin 2 π t T + sin 2 π Δ t T cos 2 π t T ] .
max / min = ( 1 + T π Δ t sin π Δ t T ) / ( 1 - T π Δ t sin π Δ t T ) .
Δ D = γ log ( max / min ) .
Δ D = γ log ( 1 + T π Δ t sin π Δ t T ) / ( 1 - T π Δ t sin π Δ t T )
Δ D 0.87 γ ( 1 - Δ t / T ) ,             for             Δ t / T 1.0.
T = ( S / 2 ω R ) ( 1 / 0.88 ) sec .
Δ D = γ log ( 1 / n ) ,
δ t = S ( 1 - n ) / ( 2 ω R ) ,
T = 1.14 S / ( 2 ω R ) + 1.14 a / b [ 1.98 σ ρ b 2 ω / E + 340 ( σ ρ b 2 / E ) 2 ω 3 ] .
ω c 1 2 [ E S / ( σ ρ R a b ) ] 1 2 .
ω c / ω L 5 [ S b / ( σ R a ) ] 1 2 .
S = 0.01 cm , b = 1.14 cm , E = 20.5 × 10 11 dynes / cm 2 , R = 14.6 cm , a = 0.39 cm , σ = 0.30 ,             ρ = 7.8 gm / cm 3 .
f c = - ( v 2 / u 2 ) ( u - z ) 2 / Δ R + ( u - z ) ,
Δ R = ( R 2 / f ) sec i ;