Abstract

The tolerance on wavelength stability for frozen-fringe holography is calculated. It is convenient to split the effect into three terms: (1) the interferometric term that depends on the path difference between the reference beam and the signal beam, (2) the holographic term that represents the difference of wave-front curvature between signal and reference beams at the hologram plate, and (3) a lateral-displacement term. It is highly desirable to reduce to a minimum all the differences mentioned and to keep down the lateral-displacement term. To do this, new designs of holographic interferometers are proposed. With a carefully designed interferometer and an object only 2 cm thick, the wavelength tolerances are within the control exercised by a well-designed resonant reflector.

© 1971 Optical Society of America

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References

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  1. R. L. Powell and K. A. Stetson, J. Opt. Soc. Am. 55, 1593 (1965).
    [CrossRef]
  2. B. P. Hildebrand, in The Engineering Uses of Holography, edited by E. R. Robertson and J. M. Harvey (Cambridge University Press, Cambridge, 1970), p. 401.
  3. G. L. Rogers, Nature (London) 166, 127 (1950).
    [CrossRef]
  4. G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A63, 193 (1952).
  5. G. L. Rogers, J. Sci. Instr. 43, 677 (1966).
    [CrossRef]

1966 (1)

G. L. Rogers, J. Sci. Instr. 43, 677 (1966).
[CrossRef]

1965 (1)

1952 (1)

G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A63, 193 (1952).

1950 (1)

G. L. Rogers, Nature (London) 166, 127 (1950).
[CrossRef]

Hildebrand, B. P.

B. P. Hildebrand, in The Engineering Uses of Holography, edited by E. R. Robertson and J. M. Harvey (Cambridge University Press, Cambridge, 1970), p. 401.

Powell, R. L.

Rogers, G. L.

G. L. Rogers, J. Sci. Instr. 43, 677 (1966).
[CrossRef]

G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A63, 193 (1952).

G. L. Rogers, Nature (London) 166, 127 (1950).
[CrossRef]

Stetson, K. A.

J. Opt. Soc. Am. (1)

J. Sci. Instr. (1)

G. L. Rogers, J. Sci. Instr. 43, 677 (1966).
[CrossRef]

Nature (London) (1)

G. L. Rogers, Nature (London) 166, 127 (1950).
[CrossRef]

Proc. Roy. Soc. (Edinburgh) (1)

G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A63, 193 (1952).

Other (1)

B. P. Hildebrand, in The Engineering Uses of Holography, edited by E. R. Robertson and J. M. Harvey (Cambridge University Press, Cambridge, 1970), p. 401.

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Figures (5)

F. 1
F. 1

Typical reflection interferometer, showing the parameters used in the calculations. p = distance from virtual image of source to the plate, q = distance of object from source and plate.

F. 2
F. 2

Compensating around the square interferometer, correcting for interferometric and holographic terms but not for the lateral term.

F. 3
F. 3

Trombone-compensated interferometer that minimizes the lateral term and corrects the others.

F. 4
F. 4

Arrangement for test experiment. PAB = 200 cm; POB = 100 cm; OB = 15 cm.

F. 5
F. 5

Test hologram. Right-hand half shows genuine frozen fringes. Left-hand half shows distorted frozen fringes. The latter get an order out of step in two thirds of the height of the blade. They are also formed in a different plane.

Equations (28)

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1 / f = 1 / p 1 / q ,
Δ = ( x 2 / 2 ) 1 / f ,
H = λ f ,
δ H = f δ λ + λ δ f ,
1 / f = 1 / p 1 / q ,
f = p q / ( p q ) .
δ f = [ p 2 / ( q p ) 2 ] δ q
δ H = f δ λ [ λ p 2 / ( q p ) 2 ] δ q .
1 / f = 1 / p 1 / q
q = p f / ( f p ) ,
δ q = ( q / f ) ( f / H ) δ H .
δ q = [ p 2 / ( f p ) 2 ] ( 1 / λ ) H .
δ q = [ p 2 / λ ( f p ) 2 ] { f δ λ [ p 2 λ / ( q p ) 2 ] δ q } .
δ q = + δ q [ q ( q p ) / p λ ] δ λ .
( N + ϕ ) λ = p 2 q initially ,
ϕ = ( p 2 q ) / λ N ,
d ϕ / d λ = ( p 2 q ) / λ 2 .
| δ λ | < λ 2 / 6 ( p 2 q ) .
λ < 0.004 Å .
d q d q < λ / 6
| d λ | < p λ 2 / 6 q ( q p ) .
d λ < 0.0033 Å .
δ s / s = δ λ / λ .
| δ s | < λ / 6 ,
| δ λ | < λ 2 / 6 s ;
< 0.08 Å ;
δ λ < 0.08 Å ;
< 0.016 Å .