Abstract

A quadratic cost functional for computing an estimate of a wave front from multiple directional derivatives is presented. This functional is robust to noise and is specially suited for moiré deflectometry, Ronchi testing, and lateral shearing interferometry.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Malacara, ed., Optical Shop Testing (Wiley, New York, 1992), Chaps. 4 and 9.
  2. R. Legarda-Sáenz, R. Rodriguez-Vera, and M. Rivera, Opt. Commun. 160, 214 (1999).
    [CrossRef]
  3. D. L. Fried, J. Opt. Soc. Am. 67, 370 (1977).
  4. R. H. Hudgin, J. Opt. Soc. Am. 67, 375 (1977).
  5. D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Sec. 10.2.
  6. M. Rivera, J. L. Marroquín, S. Botello, and M. Servin, Appl. Opt. 39, 284 (2000).
    [CrossRef]
  7. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).
  8. Essilor International, “Progressive multifocal ophthalmic lens,” U.S. patent5,272,495 (December21, 1993) .

2000 (1)

1999 (1)

R. Legarda-Sáenz, R. Rodriguez-Vera, and M. Rivera, Opt. Commun. 160, 214 (1999).
[CrossRef]

1977 (2)

Botello, S.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Fried, D. L.

Hudgin, R. H.

Legarda-Sáenz, R.

R. Legarda-Sáenz, R. Rodriguez-Vera, and M. Rivera, Opt. Commun. 160, 214 (1999).
[CrossRef]

Malacara, D.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Sec. 10.2.

Malacara, Z.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Sec. 10.2.

Marroquín, J. L.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Rivera, M.

M. Rivera, J. L. Marroquín, S. Botello, and M. Servin, Appl. Opt. 39, 284 (2000).
[CrossRef]

R. Legarda-Sáenz, R. Rodriguez-Vera, and M. Rivera, Opt. Commun. 160, 214 (1999).
[CrossRef]

Rodriguez-Vera, R.

R. Legarda-Sáenz, R. Rodriguez-Vera, and M. Rivera, Opt. Commun. 160, 214 (1999).
[CrossRef]

Servin, M.

M. Rivera, J. L. Marroquín, S. Botello, and M. Servin, Appl. Opt. 39, 284 (2000).
[CrossRef]

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Sec. 10.2.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

R. Legarda-Sáenz, R. Rodriguez-Vera, and M. Rivera, Opt. Commun. 160, 214 (1999).
[CrossRef]

Other (4)

D. Malacara, ed., Optical Shop Testing (Wiley, New York, 1992), Chaps. 4 and 9.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Sec. 10.2.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Essilor International, “Progressive multifocal ophthalmic lens,” U.S. patent5,272,495 (December21, 1993) .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

(a) Synthetic wavefront. (b)–(d) Computed wave fronts with K equal to (b) 2, (c) 8, and (d) 32 fringe patterns.

Fig. 2
Fig. 2

(a) Real example of unwrapped phases used in estimation of a wave front from moiré deflectometry. (b), (c) Surface estimates by use of (b) Eq. (2) with θ equal to 0° and 90° and (c) Eq. (5) with θ=0°168°, in steps of 24°.

Equations (6)

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

Φi,j=W·v+ni,j, Φi,j=αWxi,j+βWyi,j+ni,j,
UWˆ=i,ji+1,jRWˆi+1,j-Wˆi,jα-Wxi,j2+i,ji,j+1RWˆi,j+1-Wˆi,jβ-Wyi,j2,
Φi,jk=αkWxi,j+βkWyi,j+ni,jk
UMWˆ=ki,ji+1,jRi,j+1Wˆi+1,j-Wˆi,jαk+Wˆi,j+1-Wˆi,jβk-Φi,jk2,
-Wˆi+1,j-Wˆi,jC1+C2+Wˆi,j+1-Wˆi,jC2+C3-Ai,j-Bi,j+Wˆi,j-Wˆi-1,jC1+Wˆi-1,j+1-Wˆi-1,jC2-Ai-1,j+Wˆi+1,j-1-Wˆi,j-1C2+Wˆi,j-Wˆi,j-1C3-Bi,j-1=0.
C1=kαk2, C2=kαk·βk, C3=kβk2, Ai,j=kαkΦi,jk, Bi,j=kβkΦi,jk.

Metrics