Abstract

Two-wavelength phase-shifting interferometry is applied to an interference phase-measuring microscope enabling the measurement of step features. The surface is effectively tested at a synthesized equivalent wavelength λeq = λaλb/|λa − λb| by subtracting phase measurements made at visible wavelengths λa and λb. The rms repeatability of the technique is λ/1000 at the equivalent wavelength. To improve the precision of the data, the phase ambiguities in the single-wavelength data are removed using the equivalent wavelength results to determine fringe orders. When this correction is made, a measurement dynamic range (feature height/rms repeatability) of 104 is obtainable. Results using this technique are shown for the measurement of an optical waveguide and a deeply modulated grating.

© 1987 Optical Society of America

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References

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  1. Y.-Y. Cheng, J. C. Wyant, “Two-Wavelength Phase Shifting Interferometry,” Appl. Opt. 23, 4539 (1984).
    [CrossRef] [PubMed]
  2. Y.-Y. Cheng, J. C. Wyant, “Multiple-Wavelength Phase-Shifting Interferometry,” Appl. Opt. 24, 804 (1985).
    [CrossRef] [PubMed]
  3. K. Creath, Y.-Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
    [CrossRef]
  4. K. Creath, J. C. Wyant, “Testing Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” J. Opt. Soc. Am. A 2(13), P58 (1985).
  5. K. Creath, J. C. Wyant, Direct Phase Measurement of Aspheric Surface Contours,” Proc. Soc. Photo-Opt. Instrum. Eng. 645, 101 (1986).
  6. B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of Surface Topography of Magnetic Tapes by Mirau Interferometry,” Appl. Opt. 24, 1489 (1985).
    [CrossRef] [PubMed]
  7. J. C. Wyant, K. N. Prettyjohns, “Three-dimensional Surface Metrology Using a Computer-Controlled Noncontact Instrument,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 292 (1986).
  8. P. Carré, “Installation et utilisation du comparateur photoelectrique et interferential du Bureau International des Poids et Mesures,” Metrologia 2, 13 (1966).
    [CrossRef]

1986 (2)

K. Creath, J. C. Wyant, Direct Phase Measurement of Aspheric Surface Contours,” Proc. Soc. Photo-Opt. Instrum. Eng. 645, 101 (1986).

J. C. Wyant, K. N. Prettyjohns, “Three-dimensional Surface Metrology Using a Computer-Controlled Noncontact Instrument,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 292 (1986).

1985 (4)

B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of Surface Topography of Magnetic Tapes by Mirau Interferometry,” Appl. Opt. 24, 1489 (1985).
[CrossRef] [PubMed]

Y.-Y. Cheng, J. C. Wyant, “Multiple-Wavelength Phase-Shifting Interferometry,” Appl. Opt. 24, 804 (1985).
[CrossRef] [PubMed]

K. Creath, Y.-Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
[CrossRef]

K. Creath, J. C. Wyant, “Testing Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” J. Opt. Soc. Am. A 2(13), P58 (1985).

1984 (1)

1966 (1)

P. Carré, “Installation et utilisation du comparateur photoelectrique et interferential du Bureau International des Poids et Mesures,” Metrologia 2, 13 (1966).
[CrossRef]

Bhushan, B.

Carré, P.

P. Carré, “Installation et utilisation du comparateur photoelectrique et interferential du Bureau International des Poids et Mesures,” Metrologia 2, 13 (1966).
[CrossRef]

Cheng, Y.-Y.

Creath, K.

K. Creath, J. C. Wyant, Direct Phase Measurement of Aspheric Surface Contours,” Proc. Soc. Photo-Opt. Instrum. Eng. 645, 101 (1986).

K. Creath, Y.-Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
[CrossRef]

K. Creath, J. C. Wyant, “Testing Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” J. Opt. Soc. Am. A 2(13), P58 (1985).

Koliopoulos, C. L.

Prettyjohns, K. N.

J. C. Wyant, K. N. Prettyjohns, “Three-dimensional Surface Metrology Using a Computer-Controlled Noncontact Instrument,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 292 (1986).

Wyant, J. C.

K. Creath, J. C. Wyant, Direct Phase Measurement of Aspheric Surface Contours,” Proc. Soc. Photo-Opt. Instrum. Eng. 645, 101 (1986).

J. C. Wyant, K. N. Prettyjohns, “Three-dimensional Surface Metrology Using a Computer-Controlled Noncontact Instrument,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 292 (1986).

K. Creath, J. C. Wyant, “Testing Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” J. Opt. Soc. Am. A 2(13), P58 (1985).

K. Creath, Y.-Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
[CrossRef]

B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of Surface Topography of Magnetic Tapes by Mirau Interferometry,” Appl. Opt. 24, 1489 (1985).
[CrossRef] [PubMed]

Y.-Y. Cheng, J. C. Wyant, “Multiple-Wavelength Phase-Shifting Interferometry,” Appl. Opt. 24, 804 (1985).
[CrossRef] [PubMed]

Y.-Y. Cheng, J. C. Wyant, “Two-Wavelength Phase Shifting Interferometry,” Appl. Opt. 23, 4539 (1984).
[CrossRef] [PubMed]

Appl. Opt. (3)

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

K. Creath, J. C. Wyant, “Testing Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” J. Opt. Soc. Am. A 2(13), P58 (1985).

Metrologia (1)

P. Carré, “Installation et utilisation du comparateur photoelectrique et interferential du Bureau International des Poids et Mesures,” Metrologia 2, 13 (1966).
[CrossRef]

Opt. Acta (1)

K. Creath, Y.-Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

K. Creath, J. C. Wyant, Direct Phase Measurement of Aspheric Surface Contours,” Proc. Soc. Photo-Opt. Instrum. Eng. 645, 101 (1986).

J. C. Wyant, K. N. Prettyjohns, “Three-dimensional Surface Metrology Using a Computer-Controlled Noncontact Instrument,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 292 (1986).

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Figures (10)

Fig. 1
Fig. 1

(A) Step height too large to measure with a single wavelength λ. (B) Fringes in region of step show possible ambiguity in fringe order.

Fig. 2
Fig. 2

Black and white photographs of (A) white light fringes of an optical waveguide, (B) same fringes with a narrowband filter in place, (C) white light fringes of a grating, and (D) fringes of grating with narrowband filter in place.

Fig. 3
Fig. 3

Synthesis of beat wavelength λeq using shorter wavelengths λa and λb.

Fig. 4
Fig. 4

Wavelength bandpass used for calculation in Eq. (6).

Fig. 5
Fig. 5

Fringe contrast vs wavelength bandwidth for different OPDs using sinc(πOPD/δc) terms of Eq. (7) at 600 nm.

Fig. 6
Fig. 6

Schematic of optical profiler using a Mirau interferometer.

Fig. 7
Fig. 7

Scanning electron micrographs of 1-μm high step in optical waveguide.

Fig. 8
Fig. 8

Profile of optical waveguide at (A) 650.9 nm and (B) 577.4 nm where step is incorrect. (C) Profile combining measurements of (A) and (B) to obtain correct step (λeq = 5.11 μm). (D) Repeatability of 5.11-μm measurement.

Fig. 9
Fig. 9

(A) Profile at 650.9 nm does not resemble a square grating. (B) Profile of grating at equivalent wavelength of 10.16 μm. (C) Repeatability of 10.16-μm measurement. (D) Profile of grating at 19.41 μm.

Fig. 10
Fig. 10

(A) Corrected profile of grating at 650.9 nm showing correct step heights and less noise. (B) Repeatability of corrected profile of (A).

Tables (1)

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Table I Equivalent Wavelengths Using 10 nm Bandpass Interference Filters

Equations (7)

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A ( x , y ) = I 0 { 1 + γ cos [ ϕ ( x , y ) - 3 α ] } ; B ( x , y ) = I 0 { 1 + γ cos [ ϕ ( x , y ) - α ] } ; C ( x , y ) = I 0 { 1 + γ cos [ ϕ ( x , y ) + α ] } ; D ( x , y ) = I 0 { 1 + γ cos [ ϕ ( x , y ) + 3 α ] } ;
ϕ = tan - 1 { [ ( A - D ) + ( B - C ) ] [ 3 ( B - C ) - ( A - D ) ] ( B + C ) - ( A + D ) }
ϕ eq ( x , y ) = 2 π OPD ( x , y ) λ eq = ϕ a ( x , y ) - ϕ b ( x , y ) ,
λ eq = λ a λ b λ a - λ b .
H ( x , y ) = 1 2 [ ϕ eq ( x , y ) λ eq 2 π ] .
I = 1 Δ λ λ - Δ λ / 2 λ + Δ λ / 2 I 0 [ 1 + γ cos ( 2 π OPD λ ) ] d λ ,
I = I 0 [ 1 + γ sinc ( π OPD δ c ) cos ( 2 π OPD λ ) ] ,

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