Abstract

A feedback control system has been designed to stabilize the position of interference fringes, particularly those which occur in holography. The result of closed loop operation of the system is that rather severe phase perturbations may occur in either of the beams, and yet be compensated for such that the fringes in the holographic recording medium are essentially stabilized. This paper discusses the design and analysis of an experimental model and its performance for phase perturbations due to acoustic and mechanical vibration, thermal drift, large perturbations, warm air turbulence, and small doppler shifts. The authors then speculate that more advanced designs may stabilize interference fringes even with larger phase perturbations such as large doppler shifts, optical frequency differences, motion of the scene, and holographic interferometry.

© 1967 Optical Society of America

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Figures (15)

Fig. 1
Fig. 1

Basic feedback control system.

Fig. 2
Fig. 2

Graphical solution of closed loop equation.

Fig. 3
Fig. 3

Closed loop phase relationships.

Fig. 4
Fig. 4

Fringe control improvement using thyratrons.

Fig. 5
Fig. 5

Optimum slit width.

Fig. 6
Fig. 6

Improvement of recorded fringes under static conditions.

Fig. 7
Fig. 7

Feedback control of fringe vibrations.

Fig. 8
Fig. 8

Poor mechanical stability experiment.

Fig. 9
Fig. 9

Large phase shift experiment.

Fig. 10
Fig. 10

Thyratron improvement of fringe phase control.

Fig. 11
Fig. 11

Feedback control of large random phase variations.

Fig. 12
Fig. 12

Compensation for doppler frequency shift.

Fig. 13
Fig. 13

Geometry for warm air turbulence experiments.

Fig. 14
Fig. 14

Reduction of fringe motion during warm air turbulence.

Fig. 15
Fig. 15

Improvement of holograms made during warm air turbulence.

Equations (8)

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u 1 = a 1 exp { j [ w t + ϕ 1 ( x , y ) + ψ 1 ( t ) ] } , u 2 = a 2 exp { j [ w t + ϕ 2 ( x , y ) + ψ 2 ( t ) + k Δ ( t ) ] } .
I = K 1 + K 2 cos [ ϕ ( x , y ) + ψ ( t ) + k Δ ( t ) ] ,
V o u t = V b o + K a m p { V b i + K p m [ K 1 + K 2 cos ( ϕ 0 + ψ + k Δ ) ] } .
Δ = K c r y { V b o + K a m p [ V b i + K p m K 1 + K p m K 2 cos ( ϕ 0 + ψ + k Δ ) ] } .
C 1 cos ( β + θ ) = θ + C 2 ,
V p m = R S l x 0 - w / 2 x 0 + w / 2 [ K 1 + K 2 cos ( ( 2 π x λ h ) ] d x ,
V p m = R S l [ K 1 w + K 2 λ h π sin ( π w λ h ) cos ( 2 π x 0 λ h ) ] .
V a c = R I max K 2 K 1 sinc ( π w λ h ) .

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