Abstract

A phase-locked laser diode interferometer with differential detection to eliminate external disturbance is proposed. In this interferometer, the measurements are implemented at two different points at the same time. The surface profile that contains the disturbance is obtained at the scanned measuring point, and the disturbance is obtained at the fixed measuring point. The exact profile is obtained by subtracting the latter from the former. The limitations and characteristics are examined theoretically. The analytical results agree well with the experimental results. The repeated measurement accuracy is estimated to be ~5 nm in this interferometer.

© 1992 Optical Society of America

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References

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  1. K. Tatsuno, Y. Tsunoda, “Diode laser direct modulation heterodyne interferometer,” Appl. Opt. 26, 37–40 (1987).
    [CrossRef] [PubMed]
  2. Y. Ishii, J. Chen, K. Murata, “Digital phase-measuring interferometry with a tunable laser diode,” Opt. Lett. 12, 233–235 (1987).
    [CrossRef] [PubMed]
  3. J. Chen, Y. Ishii, K. Murata, “Heterodyne interferometry with a frequency-modulated laser diode,” Appl. Opt. 27, 124–128 (1988).
    [CrossRef] [PubMed]
  4. T. Yoshino, M. Nara, S. Mnatzakanian, B. S. Lee, T. C. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 892–897 (1987).
    [CrossRef] [PubMed]
  5. O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
    [CrossRef]
  6. T. Suzuki, O. Sasaki, T. Maruyama, “Phase locked laser diode interferometry for surface profile measurement,” Appl. Opt. 28, 4407–4410 (1989).
    [CrossRef] [PubMed]
  7. T. Suzuki, O. Sasaki, K. Higuchi, T. Maruyama, “Phase-locked laser diode interferometer: high-speed feedback control system,” Appl. Opt. 30, 3622–3626 (1991).
    [CrossRef] [PubMed]
  8. D. T. Moore, R. P. Murray, F. B. Neves, “Large aperture ac interferometer for optical testing,” Appl. Opt. 17, 3959–3963 (1978).
    [CrossRef] [PubMed]
  9. G. W. Johnson, D. C. Leiner, D. T. Moore, “Phase-locked interferometry,” Opt. Eng. 18, 46–52 (1979).
  10. H. J. Matthews, D. K. Hamilton, C. J. R. Sheppard, “Surface profiling by phase-locked interferometry,” Appl. Opt. 25, 2372–2374 (1986).
    [CrossRef] [PubMed]
  11. O. Sasaki, H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
    [CrossRef] [PubMed]
  12. O. Sasaki, H. Okazaki, “Analysis of measurement accuracy in sinusoidal phase modulating interferometry,” Appl. Opt. 25, 3152–3158 (1986).
    [CrossRef] [PubMed]
  13. O. Sasaki, H. Okazaki, M. Sakai, “Sinusoidal phase modulating interferometer using the integrating-bucket method,” Appl. Opt. 26, 1089–1093 (1987).
    [CrossRef] [PubMed]

1991

1990

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

1989

1988

1987

1986

1979

G. W. Johnson, D. C. Leiner, D. T. Moore, “Phase-locked interferometry,” Opt. Eng. 18, 46–52 (1979).

1978

Chen, J.

Hamilton, D. K.

Higuchi, K.

Ishii, Y.

Johnson, G. W.

G. W. Johnson, D. C. Leiner, D. T. Moore, “Phase-locked interferometry,” Opt. Eng. 18, 46–52 (1979).

Lee, B. S.

Leiner, D. C.

G. W. Johnson, D. C. Leiner, D. T. Moore, “Phase-locked interferometry,” Opt. Eng. 18, 46–52 (1979).

Maruyama, T.

Matthews, H. J.

Mnatzakanian, S.

Moore, D. T.

G. W. Johnson, D. C. Leiner, D. T. Moore, “Phase-locked interferometry,” Opt. Eng. 18, 46–52 (1979).

D. T. Moore, R. P. Murray, F. B. Neves, “Large aperture ac interferometer for optical testing,” Appl. Opt. 17, 3959–3963 (1978).
[CrossRef] [PubMed]

Murata, K.

Murray, R. P.

Nara, M.

Neves, F. B.

Okazaki, H.

Sakai, M.

Sasaki, O.

Sheppard, C. J. R.

Strand, T. C.

Suzuki, T.

Takahashi, K.

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Tatsuno, K.

Tsunoda, Y.

Yoshino, T.

Appl. Opt.

K. Tatsuno, Y. Tsunoda, “Diode laser direct modulation heterodyne interferometer,” Appl. Opt. 26, 37–40 (1987).
[CrossRef] [PubMed]

J. Chen, Y. Ishii, K. Murata, “Heterodyne interferometry with a frequency-modulated laser diode,” Appl. Opt. 27, 124–128 (1988).
[CrossRef] [PubMed]

T. Yoshino, M. Nara, S. Mnatzakanian, B. S. Lee, T. C. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 892–897 (1987).
[CrossRef] [PubMed]

T. Suzuki, O. Sasaki, T. Maruyama, “Phase locked laser diode interferometry for surface profile measurement,” Appl. Opt. 28, 4407–4410 (1989).
[CrossRef] [PubMed]

T. Suzuki, O. Sasaki, K. Higuchi, T. Maruyama, “Phase-locked laser diode interferometer: high-speed feedback control system,” Appl. Opt. 30, 3622–3626 (1991).
[CrossRef] [PubMed]

D. T. Moore, R. P. Murray, F. B. Neves, “Large aperture ac interferometer for optical testing,” Appl. Opt. 17, 3959–3963 (1978).
[CrossRef] [PubMed]

H. J. Matthews, D. K. Hamilton, C. J. R. Sheppard, “Surface profiling by phase-locked interferometry,” Appl. Opt. 25, 2372–2374 (1986).
[CrossRef] [PubMed]

O. Sasaki, H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
[CrossRef] [PubMed]

O. Sasaki, H. Okazaki, “Analysis of measurement accuracy in sinusoidal phase modulating interferometry,” Appl. Opt. 25, 3152–3158 (1986).
[CrossRef] [PubMed]

O. Sasaki, H. Okazaki, M. Sakai, “Sinusoidal phase modulating interferometer using the integrating-bucket method,” Appl. Opt. 26, 1089–1093 (1987).
[CrossRef] [PubMed]

Opt. Eng.

G. W. Johnson, D. C. Leiner, D. T. Moore, “Phase-locked interferometry,” Opt. Eng. 18, 46–52 (1979).

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Opt. Lett.

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Figures (10)

Fig. 1
Fig. 1

Experimental setup of a differential-type PLLD interferometer: M, mirror; BS, beam splitter; L’s, lenses; LD, laser diode; LM, laser diode modulator; FBC, feedback controller.

Fig. 2
Fig. 2

Block diagram of the FBC: SH’s, sample-and-hold circuits; PI’s, proportional-integral controllers; SW, switch; AMP, amplifier; int, integrator.

Fig. 3
Fig. 3

Generation of the feedback signals: (a) modulation current, (b) interference signals, time chart of the sample-and-hold (SH) circuits, (c) SH1, (d) SH2, (e) SH3, (f) SH4, (g) control (CNT) signal for switch SW.

Fig. 4
Fig. 4

Block diagram of the discrete-time-control system for the scanned measuring point x.

Fig. 5
Fig. 5

Series of the measured data lined up along the evolution of the disturbance d (t).

Fig. 6
Fig. 6

Disturbances measured at (a) point p, (b) point x, (c) the output of the differential amplifier.

Fig. 7
Fig. 7

Dependence of the rms value E of the remaining error on (a) the amplitude of the disturbance, (b) the frequency of the disturbance, (c) the reflective ratio R. ○, Experimental plots; solid and dashed curves, theoretical calculations.

Fig. 8
Fig. 8

Surface profiles measured with (a) a Talystep instrument, (b) a conventional PLLD interferometer, (c) differential-type PLLD interferometer.

Fig. 9
Fig. 9

Experimental results: (a) surface profile that contains the external disturbance measured at the scanned measuring point x, (b) external disturbance measured at the fixed measuring point p, (c) exact surface profile obtained by differential detection.

Fig. 10
Fig. 10

Experimental results obtained after a few minutes by using the same conditions as in Fig. 9; (a), (b), and (c) correspond to Figs. 9(a), 9(b), and 9(c), respectively.

Equations (27)

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I m ( t ) = a cos ω c t .
S ( t , x ) = S 1 + S x cos [ z cos ω c t + α ( x ) + δ ( t ) ] ,
S ( t , p ) = S 2 + S p cos [ z cos ω c t + α ( p ) + δ ( t ) ] ,
α ( x ) + δ ( t ) = { 4 π / [ λ 0 + λ c ( x ) ] } [ D 0 + D ( x ) + d ( t ) ] ,
α ( p ) + δ ( t ) = { 4 π / [ λ 0 + λ c ( p ) ] } [ D 0 + D ( p ) + d ( t ) ] ,
D ( x ) + d ( t ) = ( D 0 / λ 0 ) β I c ( t , x ) ,
D ( p ) + d ( t ) = ( D 0 / λ 0 ) β I c ( t , p ) .
D ( x ) - D ( p ) = ( D 0 / λ 0 ) β [ I c ( t , x ) - I c ( t , p ) ] = K c [ I c ( t , x ) - I c ( t , p ) ] ,
Y ( t , p ) = y 1 ( t , p ) - y 2 ( t , p ) = K r 1 sin [ α ( p ) + δ ( t ) ] ,
Y ( t , x ) = y 1 ( t , x ) - y 2 ( t , x ) = K r 2 sin [ α ( x ) + δ ( t ) ] ,
G h ( s ) = [ 1 - exp ( - T c s ) ] / s ,
G c ( s ) = K d [ K p + ( 1 / T I s ) ] ,
G s ( s ) = K 1 ,
G a ( s ) = 4 π β D 0 / λ 0 2 ,
G d ( s ) = 4 π / λ 0 .
I p ( z ) = E ( z ) Z { G h ( s ) G c ( s ) } ,
E ( z ) = - Z { G d ( s ) G s ( s ) D ( s ) } / [ 1 + Z { G s ( s ) G h ( s ) G c ( s ) G a ( s ) } ] ,
d ( t ) = v sin ω d ( t ) ,
D ( z ) = v z sin ω d T c z 2 - 2 z cos ω d T c + 1 .
I p ( z ) = b 1 z + b 0 a 1 z + a 0 D ( z ) ,
a 1 = ( 1 + K 1 K 2 K P ) T I 2 , a 0 = T I { T c K 1 K 2 - T I ( 1 - K 1 K 2 K P ) } , b 1 = K 1 K 3 T 1 K d K P T I ,             b 0 = K 1 K 3 T I K d ( T c - K P T I ) .
d P ( k T c ) = ( D 0 / λ 0 ) β I P ( k T c ) .
D ( z , 1 / 2 ) = v ( z + 1 ) sin [ ω d ( T c / 2 ) ] z 2 - 2 z cos ω d T c + 1 .
I x ( z ) = - b 1 z + b 0 a 1 z + a 0 D ( z , 1 / 2 ) ,
d x ( k T c ) = ( D 0 / λ 0 ) β I x ( k T c ) ,
e d [ ( 2 n - 1 ) T ] = ( d p ( n T c ) - { d x [ ( n - 1 ) T c ] + d x ( n T c ) } / 2 ) , e d ( 2 n T ) = ( { d p ( n T c ) + d p [ ( n + 1 ) T c ] } / 2 - d x ( n T c ) ) ,
R = K r 1 / K r 2 ,

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