Abstract

An optical fiber bundle displacement sensor with subnanometer order resolution and low thermal drift is proposed. The setup is based on a carrier amplifier system and involves techniques to eliminate fluctuation in the light power of the source. The achieved noise level of the sensor was 0.03nm/Hz. The stability was estimated by comparing the outputs of two different sensors from the same target for 4 ks (67 min). The relative displacements between the fiber bundle ends of the two sensors and the target surface varied in the area of 400 nm depending on the ambient temperature variation at 2 °C. However, the difference in output between the two sensor systems is within 2 nm for more than 1 hour of measurement. It is expected that it would be reduced to within the area of 0.1 nm if the ambient temperature were controlled to within ±0.1 °C. It is concluded that the stability of the sensors is sufficiently good to be used with nanotechnological instruments.

© 1995 Optical Society of America

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References

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  1. K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
    [CrossRef] [PubMed]
  2. G. Makosch, B. Drollinger, “Surface profile measurement with a scanning differential ac interferrometer,” Appl. Opt. 23, 4544–4553 (1984).
    [CrossRef] [PubMed]
  3. A. Bergamin, G. Cavagnero, G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3081 (1993).
    [CrossRef]
  4. T. Kohno, N. Ozawa, K. Miyamoto, T. Musha, “High precision optical surface sensor,” Appl. Opt. 27, 103–108 (1988).
    [CrossRef] [PubMed]
  5. J. A. Simpson, “Use of a microscope as a noncontacting microdisplacement measurement device,” Rev. Sci. Instrum. 42, 1371–1380 (1971).
    [CrossRef]
  6. R. V. Jones, J. C. S. Richards, “Recording optical lever,” J. Sci. Instrum. 36, 90–94 (1959).
    [CrossRef]
  7. J. Simon, “New noncontact device for measuring small microdisplacements,” Appl. Opt. 9, 2337–2340 (1970).
    [CrossRef] [PubMed]
  8. R. G. Goldman, W. R. Marklein, “Electro-optical distance gage,” U.S. patent3,263,087 (6July1966).
  9. A. W. Hartman, F. W. Rosberry, J. A. Simpson, “Noncontacting length comparator with 10 nanometer precision,” Opt. Eng. 12, 95–101 (1973).
  10. Nano Scope III, Digital Instruments, Santa Barbara, Calif.
  11. SFA-300, Seiko Instruments, Tokyo, Japan.
  12. C. D. Kissinger, “Fiber optic proximity probe,” U.S. patent3,327,584 (27June1967).
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    [CrossRef] [PubMed]
  14. C. M. Davis, “Fiber optic sensors: an overview,” Opt. Eng. 24, 347–351 (1985).
  15. P. J. Murphy, T. P. Coursolle, “Fiber optic displacement sensor employing a graded index lens,” Appl. Opt. 29, 544–547 (1990).
    [CrossRef] [PubMed]
  16. A. Shimamoto, K. Tanaka, “Geometrical analysis of an optical fiber bundle displacement sensor,” to be submitted to Appl. Opt.
  17. E. O. Doebelin, Measurement Systems: Application and Design, International Student Edition (McGraw-Hill, New York, 1975), Chap. 10, p. 616.

1993

A. Bergamin, G. Cavagnero, G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3081 (1993).
[CrossRef]

1990

1988

1985

C. M. Davis, “Fiber optic sensors: an overview,” Opt. Eng. 24, 347–351 (1985).

1984

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef] [PubMed]

G. Makosch, B. Drollinger, “Surface profile measurement with a scanning differential ac interferrometer,” Appl. Opt. 23, 4544–4553 (1984).
[CrossRef] [PubMed]

1979

1973

A. W. Hartman, F. W. Rosberry, J. A. Simpson, “Noncontacting length comparator with 10 nanometer precision,” Opt. Eng. 12, 95–101 (1973).

1971

J. A. Simpson, “Use of a microscope as a noncontacting microdisplacement measurement device,” Rev. Sci. Instrum. 42, 1371–1380 (1971).
[CrossRef]

1970

1959

R. V. Jones, J. C. S. Richards, “Recording optical lever,” J. Sci. Instrum. 36, 90–94 (1959).
[CrossRef]

Bennett, J. M.

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef] [PubMed]

Bergamin, A.

A. Bergamin, G. Cavagnero, G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3081 (1993).
[CrossRef]

Cavagnero, G.

A. Bergamin, G. Cavagnero, G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3081 (1993).
[CrossRef]

Cook, R. O.

Coursolle, T. P.

Davis, C. M.

C. M. Davis, “Fiber optic sensors: an overview,” Opt. Eng. 24, 347–351 (1985).

Doebelin, E. O.

E. O. Doebelin, Measurement Systems: Application and Design, International Student Edition (McGraw-Hill, New York, 1975), Chap. 10, p. 616.

Drollinger, B.

G. Makosch, B. Drollinger, “Surface profile measurement with a scanning differential ac interferrometer,” Appl. Opt. 23, 4544–4553 (1984).
[CrossRef] [PubMed]

Goldman, R. G.

R. G. Goldman, W. R. Marklein, “Electro-optical distance gage,” U.S. patent3,263,087 (6July1966).

Guenther, K. H.

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef] [PubMed]

Hamm, C. W.

Hartman, A. W.

A. W. Hartman, F. W. Rosberry, J. A. Simpson, “Noncontacting length comparator with 10 nanometer precision,” Opt. Eng. 12, 95–101 (1973).

Jones, R. V.

R. V. Jones, J. C. S. Richards, “Recording optical lever,” J. Sci. Instrum. 36, 90–94 (1959).
[CrossRef]

Kissinger, C. D.

C. D. Kissinger, “Fiber optic proximity probe,” U.S. patent3,327,584 (27June1967).

Kohno, T.

Makosch, G.

G. Makosch, B. Drollinger, “Surface profile measurement with a scanning differential ac interferrometer,” Appl. Opt. 23, 4544–4553 (1984).
[CrossRef] [PubMed]

Mana, G.

A. Bergamin, G. Cavagnero, G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3081 (1993).
[CrossRef]

Marklein, W. R.

R. G. Goldman, W. R. Marklein, “Electro-optical distance gage,” U.S. patent3,263,087 (6July1966).

Miyamoto, K.

Murphy, P. J.

Musha, T.

Ozawa, N.

Richards, J. C. S.

R. V. Jones, J. C. S. Richards, “Recording optical lever,” J. Sci. Instrum. 36, 90–94 (1959).
[CrossRef]

Rosberry, F. W.

A. W. Hartman, F. W. Rosberry, J. A. Simpson, “Noncontacting length comparator with 10 nanometer precision,” Opt. Eng. 12, 95–101 (1973).

Shimamoto, A.

A. Shimamoto, K. Tanaka, “Geometrical analysis of an optical fiber bundle displacement sensor,” to be submitted to Appl. Opt.

Simon, J.

Simpson, J. A.

A. W. Hartman, F. W. Rosberry, J. A. Simpson, “Noncontacting length comparator with 10 nanometer precision,” Opt. Eng. 12, 95–101 (1973).

J. A. Simpson, “Use of a microscope as a noncontacting microdisplacement measurement device,” Rev. Sci. Instrum. 42, 1371–1380 (1971).
[CrossRef]

Tanaka, K.

A. Shimamoto, K. Tanaka, “Geometrical analysis of an optical fiber bundle displacement sensor,” to be submitted to Appl. Opt.

Wierer, P. G.

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef] [PubMed]

Appl. Opt.

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef] [PubMed]

G. Makosch, B. Drollinger, “Surface profile measurement with a scanning differential ac interferrometer,” Appl. Opt. 23, 4544–4553 (1984).
[CrossRef] [PubMed]

Appl. Opt.

J. Sci. Instrum.

R. V. Jones, J. C. S. Richards, “Recording optical lever,” J. Sci. Instrum. 36, 90–94 (1959).
[CrossRef]

Opt. Eng.

C. M. Davis, “Fiber optic sensors: an overview,” Opt. Eng. 24, 347–351 (1985).

A. W. Hartman, F. W. Rosberry, J. A. Simpson, “Noncontacting length comparator with 10 nanometer precision,” Opt. Eng. 12, 95–101 (1973).

Rev. Sci. Instrum.

J. A. Simpson, “Use of a microscope as a noncontacting microdisplacement measurement device,” Rev. Sci. Instrum. 42, 1371–1380 (1971).
[CrossRef]

Rev. Sci. Instrum.

A. Bergamin, G. Cavagnero, G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3081 (1993).
[CrossRef]

Other

R. G. Goldman, W. R. Marklein, “Electro-optical distance gage,” U.S. patent3,263,087 (6July1966).

Nano Scope III, Digital Instruments, Santa Barbara, Calif.

SFA-300, Seiko Instruments, Tokyo, Japan.

C. D. Kissinger, “Fiber optic proximity probe,” U.S. patent3,327,584 (27June1967).

A. Shimamoto, K. Tanaka, “Geometrical analysis of an optical fiber bundle displacement sensor,” to be submitted to Appl. Opt.

E. O. Doebelin, Measurement Systems: Application and Design, International Student Edition (McGraw-Hill, New York, 1975), Chap. 10, p. 616.

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Figures (8)

Fig. 1
Fig. 1

Schematic illustration of a basic optical fiber displacement sensor.

Fig. 2
Fig. 2

Receiving light power P r , versus gap y between the fiber bundle end and the target surface.

Fig. 3
Fig. 3

Block diagram of the developed ac-modulated fiber displacement sensor: PSD, phase sensitive demodulator.

Fig. 4
Fig. 4

Schematic setup for the calibration of sensors: AD, analog to digital; GPIB, general-purpose interface bus; PID, proportional-integral-derivative feedback.

Fig. 5
Fig. 5

Output Γ for sensors #1 and #2 versus gap y in the no-bias operation mode. y 01 and y 02 are the driving points in this study.

Fig. 6
Fig. 6

Noise level of the sensors. The measurement was done by feedback from the output of sensor #2, and the output of sensor #1 was monitored. The time constants of the low-pass filter varied at two levels: (a) 10 ms and (b) 100 ms.

Fig. 7
Fig. 7

Relation between the noise level per unit noise bandwidth N dis ¯ and peak light power P max. The calculation was conducted under the conditions G a = 1 and T = 300 K.

Fig. 8
Fig. 8

Outputs (lower) and the difference (upper) between the outputs of the two sensors versus testing time.

Tables (1)

Tables Icon

Table 1 Typical Values Related to Noise Level and Thermal Drift

Equations (22)

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S ( y ) = d P r ¯ ( y ) / d y .
v out = R f r P r ( y ) + R f I b ,
Δ v out = v out ( y 0 , T ) y Δ y + v out ( y 0 , T ) T Δ T ,
v out ( y 0 , T ) y = P r ( y 0 ) y R f ( T ) r ( T ) = P max S ( y 0 ) R f ( T ) r ( T ) ,
Δ v out P max S ( y 0 ) R f ( T ) r ( T ) = Δ y + [ ( α R f + α r ) P r ( y 0 ) P max S ( y 0 ) + ( α R f + α I b ) I b P max S ( y 0 ) r ] Δ T ,
P dis = K dis P r ¯ ( y ) P in ,
P ref = K ref P in ,
V dis = F dis P dis ,
V ref = F ref P ref ,
V dif = V dis - G a V ref ,
Γ = G dif G ref [ F dis K dis P r ¯ ( y ) F ref K ref - G a ] = G dif G ref ( F dis K dis F ref K ref ) [ P r ¯ ( y ) - G a F ref K ref F dis K dis ] .
Γ = P r ¯ ( y ) .
G a F ref K ref / F dis K dis = G a G dif / G ref = P r ¯ ( y 0 ) .
Γ = A [ P r ¯ ( y 0 + Δ y ) - P r ¯ ( y 0 ) ] ,
= A S ( y 0 ) Δ y .
B = 0 Re ( 1 1 + j 2 π τ f ) d f = 1 / ( 4 τ ) ,
N ¯ total = N ¯ 1 2 + N ¯ 2 2 ,
i sh = ( 2 e I B ) 1 / 2 ,
v J = ( 4 k T R B ) 1 / 2 ,
N dis = [ G dif / G ref V ref S ( y 0 ) ] { [ ( i sh 1 R f ) 2 + v J 1 2 ] + [ ( G a i sh 2 R f ) 2 + ( G a v J 2 ) 2 ] } 1 / 2
= { 2 e [ P r ¯ ( y 0 ) P max r + G a 2 P ref P max 2 r ] + 4 k T ( 1 + G a 2 ) P max 2 R f r 2 } 1 / 2 × B 1 / 2 S ( y 0 ) ,
N dis = [ 2 e P r ¯ ( y 0 ) P max r ( 1 + G a ) + 4 k T ( 1 + G a 2 ) P max 2 R f r 2 ] 1 / 2 B 1 / 2 S ( y 0 ) .

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