Abstract

We validate the quantitative analysis of Ronchigrams for wavefront sensing through detailed numerical simulations. Analysis of the experimental Ronchigrams provides the wavefront aberrations, the F/# of the beam and the distance of the Ronchi ruling from the paraxial focus. These retrieved parameters are used to numerically simulate the Ronchigrams with excellent agreement. This favorable comparison validates the accuracy of the wavefront recovery and provides a tool to examine the accuracy and robustness of this wavefront measurement technique.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. R. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt. 32(10), 1737 (1993).
    [CrossRef] [PubMed]
  2. M. Guizar-Sicairos and J. R. Fienup, “Measurement of coherent x-ray focused beams by phase retrieval with transverse translation diversity,” Opt. Express 17(4), 2670–2685 (2009).
    [CrossRef] [PubMed]
  3. G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express 14(2), 474–486 (2006).
    [CrossRef] [PubMed]
  4. S. Lee and J. Sasian, “Ronchigram quantification via a non-complementary dark-space effect,” Opt. Express 17(3), 1854–1858 (2009).
    [CrossRef] [PubMed]
  5. V. Ronchi, “Forty Years of History of a Grating Interferometer,” Appl. Opt. 3(4), 437–451 (1964).
    [CrossRef]
  6. T. Yatagai, “Fringe scanning Ronchi test for aspherical surfaces,” Appl. Opt. 23(20), 3676–3679 (1984).
    [CrossRef] [PubMed]
  7. S. Lee, “Direct determination of f-number by using Ronchi test,” Opt. Express 17(7), 5107–5111 (2009).
    [CrossRef] [PubMed]
  8. J. Jeong, B. Lee, and S. Lee, “Determination of paraxial image plane location by using Ronchi test,” Opt. Express . 18(17) 18249-18253 (2010).
    [CrossRef] [PubMed]
  9. There are many different conventions, but we followed the one in J. C. Wyant and K. Creath, “Basic Wavefront Aberration Theory for Optical Metrology,” in Applied Optics and Optical Engineering, XI, 1992, Academic Press, Inc.
  10. J. W. Goodman, Introduction to Fourier Optics, 3rd Ed. (Roberts & Company, Englewood, 2005).
  11. D. Malacara, Optical Shop Testing, 2nd Ed., Ch. 9 (A Wiley-Interscience Publication, 1992).

2010 (1)

2009 (3)

2006 (1)

1993 (1)

1984 (1)

1964 (1)

Brady, G. R.

Fienup, J. R.

Guizar-Sicairos, M.

Jeong, J.

Lee, B.

Lee, S.

Ronchi, V.

Sasian, J.

Yatagai, T.

Appl. Opt. (3)

Opt. Express (5)

Other (3)

There are many different conventions, but we followed the one in J. C. Wyant and K. Creath, “Basic Wavefront Aberration Theory for Optical Metrology,” in Applied Optics and Optical Engineering, XI, 1992, Academic Press, Inc.

J. W. Goodman, Introduction to Fourier Optics, 3rd Ed. (Roberts & Company, Englewood, 2005).

D. Malacara, Optical Shop Testing, 2nd Ed., Ch. 9 (A Wiley-Interscience Publication, 1992).

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 (5)

Fig. 1
Fig. 1

Ronchi test setup for measuring transverse ray aberrations in a beam.

Fig. 2
Fig. 2

π-phase Ronchigrams with vertical ruling at (a) 13.00, (b) 13.50, (c) 14.00, (d) 14.50, and (e) 15.00 mm of the longitudinal translation stage and (f) thru (j) are their corresponding simulated images. All images are cropped to 512 by 512 pixels from the original sizes.

Fig. 3
Fig. 3

Defocus a3 (squares) and spherical aberration a8 (circles) as a function of ruling’s longitudinal position. The accompanied lines are the fitted lines. These values were determined by the quantitative Ronchigram analysis using F/# = 5.24, as retrieved from the data.

Fig. 4
Fig. 4

π-phase Ronchigrams with horizontal ruling at (a) 13.00, (b) 13.50, (c) 14.00, (d) 14.50, and (e) 15.00 mm of the longitudinal translation stage and (f) thru (j) are their corresponding simulated images. All images are cropped to 512 by 512 pixels from the original sizes.

Fig. 5
Fig. 5

Upper left quadrants of (a) Fig. 2(b) and (b) its corresponding simulated image in their original sizes. For better visualization, in the simulation the intensity was saturated by 40%.

Tables (1)

Tables Icon

Table 1 Third-order aberrations at various locations in unit of waves [7].

Equations (3)

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

u 2 ( x , y ) = e i k z i λ z e i k 2 z ( x 2 + y 2 ) u 1 ( α , β ) e i k 2 z ( α 2 + β 2 ) e i 2 π λ z ( x α + y β ) d α d β ,
u 2 ( x , y ) = u 1 ( x , y ) h 12 ( x , y ; z ) ,
h 12 ( x , y ; z ) = exp ( i k z ) i λ z exp [ i π λ z ( x 2 + y 2 ) ] .

Metrics