Abstract

Light reflected by a nondielectric material experiences a phase change on reflection that differs from light reflected by a dielectric material and other nondielectric materials. The complex degree of coherence for small optical path differences is derived for two-beam interference when the illumination source is extended, incoherent, and quasimonochromatic. An analysis of the two-beam interference pattern reveals a simple relationship between the phase of the interference pattern at the point of maximum fringe visibility and the material-dependent phase change on reflection.

© 1994 Optical Society of America

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References

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  1. G. S. Kino, S. C. Chim, Appl. Opt. 29, 3775 (1990).
    [CrossRef] [PubMed]
  2. B. Bhushan, J. C. Wyant, C. L. Koliopoulos, Appl. Opt. 24, 1489 (1985).
    [CrossRef] [PubMed]
  3. B. S. Lee, T. C. Strand, Appl. Opt. 29, 3784 (1990).
    [CrossRef] [PubMed]
  4. Y. Li, F. E. Talke, Trans. ASME 112, 670 (1990).
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 10.4.2.
  6. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 13.4.1.
  7. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), Vols. 1 and 2.
  8. G. Hass, L. Hadley, in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 118–138.

1990 (3)

1985 (1)

Bhushan, B.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 10.4.2.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 13.4.1.

Chim, S. C.

Hadley, L.

G. Hass, L. Hadley, in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 118–138.

Hass, G.

G. Hass, L. Hadley, in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 118–138.

Kino, G. S.

Koliopoulos, C. L.

Lee, B. S.

Li, Y.

Y. Li, F. E. Talke, Trans. ASME 112, 670 (1990).
[CrossRef]

Strand, T. C.

Talke, F. E.

Y. Li, F. E. Talke, Trans. ASME 112, 670 (1990).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 10.4.2.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 13.4.1.

Wyant, J. C.

Appl. Opt. (3)

Trans. ASME (1)

Y. Li, F. E. Talke, Trans. ASME 112, 670 (1990).
[CrossRef]

Other (4)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 10.4.2.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 13.4.1.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), Vols. 1 and 2.

G. Hass, L. Hadley, in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 118–138.

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Figures (2)

Fig. 1
Fig. 1

Diffraction of a spherical converging wave by a circular aperture in a two-beam Mirau interferometer showing the amplitude and phase terms of a ray traversing the interferometer.

Fig. 2
Fig. 2

Optomechanical layout of the apparatus used (right) and an interference pattern obtained with the apparatus, together with its fringe visibility curve (left). PZT, piezoelectric transducer.

Tables (1)

Tables Icon

Table 1 Comparison of Measured and Calculated Phase-Change Values

Equations (10)

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I ( Δ z ) = I 1 + I 2 + 2 I 1 I 2 Re [ γ 12 ( Δ z ) ] ,
γ 12 ( Δ z ) W I ( Q ) R 1 R 2 exp [ i ( 4 π λ 0 Δ R + Δ ϕ ) ] d Q ,
Δ R Δ z - Δ z r 2 2 R 2 .
γ 12 ( Δ z ) exp [ i ( 4 π λ 0 Δ z ) ] × 0 a 0 2 π exp { - i [ 2 π λ 0 Δ z R 2 r 2 - Δ ϕ ( r ) ] } r d r d φ ,
Ψ 1 ( n , k , θ ) = [ τ bs 2 ρ ts exp i ( 2 ϕ T bs + ϕ ts ) ] TE + [ τ bs 2 ρ ts exp i ( 2 ϕ T bs + ϕ ts ) ] TM ,
ϕ 1 ( n , k , θ ) = arctan Im [ Ψ 1 ( n , k , θ ) ] / Re [ Ψ 1 ( n , k , θ ) ] ,
ϕ ( r ) = ϕ 0 ( 1 + κ NA 2 r 2 ) ,
Re [ γ 12 ( Δ z ) ] = cos { 4 π λ 0 ( 1 - NA 2 4 ) Δ z + [ Δ ϕ 0 + ( κ 1 ϕ 01 - κ 2 ϕ 02 ) 2 NA 2 ] } × sinc { [ π λ 0 Δ z - ( κ 1 ϕ 01 - κ 2 ϕ 02 ) 2 ] NA 2 } .
I = I 1 + I 2 + 2 I 1 I 2 cos [ Δ ϕ 0 + 2 ( κ 1 ϕ 01 - κ 2 ϕ 02 ) ] .
ϕ 0 ts = Φ 1 - Φ dielectric 1 + 2 κ 1 .

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