Abstract

The theoretical detection limit on angle deflection measurement when the quasi-critical internal-reflection method is used is calculated and compared with the more common method of using a bicell position-sensitive detector. Simple formulas for the sensitivity and resolution when the system is shot noise limited are given. It is shown that, even though the bicell detector is potentially much more sensitive for wide and well collimated beams, under typical laboratory restrictions, the internal reflection method may be more sensitive and have better resolution. It is argued that the internal-reflection method may be a tool in developing compact sensors based on the optical beam deflection method.

© 1997 Optical Society of America

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References

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  1. S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
    [CrossRef]
  2. C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
    [CrossRef]
  3. The Autoprobe C P (AFM microscope), Park Scientific Instruments, Sunnyvale, Calif.
  4. J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
    [CrossRef]
  5. A. Salazar, A. Sanchez-Lavega, J. Fernandez, “Theory of thermal diffusivity determination by the ‘Mirage’ technique in solids,” J. Appl. Phys. 65, 4150–4156 (1989).
    [CrossRef]
  6. G. Y. Chang, R. B. Givens, J. W. M. Spicer, R. Osiander, J. C. Murphy, “Optical beam deflection imaging of the electron beam interaction volume in semiconductors,” Appl. Phys. Lett. 63, 645–647 (1993).
    [CrossRef]
  7. G. C. Wetsel, S. E. McBride, R. J. Warmack, B. Van de Sande, “Calibration of scanning tunneling microscope transducers using optical beam deflection,” Appl. Phys. Lett. 55, 528–530 (1989).
    [CrossRef]
  8. S. R. Cook, M. A. Hoffbauer, J. B. Cross, “A specialized torsion balance designed to measure the absolute flux density of hyperthermal molecular beams containing reactive species,” Rev. Sci. Instrum. 67, 1781–1789 (1996).
    [CrossRef]
  9. M. Rosete-Aguilar, R. Díaz Uribe, “Profile testing of spherical surfaces by laser deflectometry,” Appl. Opt. 32, 4690–4697 (1993) and references therein.
  10. D. Royer, M. H. Norory, M. Fink, “Optical generation and detection of elastic waves in solids,” J. Phys. III, Coloque C7-4, 673–680 (1995).
  11. A. García-Valenzuela, R. Díaz-Uribe, “Approach to improve the angle sensitivity and resolution of the optical beam deflection method using a passive interferometer and a Ronchi grating,” to be published in Opt. Eng. (1997).
  12. T. Kohno, N. Ozawa, K. Miyamoto, T. Musha, “High precision optical surface sensor,” Appl. Opt. 27, 103–108 (1988).
    [CrossRef] [PubMed]
  13. 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]
  14. 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]
  15. H. M. Lai, F. C. Cheng, W. K. Tang, “Goos–Hänchen effect around and off the critical angle,” J. Opt. Soc. Am. A 3, 550–557 (1986) and references therein.
  16. R. E. Collin, Antennas and Radiowave Propagation (McGraw-Hill, New York, 1985), Appendix to Chap. 4, pp. 284–286.
  17. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

1996 (2)

S. R. Cook, M. A. Hoffbauer, J. B. Cross, “A specialized torsion balance designed to measure the absolute flux density of hyperthermal molecular beams containing reactive species,” Rev. Sci. Instrum. 67, 1781–1789 (1996).
[CrossRef]

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]

1995 (1)

D. Royer, M. H. Norory, M. Fink, “Optical generation and detection of elastic waves in solids,” J. Phys. III, Coloque C7-4, 673–680 (1995).

1993 (2)

G. Y. Chang, R. B. Givens, J. W. M. Spicer, R. Osiander, J. C. Murphy, “Optical beam deflection imaging of the electron beam interaction volume in semiconductors,” Appl. Phys. Lett. 63, 645–647 (1993).
[CrossRef]

M. Rosete-Aguilar, R. Díaz Uribe, “Profile testing of spherical surfaces by laser deflectometry,” Appl. Opt. 32, 4690–4697 (1993) and references therein.

1992 (2)

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]

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

1989 (3)

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

A. Salazar, A. Sanchez-Lavega, J. Fernandez, “Theory of thermal diffusivity determination by the ‘Mirage’ technique in solids,” J. Appl. Phys. 65, 4150–4156 (1989).
[CrossRef]

G. C. Wetsel, S. E. McBride, R. J. Warmack, B. Van de Sande, “Calibration of scanning tunneling microscope transducers using optical beam deflection,” Appl. Phys. Lett. 55, 528–530 (1989).
[CrossRef]

1988 (1)

1986 (1)

1980 (1)

J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
[CrossRef]

Aamodt, L. C.

J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (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 implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Chang, G. Y.

G. Y. Chang, R. B. Givens, J. W. M. Spicer, R. Osiander, J. C. Murphy, “Optical beam deflection imaging of the electron beam interaction volume in semiconductors,” Appl. Phys. Lett. 63, 645–647 (1993).
[CrossRef]

Cheng, F. C.

Collin, R. E.

R. E. Collin, Antennas and Radiowave Propagation (McGraw-Hill, New York, 1985), Appendix to Chap. 4, pp. 284–286.

Cook, S. R.

S. R. Cook, M. A. Hoffbauer, J. B. Cross, “A specialized torsion balance designed to measure the absolute flux density of hyperthermal molecular beams containing reactive species,” Rev. Sci. Instrum. 67, 1781–1789 (1996).
[CrossRef]

Cross, J. B.

S. R. Cook, M. A. Hoffbauer, J. B. Cross, “A specialized torsion balance designed to measure the absolute flux density of hyperthermal molecular beams containing reactive species,” Rev. Sci. Instrum. 67, 1781–1789 (1996).
[CrossRef]

De Grooth, B. G.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Díaz Uribe, R.

Díaz-Uribe, R.

A. García-Valenzuela, R. Díaz-Uribe, “Approach to improve the angle sensitivity and resolution of the optical beam deflection method using a passive interferometer and a Ronchi grating,” to be published in Opt. Eng. (1997).

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 implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Fernandez, J.

A. Salazar, A. Sanchez-Lavega, J. Fernandez, “Theory of thermal diffusivity determination by the ‘Mirage’ technique in solids,” J. Appl. Phys. 65, 4150–4156 (1989).
[CrossRef]

Fink, M.

D. Royer, M. H. Norory, M. Fink, “Optical generation and detection of elastic waves in solids,” J. Phys. III, Coloque C7-4, 673–680 (1995).

García-Valenzuela, A.

A. García-Valenzuela, R. Díaz-Uribe, “Approach to improve the angle sensitivity and resolution of the optical beam deflection method using a passive interferometer and a Ronchi grating,” to be published in Opt. Eng. (1997).

Givens, R. B.

G. Y. Chang, R. B. Givens, J. W. M. Spicer, R. Osiander, J. C. Murphy, “Optical beam deflection imaging of the electron beam interaction volume in semiconductors,” Appl. Phys. Lett. 63, 645–647 (1993).
[CrossRef]

Greve, J.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[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 implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (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 implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (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 implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Hoffbauer, M. A.

S. R. Cook, M. A. Hoffbauer, J. B. Cross, “A specialized torsion balance designed to measure the absolute flux density of hyperthermal molecular beams containing reactive species,” Rev. Sci. Instrum. 67, 1781–1789 (1996).
[CrossRef]

Huang, P. S.

Kamada, O.

Kiyono, S.

Kohno, T.

Lai, H. M.

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 implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (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 implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

McBride, S. E.

G. C. Wetsel, S. E. McBride, R. J. Warmack, B. Van de Sande, “Calibration of scanning tunneling microscope transducers using optical beam deflection,” Appl. Phys. Lett. 55, 528–530 (1989).
[CrossRef]

Miyamoto, K.

Murphy, J. C.

G. Y. Chang, R. B. Givens, J. W. M. Spicer, R. Osiander, J. C. Murphy, “Optical beam deflection imaging of the electron beam interaction volume in semiconductors,” Appl. Phys. Lett. 63, 645–647 (1993).
[CrossRef]

J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
[CrossRef]

Musha, T.

Ni, J.

Norory, M. H.

D. Royer, M. H. Norory, M. Fink, “Optical generation and detection of elastic waves in solids,” J. Phys. III, Coloque C7-4, 673–680 (1995).

Osiander, R.

G. Y. Chang, R. B. Givens, J. W. M. Spicer, R. Osiander, J. C. Murphy, “Optical beam deflection imaging of the electron beam interaction volume in semiconductors,” Appl. Phys. Lett. 63, 645–647 (1993).
[CrossRef]

Ozawa, N.

Putman, C. A. J.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Rosete-Aguilar, M.

Royer, D.

D. Royer, M. H. Norory, M. Fink, “Optical generation and detection of elastic waves in solids,” J. Phys. III, Coloque C7-4, 673–680 (1995).

Salazar, A.

A. Salazar, A. Sanchez-Lavega, J. Fernandez, “Theory of thermal diffusivity determination by the ‘Mirage’ technique in solids,” J. Appl. Phys. 65, 4150–4156 (1989).
[CrossRef]

Sanchez-Lavega, A.

A. Salazar, A. Sanchez-Lavega, J. Fernandez, “Theory of thermal diffusivity determination by the ‘Mirage’ technique in solids,” J. Appl. Phys. 65, 4150–4156 (1989).
[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 implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Spicer, J. W. M.

G. Y. Chang, R. B. Givens, J. W. M. Spicer, R. Osiander, J. C. Murphy, “Optical beam deflection imaging of the electron beam interaction volume in semiconductors,” Appl. Phys. Lett. 63, 645–647 (1993).
[CrossRef]

Tang, W. K.

van de Hulst, N. F.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Van de Sande, B.

G. C. Wetsel, S. E. McBride, R. J. Warmack, B. Van de Sande, “Calibration of scanning tunneling microscope transducers using optical beam deflection,” Appl. Phys. Lett. 55, 528–530 (1989).
[CrossRef]

Warmack, R. J.

G. C. Wetsel, S. E. McBride, R. J. Warmack, B. Van de Sande, “Calibration of scanning tunneling microscope transducers using optical beam deflection,” Appl. Phys. Lett. 55, 528–530 (1989).
[CrossRef]

Wetsel, G. C.

G. C. Wetsel, S. E. McBride, R. J. Warmack, B. Van de Sande, “Calibration of scanning tunneling microscope transducers using optical beam deflection,” Appl. Phys. Lett. 55, 528–530 (1989).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

Appl. Opt. (4)

Appl. Phys. Lett. (2)

G. Y. Chang, R. B. Givens, J. W. M. Spicer, R. Osiander, J. C. Murphy, “Optical beam deflection imaging of the electron beam interaction volume in semiconductors,” Appl. Phys. Lett. 63, 645–647 (1993).
[CrossRef]

G. C. Wetsel, S. E. McBride, R. J. Warmack, B. Van de Sande, “Calibration of scanning tunneling microscope transducers using optical beam deflection,” Appl. Phys. Lett. 55, 528–530 (1989).
[CrossRef]

J. Appl. Phys. (4)

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
[CrossRef]

A. Salazar, A. Sanchez-Lavega, J. Fernandez, “Theory of thermal diffusivity determination by the ‘Mirage’ technique in solids,” J. Appl. Phys. 65, 4150–4156 (1989).
[CrossRef]

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

J. Phys. III, Coloque (1)

D. Royer, M. H. Norory, M. Fink, “Optical generation and detection of elastic waves in solids,” J. Phys. III, Coloque C7-4, 673–680 (1995).

Rev. Sci. Instrum. (1)

S. R. Cook, M. A. Hoffbauer, J. B. Cross, “A specialized torsion balance designed to measure the absolute flux density of hyperthermal molecular beams containing reactive species,” Rev. Sci. Instrum. 67, 1781–1789 (1996).
[CrossRef]

Other (4)

A. García-Valenzuela, R. Díaz-Uribe, “Approach to improve the angle sensitivity and resolution of the optical beam deflection method using a passive interferometer and a Ronchi grating,” to be published in Opt. Eng. (1997).

R. E. Collin, Antennas and Radiowave Propagation (McGraw-Hill, New York, 1985), Appendix to Chap. 4, pp. 284–286.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

The Autoprobe C P (AFM microscope), Park Scientific Instruments, Sunnyvale, Calif.

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Figures (4)

Fig. 1
Fig. 1

Schematic illustration of the internal-reflection method used to measure optical-beam deflections. The coordinate systems used in the analysis are shown. The beam's axis on entrance to the prism coincides with the x′ axis shown. The location of the beam waist is assumed to be at the primed system's origin. Although this origin is shown within the prism, it may well be outside. The angle of incidence to the entrance and exit faces of the prism are assumed to be near zero.

Fig. 2
Fig. 2

Plot of the integral I(η). The integral was done numerically.

Fig. 3
Fig. 3

Plot of the factor M = (4n12/n02)[2n0n1(n12 - n02)-1/2]1/2 as a function n1 and for n0 = 1. Some glasses corresponding to the value of n1 in the figure are also shown.

Fig. 4
Fig. 4

Plot of the ratio R between the sensitivity of the internal-reflection method and the sensitivity when a bicell detector as a function of the waist radius w0 is used. The distance to the bicell detector is assumed to be fixed at 0.5 m (continuous curve). If the bicell detector is free to move as far as needed to achieve the maximum sensitivity, R follows the dashed curve for w0 > 317 µm.

Equations (25)

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Hx, y, z=Aw024π - - Qˆk×exp-w024kz2+ky2×expjkzz+jkyy+jk12-kz2-ky21/2xdkzdky,
Hx, y, z=Aw024π - - Qˆk×exp-w024kz2+ky sin θi-kx cos θi2×expjkzz+jkyy+jkxx+jkx sin θi+ky cos θiR dkzdkysin θi,
fk=ky-n12n02k02-k12+ky21/2ky+n12n02k02-k12+ky21/2.
Hrx, y, z=Aw024π - - Qˆkfk×exp-w024kz2+ky sin θi-kx cos θi2×expjkzz-jkyy+jkxx+jkx sin θi+ky cos θiR dkzdkysin θi.
Hrr, θ, φ=Aw024π 2πkxx expjk1rr sin θi×exp-w024kzs2+kys sin θi-kxs cos θi2×expjkxs sin θi+kys cos θiRfksQˆks,
s=cμ02n1Hrr2aˆr,
Pr=limr cμ02n1 0π/2 02π r2 sin θsHrr2 dφsdθs= Bk12 0π/2 02πsin2 θs cos2 φsfks2sin2 θi×exp-w022kzs2+kys sin θi-kxs cos θi2×sin θs dφsdθs,
θi=θc-γi,  θs=θc-γs,
fks2=1k12-k02>kys21-4n12n02kyskys2-k12-k021/2k12-k02>kys2.
fks2=1θs>θc1-D γsθs<θc,
Pr=Bk12 sin θc 0π/2 02π fks2×exp-w02k122 φs2 sin2 θc-w02k122 γs-γi2×dφs-1dγs
Pr=-B 2πk1w0 - exp-w02k122 γs-γi2dγs-D 0 γs exp-w02k122 γs-γi2dγs,
dPr/dθi=-D P02π1/2 w03k13 0 γs γs-γi×exp-w02k122 γs-γi2dγs.
u=w0k1γs,  η=w0k1γi,
dPr/dθi=Dw0k12π1/2 P0Iη,
Iη=0 uu-ηexp-12 u-η2du.
dPr/dθi=1.28D w0k12π1/2 P0=1.28M w0λ1/2 P0,
dS/dθi=1.28κM w0λ1/2 Po.
dS/dθ=22π1/2κPo w0λ.
MDA=11.28M 2qBκPo1/2 λwo1/2
MDA=qB4πκPo1/2 λwo
Hr, θ, φ=πAw02 jk0 cos θ expjk1r2πr×exp-w024 k1 sin θ sin φ2+k1 sin θ cos φ2ây×rây×r,
s=cμ02n1 Hr2âr,
cμ02n1 Aw02/222πk12 01 1-s1/2 exp-w02k122 s ds2,
P0=cμ02n1 Aw02/222πk12 1w02k12 1-exp-w02k122.

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