Abstract

We describe a configuration that can be used for two-wavelength phase-shifting in-line interferometry based on polarizing separation. The experiment is conducted on a sample with a step height of 1.34μm nominally. In this paper, five- and seven-phase step algorithms have been compared for their effectiveness in reducing the noise in the phase maps. The noise is further reduced by the application of the flat fielding method. The recorded interferograms are processed using seven-phase step algorithm to obtain the phase map for each wavelength separately. The independent phase maps are subtracted and a phase map for the beat-wavelength is obtained and converted to height map. The results extracted from the seven-phase step algorithm have been compared with the results extracted from the single shot off-axis geometry and the results are in agreement.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1980), pp. 459–490.
  2. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15, 7231–7242 (2007).
    [CrossRef] [PubMed]
  3. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1988), pp. 349–393.
  4. U. P. Kumar, B. Bhaduri, M. P. Kothiyal, and N. K. Mohan, “Two wavelength micro-interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
    [CrossRef]
  5. K. Creath, Y. Cheng, and J. C. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Opt. Acta 32, 1455–1464 (1985).
    [CrossRef]
  6. Y. Y. Cheng and J. C. Wyant, “Two wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [CrossRef] [PubMed]
  7. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [CrossRef] [PubMed]
  8. J. Schmit and P. Hariharan, “Two-wavelength interferometry profilometry with a phase-step error-compensating algorithm,” Opt. Eng. 45, 115602–1–115603–3 (2006).
    [CrossRef]
  9. D. Kim and S. Kim, “Direct spectral phase calculation for dispersive interferometric thickness profilometry,” Opt. Express 12, 5117–5124 (2004).
    [CrossRef] [PubMed]
  10. S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13, 1382–1387 (2002).
    [CrossRef]
  11. Y. Y. Cheng and J. C. Wyant, “Multiple-wavelength phase-shifting interferometry,” Appl. Opt. 24, 804–807 (1985).
    [CrossRef] [PubMed]
  12. D. Kim, J. W. You, and S. Kim, “White light on-axis digital holographic microscopy based on spectral phase shifting,” Opt. Express 14, 229–234 (2006).
    [CrossRef] [PubMed]
  13. J. You, S. Kim, and D. Kim, “High speed volumetric thickness profile measurement based on full-field wavelength scanning interferometer,” Opt. Express 16, 21022–21031 (2008).
    [CrossRef] [PubMed]
  14. P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
    [CrossRef]
  15. H. Fan, I. Reading, and Z. P. Fang, “Research on tilted coherent plane white-light Interferometry for wafer bump 3D inspection,” SIM Tech Tech Rep 7, 59–63 (2006).
  16. P. de Groot and L. Deck, “Three-dimensional imaging by sub-Nyquist sampling of white-light interferograms,” Opt. Lett. 18, 1462–1464 (1993).
    [CrossRef] [PubMed]
  17. P. de Groot, “Surface profiling by frequency-domain analysis of white light Interferograms,” Proc. SPIE 2248, 101–104 (1994).
    [CrossRef]
  18. D. G. Abdelsalam, R. Magnusson, and D. Kim, “Single-shot dual wavelength digital holography based on polarizing separation,” Appl. Opt. 50, 3360–3368 (2011).
    [CrossRef] [PubMed]
  19. T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27–37 (2002).
    [CrossRef] [PubMed]
  20. K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, W.R.Robinson and G.T.Reid, eds. (Institute of Physics Publishing, 1993), Chap. 4.
  21. S. B. Howell, Handbook of CCD Astronomy (Cambridge, 2006).
  22. 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,” Opt. Lasers Eng. 48, 543–547 (2010).
    [CrossRef]
  23. 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).
    [CrossRef]
  24. D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor and Francis Group, 2005), pp. 384–385.
  25. F. Pan, W. Xiao, S. Liu, F. J. Wang, L. Rong, and R. Li, “Coherent noise reduction in digital holographic phase contrast microscopy by slightly shifting object,” Opt. Express 19, 3863–3869 (2011).
    [CrossRef]
  26. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
    [CrossRef]
  27. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [CrossRef]
  28. H. Lee, S. Kim, and D. Kim, “Two step on-axis digital holography using dual-channel Mach-Zehnder interferometer and matched filter algorithm,” J. Opt. Soc. Korea 14, 363–367(2010).
    [CrossRef]
  29. D. G. Abdelsalam, B. J. Baek, Y. J. Cho, and D. Kim, “Surface form measurement using single-shot off-axis Fizeau interferometer,” J. Opt. Soc. Korea 14, 409–414 (2010).
    [CrossRef]
  30. Y. Cheng and J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,” Appl. Opt. 24, 3049–3052 (1985).
    [CrossRef] [PubMed]
  31. R. A. Nicolaus, “Precise method to determining systematic errors in phase-shifting interferometry on Fizeau interference,” Appl. Opt. 32, 6380–6386 (1993).
    [CrossRef] [PubMed]
  32. E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation: application in digital holographic microscopy,” Opt. Commun. 182, 59–69 (2000).
    [CrossRef]

2011

F. Pan, W. Xiao, S. Liu, F. J. Wang, L. Rong, and R. Li, “Coherent noise reduction in digital holographic phase contrast microscopy by slightly shifting object,” Opt. Express 19, 3863–3869 (2011).
[CrossRef]

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

2010

H. Lee, S. Kim, and D. Kim, “Two step on-axis digital holography using dual-channel Mach-Zehnder interferometer and matched filter algorithm,” J. Opt. Soc. Korea 14, 363–367(2010).
[CrossRef]

D. G. Abdelsalam, B. J. Baek, Y. J. Cho, and D. Kim, “Surface form measurement using single-shot off-axis Fizeau interferometer,” 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,” Opt. Lasers 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).
[CrossRef]

2009

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

2008

2007

2006

D. Kim, J. W. You, and S. Kim, “White light on-axis digital holographic microscopy based on spectral phase shifting,” Opt. Express 14, 229–234 (2006).
[CrossRef] [PubMed]

J. Schmit and P. Hariharan, “Two-wavelength interferometry profilometry with a phase-step error-compensating algorithm,” Opt. Eng. 45, 115602–1–115603–3 (2006).
[CrossRef]

H. Fan, I. Reading, and Z. P. Fang, “Research on tilted coherent plane white-light Interferometry for wafer bump 3D inspection,” SIM Tech Tech Rep 7, 59–63 (2006).

2004

2002

T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27–37 (2002).
[CrossRef] [PubMed]

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13, 1382–1387 (2002).
[CrossRef]

2000

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation: application in digital holographic microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
[CrossRef]

1999

1995

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

1994

P. de Groot, “Surface profiling by frequency-domain analysis of white light Interferograms,” Proc. SPIE 2248, 101–104 (1994).
[CrossRef]

1993

1987

1985

1984

Abdelsalam, D. G.

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

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,” Opt. Lasers Eng. 48, 543–547 (2010).
[CrossRef]

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

Baek, B. J.

Beghuin, D.

Bevilacqua, F.

Bhaduri, B.

U. P. Kumar, B. Bhaduri, M. P. Kothiyal, and N. K. Mohan, “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.

Charrière, F.

Cheng, Y.

K. Creath, Y. Cheng, and J. C. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Opt. Acta 32, 1455–1464 (1985).
[CrossRef]

Y. Cheng and J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,” Appl. Opt. 24, 3049–3052 (1985).
[CrossRef] [PubMed]

Cheng, Y. Y.

Cho, Y. J.

Colomb, T.

Creath, K.

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
[CrossRef] [PubMed]

K. Creath, Y. Cheng, and J. C. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Opt. Acta 32, 1455–1464 (1985).
[CrossRef]

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, W.R.Robinson and G.T.Reid, eds. (Institute of Physics Publishing, 1993), Chap. 4.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1988), pp. 349–393.

Cuche, E.

Dahlgren, P.

de Groot, P.

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

P. de Groot, “Surface profiling by frequency-domain analysis of white light Interferograms,” Proc. SPIE 2248, 101–104 (1994).
[CrossRef]

P. de Groot and L. Deck, “Three-dimensional imaging by sub-Nyquist sampling of white-light interferograms,” Opt. Lett. 18, 1462–1464 (1993).
[CrossRef] [PubMed]

Deck, L.

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

P. de Groot and L. Deck, “Three-dimensional imaging by sub-Nyquist sampling of white-light interferograms,” Opt. Lett. 18, 1462–1464 (1993).
[CrossRef] [PubMed]

Depeursinge, C.

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).
[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,” Opt. Lasers Eng. 48, 543–547 (2010).
[CrossRef]

Emery, Y.

Fan, H.

H. Fan, I. Reading, and Z. P. Fang, “Research on tilted coherent plane white-light Interferometry for wafer bump 3D inspection,” SIM Tech Tech Rep 7, 59–63 (2006).

Fang, Z. P.

H. Fan, I. Reading, and Z. P. Fang, “Research on tilted coherent plane white-light Interferometry for wafer bump 3D inspection,” SIM Tech Tech Rep 7, 59–63 (2006).

Hariharan, P.

J. Schmit and P. Hariharan, “Two-wavelength interferometry profilometry with a phase-step error-compensating algorithm,” Opt. Eng. 45, 115602–1–115603–3 (2006).
[CrossRef]

Howell, S. B.

S. B. Howell, Handbook of CCD Astronomy (Cambridge, 2006).

Kim, D.

Kim, S.

Kothiyal, M. P.

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

Kühn, J.

Kumar, U. P.

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

Lee, C. C.

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13, 1382–1387 (2002).
[CrossRef]

Lee, H.

Li, R.

F. Pan, W. Xiao, S. Liu, F. J. Wang, L. Rong, and R. Li, “Coherent noise reduction in digital holographic phase contrast microscopy by slightly shifting object,” Opt. Express 19, 3863–3869 (2011).
[CrossRef]

Liu, S.

F. Pan, W. Xiao, S. Liu, F. J. Wang, L. Rong, and R. Li, “Coherent noise reduction in digital holographic phase contrast microscopy by slightly shifting object,” Opt. Express 19, 3863–3869 (2011).
[CrossRef]

Lu, S. H.

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13, 1382–1387 (2002).
[CrossRef]

Magnusson, R.

Malacara, D.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor and Francis Group, 2005), pp. 384–385.

Malacara, Z.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor and Francis Group, 2005), pp. 384–385.

Marquet, P.

Mohan, N. K.

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

Montfort, F.

Nicolaus, R. A.

Pan, F.

F. Pan, W. Xiao, S. Liu, F. J. Wang, L. Rong, and R. Li, “Coherent noise reduction in digital holographic phase contrast microscopy by slightly shifting object,” Opt. Express 19, 3863–3869 (2011).
[CrossRef]

Reading, I.

H. Fan, I. Reading, and Z. P. Fang, “Research on tilted coherent plane white-light Interferometry for wafer bump 3D inspection,” SIM Tech Tech Rep 7, 59–63 (2006).

Rong, L.

F. Pan, W. Xiao, S. Liu, F. J. Wang, L. Rong, and R. Li, “Coherent noise reduction in digital holographic phase contrast microscopy by slightly shifting object,” Opt. Express 19, 3863–3869 (2011).
[CrossRef]

Schmit, J.

J. Schmit and P. Hariharan, “Two-wavelength interferometry profilometry with a phase-step error-compensating algorithm,” Opt. Eng. 45, 115602–1–115603–3 (2006).
[CrossRef]

Servin, M.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor and Francis Group, 2005), pp. 384–385.

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,” Opt. Lasers 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).
[CrossRef]

Wang, F. J.

F. Pan, W. Xiao, S. Liu, F. J. Wang, L. Rong, and R. Li, “Coherent noise reduction in digital holographic phase contrast microscopy by slightly shifting object,” Opt. Express 19, 3863–3869 (2011).
[CrossRef]

Wolf, E.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1988), pp. 349–393.

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

Wyant, J. C.

Xiao, W.

F. Pan, W. Xiao, S. Liu, F. J. Wang, L. Rong, and R. Li, “Coherent noise reduction in digital holographic phase contrast microscopy by slightly shifting object,” Opt. Express 19, 3863–3869 (2011).
[CrossRef]

You, J.

You, J. W.

Appl. Opt.

J. Mod. Opt.

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

J. Opt. Soc. Korea

Meas. Sci. Technol.

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13, 1382–1387 (2002).
[CrossRef]

Opt. Acta

K. Creath, Y. Cheng, and J. C. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Opt. Acta 32, 1455–1464 (1985).
[CrossRef]

Opt. Commun.

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation: application in digital holographic microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

Opt. Eng.

J. Schmit and P. Hariharan, “Two-wavelength interferometry profilometry with a phase-step error-compensating algorithm,” Opt. Eng. 45, 115602–1–115603–3 (2006).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

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

Opt. Lett.

Proc. SPIE

P. de Groot, “Surface profiling by frequency-domain analysis of white light Interferograms,” Proc. SPIE 2248, 101–104 (1994).
[CrossRef]

SIM Tech Tech Rep

H. Fan, I. Reading, and Z. P. Fang, “Research on tilted coherent plane white-light Interferometry for wafer bump 3D inspection,” SIM Tech Tech Rep 7, 59–63 (2006).

Other

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1988), pp. 349–393.

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

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, W.R.Robinson and G.T.Reid, eds. (Institute of Physics Publishing, 1993), Chap. 4.

S. B. Howell, Handbook of CCD Astronomy (Cambridge, 2006).

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor and Francis Group, 2005), pp. 384–385.

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 (11)

Fig. 1
Fig. 1

Image correction with flat fielding (a) imaging interferogram at 635 nm before correction with the flat fielding method, (b) after correction with flat fielding, (c) imaging interferogram at 675 nm before correction with the flat fielding method, and (d) after correction with flat fielding.

Fig. 2
Fig. 2

Uneven illumination that produces darkness at the edges of the image (a) inhomogenity of the laser beam, and (b) shadow detection of the dust particles hanging at the CCD camera aperture.

Fig. 3
Fig. 3

Schematic diagram of the in-line phase-shifting dual-wavelength optical setup.

Fig. 4
Fig. 4

Interferograms of step height measurement of the sample (a) at 635 nm , (b) at 675 nm , (c) wrapped phase map of (a), and (d) wrapped phase map of (b).

Fig. 5
Fig. 5

In-line interferograms captured by the CCD camera at (a–g) λ 1 = 635 nm with 0.0, 0.5 π , 1.0 π , 1.5 π , 2.0 π , 2.5 π , and 3.0 π radian phase shifts, respectively, and (h–n) λ 2 = 675 nm with 0.0, 0.5 π , 1.0 π , 1.5 π , 2.0 π , 2.5 π , and 3.0 π radian phase shifts, respectively.

Fig. 6
Fig. 6

Wrapped phase maps and the corresponding 2D phase profiles using five- and seven-phase step algorithms for λ 1 = 635 nm (a) phase map measured with five-step algorithm, (b) phase map measured with seven-step algorithm, (c) 2D phase profile along the selected line of (a), and (d) 2D phase profile along the selected line of (b).

Fig. 7
Fig. 7

Surface height measurement of the sample at the beat wavelength (a) height map before correction with flat fielding, (b) height map after correction with flat fielding, (c) 2D surface profile along the selected line of (a), and (d) 2D surface profile along the selected line of (b).

Fig. 8
Fig. 8

2D surface profile of Fig. 7d after applying the rms method for the distributed height.

Fig. 9
Fig. 9

Reconstruction steps of the spatial filtering based dual wavelength off-axis interferometry (imaging scheme) (a) off-axis interferogram, (b) Fourier transformed spatial frequency domain data, (c) object phase map on the synthetic beat-wavelength, and (d) 2D surface profile along the selected line of (c) after applying the rms for the distributed height.

Fig. 10
Fig. 10

Flowchart of the algorithm that is used to analyze the off-axis interferogram containing both wavelengths.

Fig. 11
Fig. 11

2D surface profile of Figs. 8, 9d after inverting up the profile of Fig. 8 to fit with Fig. 9d.

Equations (8)

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

I C = [ M ( I R I B ) ] / ( I F I B ) ,
I j + 1 ( x , y ) = I O + I R + 2 I O I R cos ( ϕ i + j π / 2 ) ,
ϕ i 5 = tan 1 ( 2 ( I 2 I 4 ) I 1 + 2 I 3 I 5 )
ϕ i 7 = tan 1 ( 4 I 2 8 I 4 + 4 I 6 I 1 + 7 I 3 7 I 5 + I 7 ) .
Φ = ϕ 1 ϕ 2 ,
Λ = λ 1 λ 2 λ 2 λ 1 .
h = Φ 4 π Λ .
h rms = [ h h ¯ ] 2 / ( N 1 ) ,

Metrics