Abstract

A measured displacement resolution of <3 nm is demonstrated with a common cathode differential photodetector combined with a laser-diode optical source and a fiber-optic collimator. Resolution, standard deviation, and differences between maxima and minima values for the residuals of the least-squares fit suggest that a coherent laser-diode source temporally correlates photoelectron flux between adjacent detector segments, suggesting reduced signal variance and associated electronic (shot) noise. For otherwise similar systems, the laser-diode source provides approximately an order of magnitude reduction in standard deviation compared with a light-emitting-diode source, which implies an equivalently improved measured (including standard deviation) resolution. Combined variances for correlated and uncorrelated detectors and their measured variances are outlined. The measured resolution is a sum of both the (ideal) mathematical variance based on the detector noise (millivolts) divided by the system sensitivity (millivolts per nanometer, and the standard deviation of the noise (nanometers).

© 1997 Optical Society of America

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References

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  1. W. E. Frank, “Detection and measurement device having a small flexible fiber transmission line,” U.S. patent3,273,447 (20September1966).
  2. C. D. Kissinger, “Fiber optic proximity probe,” U.S. patent3,327,584 (27June1967).
  3. R. O. Cook, C. W. Hamm, “Fiber optic lever displacement transducer,” Appl. Opt. 34, 5854–5860 (1995).
  4. A. Shimamoto, K. Tanaka, “Geometrical analysis on an optical fiber bundle displacement sensor,” Appl. Opt. 35, 6767–6774 (1996).
    [CrossRef] [PubMed]
  5. “Dual-photodiode edge displacement sensor,” NASA Tech. Briefs 21 (1), 33–34 (1997).
  6. J. L. Remo, “Optical edge sensors for large aperture segmented arrays,” (5June1995).
  7. J. L. Remo, “High resolution optic displacement measurement using a photodiode sensor,” Opt. Eng. 36 (August1997).
  8. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
    [CrossRef]
  9. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
    [CrossRef]
  10. A. J. den Dekker, A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997).
    [CrossRef]
  11. J. Fradkin, AIP Handbook of Modern Sensors (American Institute of Physics, New York, 1993).

1997 (3)

“Dual-photodiode edge displacement sensor,” NASA Tech. Briefs 21 (1), 33–34 (1997).

J. L. Remo, “High resolution optic displacement measurement using a photodiode sensor,” Opt. Eng. 36 (August1997).

A. J. den Dekker, A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997).
[CrossRef]

1996 (1)

1995 (1)

Cook, R. O.

den Dekker, A. J.

Fradkin, J.

J. Fradkin, AIP Handbook of Modern Sensors (American Institute of Physics, New York, 1993).

Frank, W. E.

W. E. Frank, “Detection and measurement device having a small flexible fiber transmission line,” U.S. patent3,273,447 (20September1966).

Hamm, C. W.

Kissinger, C. D.

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

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

Remo, J. L.

J. L. Remo, “High resolution optic displacement measurement using a photodiode sensor,” Opt. Eng. 36 (August1997).

J. L. Remo, “Optical edge sensors for large aperture segmented arrays,” (5June1995).

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Shimamoto, A.

Tanaka, K.

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

van den Bos, A.

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

NASA Tech. Briefs (1)

“Dual-photodiode edge displacement sensor,” NASA Tech. Briefs 21 (1), 33–34 (1997).

Opt. Eng. (1)

J. L. Remo, “High resolution optic displacement measurement using a photodiode sensor,” Opt. Eng. 36 (August1997).

Other (6)

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

J. Fradkin, AIP Handbook of Modern Sensors (American Institute of Physics, New York, 1993).

J. L. Remo, “Optical edge sensors for large aperture segmented arrays,” (5June1995).

W. E. Frank, “Detection and measurement device having a small flexible fiber transmission line,” U.S. patent3,273,447 (20September1966).

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

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for either the laser diode (LD) or the light emitting diode (LED), which provide the light source to the fiber optic (FO). A digital piezotranslator displaces the FO laterally across the dual photodiode (DPD) surface.

Fig. 2
Fig. 2

Schematic diagram of the photodiode current and voltage conversion to a displacement signal. Voltages provide differential inputs for an analog-to-digital converter. The photons supplied by a given FO aperture impinge on both segments of the DPD; however, not all the photons generate photoelectrons.

Fig. 3
Fig. 3

Relationship between the photon flux, photoelectron generation, current pulse, and shot noise superimposed on the mean electric current generated by a single segment of the DPD (adapted from Ref. 9). The individual pulse trains from the two segments of the DPD are temporally correlated within a time duration τ, which implies that the noise can be partially extracted when the signals from each of the segments are subtracted.

Fig. 4
Fig. 4

Scan across both segments of the DPD by an LED source. The complementary and symmetrical nature of the two curves, each corresponding to a segment of the DPD, is clearly shown. Here the LED sensitivity is ∼0.012 mV/nm, which is quite low compared with that of the LD source, which yields the exact same curve, but with a sensitivity an order of magnitude greater than that of the LED.

Fig. 5
Fig. 5

Residuals of a least-squares fit over 10-nm steps introducing a very low noise level when a LD is used. Here, with the silica FO collimator, the standard deviation is only 1.5 nm, and the difference between max and min, a measure of the noise, is only 8 nm and is ideally symmetrical.

Fig. 6
Fig. 6

(a) Photodiode output and (b) the residuals of the least-squares fit for the LD displacement measurements taken over 50-nm steps with a higher noise level than the 10-nm-step measurements. The max - min = 13.3 nm is much larger than that for the 10-nm steps.

Fig. 7
Fig. 7

(a) DPD output and (b) residuals of the least-squares fit for 10-nm steps given for the six channels of fiber-optic bundles, where each bundle consists of several 100-µm glass fibers with a collective aperture of 1.4 mm. Details of this system can be found in Ref. 7.

Fig. 8
Fig. 8

(a) DPD output and (b) residuals of the least-squares fit for 50-nm steps given for the six-channel fiber-optic bundle described in Fig. 7.

Tables (1)

Tables Icon

Table 1 Resolution R in Nanometers for Three Types of Lateral Displacement Sensors Summarized for 10-nm Steps across a 2000-nm Range

Equations (24)

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ϕ=n/τ.
I=eηn/τ,
=eηϕ,
σ2=n.
ϕ=σ2/τ,
I=eησ2/τ.
iSN2=2eI/τ
=2ηeσ/τ2.
R0=inherent detector photoelectric variance noise in mV/sensitivity mV/μm=σd2/S,
R=photoelectron variance/square mean current=σi2/i2=1/ηn.
V2=V12+V22.
σi2=Vi-Vi2.
σ2=σ12+σ22.
V2=αV1,
V2=1+α2V12,
σ2=1+α2V1-V12.
V=V1+V2.
σ2=σ12+σ22+2C12,
C12=V1-V1V2-V2.
V=1+αV1,
σ2=1+α2σ12.
Rm=σc2/S,
σc2=σd2+σS.
Rm=σd2/S+1+ασ1.

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