Abstract

We present a simple method for increasing the number of data points obtained during performance of profilometric measurements with the Ronchi test. The method is based on multiple ronchigram acquisitions that are superimposed after a few very simple data-processing operations. The measurement method, experimental setup, and data processing are described in detail from the ronchigram to the measured profile, and experimental results for a concave surface of an spherical ophthalmic lens are provided. The radius of curvature values measured for that surface are compared with the ones obtained with a high-precision radioscope, showing very good agreement and demonstrating the capability of the technique to measure topographic profiles of reflective samples.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Cornejo-Rodríguez, “Ronchi test,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), Chap. 9.
  2. A. Cordero-Dávila, A. Cornejo-Rodríguez, O. Cardona-Núñez, “Ronchi and Hartmann tests with the same mathematical theory,” Appl. Opt. 31, 2370–2376 (1992).
    [CrossRef] [PubMed]
  3. K. Patorski, “Heuristic explanation of grating shearing interferometry using incoherent illumination,” Opt. Acta 31, 33–38 (1984).
    [CrossRef]
  4. T. Yatagai, “Fringe scanning Ronchi test for aspherical surfaces,” Appl. Opt. 23, 3676–3679 (1984).
    [CrossRef] [PubMed]
  5. K. Hibino, D. I. Farrant, B. K. Ward, B. F. Oreb, “Dynamic range of Ronchi test with a phase-shifted sinusoidal grating,” Appl. Opt. 36, 6178–6189 (1997).
    [CrossRef]
  6. A. Cornejo, D. Malacara, “Ronchi test of aspherical surfaces, analysis, and accuracy,” Appl. Opt. 9, 1897–1901 (1970).
    [PubMed]
  7. M. P. Rimmer, J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14, 142–150 (1975).
    [CrossRef] [PubMed]
  8. W. Meyers, H. P. Stahl, “Contouring of a free oil surface,” in Interferometry, Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, G. T. Reid, eds. Proc. SPIE1755, 84–94 (1992).
    [CrossRef]
  9. S. Royo, “Topographic measurements of non-rotationally symmetrical surfaces using Ronchi deflectometry,” Ph.D. dissertation (Technical University of Catalonia, Terrassa, Spain, 1999).

1997 (1)

1992 (1)

1984 (2)

K. Patorski, “Heuristic explanation of grating shearing interferometry using incoherent illumination,” Opt. Acta 31, 33–38 (1984).
[CrossRef]

T. Yatagai, “Fringe scanning Ronchi test for aspherical surfaces,” Appl. Opt. 23, 3676–3679 (1984).
[CrossRef] [PubMed]

1975 (1)

1970 (1)

Cardona-Núñez, O.

Cordero-Dávila, A.

Cornejo, A.

Cornejo-Rodríguez, A.

A. Cordero-Dávila, A. Cornejo-Rodríguez, O. Cardona-Núñez, “Ronchi and Hartmann tests with the same mathematical theory,” Appl. Opt. 31, 2370–2376 (1992).
[CrossRef] [PubMed]

A. Cornejo-Rodríguez, “Ronchi test,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), Chap. 9.

Farrant, D. I.

Hibino, K.

Malacara, D.

Meyers, W.

W. Meyers, H. P. Stahl, “Contouring of a free oil surface,” in Interferometry, Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, G. T. Reid, eds. Proc. SPIE1755, 84–94 (1992).
[CrossRef]

Oreb, B. F.

Patorski, K.

K. Patorski, “Heuristic explanation of grating shearing interferometry using incoherent illumination,” Opt. Acta 31, 33–38 (1984).
[CrossRef]

Rimmer, M. P.

Royo, S.

S. Royo, “Topographic measurements of non-rotationally symmetrical surfaces using Ronchi deflectometry,” Ph.D. dissertation (Technical University of Catalonia, Terrassa, Spain, 1999).

Stahl, H. P.

W. Meyers, H. P. Stahl, “Contouring of a free oil surface,” in Interferometry, Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, G. T. Reid, eds. Proc. SPIE1755, 84–94 (1992).
[CrossRef]

Ward, B. K.

Wyant, J. C.

Yatagai, T.

Appl. Opt. (5)

Opt. Acta (1)

K. Patorski, “Heuristic explanation of grating shearing interferometry using incoherent illumination,” Opt. Acta 31, 33–38 (1984).
[CrossRef]

Other (3)

A. Cornejo-Rodríguez, “Ronchi test,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), Chap. 9.

W. Meyers, H. P. Stahl, “Contouring of a free oil surface,” in Interferometry, Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, G. T. Reid, eds. Proc. SPIE1755, 84–94 (1992).
[CrossRef]

S. Royo, “Topographic measurements of non-rotationally symmetrical surfaces using Ronchi deflectometry,” Ph.D. dissertation (Technical University of Catalonia, Terrassa, Spain, 1999).

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 (8)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Measurement of the slope and position of one ray reflected on the sample at the Ronchi ruling plane. With the objective focused at infinity, each pixel receives only rays with a given slope. Position at the ruling plane is obtained with a reference ruling line.

Fig. 3
Fig. 3

Data processing from the ronchigram to the surface profile.

Fig. 4
Fig. 4

Ray-tracing schematics. Reflected rays are ray traced backwards to calculate the local normal to the sample at the point where the rays leave the surface.

Fig. 5
Fig. 5

First pair of ronchigrams: (a) ruling lines along the X axis (X ronchigram) and (b) ruling lines along the Y axis (Y ronchigram).

Fig. 6
Fig. 6

Superposition of eroded ronchigrams. Each intersection of orthogonal lines is a valid sampling point. (a) Nonmicrostepped experiment and (b) microstepped experiment.

Fig. 7
Fig. 7

Three-dimensional surface reconstruction: (a) nonmicrostepped experiment and (b) microstepped experiment.

Fig. 8
Fig. 8

Contour plot surface reconstruction: (a) nonmicrostepped experiment, contour step 72 µm and (b) microstepped experiment, contour step 9 µm. Data points in the nonmicrostepped experiment have been enlarged to improve their visibility. Each plotted point is a measured data point with a gray value determined by its measured height.

Tables (1)

Tables Icon

Table 1 Three-Dimensional Fitting Results for the Measured Surface with Eq. (1)a

Equations (1)

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

z=1Rx-x02+y-y021/21+1-x-x02+y-y02R21/2,

Metrics