Abstract

We investigate an internal-transmission method for measuring microdeflections of an optical beam as a potential tool for the development of new compact and stable optical sensors. We calculate the detection limits of the internal-transmission method when an ideal coherent optical source and an ideal quasi-monochromatic thermallike source are used. The proposed method is compared with an internal-reflection method previously studied. It is found theoretically and verified experimentally that the transmission method may have better resolution than the reflection method. We also compare the calculated sensitivity as a function of the angle of incidence with experimental results for both methods.

© 1998 Optical Society of America

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  1. A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the mirage effect,” Appl. Phys. Lett. 36, 130–132 (1980).
    [CrossRef]
  2. W. B. Jackson, N. M. Amer, A. C. Boccara, D. Fournier, “Photothermal deflection spectroscopy and detection,” Appl. Opt. 20, 1333–1344 (1981).
    [CrossRef] [PubMed]
  3. H. Sontag, A. C. Tam, “Optical monitoring of photoacoustic pulse propagation in silicon wafers,” Appl. Phys. Lett. 46, 725–727 (1985).
    [CrossRef]
  4. L. Noui, R. J. Dewhurst, “A beam deflection technique for photoacoustic lamb wave measurements,” in Photoacoustic and Photothermal Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, ed. (Springer-Verlag, Berlin, 1990), pp. 278–281.
    [CrossRef]
  5. E. Moreels, C. de Greef, R. Finsy, “Laser light refractometer,” Appl. Opt. 23, 3010–3013 (1984).
    [CrossRef] [PubMed]
  6. G. Meyer, N. M. Meyer, “Novel approach to atomic force microscopy,” Bull. Am. Phys. Soc. 33, 319–321 (1988); Appl. Phys. Lett. 53, 2400–2402 (1988).
  7. S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
    [CrossRef]
  8. A. García-Valenzuela, “Limits of different detection schemes used in the optical beam deflection method,” J. Appl. Phys. 82, 985–988 (1997).
    [CrossRef]
  9. P. S. Huang, S. Kiyono, O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
    [CrossRef] [PubMed]
  10. A. García-Valenzuela, R. Díaz-Uribe, “Detection limits of an internal-reflection sensor for the optical beam deflection method,” Appl. Opt. 36, 4456–4462 (1997).
    [CrossRef] [PubMed]
  11. P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect using elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
    [CrossRef] [PubMed]
  12. M. Tur, E. Shafir, K. Bløtekjaer, “Source-induced noise in optical systems driven by low-coherence sources,” J. Lightwave Technol. 8, 183–189 (1990).
    [CrossRef]
  13. A. García-Valenzuela, J. Villatoro, “Noise in optical measurements of cantilever deflections,” J. Appl. Phys. 84, 58–63 (1998).
    [CrossRef]
  14. R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 8, p. 132.

1998

A. García-Valenzuela, J. Villatoro, “Noise in optical measurements of cantilever deflections,” J. Appl. Phys. 84, 58–63 (1998).
[CrossRef]

1997

A. García-Valenzuela, R. Díaz-Uribe, “Detection limits of an internal-reflection sensor for the optical beam deflection method,” Appl. Opt. 36, 4456–4462 (1997).
[CrossRef] [PubMed]

A. García-Valenzuela, “Limits of different detection schemes used in the optical beam deflection method,” J. Appl. Phys. 82, 985–988 (1997).
[CrossRef]

1996

1992

1990

M. Tur, E. Shafir, K. Bløtekjaer, “Source-induced noise in optical systems driven by low-coherence sources,” J. Lightwave Technol. 8, 183–189 (1990).
[CrossRef]

1989

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
[CrossRef]

1988

G. Meyer, N. M. Meyer, “Novel approach to atomic force microscopy,” Bull. Am. Phys. Soc. 33, 319–321 (1988); Appl. Phys. Lett. 53, 2400–2402 (1988).

1985

H. Sontag, A. C. Tam, “Optical monitoring of photoacoustic pulse propagation in silicon wafers,” Appl. Phys. Lett. 46, 725–727 (1985).
[CrossRef]

1984

1981

1980

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the mirage effect,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Alexander, S.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
[CrossRef]

Amer, N. M.

Badoz, J.

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the mirage effect,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Bløtekjaer, K.

M. Tur, E. Shafir, K. Bløtekjaer, “Source-induced noise in optical systems driven by low-coherence sources,” J. Lightwave Technol. 8, 183–189 (1990).
[CrossRef]

Boccara, A. C.

W. B. Jackson, N. M. Amer, A. C. Boccara, D. Fournier, “Photothermal deflection spectroscopy and detection,” Appl. Opt. 20, 1333–1344 (1981).
[CrossRef] [PubMed]

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the mirage effect,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 8, p. 132.

de Greef, C.

Dewhurst, R. J.

L. Noui, R. J. Dewhurst, “A beam deflection technique for photoacoustic lamb wave measurements,” in Photoacoustic and Photothermal Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, ed. (Springer-Verlag, Berlin, 1990), pp. 278–281.
[CrossRef]

Díaz-Uribe, R.

Elings, V.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
[CrossRef]

Finsy, R.

Fournier, D.

W. B. Jackson, N. M. Amer, A. C. Boccara, D. Fournier, “Photothermal deflection spectroscopy and detection,” Appl. Opt. 20, 1333–1344 (1981).
[CrossRef] [PubMed]

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the mirage effect,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

García-Valenzuela, A.

A. García-Valenzuela, J. Villatoro, “Noise in optical measurements of cantilever deflections,” J. Appl. Phys. 84, 58–63 (1998).
[CrossRef]

A. García-Valenzuela, R. Díaz-Uribe, “Detection limits of an internal-reflection sensor for the optical beam deflection method,” Appl. Opt. 36, 4456–4462 (1997).
[CrossRef] [PubMed]

A. García-Valenzuela, “Limits of different detection schemes used in the optical beam deflection method,” J. Appl. Phys. 82, 985–988 (1997).
[CrossRef]

Gurley, J.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
[CrossRef]

Hansma, P. K.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
[CrossRef]

Hellemans, L.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
[CrossRef]

Huang, P. S.

Jackson, W. B.

Kamada, O.

Kiyono, S.

Longmire, M.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
[CrossRef]

Marti, O.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
[CrossRef]

Meyer, G.

G. Meyer, N. M. Meyer, “Novel approach to atomic force microscopy,” Bull. Am. Phys. Soc. 33, 319–321 (1988); Appl. Phys. Lett. 53, 2400–2402 (1988).

Meyer, N. M.

G. Meyer, N. M. Meyer, “Novel approach to atomic force microscopy,” Bull. Am. Phys. Soc. 33, 319–321 (1988); Appl. Phys. Lett. 53, 2400–2402 (1988).

Moreels, E.

Ni, J.

Noui, L.

L. Noui, R. J. Dewhurst, “A beam deflection technique for photoacoustic lamb wave measurements,” in Photoacoustic and Photothermal Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, ed. (Springer-Verlag, Berlin, 1990), pp. 278–281.
[CrossRef]

Schneir, J.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
[CrossRef]

Shafir, E.

M. Tur, E. Shafir, K. Bløtekjaer, “Source-induced noise in optical systems driven by low-coherence sources,” J. Lightwave Technol. 8, 183–189 (1990).
[CrossRef]

Sontag, H.

H. Sontag, A. C. Tam, “Optical monitoring of photoacoustic pulse propagation in silicon wafers,” Appl. Phys. Lett. 46, 725–727 (1985).
[CrossRef]

Tam, A. C.

H. Sontag, A. C. Tam, “Optical monitoring of photoacoustic pulse propagation in silicon wafers,” Appl. Phys. Lett. 46, 725–727 (1985).
[CrossRef]

Tur, M.

M. Tur, E. Shafir, K. Bløtekjaer, “Source-induced noise in optical systems driven by low-coherence sources,” J. Lightwave Technol. 8, 183–189 (1990).
[CrossRef]

Villatoro, J.

A. García-Valenzuela, J. Villatoro, “Noise in optical measurements of cantilever deflections,” J. Appl. Phys. 84, 58–63 (1998).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

H. Sontag, A. C. Tam, “Optical monitoring of photoacoustic pulse propagation in silicon wafers,” Appl. Phys. Lett. 46, 725–727 (1985).
[CrossRef]

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the mirage effect,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Bull. Am. Phys. Soc.

G. Meyer, N. M. Meyer, “Novel approach to atomic force microscopy,” Bull. Am. Phys. Soc. 33, 319–321 (1988); Appl. Phys. Lett. 53, 2400–2402 (1988).

J. Appl. Phys.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope using an optical lever,” J. Appl. Phys. 65, 1164–1167 (1989).
[CrossRef]

A. García-Valenzuela, “Limits of different detection schemes used in the optical beam deflection method,” J. Appl. Phys. 82, 985–988 (1997).
[CrossRef]

A. García-Valenzuela, J. Villatoro, “Noise in optical measurements of cantilever deflections,” J. Appl. Phys. 84, 58–63 (1998).
[CrossRef]

J. Lightwave Technol.

M. Tur, E. Shafir, K. Bløtekjaer, “Source-induced noise in optical systems driven by low-coherence sources,” J. Lightwave Technol. 8, 183–189 (1990).
[CrossRef]

Other

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 8, p. 132.

L. Noui, R. J. Dewhurst, “A beam deflection technique for photoacoustic lamb wave measurements,” in Photoacoustic and Photothermal Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, ed. (Springer-Verlag, Berlin, 1990), pp. 278–281.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic illustration of the internal-reflection and internal-transmission methods used to measure optical beam deflection. The beam’s axis on the entrance to the prism coincides with the x′ axis shown. The location of the beam’s waist is assumed to be at the primed system’s origin.

Fig. 2
Fig. 2

Plot of I t (v) as a function of v = w 0 k 1γ i , where γ i = θ c - θ i [Eq. (3)].

Fig. 3
Fig. 3

Schematic illustration of the experimental setup: M’s, mirrors; PZT, piezoelectric; CL’s, converging lenses; SD’s, silicon detectors.

Fig. 4
Fig. 4

Normalized signal amplitude as a function of the angle of incidence. Continuous curve, theoretical sensitivity. Filled circles and triangles, values of the reflected and the transmitted optical power, respectively. Vertical line, value of the critical angle.

Fig. 5
Fig. 5

Fourier transform of the signal-current output of the detector. The SNR (in decibels) is marked by the arrows. The SNR of (a) the reflected and (b) the transmitted beams is shown. The highest peaks correspond to the signal at 2.0 kHz.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

H r = A   - - Q ˆ k exp - w 0 2 4 k y 2 + k z 2 × exp j k 1 2 - k z 2 - k y 2 1 / 2   x + k y y + k z z d k z d k y ,
P r = - C   2 π k 1 w 0 - exp - w 0 2 k 1 2 2 γ s - γ i 2 d γ s - D   0 γ s exp - w 0 2 k 1 2 2 γ s - γ i 2 d γ s ,
P r = P 0 - DP 0 2 π w 0 k 1   I t v , I t v = 0 u exp - 1 / 2 u - v 2 d u .
P t = DP 0 2 π w 0 k 1 1 / 2   I t v .
P t 1.9   DP 0 2 π w 0 k 1 1 / 2 = TP 0 λ / w 0 , ,
P N ν = P d 2 π Δ ν ,
i SIN 2 t 1 / 2 = κ P d 2 π Δ ν   B 1 / 2 ,
i SN 2 t 1 / 2 = 2 q κ P d B 1 / 2 .
MDA = i SN 2 t 1 / 2 + i SIN 2 t 1 / 2 / S / θ i ,
S θ i = 1.28 M κ w 0 / λ ¯   P 0 ,
P d / P 0 γ
MDA = B γ π Δ ν + 2 q γ κ P 0 1 / 2 λ ¯ / w 0 1.28 M ,
G = w 0 / λ ¯ 1 / 4 / T .
G = w 0 / λ ¯ / T ,
θ = θ ¯ + δ θ   sin 2 π ft .
θ p θ = 1 n 1 cos   θ cos   θ p ,
P r θ ¯ i + δ θ i P r θ ¯ i + P r θ i   δ θ i ,
P r θ i = MP 0 w 0 λ 1 / 2 0 u u - v exp - 1 / 2 u - v 2 d u
i ac = κ   P r θ i   δ θ i   sin 2 π ft .

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