Abstract

An active stabilization system for à holographic setup based on detection of phase shift between the interference pattern and a reference hologram is described. Its basic feature is the possibility of operating for 0, π, or ±π/2 at will, always in a null-detection mode. The reference hologram may be a previously recorded permanent hologram or a real-time (even reversible) one. The use of the open loop response of the stabilization system is developed for analyzing its performance, which allows closer insight into parameters limiting its behavior. The effects of different noise sources are analyzed in detail. The real-time effect in a positive resist is successfully employed for operating the stabilization setup for recording an improved grating in this material.

© 1988 Optical Society of America

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References

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  1. D. B. Naumann, H. W. Rose, “Improvement of Recorded Holographic Fringes by Feedback Control,” Appl. Opt. 6, 1097 (1967).
    [CrossRef]
  2. S. Johansson, L.-E. Nilsson, K. Biedermann, K. Kleveby, “Holographic Diffraction Gratings with Asymmetric Groove Profiles,” in Proceedings, ICO Jerusalem 1976 Conference on Holography and Optical Data Processing (Pergamon, New York, 1976), p. 521.
  3. D. R. MacQuigg, “Hologram Fringe Stabilization Method,” Appl. Opt. 16, 291 (1977).
    [CrossRef] [PubMed]
  4. G. R. Little, “Phase Stabilization and Control Techique with Improved Precision,” Appl. Opt. 25, 1971 (1986).
    [CrossRef]
  5. A. A. Kamshilin, J. Frejlich, L. Cescato, “Photorefractive Crystals for the Stabilization of the Holographic Setup,” Appl. Opt. 25, 2375 (1986).
    [CrossRef] [PubMed]
  6. L. F. Mollenauer, W. J. Tomlinson, “Piecewise Interferometric Generation of Precision Gratings,” Appl. Opt. 16, 555 (1977).
    [CrossRef] [PubMed]
  7. W. J. Tomlinson, L. F. MoIIenauer, “Balance Interferometers with Simply Adjustable Interference Angles,” Appl. Opt. 16, 1806 (1977).
    [CrossRef] [PubMed]
  8. J. L. Horner, “Additional Property of Interferometer Symmetry,” Appl. Opt. 17, 505 (1978).
    [CrossRef] [PubMed]
  9. D. L. Staebler, J. A. Amodei, “Coupled-Wave Analysis of Holographic Storage in LiNbO3,” J. Appl. Phys. 43, 1042 (1972).
    [CrossRef]
  10. R. C. Weyrick, Fundamentals of Automatic Control (McGraw-Hill, New York, 1975), Chap. 6.
  11. J. Frejlich, L. H. Cescato, “Analysis of a Phase-Modulating Recording Mechanism in Negative Photoresist,” J. Opt. Soc. Am. 71, 873 (1981).
    [CrossRef]
  12. C. C. Guest, T. K. Gaylord, “Phase Stabilization System for Holographic Optical Data Processing,” Appl. Opt. 24, 2140 (1985).
    [CrossRef] [PubMed]
  13. J. Frejlich, L. Cescato, G. F. Mendes, “Active Stabilization for Real-Time Holographic Recording,” in Proceedings, International Optical Computing Conference, Jerusalem, Israel (July 1986).
  14. S. P. Vorobev, “Effect of Instability in Interference Pattern Location on Hologram Quality,” Sov. J. Opt. Technol. 50(9), 539 (1983).

1986 (2)

1985 (1)

1983 (1)

S. P. Vorobev, “Effect of Instability in Interference Pattern Location on Hologram Quality,” Sov. J. Opt. Technol. 50(9), 539 (1983).

1981 (1)

1978 (1)

1977 (3)

1972 (1)

D. L. Staebler, J. A. Amodei, “Coupled-Wave Analysis of Holographic Storage in LiNbO3,” J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

1967 (1)

Amodei, J. A.

D. L. Staebler, J. A. Amodei, “Coupled-Wave Analysis of Holographic Storage in LiNbO3,” J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Biedermann, K.

S. Johansson, L.-E. Nilsson, K. Biedermann, K. Kleveby, “Holographic Diffraction Gratings with Asymmetric Groove Profiles,” in Proceedings, ICO Jerusalem 1976 Conference on Holography and Optical Data Processing (Pergamon, New York, 1976), p. 521.

Cescato, L.

A. A. Kamshilin, J. Frejlich, L. Cescato, “Photorefractive Crystals for the Stabilization of the Holographic Setup,” Appl. Opt. 25, 2375 (1986).
[CrossRef] [PubMed]

J. Frejlich, L. Cescato, G. F. Mendes, “Active Stabilization for Real-Time Holographic Recording,” in Proceedings, International Optical Computing Conference, Jerusalem, Israel (July 1986).

Cescato, L. H.

Frejlich, J.

Gaylord, T. K.

Guest, C. C.

Horner, J. L.

Johansson, S.

S. Johansson, L.-E. Nilsson, K. Biedermann, K. Kleveby, “Holographic Diffraction Gratings with Asymmetric Groove Profiles,” in Proceedings, ICO Jerusalem 1976 Conference on Holography and Optical Data Processing (Pergamon, New York, 1976), p. 521.

Kamshilin, A. A.

Kleveby, K.

S. Johansson, L.-E. Nilsson, K. Biedermann, K. Kleveby, “Holographic Diffraction Gratings with Asymmetric Groove Profiles,” in Proceedings, ICO Jerusalem 1976 Conference on Holography and Optical Data Processing (Pergamon, New York, 1976), p. 521.

Little, G. R.

G. R. Little, “Phase Stabilization and Control Techique with Improved Precision,” Appl. Opt. 25, 1971 (1986).
[CrossRef]

MacQuigg, D. R.

Mendes, G. F.

J. Frejlich, L. Cescato, G. F. Mendes, “Active Stabilization for Real-Time Holographic Recording,” in Proceedings, International Optical Computing Conference, Jerusalem, Israel (July 1986).

MoIIenauer, L. F.

Mollenauer, L. F.

Naumann, D. B.

Nilsson, L.-E.

S. Johansson, L.-E. Nilsson, K. Biedermann, K. Kleveby, “Holographic Diffraction Gratings with Asymmetric Groove Profiles,” in Proceedings, ICO Jerusalem 1976 Conference on Holography and Optical Data Processing (Pergamon, New York, 1976), p. 521.

Rose, H. W.

Staebler, D. L.

D. L. Staebler, J. A. Amodei, “Coupled-Wave Analysis of Holographic Storage in LiNbO3,” J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Tomlinson, W. J.

Vorobev, S. P.

S. P. Vorobev, “Effect of Instability in Interference Pattern Location on Hologram Quality,” Sov. J. Opt. Technol. 50(9), 539 (1983).

Weyrick, R. C.

R. C. Weyrick, Fundamentals of Automatic Control (McGraw-Hill, New York, 1975), Chap. 6.

Appl. Opt. (8)

J. Appl. Phys. (1)

D. L. Staebler, J. A. Amodei, “Coupled-Wave Analysis of Holographic Storage in LiNbO3,” J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

J. Opt. Soc. Am. (1)

Sov. J. Opt. Technol. (1)

S. P. Vorobev, “Effect of Instability in Interference Pattern Location on Hologram Quality,” Sov. J. Opt. Technol. 50(9), 539 (1983).

Other (3)

J. Frejlich, L. Cescato, G. F. Mendes, “Active Stabilization for Real-Time Holographic Recording,” in Proceedings, International Optical Computing Conference, Jerusalem, Israel (July 1986).

S. Johansson, L.-E. Nilsson, K. Biedermann, K. Kleveby, “Holographic Diffraction Gratings with Asymmetric Groove Profiles,” in Proceedings, ICO Jerusalem 1976 Conference on Holography and Optical Data Processing (Pergamon, New York, 1976), p. 521.

R. C. Weyrick, Fundamentals of Automatic Control (McGraw-Hill, New York, 1975), Chap. 6.

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Figures (10)

Fig. 1
Fig. 1

Holographic setup: M1 and M3 are fixed mirrors; M2 is PZT-driven and M4 may slide and rotate around a vertical axis at R; SF1 and SF2 are spatial filters; L1 and L2 are the corresponding collimating lenses; BS is a beam splitter slab. A 4579-Å argon-ion laser line beam is split into two collimated beams of equal intensities I1 and I2 which interfere at a previously recorded permanent hologram at H. If properly adjusted this setup allows easy change of angle 2θ, maintaining a zero-path difference condition. A PIN detector (D) is connected to a lock-in amplifier whose output is fed to the PZT source (HV). A dither signal to the PZT is provided by an oscillator (OSC).

Fig. 2
Fig. 2

Two-wave mixing scheme at the recorded hologram in the holographic setup. ∑1(∑2), Σ 1 ( Σ 2 ), and Σ 2 ( Σ 1 ), represent wavefronts propagating in direction R ^ (Ŝ) along which irradiance IR(IS) is measured. ∑1, Σ i , and Σ i are the incident, transmitted, and diffracted waves, respectively.

Fig. 3
Fig. 3

Flow chart of the active stabilization system.

Fig. 4
Fig. 4

Open loop systems rms response VΩ produced by the voltage pulse VS applied to the PZT for I (μW/cm2) = 37 (×), 40 (■), 67.5 (○), 68 (+), and 97.5 (□) for vd = 0.5 V and Ω/2π 3470 Hz.

Fig. 5
Fig. 5

Open loop rms response vs dither frequency for I = 58 μW/cm2 and vd = 0.5 V.

Fig. 6
Fig. 6

Open loop rms response vs moirelike fringe period-to-detector size ratio for I = 46 μW/cm2, vd = 0.5 V, 3470 Hz, and an effective detector diameter of 3 mm. The continuous line represents experimental data. Single spots are computed values assuming straight parallel fringes for the interference pattern.

Fig. 7
Fig. 7

Laser light noise-to-intensity ratio (rms) measured at the lock-in amplifier for the latter tuned from 100 to 4000 Hz successively

Fig. 8
Fig. 8

Noise measurement. All rms noises VΩN, VΩS, and VEN as measured in the lock-in amplifier output recording for open loop operation are shown for I1I2 = 40 μW/cm2, Ω/2π = 3470 Hz, and vd varying from 0.5 to 8 V.

Fig. 9
Fig. 9

Closed loop operation. The recording of the lock-in amplifier output is shown for I = 85 μW/cm2, vd = 0.5 V, and Ω/2π = 600 Hz, allowing computation of ΔVΩ referred to in Eq. (30). Large spikes observed there correspond to large perturbations in the laboratory. For comparison the recording corresponding to the nonstabilized setup is also shown. VΩN as measured in each one of both beams and the electronic noise VEN are also shown here.

Fig. 10
Fig. 10

Recording a 1.7-μm period grating onto a Shipley AZ-1350 photoresist film in the holographic setup of Fig. 1. Shallow (a) and deep (b) modulated gratings were recorded using the stabilization system in the second derivative operating mode profiting from real-time effects of this photoresist. Shallow (c) and deep (d) modulated gratings as before but without stabilization. Note the striking difference in border definition with and without stabilization (scanning electron microscopy).

Tables (1)

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Table I Stabilization Performance

Equations (33)

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δ = δ 0 cos ( K x ) ,
I 0 = I 1 + I 2 + 2 I 1 I 2 cos ( K x - ψ ) ,
I R = I 1 η 0 + I 2 η 1 - 2 I 1 I 2 η 0 η 1 sin ψ ,
I S = I 2 η 0 + I 1 η 1 + 2 I 1 I 2 η 0 η 1 sin ψ ,
ψ + ψ d sin Ω t ,
ψ d K PZT Ω · v d 1 ,
I R = I 1 η 0 + I 2 η 1 - 2 I 1 I 2 η 0 η 1 sin ( ψ + ψ d sin Ω t ) .
I R = I R 0 + ɛ + I Ω sin Ω t - I 2 Ω cos 2 Ω t ,
I R 0 I 1 η 0 + I 2 η 1 - 2 I η 0 η 1 sin ψ             with I I 1 I 2 ,
ɛ 2 I η 0 η 1 ( ψ d / 2 ) 2 sin ψ ,
I Ω - 2 I η 0 η 1 ψ d cos ψ = ψ d I R 0 / ψ ,
I 2 Ω 2 I η 0 η 1 ( ψ d / 2 ) 2 sin ψ = ( ψ d / 2 ) 2 2 I R 0 / ψ 2 .
V Ω = ( V Ω ) M cos ψ             with             ( V Ω ) M 2 K p I η 0 η 1 K PZT Ω v d ,
ψ PZT = K PZT 0 V 0 + ψ f ,
ψ f = A cos ψ ,
A K PZT 0 K 0 K l ( V Ω ) M ,
ψ = ψ N + ψ PZT
ψ = K PZT 0 V 0 + ψ N + A cos ψ ,
( ψ - K PZT 0 V 0 ) / A = cos ψ
ψ f / ψ N = - 1
ψ / ψ N = 0.
ψ f / ψ N = - A sin ψ / ( 1 + A sin ψ ) - 1 ,
ψ / ψ N = 1 / ( 1 + A sin ψ ) 0 ,
ψ f = B sin ψ             with             B ( ψ d / 4 ) A .
V Ω = ( V Ω ) M cos ( K PZT 0 V S ± π / 2 ) = ± ( V Ω ) M sin ( K PZT 0 V S ) .
Δ ψ ψ N / A ,
ψ f = K PZT 0 K 0 K l ( V Ω + V N ) .
( Δ ψ ) N = K PZT 0 K 0 K l / SNR 0 1 / ( V Ω ) M + K PZT 0 K 0 K l 1 / SNR 0
SNR 0 ( V Ω ) M / V N .
Δ ψ Δ V Ω / ( V Ω ) M ,
ψ N K 0 K PZT 0 ( K l Δ V Ω ) .
V N = V Ω N ( η 1 + η 0 + 2 η 1 η 0 ) + V E N ,
V Ω N ( η 1 + η 0 ± 2 η 1 η 0 ) V E N ,

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