Abstract

An implementation of the well-known Ronchi test technique, which allows for the profilometric measurement of nonrotationally symmetrical surfaces, is presented and applied to the measurement of toroidal surfaces. Both the experimental setup and the data-processing procedures are described, and parameters such as the radius of curvature of the sample surface, the orientation of its principal meridians, and the position of its vertex are measured by means of the values of the local normal to the surface obtained at a set of sampling points. Integration of these local normal values allows for the reconstruction of the three-dimensional profile of the toroidal surface considered with micrometric accuracy, and submicrometric surface details may be calculated by use of surface-fitting procedures. The density of sampling points on the surface may be tailored to fit test requirements, within certain limits that depend on selection of experimental setup.

© 2000 Optical Society of America

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References

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  1. A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992).
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    [CrossRef]
  3. J. Arasa, S. Royo, C. Pizarro, “Toroidal surface profilometries through Ronchi deflectometry: constancy under rotation of the sample,” in Applications of Photonic Technology, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 909–915 (1998).
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    [CrossRef]
  5. K. Stultz, H. P. Stahl, “A discussion of techniques that separate orthogonal data produced by Ronchi cross-grating patterns,” in Current Developments in Optical Design and Optical Engineering, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 226–232 (1994).
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. D. S. Wan, M. W. Chang, “Effects of grating spacing on the Ronchi test,” Opt. Eng. 32, 1084–1090 (1993).
    [CrossRef]
  9. L. Carretero, A. González, A. Fimia, I. Pascual, “Application of the Ronchi test to intraocular lenses: a comparison of theoretical and measured results,” Appl. Opt. 32, 4132–4137 (1993).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. H. J. Lee, S. W. Kim, “Precision profile measurement of aspheric surfaces by improved Ronchi test,” Opt. Eng. 38, 1041–1047 (1999).
    [CrossRef]
  13. D. Malacara, A. Cornejo, “Null Ronchi test for aspherical surfaces,” Appl. Opt. 13, 1778–1780 (1974).
    [CrossRef] [PubMed]
  14. E. Mobsby, “A Ronchi null test for paraboloids,” Sky Telesc. 48, 325–330 (1974).
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1999 (1)

H. J. Lee, S. W. Kim, “Precision profile measurement of aspheric surfaces by improved Ronchi test,” Opt. Eng. 38, 1041–1047 (1999).
[CrossRef]

1998 (1)

1997 (1)

1993 (2)

1992 (1)

1990 (1)

1988 (1)

1986 (1)

1974 (2)

D. Malacara, A. Cornejo, “Null Ronchi test for aspherical surfaces,” Appl. Opt. 13, 1778–1780 (1974).
[CrossRef] [PubMed]

E. Mobsby, “A Ronchi null test for paraboloids,” Sky Telesc. 48, 325–330 (1974).

Arasa, J.

J. Arasa, S. Royo, C. Pizarro, “Toroidal surface profilometries through Ronchi deflectometry: constancy under rotation of the sample,” in Applications of Photonic Technology, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 909–915 (1998).

Award, B. K.

Cardona-Núñez, O.

Carretero, L.

Chang, M. W.

D. S. Wan, M. W. Chang, “Effects of grating spacing on the Ronchi test,” Opt. Eng. 32, 1084–1090 (1993).
[CrossRef]

Cordero-Dávila, A.

Cornejo, A.

Cornejo-Rodriguez, A.

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

Cornejo-Rodríguez, A.

Farrant, D. I.

Fimia, A.

González, A.

Hibino, K.

Jalie, M.

M. Jalie, The Principles of Ophthalmic Lenses (Association of British Dispensing Opticians, London, 1980).

Kim, S. W.

H. J. Lee, S. W. Kim, “Precision profile measurement of aspheric surfaces by improved Ronchi test,” Opt. Eng. 38, 1041–1047 (1999).
[CrossRef]

Lee, H. J.

H. J. Lee, S. W. Kim, “Precision profile measurement of aspheric surfaces by improved Ronchi test,” Opt. Eng. 38, 1041–1047 (1999).
[CrossRef]

Luna-Aguilar, E.

Malacara, D.

Menchaca, C.

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).

Mobsby, E.

E. Mobsby, “A Ronchi null test for paraboloids,” Sky Telesc. 48, 325–330 (1974).

Omura, K.

Oreb, B. F.

Pascual, I.

Percino-Zacarías, M. E.

Pizarro, C.

J. Arasa, S. Royo, C. Pizarro, “Toroidal surface profilometries through Ronchi deflectometry: constancy under rotation of the sample,” in Applications of Photonic Technology, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 909–915 (1998).

Royo, S.

J. Arasa, S. Royo, C. Pizarro, “Toroidal surface profilometries through Ronchi deflectometry: constancy under rotation of the sample,” in Applications of Photonic Technology, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 909–915 (1998).

S. Royo, “Topographic measurements of non-rotationally symmetrical concave 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).

K. Stultz, H. P. Stahl, “A discussion of techniques that separate orthogonal data produced by Ronchi cross-grating patterns,” in Current Developments in Optical Design and Optical Engineering, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 226–232 (1994).

Stultz, K.

K. Stultz, H. P. Stahl, “A discussion of techniques that separate orthogonal data produced by Ronchi cross-grating patterns,” in Current Developments in Optical Design and Optical Engineering, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 226–232 (1994).

Vázquez-Montiel, S.

Wan, D. S.

D. S. Wan, M. W. Chang, “Effects of grating spacing on the Ronchi test,” Opt. Eng. 32, 1084–1090 (1993).
[CrossRef]

Yatagai, T.

Zárate-Vázquez, S.

Appl. Opt. (8)

Opt. Eng. (2)

H. J. Lee, S. W. Kim, “Precision profile measurement of aspheric surfaces by improved Ronchi test,” Opt. Eng. 38, 1041–1047 (1999).
[CrossRef]

D. S. Wan, M. W. Chang, “Effects of grating spacing on the Ronchi test,” Opt. Eng. 32, 1084–1090 (1993).
[CrossRef]

Sky Telesc. (1)

E. Mobsby, “A Ronchi null test for paraboloids,” Sky Telesc. 48, 325–330 (1974).

Other (6)

M. Jalie, The Principles of Ophthalmic Lenses (Association of British Dispensing Opticians, London, 1980).

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

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

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).

K. Stultz, H. P. Stahl, “A discussion of techniques that separate orthogonal data produced by Ronchi cross-grating patterns,” in Current Developments in Optical Design and Optical Engineering, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 226–232 (1994).

J. Arasa, S. Royo, C. Pizarro, “Toroidal surface profilometries through Ronchi deflectometry: constancy under rotation of the sample,” in Applications of Photonic Technology, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 909–915 (1998).

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Figures (9)

Fig. 1
Fig. 1

Toroidal surface and the parameters used for its mathematical description.

Fig. 2
Fig. 2

Experimental setup. RGB: red, green, blue.

Fig. 3
Fig. 3

Data-processing operations from the ronchigram to the surface profile. 2-D, two dimensional; 3-D, three dimensional.

Fig. 4
Fig. 4

Experimental ronchigrams for the sample surface: (a) X ronchigram, ruling lines placed horizontally; (b) Y ronchigram, ruling lines placed vertically.

Fig. 5
Fig. 5

Intersection of 1-pixel-wide line patterns: (a) nonmicrostepped experiment yielding 68 sampling points on the sample surface; (b) microstepped experiment yielding 7950 sampling points on the sample surface.

Fig. 6
Fig. 6

G60 orientation: local normal slope against position curves along the principal meridians of the sample: (a) cross curve; (b) base curve.

Fig. 7
Fig. 7

G60 orientation: three-dimensional profile of the surface obtained by integration of the local normals: (a) three-dimensional plot, (b) contour plot. Each contour step equals a height step of 16 µm.

Fig. 8
Fig. 8

Measured surface profiles, as contour plots, at the three additional orientations measured. Each contour step equals 16 µm. (a) G00 orientation, (b) G30 orientation; (c) G90 orientation.

Fig. 9
Fig. 9

Residuals obtained by subtraction of the measured profile from the best-fit profile. Each contour step equals 47 nm. (a) G00 orientation, (b) G30 orientation, (c) G60 orientation, (d) G90 orientation. Features that deviate from the ideal surface may be seen to rotate as the sample is rotated.

Tables (3)

Tables Icon

Table 1 G60 Orientation: Results of Fitting the Plots in Fig. 6 to Eq. (5)

Tables Icon

Table 2 Orientation G60: Results of the Three-Dimensional Fitting of a Tilted and Decentered Spherocylindrical Surface (Eq. 3) to the Measured Profile

Tables Icon

Table 3 Results for the Sample in the Three Additional Orientations Measured

Equations (5)

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

x=a+b cos ϕcos , y=a+b cos ϕsin , z=b sin ϕ,
z=x2/R1+y2/R21+1-x2/R1+y2/R22x2+y21/2,
x-x0=xS cos θ+yS sin θ, y-y0=-xS sin θ+yS cos θ, z=x-x02/R1+y-y02/R21+1-x-x02/R1+y-y02/R22x-x02+y-y021/2,
ui=nXiΔx/f, vi=nYiΔy/f,
NJ60=CJ60J+KJ

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