Abstract

The purposes of the paper are threefold: (1) to show the possibility to perform parallel phase-shifting Fizeau interferometry by using a quarter waveplate with high flatness as a reference, (2) to present a comparative study between the phase-shifting algorithm and the off-axis geometry in surface microtopography measurement, and (3) to show the advantages of using the proposed common path Fizeau interferometry over the quasi-common path Michelson interferometry in terms of accuracy in measurement. The compelling advantage of the proposed parallel phase-shifting Fizeau interferometric technique is the long-term stability that leads to measuring objects with a high degree of accuracy.

© 2012 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1980), pp. 459–490.
  2. D. G. Abdelsalam and D. Kim, “Two-wavelength in-line phase-shifting based on polarizing separation for accurate surface profiling,” Appl. Opt. 50, 6153–6161 (2011).
    [CrossRef]
  3. Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
    [CrossRef]
  4. D. G. Abdelsalam and D. Kim, “Single-shot, dual-wavelength digital holography based on polarizing separation,” Appl. Opt. 50, 3360–3368 (2011).
    [CrossRef]
  5. T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. 45, 4873–4877 (2006).
    [CrossRef]
  6. M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Proc. SPIE 5531, 304–314 (2004).
    [CrossRef]
  7. D. G. Abdelsalam, M. S. Shaalan, and M. M. Eloker, “Surface microtopography measurement of a standard flat surface by multiple-beam interference fringes at reflection,” Optic. Laser. Eng. 48, 543–547 (2010).
    [CrossRef]
  8. D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48, 643–649 (2010).
  9. P. Gao, B. Yao, I. Harder, J. Min, R. Guo, J. Zheng, and T. Ye, “Parallel two-step phase-shifting digital holograph microscopy based on a grating pair,” J. Opt. Soc. Am. A 28, 434–440 (2011).
    [CrossRef]
  10. U. Kumar, B. Bhaduri, M. Kothiyal, and M. Krishna, “Two wavelength micro interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
    [CrossRef]
  11. Q. Kemao, “A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 40, 1091–1098 (2008).
    [CrossRef]
  12. D. G. Abdelsalam, B. J. Baek, Y. J. Cho, and D. Kim, “Surface form measurement using single shot off-axis Fizeau interferometry,” J. Opt. Soc. Korea 14, 409–414 (2010).
    [CrossRef]
  13. P. Gao, B. Yao, J. Min, R. Guo, J. Zheng, T. Ye, I. Harder, V. Nercissian, and K. Mantel, “Parallel two-step phase-shifting point-diffraction interferometry for microscopy based on a pair of cube beamsplitters,” Opt. Express 19, 1930–1935 (2011).
    [CrossRef]

2011

2010

D. G. Abdelsalam, B. J. Baek, Y. J. Cho, and D. Kim, “Surface form measurement using single shot off-axis Fizeau interferometry,” J. Opt. Soc. Korea 14, 409–414 (2010).
[CrossRef]

D. G. Abdelsalam, M. S. Shaalan, and M. M. Eloker, “Surface microtopography measurement of a standard flat surface by multiple-beam interference fringes at reflection,” Optic. Laser. Eng. 48, 543–547 (2010).
[CrossRef]

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48, 643–649 (2010).

2009

U. Kumar, B. Bhaduri, M. Kothiyal, and M. Krishna, “Two wavelength micro interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[CrossRef]

2008

Q. Kemao, “A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 40, 1091–1098 (2008).
[CrossRef]

2006

2004

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Abdelsalam, D. G.

D. G. Abdelsalam and D. Kim, “Two-wavelength in-line phase-shifting based on polarizing separation for accurate surface profiling,” Appl. Opt. 50, 6153–6161 (2011).
[CrossRef]

D. G. Abdelsalam and D. Kim, “Single-shot, dual-wavelength digital holography based on polarizing separation,” Appl. Opt. 50, 3360–3368 (2011).
[CrossRef]

D. G. Abdelsalam, M. S. Shaalan, and M. M. Eloker, “Surface microtopography measurement of a standard flat surface by multiple-beam interference fringes at reflection,” Optic. Laser. Eng. 48, 543–547 (2010).
[CrossRef]

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48, 643–649 (2010).

D. G. Abdelsalam, B. J. Baek, Y. J. Cho, and D. Kim, “Surface form measurement using single shot off-axis Fizeau interferometry,” J. Opt. Soc. Korea 14, 409–414 (2010).
[CrossRef]

Awatsuji, Y.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Baek, B. J.

Bhaduri, B.

U. Kumar, B. Bhaduri, M. Kothiyal, and M. Krishna, “Two wavelength micro interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1980), pp. 459–490.

Brock, N.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Cho, Y. J.

Eloker, M. M.

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48, 643–649 (2010).

D. G. Abdelsalam, M. S. Shaalan, and M. M. Eloker, “Surface microtopography measurement of a standard flat surface by multiple-beam interference fringes at reflection,” Optic. Laser. Eng. 48, 543–547 (2010).
[CrossRef]

Gao, P.

Guo, R.

Harder, I.

Hayes, J.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Kemao, Q.

Q. Kemao, “A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 40, 1091–1098 (2008).
[CrossRef]

Kim, D.

Kothiyal, M.

U. Kumar, B. Bhaduri, M. Kothiyal, and M. Krishna, “Two wavelength micro interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[CrossRef]

Krishna, M.

U. Kumar, B. Bhaduri, M. Kothiyal, and M. Krishna, “Two wavelength micro interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[CrossRef]

Kubota, T.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Kumar, U.

U. Kumar, B. Bhaduri, M. Kothiyal, and M. Krishna, “Two wavelength micro interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[CrossRef]

Mantel, K.

Millerd, J.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Min, J.

Murata, S.

Nercissian, V.

Nitanai, E.

Nomura, T.

North-Morris, M.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Novak, M.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Numata, T.

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Shaalan, M. S.

D. G. Abdelsalam, M. S. Shaalan, and M. M. Eloker, “Surface microtopography measurement of a standard flat surface by multiple-beam interference fringes at reflection,” Optic. Laser. Eng. 48, 543–547 (2010).
[CrossRef]

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48, 643–649 (2010).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1980), pp. 459–490.

Wyant, J.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Yao, B.

Ye, T.

Zheng, J.

Appl. Opt.

Appl. Phys. Lett.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Korea

Opt. Express

Opt. Laser Technol.

Q. Kemao, “A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 40, 1091–1098 (2008).
[CrossRef]

Opt. Lasers Eng.

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48, 643–649 (2010).

U. Kumar, B. Bhaduri, M. Kothiyal, and M. Krishna, “Two wavelength micro interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[CrossRef]

Optic. Laser. Eng.

D. G. Abdelsalam, M. S. Shaalan, and M. M. Eloker, “Surface microtopography measurement of a standard flat surface by multiple-beam interference fringes at reflection,” Optic. Laser. Eng. 48, 543–547 (2010).
[CrossRef]

Proc. SPIE

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1980), pp. 459–490.

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Figures (8)

Fig. 1.
Fig. 1.

Configuration for single-shot parallel phase shifting. (a) quasi-common path Michelson type; (b) common path Fizeau type. BE, beam expander; L1L2, achromatic lenses with focal lengths f1=300mm, f2=f150mm.

Fig. 2.
Fig. 2.

Experimental results of the single-shot, four-step phase-shifting interferometry with on-axis Fizeau interferometer; (a) intensity images of a spherical object with phase shift of 0, π/2, π, and 3π/2 between the object and reference waves; (b) wrapped phase map resulting from the four-frames of (a); (c) 3D unwrapped phase map with 250×250 pixels.

Fig. 3.
Fig. 3.

2D surface phase along 240 pixels in the x-direction of Fig. 2(c).

Fig. 4.
Fig. 4.

Experimental results of the single-shot, four-step phase-shifting interferometry using on-axis Fizeau interferometer; (a) intensity images of a step object with phase shift of 0, π/2, π, and 3π/2 between the object and reference waves; (b) unwrapped phase map resulting from the four-frames of (a).

Fig. 5.
Fig. 5.

2D surface phase; black line is the proposed method along the x-direction of Fig. 4(b), and the red line is measured with WSI.

Fig. 6.
Fig. 6.

Experimental results of the single-shot, off-axis geometry using on-axis Fizeau interferometer; (a) off-axis interferogram; (b) Fourier transformed spatial frequency domain data; (c) 3D unwrapped phase map (250×250 pixels).

Fig. 7.
Fig. 7.

2D surface phase along 240 pixels in the x-direction of Fig. 6(c).

Fig. 8.
Fig. 8.

Stability test for the proposed common path Fizeau type against the quasi-common path Michelson type.

Equations (4)

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Ij(x,y)=IO+IR+2IOIRcos(ϕ+(j1)π2),
ϕ=tan1((I4I2)(I1I3)).
I(m,n)=Ψ=|O|2+|R|2+R*O+RO*,
RD(m,n)=ARexpi(2π/λ)(kxmΔx+kynΔy),

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