Abstract

A type of a transmission phase-shifting laser microscope, believed to be new, has been developed. In this microscope a biprism located between a magnifying lens and an observation plane was used as a beam splitter. The biprism is laterally translated to introduce phase shifts required for quantitative phase measurement with a phase-shifting technique. The disturbance caused by a Fresnel-diffracted wave from the splitting edge of the biprism is reduced by placement of a linear beam stopper at the center of an intermediate image plane. As the first application, the developed microscope is used to measure a refractive-index distribution in optical waveguides. A difference of refractive indices of less than 6 × 10-5 is clearly measured in the submicrometer region.

© 2002 Optical Society of America

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References

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  1. J. H. Bruning, D. R. Herriott, J.E. Gallagher, D. P. Rosenfeld, A. D. White, J. Brangaccio, “Digital wavefront measuring interferometry for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  2. K. Creath, “Phase-measurement interferometry techniques,” Prog. Optics349–393 (1988).
  3. J. F. Biegen, R. A. Smythe, “High resolution phase measuring laser interferometric microscope for engineering surface metrology,” in Surface Measurement and Characterization, J. Bennett, ed., Proc. SPIE1009, 35–45 (1988).
    [CrossRef]
  4. J. Chen, Y. Ishii, K. Murata, “Heterodyne interferometry with a frequency-modulated laser diode,” Appl. Opt. 27, 124–128 (1988).
    [CrossRef] [PubMed]
  5. Q. Ru, J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).
  6. G. Möllenstedt, H. Dücker, “Beobachtungen und Messungen an biprisma-Interferenzen mit Electronenwellen,” Z. Phys. 145, 377–397 (1956).
    [CrossRef]

1992 (1)

Q. Ru, J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

1988 (2)

1974 (1)

1956 (1)

G. Möllenstedt, H. Dücker, “Beobachtungen und Messungen an biprisma-Interferenzen mit Electronenwellen,” Z. Phys. 145, 377–397 (1956).
[CrossRef]

Biegen, J. F.

J. F. Biegen, R. A. Smythe, “High resolution phase measuring laser interferometric microscope for engineering surface metrology,” in Surface Measurement and Characterization, J. Bennett, ed., Proc. SPIE1009, 35–45 (1988).
[CrossRef]

Brangaccio, J.

Bruning, J. H.

Chen, J.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” Prog. Optics349–393 (1988).

Dücker, H.

G. Möllenstedt, H. Dücker, “Beobachtungen und Messungen an biprisma-Interferenzen mit Electronenwellen,” Z. Phys. 145, 377–397 (1956).
[CrossRef]

Endo, J.

Q. Ru, J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

Gallagher, J.E.

Herriott, D. R.

Ishii, Y.

Möllenstedt, G.

G. Möllenstedt, H. Dücker, “Beobachtungen und Messungen an biprisma-Interferenzen mit Electronenwellen,” Z. Phys. 145, 377–397 (1956).
[CrossRef]

Murata, K.

Rosenfeld, D. P.

Ru, Q.

Q. Ru, J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

Smythe, R. A.

J. F. Biegen, R. A. Smythe, “High resolution phase measuring laser interferometric microscope for engineering surface metrology,” in Surface Measurement and Characterization, J. Bennett, ed., Proc. SPIE1009, 35–45 (1988).
[CrossRef]

Tanji, T.

Q. Ru, J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

Tonomura, A.

Q. Ru, J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

White, A. D.

Appl. Opt. (2)

Optik (1)

Q. Ru, J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

Prog. Optics (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Optics349–393 (1988).

Z. Phys. (1)

G. Möllenstedt, H. Dücker, “Beobachtungen und Messungen an biprisma-Interferenzen mit Electronenwellen,” Z. Phys. 145, 377–397 (1956).
[CrossRef]

Other (1)

J. F. Biegen, R. A. Smythe, “High resolution phase measuring laser interferometric microscope for engineering surface metrology,” in Surface Measurement and Characterization, J. Bennett, ed., Proc. SPIE1009, 35–45 (1988).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Optical paths of two interfering beams.

Fig. 2
Fig. 2

Transmission phase-shifting laser microscope.

Fig. 3
Fig. 3

Example of calibration curve for biprism movement.

Fig. 4
Fig. 4

Fabrication of optical waveguide.

Fig. 5
Fig. 5

Example of interferogram.

Fig. 6
Fig. 6

Effect of Fresnel-diffracted wave on phase distribution.

Fig. 7
Fig. 7

Phase distribution of optical waveguide obtained with beam-stopper method.

Fig. 8
Fig. 8

Contour map of refractive-index distribution inside and outside the optical waveguide.

Fig. 9
Fig. 9

Contour maps of three different waveguides on the same substrate.

Tables (1)

Tables Icon

Table 1 Calculated Values of Incident Angle to the Biprism β0, Carrier-Fringe Spacing D p on the Observation Plane and Amount of Image Shift Δx as a Function of the Distance from the Axis on the Image Plane

Equations (26)

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uox, y=|uox, y|expikz+ϕx, y,
urx, y=|urx, y|expikz.
uox, y=|uox, y|expikx sin θ+z cos θ+ϕx, y,
urx, y=|urx, y|expik-x sin θ+z cos θ,
uox, y=|uox, y|expikx sin θ+z cos θ+ϕx, y+ϕp,
urx, y=|urx, y|expik-x sin θ+z cos θ-ϕp.
Ix, y=|uox, y|2+|urx, y|2+2|uox, y|urx, y|cos2kx sin θ+ϕx, y+2ϕp
2ϕp=2πmMm=1, 2, 3,  , M.
2kx sin θ+ϕx, y=tan-1m=1M Ix, y; msin2πmMm=1M Ix, y; mcos2πmM,
2kx sin θ=2πx/d,
θp=n-1α,
dp=λ/2θp.
do=Li+LsLsλ2θp,
β1=sin-11/nsin β0,
β2=αp-β1,
β3=sin-1n sin β2
=sin-1n sinαp-β1,
RR¯=RN¯cos β2
=xpsin αpcosαp-β1,
RS¯=RR¯cos β1cosβ3-αp.
Δϕ=2×2πRR¯λ-RS¯λ=4πxpλsin αpcosαp-β1n-cos β1cosβ3-αp,
Δϕ=4πxpλn-1αp=2πxpdp
B=C+A sin2πV/V0+D,
V0/M,
Δϕ=2πt n2-n1n1n1λ0,
Δx=RS=RR sin β1+RR cos β1 tanβ3-αp=xpsin αpcosαp-β1sin β1+cos β1 tanβ3-αp.

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