Abstract

Digital phase-shifting interferometry (PSI), a technique widely used in optical testing, requires interferograms collected at optical phase differences separated by a definite phase step. The five-frame interferogram-collecting sequence suggested by Hariharan et al. [Appl. Opt. 26, 2504 (1987)] is extremely effective in significantly reducing the errors in height profiles derived using PSI that are caused by phase-step errors. In this Letter, we report on a class of five-frame sequence that, owing to its mathematical equivalence with the one suggested by Hariharan et al. and its ease of execution, is more commonly used but is much less effective in reducing the height profile errors caused by phase-step errors.

© 2011 Optical Society of America

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References

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  1. C. T. Farrell and M. A. Player, Meas. Sci. Technol. 5, 648 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. K. M. Hurst, C. B. Roberts, and W. R. Ashurst, Tribol. Lett. 35, 9 (2009).
    [CrossRef]
  4. P. Hariharan, B. F. Oreb, and T. Eiju, Appl. Opt. 26, 2504 (1987).
    [CrossRef] [PubMed]

2009

K. M. Hurst, C. B. Roberts, and W. R. Ashurst, Tribol. Lett. 35, 9 (2009).
[CrossRef]

2005

1994

C. T. Farrell and M. A. Player, Meas. Sci. Technol. 5, 648 (1994).
[CrossRef]

1987

Ashurst, W. R.

K. M. Hurst, C. B. Roberts, and W. R. Ashurst, Tribol. Lett. 35, 9 (2009).
[CrossRef]

Corwin, A. D.

de Boer, M. P.

Eiju, T.

Farrell, C. T.

C. T. Farrell and M. A. Player, Meas. Sci. Technol. 5, 648 (1994).
[CrossRef]

Hariharan, P.

Hurst, K. M.

K. M. Hurst, C. B. Roberts, and W. R. Ashurst, Tribol. Lett. 35, 9 (2009).
[CrossRef]

Oreb, B. F.

Player, M. A.

C. T. Farrell and M. A. Player, Meas. Sci. Technol. 5, 648 (1994).
[CrossRef]

Roberts, C. B.

K. M. Hurst, C. B. Roberts, and W. R. Ashurst, Tribol. Lett. 35, 9 (2009).
[CrossRef]

Sinclair, M. B.

Appl. Opt.

Meas. Sci. Technol.

C. T. Farrell and M. A. Player, Meas. Sci. Technol. 5, 648 (1994).
[CrossRef]

Tribol. Lett.

K. M. Hurst, C. B. Roberts, and W. R. Ashurst, Tribol. Lett. 35, 9 (2009).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Error in ϕ ( Δ ϕ ) for different imposed percentage error ( % ϵ ) in α.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

I 1 = A + B + 2 A B cos ( ϕ ± 2 α ) ,
I 2 = A + B + 2 A B cos ( ϕ ± α ) ,
I 3 = A + B + 2 A B cos ( ϕ ) ,
I 4 = A + B + 2 A B cos ( ϕ α ) ,
I 5 = A + B + 2 A B cos ( ϕ 2 α ) .
I 1 = A + B + 2 A B cos ( ϕ ) ,
I 2 = A + B + 2 A B cos ( ϕ ± α ) ,
I 3 = A + B + 2 A B cos ( ϕ ± 2 α ) ,
I 4 = A + B + 2 A B cos ( ϕ ± 3 α ) ,
I 5 = A + B + 2 A B cos ( ϕ ± 4 α ) .
tan ϕ = ± 2 ( I 2 I 4 ) 2 I 3 I 1 I 5 .
Δ ϕ = ϵ 2 8 sin 2 ϕ ,
Δ ϕ = ± 2 ϵ .

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