Abstract

A modification to the usual phase shifting interferometry algorithm permits measurements to be taken fast enough to essentially freeze out vibrations. Only two interferograms are time critical in this 2 + 1 algorithm; the third is null. The implemented system acquires the two time critical interferograms with a 1-millisecond separation on either side of the interline transfer of a standard CCD video camera, resulting in a reduction in sensitivity to vibration of 1–2 orders of magnitude. The required phase shift is achieved via frequency shifting. Laboratory tests comparing this system with a commercial phase shifting package reveal comparable rms errors when vibrations are low; as expected from an analysis of potential phase errors. However, the 2 + 1 system also succeeded when vibrations were large enough to wash out video rate fringes.

© 1990 Optical Society of America

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References

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  1. J. R. P. Angel, P. Wizinowich, “A Method for Phase Shifting Interferometry in the Presence of Vibration,” ESO Proc. 30, 561–567 (1988).
  2. J. R. P. Angel, N. J. Woolf, “15 Meter MMT Design Study,” Astrophys. J. 301, 478–501 (1986).
    [CrossRef]
  3. P. A. Strittmatter, “Columbus Project Overview,” ESO Proc. 30, 29–46 (1988).
  4. C. Roddier, F. Roddier, “Interferogram Analysis Using Fourier Transform Techniques,” Appl. Opt. 26, 1668–1673 (1987).
    [CrossRef] [PubMed]
  5. J. L. McLaughlin, B. A. Horowitz, “Real-Time Snapshot Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 680, 35–43 (1987).
  6. R. Smythe, R. Moore, “Instantaneous Phase Measuring Interferometry,” Opt. Eng. 23, 361–364 (1984).
    [CrossRef]
  7. O. Y. Kwon, D. M. Shough, R. A. Williams, “Stroboscopic Phase-Shifting Interferometry,” Opt. Lett. 12, 855–857 (1987).
    [CrossRef] [PubMed]
  8. K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
    [CrossRef]
  9. N. A. Massie, “Real-Time Digital Heterodyne Interferometry: A System,” Appl. Opt. 19, 154–160 (1980).
    [CrossRef] [PubMed]
  10. R. V. Shack, G. W. Hopkins, “The Shack Interferometer,” Opt. Eng. 18, 226–228 (1979).
  11. “Phase Analysis Software Manual,” version 1.22 (Phase Shift Technology, Tucson, AZ, 1988).

1988 (3)

J. R. P. Angel, P. Wizinowich, “A Method for Phase Shifting Interferometry in the Presence of Vibration,” ESO Proc. 30, 561–567 (1988).

P. A. Strittmatter, “Columbus Project Overview,” ESO Proc. 30, 29–46 (1988).

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

1987 (3)

1986 (1)

J. R. P. Angel, N. J. Woolf, “15 Meter MMT Design Study,” Astrophys. J. 301, 478–501 (1986).
[CrossRef]

1984 (1)

R. Smythe, R. Moore, “Instantaneous Phase Measuring Interferometry,” Opt. Eng. 23, 361–364 (1984).
[CrossRef]

1980 (1)

1979 (1)

R. V. Shack, G. W. Hopkins, “The Shack Interferometer,” Opt. Eng. 18, 226–228 (1979).

Angel, J. R. P.

J. R. P. Angel, P. Wizinowich, “A Method for Phase Shifting Interferometry in the Presence of Vibration,” ESO Proc. 30, 561–567 (1988).

J. R. P. Angel, N. J. Woolf, “15 Meter MMT Design Study,” Astrophys. J. 301, 478–501 (1986).
[CrossRef]

Creath, K.

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

Hopkins, G. W.

R. V. Shack, G. W. Hopkins, “The Shack Interferometer,” Opt. Eng. 18, 226–228 (1979).

Horowitz, B. A.

J. L. McLaughlin, B. A. Horowitz, “Real-Time Snapshot Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 680, 35–43 (1987).

Kwon, O. Y.

Massie, N. A.

McLaughlin, J. L.

J. L. McLaughlin, B. A. Horowitz, “Real-Time Snapshot Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 680, 35–43 (1987).

Moore, R.

R. Smythe, R. Moore, “Instantaneous Phase Measuring Interferometry,” Opt. Eng. 23, 361–364 (1984).
[CrossRef]

Roddier, C.

Roddier, F.

Shack, R. V.

R. V. Shack, G. W. Hopkins, “The Shack Interferometer,” Opt. Eng. 18, 226–228 (1979).

Shough, D. M.

Smythe, R.

R. Smythe, R. Moore, “Instantaneous Phase Measuring Interferometry,” Opt. Eng. 23, 361–364 (1984).
[CrossRef]

Strittmatter, P. A.

P. A. Strittmatter, “Columbus Project Overview,” ESO Proc. 30, 29–46 (1988).

Williams, R. A.

Wizinowich, P.

J. R. P. Angel, P. Wizinowich, “A Method for Phase Shifting Interferometry in the Presence of Vibration,” ESO Proc. 30, 561–567 (1988).

Woolf, N. J.

J. R. P. Angel, N. J. Woolf, “15 Meter MMT Design Study,” Astrophys. J. 301, 478–501 (1986).
[CrossRef]

Appl. Opt. (2)

Astrophys. J. (1)

J. R. P. Angel, N. J. Woolf, “15 Meter MMT Design Study,” Astrophys. J. 301, 478–501 (1986).
[CrossRef]

ESO Proc. (2)

P. A. Strittmatter, “Columbus Project Overview,” ESO Proc. 30, 29–46 (1988).

J. R. P. Angel, P. Wizinowich, “A Method for Phase Shifting Interferometry in the Presence of Vibration,” ESO Proc. 30, 561–567 (1988).

Opt. Eng. (2)

R. V. Shack, G. W. Hopkins, “The Shack Interferometer,” Opt. Eng. 18, 226–228 (1979).

R. Smythe, R. Moore, “Instantaneous Phase Measuring Interferometry,” Opt. Eng. 23, 361–364 (1984).
[CrossRef]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. L. McLaughlin, B. A. Horowitz, “Real-Time Snapshot Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 680, 35–43 (1987).

Prog. Opt. (1)

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

Other (1)

“Phase Analysis Software Manual,” version 1.22 (Phase Shift Technology, Tucson, AZ, 1988).

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Figures (9)

Fig. 1
Fig. 1

Frequency shifter. The beam from the laser, polarized at 45° to the polarizing beam splitter, is divided into two orthogonally polarized components. The rotating prism turntable causes the upper and lower beams to experience shifts in angular frequency of +Δω and −Δω, respectively. A double pass of a λ/4 plate rotates the polarization axis by 90° allowing the two frequency shifted components to be recombined by the polarizing beam splitter.

Fig. 2
Fig. 2

Frequency selector and interferometer. The Pockels cell and polarizing beam splitter act as a switch for the two orthogonally polarized frequency components. The polarizing beam splitter transmits light polarized in the plane of the page. The Pockels cell can rapidly change the polarization orientation and, hence, the frequency component entering the Shack cube interferometer shown.

Fig. 3
Fig. 3

Frequency shifter/selector package. The prism turntable motor extends below the L-shaped (23 × 15 cm) baseplate. The laser beam enters from the laser at the top of the photo and exits the package through the shutter at the top of the L. Refer to Figs. 1 and 2.

Fig. 4
Fig. 4

Sequence of interferograms. Three interferograms are required by the 2 + 1 interferogram. The 2 time critical interferograms are obtained by opening a shutter for 1 ms on either side of the interline transfer between two CCD integrations or fields. The Pockels cell voltage, and hence the frequency component entering the interferometer, is switched at the instant of interline transfer. The +1 or null interferogram may be obtained in a similar manner during a third CCD field.

Fig. 5
Fig. 5

Video rate interferograms in the high vibration case. The two fields of a single video frame were separated to obtain these two 1/60th of a second interferogram exposures. The fringes are almost completely washed out by vibrations and can be seen to move around on the video monitor.

Fig. 6
Fig. 6

Two 2 + 1 90° phase shifted interferograms in the high vibration case; these interferograms demonstrate how vibrations are essentially frozen out by the 2 + 1 phase shifting system.

Fig. 7
Fig. 7

Phase map in the high vibration case. The 2 + 1 algorithm was used to reduce the interferograms shown in Fig. 6 and a null interferogram. The resultant phase map is plotted as intensity with brighter areas representing higher areas on the surface. The 2π discontinuities present in the map at the top were removed for the bottom phase map.

Fig. 8
Fig. 8

Phase error plots for simulated phase shift errors and second- and third-order nonlinear detection errors. The number of fringes of phase error is plotted vs optical path difference in the left column, for a −10% simulated error. The peak-to-valley phase error is plotted vs percent of simulated error in the right column.

Fig. 9
Fig. 9

Phase error plots, similar to Fig. 8, for simulated intensity matching and frequency contamination errors.

Tables (1)

Tables Icon

Table 1 Summary of 2 + 1 Algorithm Error Analysis (Number of Fringes of Phase Error (Peak-to-Valley) Resulting from a −5 % Simulated Error)

Equations (7)

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I ( x , y ) = I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 cos [ ϕ ( x , y ) + α ( t ) ] ,
I A ( x , y ) = I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 cos ϕ , I B ( x , y ) = I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 cos ( ϕ - π / 2 ) = I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 sin ϕ .
I C ( x , y ) = ½ [ I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 cos ϕ ] + ½ [ I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 cos ( ϕ + π ) ] = I 1 + I 2 .
OPD ( x , y ) = λ 2 π tan - 1 I B ( x , y ) - I C ( x , y ) I A ( x , y ) - I C ( x , y ) .
2 Δ ω = c α OPD = 2 π 8 ω t r λ ,
I A ( x , y ) = I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 sin ϕ , I B ( x , y ) = I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 cos ϕ ,
I C ( x , y ) = ½ [ I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 cos ( ϕ - π / 2 ) ] + ½ [ I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 cos ( ϕ + π / 2 ) ] = ( I 1 + I 2 ) .

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