Abstract

In this work we present an experimental proposal to evaluate optical surfaces with high slopes or with infrared wavelengths based on the Ronchi test as well as on the concept of equivalent wavelength. A spatial modulator is used in the implementation of the Ronchi test, and a white LED with different color filters is employed in order to generate different wavelengths. Two Ronchigrams with incoherent light, each one for a different color, are registered and computationally processed, thus generating a third one with an equivalent wavelength. The results obtained show that it is possible to generate patterns with traditional rulings and substructured sequences of Katyl. Additionally, we discuss some of the limitations of employing different rulings. Finally, we found that appropriate image enhancing algorithms allow us to improve the visibility of the resulting fringes and thus obtain a better analysis.

© 2012 Optical Society of America

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References

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  1. J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. 10, 2113–2118 (1971).
    [CrossRef]
  2. W. B. Ribbens, “Surface roughness measurement by two wavelength holographic interferometry,” Appl. Opt. 13, 1085–1088 (1974).
    [CrossRef]
  3. K. Creath, “Step height measurement using two-wavelength phase shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [CrossRef]
  4. J. A MacGovern and J. C. Wyant, “Computer generated holograms for testing optical elements,” Appl. Opt. 10, 619–624 (1971).
    [CrossRef]
  5. B. P. Hildebrand and K. A. Haines, “Multiple-wavelength and multiple-source holography applied to contour generation,” J. Opt. Soc. Am. 57, 155–162 (1967).
    [CrossRef]
  6. S. J. Zelenka and R. J. Varner, “Multiple-index holographic contouring,” Appl. Opt. 8, 1431–1434 (1969).
    [CrossRef]
  7. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [CrossRef]
  8. K. M. Leung, T. C. Lee, and G. E. Bernal, “Two-wavelength contouring with the automated thermoplastic holographic camera,” Proc. SPIE 0192, 184–189 (1979).
  9. J. C. Wyant, B. F. Oreb, and P. Hariharan, “Testing aspherics using two-wavelength holography: use of digital electronic techniques,” Appl. Opt. 23, 4020–4023 (1984).
    [CrossRef]
  10. P. D. Groot and S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. 30, 4026–4033 (1991).
    [CrossRef]
  11. A. A. Garcia, A. F. S. Granados, and R. A. Cornejo, “Wavefront determination using the Ronchi test with synthetic wavelength,” Proc. SPIE 8011, 8011D-1, (2011).
  12. A. R. Cornejo, “Ronchi test,” in Optical Shop Testing, D. Malacara, ed. (Wiley Interscience2007), pp. 317–360.
  13. J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 85–88 (1964).
    [CrossRef]
  14. R. Barakat, “General diffraction theory of optical aberration tests, from the point of view of spatial filtering,” J. Opt. Soc. Am. 59, 1432–1439 (1969).
    [CrossRef]
  15. W. S Meyers and H. P. Stahl, “Sensitivity of two-channel Ronchi test to grating misalignment,” Proc. SPIE 1994, 90–101 (1994).
    [CrossRef]
  16. A. Cornejo and D. Malacara, “Ronchi test of aspherical surfaces, analysis, and accuracy,” Appl. Opt. 9, 1897–1901 (1897).
  17. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2008).
  18. R. H. Katyl, “Moiré screens coded with pseudo-random sequences,” Appl. Opt. 11, 2278–2285 (1972).
    [CrossRef]
  19. L. Yaoltzin and Z. Yaoltzin, “Prueba de Ronchi con rejillas sub-estructuradas,” Master’s thesis (INAOE, 2005).
  20. G. M. Campos and A. F. Granados, “Interferometric Ronchi test by using sub-structured gratings,” Proc. SPIE 7390, 73901B (2009).
    [CrossRef]
  21. L. J. Salinas, A. F. Granados, R. A. Cornejo, E. Luna, J. J. E. Sánchez, and J. M. C. Hernández, “Ronchi test with variable-frequency rulings,” Opt. Eng. 48, 013604 (2009).
    [CrossRef]

2011

A. A. Garcia, A. F. S. Granados, and R. A. Cornejo, “Wavefront determination using the Ronchi test with synthetic wavelength,” Proc. SPIE 8011, 8011D-1, (2011).

2009

G. M. Campos and A. F. Granados, “Interferometric Ronchi test by using sub-structured gratings,” Proc. SPIE 7390, 73901B (2009).
[CrossRef]

L. J. Salinas, A. F. Granados, R. A. Cornejo, E. Luna, J. J. E. Sánchez, and J. M. C. Hernández, “Ronchi test with variable-frequency rulings,” Opt. Eng. 48, 013604 (2009).
[CrossRef]

1994

W. S Meyers and H. P. Stahl, “Sensitivity of two-channel Ronchi test to grating misalignment,” Proc. SPIE 1994, 90–101 (1994).
[CrossRef]

1991

1987

1984

1979

K. M. Leung, T. C. Lee, and G. E. Bernal, “Two-wavelength contouring with the automated thermoplastic holographic camera,” Proc. SPIE 0192, 184–189 (1979).

1974

1973

1972

1971

1969

1967

1964

J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 85–88 (1964).
[CrossRef]

1897

Barakat, R.

Bernal, G. E.

K. M. Leung, T. C. Lee, and G. E. Bernal, “Two-wavelength contouring with the automated thermoplastic holographic camera,” Proc. SPIE 0192, 184–189 (1979).

Campos, G. M.

G. M. Campos and A. F. Granados, “Interferometric Ronchi test by using sub-structured gratings,” Proc. SPIE 7390, 73901B (2009).
[CrossRef]

Cornejo, A.

Cornejo, A. R.

A. R. Cornejo, “Ronchi test,” in Optical Shop Testing, D. Malacara, ed. (Wiley Interscience2007), pp. 317–360.

Cornejo, R. A.

A. A. Garcia, A. F. S. Granados, and R. A. Cornejo, “Wavefront determination using the Ronchi test with synthetic wavelength,” Proc. SPIE 8011, 8011D-1, (2011).

L. J. Salinas, A. F. Granados, R. A. Cornejo, E. Luna, J. J. E. Sánchez, and J. M. C. Hernández, “Ronchi test with variable-frequency rulings,” Opt. Eng. 48, 013604 (2009).
[CrossRef]

Creath, K.

Garcia, A. A.

A. A. Garcia, A. F. S. Granados, and R. A. Cornejo, “Wavefront determination using the Ronchi test with synthetic wavelength,” Proc. SPIE 8011, 8011D-1, (2011).

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2008).

Granados, A. F.

G. M. Campos and A. F. Granados, “Interferometric Ronchi test by using sub-structured gratings,” Proc. SPIE 7390, 73901B (2009).
[CrossRef]

L. J. Salinas, A. F. Granados, R. A. Cornejo, E. Luna, J. J. E. Sánchez, and J. M. C. Hernández, “Ronchi test with variable-frequency rulings,” Opt. Eng. 48, 013604 (2009).
[CrossRef]

Granados, A. F. S.

A. A. Garcia, A. F. S. Granados, and R. A. Cornejo, “Wavefront determination using the Ronchi test with synthetic wavelength,” Proc. SPIE 8011, 8011D-1, (2011).

Groot, P. D.

Haines, K. A.

Hariharan, P.

Hernández, J. M. C.

L. J. Salinas, A. F. Granados, R. A. Cornejo, E. Luna, J. J. E. Sánchez, and J. M. C. Hernández, “Ronchi test with variable-frequency rulings,” Opt. Eng. 48, 013604 (2009).
[CrossRef]

Hildebrand, B. P.

Katyl, R. H.

Kishner, S.

Lee, T. C.

K. M. Leung, T. C. Lee, and G. E. Bernal, “Two-wavelength contouring with the automated thermoplastic holographic camera,” Proc. SPIE 0192, 184–189 (1979).

Leung, K. M.

K. M. Leung, T. C. Lee, and G. E. Bernal, “Two-wavelength contouring with the automated thermoplastic holographic camera,” Proc. SPIE 0192, 184–189 (1979).

Luna, E.

L. J. Salinas, A. F. Granados, R. A. Cornejo, E. Luna, J. J. E. Sánchez, and J. M. C. Hernández, “Ronchi test with variable-frequency rulings,” Opt. Eng. 48, 013604 (2009).
[CrossRef]

MacGovern, J. A

Malacara, D.

Meyers, W. S

W. S Meyers and H. P. Stahl, “Sensitivity of two-channel Ronchi test to grating misalignment,” Proc. SPIE 1994, 90–101 (1994).
[CrossRef]

Oreb, B. F.

Polhemus, C.

Rayces, J. L.

J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 85–88 (1964).
[CrossRef]

Ribbens, W. B.

Salinas, L. J.

L. J. Salinas, A. F. Granados, R. A. Cornejo, E. Luna, J. J. E. Sánchez, and J. M. C. Hernández, “Ronchi test with variable-frequency rulings,” Opt. Eng. 48, 013604 (2009).
[CrossRef]

Sánchez, J. J. E.

L. J. Salinas, A. F. Granados, R. A. Cornejo, E. Luna, J. J. E. Sánchez, and J. M. C. Hernández, “Ronchi test with variable-frequency rulings,” Opt. Eng. 48, 013604 (2009).
[CrossRef]

Stahl, H. P.

W. S Meyers and H. P. Stahl, “Sensitivity of two-channel Ronchi test to grating misalignment,” Proc. SPIE 1994, 90–101 (1994).
[CrossRef]

Varner, R. J.

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2008).

Wyant, J. C.

Yaoltzin, L.

L. Yaoltzin and Z. Yaoltzin, “Prueba de Ronchi con rejillas sub-estructuradas,” Master’s thesis (INAOE, 2005).

Yaoltzin, Z.

L. Yaoltzin and Z. Yaoltzin, “Prueba de Ronchi con rejillas sub-estructuradas,” Master’s thesis (INAOE, 2005).

Zelenka, S. J.

Appl. Opt.

J. Opt. Soc. Am.

Opt. Acta

J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 85–88 (1964).
[CrossRef]

Opt. Eng.

L. J. Salinas, A. F. Granados, R. A. Cornejo, E. Luna, J. J. E. Sánchez, and J. M. C. Hernández, “Ronchi test with variable-frequency rulings,” Opt. Eng. 48, 013604 (2009).
[CrossRef]

Proc. SPIE

G. M. Campos and A. F. Granados, “Interferometric Ronchi test by using sub-structured gratings,” Proc. SPIE 7390, 73901B (2009).
[CrossRef]

A. A. Garcia, A. F. S. Granados, and R. A. Cornejo, “Wavefront determination using the Ronchi test with synthetic wavelength,” Proc. SPIE 8011, 8011D-1, (2011).

W. S Meyers and H. P. Stahl, “Sensitivity of two-channel Ronchi test to grating misalignment,” Proc. SPIE 1994, 90–101 (1994).
[CrossRef]

K. M. Leung, T. C. Lee, and G. E. Bernal, “Two-wavelength contouring with the automated thermoplastic holographic camera,” Proc. SPIE 0192, 184–189 (1979).

Other

L. Yaoltzin and Z. Yaoltzin, “Prueba de Ronchi con rejillas sub-estructuradas,” Master’s thesis (INAOE, 2005).

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2008).

A. R. Cornejo, “Ronchi test,” in Optical Shop Testing, D. Malacara, ed. (Wiley Interscience2007), pp. 317–360.

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Figures (14)

Fig. 1.
Fig. 1.

Experimental arrangement of the Ronchi test.

Fig. 2.
Fig. 2.

Planes to describe the Ronchi test since the point of view of Fourier theory. A, Exit pupil of the surface under test. B, Frequency modulation plane. C, Image plane.

Fig. 3.
Fig. 3.

Fringe visibility modification with gamma-correction. (a) and (b) Profiles of Ronchigrams registered with λ1 and λ2, respectively, without the application of gamma-correction; (c), profile of the Ronchigram with equivalent wavelength generated with Ronchigrams of (a) and (b). (d) and (e) profiles of Ronchigrams registered with λ1 and λ2, respectively, applying the gamma-correction with γ=0.6; (f) profile of the Ronchigram with equivalent wavelength generated with Ronchigrams of (d) and (e).

Fig. 4.
Fig. 4.

Ronchigrams with equivalent wavelength modified with gamma-correction. (a) Ronchigram corresponding to the profile shown in Fig. 3(c); (b) Ronchigram corresponding to the profile shown in Fig. 3(f).

Fig. 5.
Fig. 5.

Improvement of the fringe visibility in Ronchigrams with equivalent wavelength applying distinct values of gamma-correction. (a) γ=0.8; (b) γ=0.2.

Fig. 6.
Fig. 6.

Behavior of the intensity distribution of Ronchigrams due to the application of distinct values of gamma-correction. (a) Without modification, γ=1.0; (b) γ=0.6; (c) γ=0.2.

Fig. 7.
Fig. 7.

Filtering process employed in this work. (a) Pattern with equivalent wavelength without filtering; (b), Fourier transform of the pattern in (a); (c), Gaussian filter; (d) filtering of frequencies; (e), filtered pattern with equivalent wavelength.

Fig. 8.
Fig. 8.

Experimental configuration of the Ronchi test employed in this work. (a) Schematic top view; (b), view from behind; (c) lateral view.

Fig. 9.
Fig. 9.

Spectral distribution of the (a) white LED; (b) color filters.

Fig. 10.
Fig. 10.

7 bit substructured rulings of the Katyl type: (a) positive and (b) negative.

Fig. 11.
Fig. 11.

Generation of a Ronchigram with equivalent wavelength for traditional Ronchi rulings. (a) Ronchigram with λ1; (b) Ronchigram with λ2; (c) Ronchigram with λeq.

Fig. 12.
Fig. 12.

Profiles of the central row pixel of Ronchigrams of Fig. 11.

Fig. 13.
Fig. 13.

Generation of a Ronchigram with equivalent wavelength and 7 bit substructured Ronchi rulings. (a) Ronchigram with λ1; (b) Ronchigram with λ2; (c) Ronchigram with λeq.

Fig. 14.
Fig. 14.

Profiles of the central pixel row of Ronchigrams of Fig. 13.

Equations (20)

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F0(x0,y0)=exp[i2πW(x0,y0)],
U(xr,yr)=F0(x0,y0)exp[i2πλr(xrx0+yry0)]dx0dy0.
G(x1,y1)=U(xr,yr)M(xr,yr)exp[i2πλr(xrx1+yry1)]dxrdyr.
M(xr,yr)=n=Bnexpi2πnpxr,
G(x1,y1)=n=BnF0(x1+λrnp,y1),
I(x,y)=I0+βcos[2πλOPD(x,y)],
OPD(x,y)=W(x,y)xΔx=α(x,y)Δx,
I(x,y)=I0+βcos[2πλqα(x,y)],
Δx=ΔxD/2=2λrpD,
λq=λΔx=pD2r,
d(λ)=λlp,
I1(x,y)=I01+β1cos[2πλq1α(x,y)],I2(x,y)=I02+β2cos[2πλq2α(x,y)].
I1(x,y)I2(x,y)={I01+β1cos[2πλq1α(x,y)]}{I02+β2cos[2πλq2α(x,y)]}.
12β1β2cos[2πα(x,y)(λq2+λq1λq1λq2)]+12β1β2cos[2πα(x,y)(λq2-λq1λq1λq2)].
λeqR=λ1λ2λ2λ1,
D0<min{f1=1λq1,f2=1λq2,f3=1λq+},
λq+=λq1λq2λq1+λq2.
If(x,y)=I01I02+12β1β2cos[2πλqRα(x,y)],
s=crγ,
H(u,v)=expD2(u,v)2σ2,

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