Abstract

Active laser diode interferometers in which the interference signal is fed back to the diode current are investigated for Twyman-Green and self-coupling interferometers. The Twyman-Green interferometer is stabilized with a stabilization factor of more than 100. By using the feedback signal of either type of interferometer, displacement is measured in a linear scale over a dynamic range of 8–9 μm with a precision of 10–60 nm. The feedback signal vs displacement shows hysteresis and multistable behavior, in accordance with theoretical results.

© 1987 Optical Society of America

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References

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  1. A. Dandrige, R. O. Miles, T. G. Giallorenzi, “Diode Laser Sensor,” Electron. Lett. 16, 948 (1980).
    [CrossRef]
  2. T. Yoshino, Y. Kawase, T. Ose, “Simple Laser Interferometer of Composite Resonator Type,” presented at Fall Meeting of Japan Society of Applied Physics (Tokyo, 1980), paper 17a-K-8.
  3. T. Yoshino, M. Nara, “Active Interferometer Using a Laser Diode,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1984), paper THA6.
  4. T. Yoshino, S. Mnatzakanian, B. Lee, T. C. Strand, “Self-Coupling Laser Diode Interferometry for Profilometry Applications,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1986), paper MI2.

1980

A. Dandrige, R. O. Miles, T. G. Giallorenzi, “Diode Laser Sensor,” Electron. Lett. 16, 948 (1980).
[CrossRef]

Dandrige, A.

A. Dandrige, R. O. Miles, T. G. Giallorenzi, “Diode Laser Sensor,” Electron. Lett. 16, 948 (1980).
[CrossRef]

Giallorenzi, T. G.

A. Dandrige, R. O. Miles, T. G. Giallorenzi, “Diode Laser Sensor,” Electron. Lett. 16, 948 (1980).
[CrossRef]

Kawase, Y.

T. Yoshino, Y. Kawase, T. Ose, “Simple Laser Interferometer of Composite Resonator Type,” presented at Fall Meeting of Japan Society of Applied Physics (Tokyo, 1980), paper 17a-K-8.

Lee, B.

T. Yoshino, S. Mnatzakanian, B. Lee, T. C. Strand, “Self-Coupling Laser Diode Interferometry for Profilometry Applications,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1986), paper MI2.

Miles, R. O.

A. Dandrige, R. O. Miles, T. G. Giallorenzi, “Diode Laser Sensor,” Electron. Lett. 16, 948 (1980).
[CrossRef]

Mnatzakanian, S.

T. Yoshino, S. Mnatzakanian, B. Lee, T. C. Strand, “Self-Coupling Laser Diode Interferometry for Profilometry Applications,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1986), paper MI2.

Nara, M.

T. Yoshino, M. Nara, “Active Interferometer Using a Laser Diode,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1984), paper THA6.

Ose, T.

T. Yoshino, Y. Kawase, T. Ose, “Simple Laser Interferometer of Composite Resonator Type,” presented at Fall Meeting of Japan Society of Applied Physics (Tokyo, 1980), paper 17a-K-8.

Strand, T. C.

T. Yoshino, S. Mnatzakanian, B. Lee, T. C. Strand, “Self-Coupling Laser Diode Interferometry for Profilometry Applications,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1986), paper MI2.

Yoshino, T.

T. Yoshino, M. Nara, “Active Interferometer Using a Laser Diode,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1984), paper THA6.

T. Yoshino, S. Mnatzakanian, B. Lee, T. C. Strand, “Self-Coupling Laser Diode Interferometry for Profilometry Applications,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1986), paper MI2.

T. Yoshino, Y. Kawase, T. Ose, “Simple Laser Interferometer of Composite Resonator Type,” presented at Fall Meeting of Japan Society of Applied Physics (Tokyo, 1980), paper 17a-K-8.

Electron. Lett.

A. Dandrige, R. O. Miles, T. G. Giallorenzi, “Diode Laser Sensor,” Electron. Lett. 16, 948 (1980).
[CrossRef]

Other

T. Yoshino, Y. Kawase, T. Ose, “Simple Laser Interferometer of Composite Resonator Type,” presented at Fall Meeting of Japan Society of Applied Physics (Tokyo, 1980), paper 17a-K-8.

T. Yoshino, M. Nara, “Active Interferometer Using a Laser Diode,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1984), paper THA6.

T. Yoshino, S. Mnatzakanian, B. Lee, T. C. Strand, “Self-Coupling Laser Diode Interferometry for Profilometry Applications,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1986), paper MI2.

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Figures (14)

Fig. 1
Fig. 1

Schematic diagram of a Twyman-Green interferometer: LD, laser diode; I0, constant current; PD, photodetector; A, amplifier; P, pinhole.

Fig. 2
Fig. 2

Graphical relation of stationary states of the feedback system from open loop characteristics.

Fig. 3
Fig. 3

Theoretical relationship between interference signal P and reflector displacement ΔD: (a) graphical solution of the stationary feedback states from open loop characteristics; (b) closed loop characteristic.

Fig. 4
Fig. 4

Experimental setup of a Twyman-Green feedback interferometer.

Fig. 5
Fig. 5

Measured dependence of laser diode frequency on injection current.

Fig. 6
Fig. 6

Frequency response of laser frequency tuning measured as a function of modulation frequency of the diode current.

Fig. 7
Fig. 7

Interference patterns in a Twyman-Green feedback interferometer when feedback loop is (a) on and (b) off.

Fig. 8
Fig. 8

Stabilization factor S measured as a function of vibration frequency of the reflector.

Fig. 9
Fig. 9

Spectrum analyzer output of the photodetector signal of a laser diode feedback interferometer of Twyman-Green type measured as a function of peak-to-peak amplitude ΔDpp of mirror vibration at 98 Hz.

Fig. 10
Fig. 10

Photodetector signal of a laser diode feedback interferometer of Twyman-Green type, measured for different feedback gain A and vibration amplitude ΔD.

Fig. 11
Fig. 11

Photodetector signal P of a laser diode feedback interferometer of Twyman-Green type, measured for different waveforms of vibration: I s is the driving current of the speaker; on and off refer to the presence or absence of feedback; (a) sinusoidal modulation; (b) nonsinusoidal modulation.

Fig. 12
Fig. 12

Schematic diagram of (a) self-coupling interferometer and (b) its equivalent system.

Fig. 13
Fig. 13

Experimental setup of a laser diode feedback self-coupling interferometer.

Fig. 14
Fig. 14

Feedback signal in a laser diode feedback self-coupling interferometer measured as a function of reflector displacement.

Equations (19)

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P = P ( δ ) .
I = A ( P - P 0 ) .
f = f 0 + χ I ,
δ = 4 π f D / c
P = P ( δ , D ) = ( P 0 - f 0 χ A ) + ( c 4 π D χ A ) δ .
P = a + b cos δ .
P = P 1 R = P 1 ( F sin 2 δ + G 1 + F sin 2 δ ) ,
[ Δ δ Δ D ] on = δ S D ,
S = 4 π χ b A D sin δ C + 1.
[ Δ δ Δ D ] off = δ D .
S = Δ δ / Δ D off Δ δ / Δ D on ,
Δ I = A Δ P Δ P .
Δ f = - f Δ D / D ,
Δ I = - f 0 χ D Δ D Δ D .
R = F sin 2 ( k D ) + G 1 + F sin 2 ( k D ) ,
F = 4 r 2 r 3 ( 1 - r 2 r 3 ) 2 ,
G = ( r 2 - r 3 1 - r 2 r 3 ) 2 ,
R = ( 1 - G ) F sin 2 ( k D ) + G ,
f = f 0 + a sin ( ω m t ) ,

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