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References

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  1. R. Crane, “Interference Phase Measurement,” Appl. Opt. 8, 538 (1969).
  2. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  3. K. D. Stumpf, “Real-Time Interferometer,” Opt. Eng. 18, 648 (1979).
    [CrossRef]
  4. N. A. Massie, “Real-Time Digital Heterodyne Interferometry: a System,” Appl. Opt. 19, 154 (1980).
    [CrossRef] [PubMed]
  5. 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]
  6. G. E. Sommargren, “Optical Heterodyne Profilometry,” Appl. Opt. 20, 610 (1981).
    [CrossRef] [PubMed]
  7. O. Sasaki, H. Okazaki, “Analysis of Measurement Accuracy in Sinusoidal Phase Modulating Interferometry,” Appl. Opt. 25, 000 (1986), same issue.
    [CrossRef]
  8. O. Sasaki, H. Okazaki, “Detection of Time-Varying Intensity Distribution with CCD Image Sensors,” Appl. Opt. 24, 2124 (1985).
    [CrossRef] [PubMed]

1986 (1)

O. Sasaki, H. Okazaki, “Analysis of Measurement Accuracy in Sinusoidal Phase Modulating Interferometry,” Appl. Opt. 25, 000 (1986), same issue.
[CrossRef]

1985 (2)

1981 (1)

1980 (1)

1979 (1)

K. D. Stumpf, “Real-Time Interferometer,” Opt. Eng. 18, 648 (1979).
[CrossRef]

1974 (1)

1969 (1)

R. Crane, “Interference Phase Measurement,” Appl. Opt. 8, 538 (1969).

Bhushan, B.

Brangaccio, D. J.

Bruning, J. H.

Crane, R.

R. Crane, “Interference Phase Measurement,” Appl. Opt. 8, 538 (1969).

Gallagher, J. E.

Herriott, D. R.

Koliopoulos, C. L.

Massie, N. A.

Okazaki, H.

O. Sasaki, H. Okazaki, “Analysis of Measurement Accuracy in Sinusoidal Phase Modulating Interferometry,” Appl. Opt. 25, 000 (1986), same issue.
[CrossRef]

O. Sasaki, H. Okazaki, “Detection of Time-Varying Intensity Distribution with CCD Image Sensors,” Appl. Opt. 24, 2124 (1985).
[CrossRef] [PubMed]

Rosenfeld, D. P.

Sasaki, O.

O. Sasaki, H. Okazaki, “Analysis of Measurement Accuracy in Sinusoidal Phase Modulating Interferometry,” Appl. Opt. 25, 000 (1986), same issue.
[CrossRef]

O. Sasaki, H. Okazaki, “Detection of Time-Varying Intensity Distribution with CCD Image Sensors,” Appl. Opt. 24, 2124 (1985).
[CrossRef] [PubMed]

Sommargren, G. E.

Stumpf, K. D.

K. D. Stumpf, “Real-Time Interferometer,” Opt. Eng. 18, 648 (1979).
[CrossRef]

White, A. D.

Wyant, J. C.

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Figures (9)

Fig. 1
Fig. 1

Sinusoidal phase modulating interferometer. Signal s(t) is detected with a CCD image sensor.

Fig. 2
Fig. 2

Relationship between amplitude z and the ratio R = |J3(z)/J1(z)|.

Fig. 3
Fig. 3

Amplitude of discrete Fourier transform of signal s(mΔt) obtained from the output g(mΔt) of the CCD image sensor.

Fig. 4
Fig. 4

Tilt and aberration of the reference wave front measured by selecting the light near the optical axis at the focal plane of the lens.

Fig. 5
Fig. 5

Surface profile of a diamond-turned aluminum disk obtained by subtracting the profile of Fig. 4 from the raw measured profile.

Fig. 6
Fig. 6

Surface profile of a diamond-turned aluminum disk measured with a Talystep instrument.

Fig. 7
Fig. 7

Surface profile of a gauge block measured using a 2-D CCD image sensor.

Fig. 8
Fig. 8

Surface profiles along the lines directed toward (a) the x axis and (b) the y axis, taken from Fig. 7.

Fig. 9
Fig. 9

Measured surface profile of another gauge block whose roughness is smaller than that of Fig. 7.

Equations (12)

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A ( t ) = a cos ( ω c t + θ ) .
s ( t ) = s 0 cos [ z cos ( ω c t + θ ) + α + n M ( t ) ] ,
F ( ω ) = F { s ( t ) } = ( 1 / 2 ) m = - ( - 1 ) m K 2 m [ N ( ω - 2 m ω c ) exp ( j α ) + N * ( - ω + 2 m ω c ) exp ( - j α ) ] + ( 1 / 2 j ) m = - ( - 1 ) m K 2 m - 1 { N [ ω - ( 2 m - 1 ) ω c ] exp ( j α ) - N * [ - ω + ( 2 m - 1 ) ω c ] exp ( - j α ) } ,
K m = J m ( z ) exp ( j m θ ) , N ( ω ) = F { exp [ j n M ( t ) ] } ,
N ( ω ) = 0             ω ω c ,
F ( 2 m ω c ) = ( - 1 ) m N s 0 cos ( α + β ) J 2 m ( z ) exp ( j 2 m θ ) , F [ ( 2 m - 1 ) ω c ] = ( - 1 ) m N s 0 sin ( α + β ) J 2 m - 1 ( z ) × exp [ j ( 2 m - 1 ) θ ]             m = 0 , ± 1 , ± 2 , ,
tan ( α + β ) = [ F ( ω c ) / J 1 ( z ) ] sgn { - Re [ F ( ω c ) ] J 1 ( z ) cos θ } [ F ( 2 ω ) / J 2 ( z ) ] sgn { - Re [ F ( 2 ω c ) ] J 2 ( z ) cos 2 θ } ,
sgn { x } = { 1 x 0 , - 1 x < 0 ,
R = F ( 3 ω c ) / F ( ω c ) = J 3 ( z ) / J 1 ( z ) ,
arg { - F ( ω c ) } = arg { J 1 ( z ) exp ( j θ ) sin α } = { θ α > 0 , θ + π α < 0 ,
g ( m Δ t ) = - T a / 2 T a / 2 s ( t + m Δ t ) d t             m = 0 , 1 , , M - 1 ,
F ( l Δ f ) = G ( l Δ f ) [ π l T a / M Δ t ) / sin ( π l T a / M Δ t ) ] ,

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