Abstract

This contribution introduces a novel image recording approach for phase retrieval in a RGB-interferometer setup with pulsed LED illumination and an oscillating reference mirror. The effective acquisition time of the interference images is below 100 μs with a repetition rate of 10 frames per second. The pulsed illumination is synchronized with the exposure gap of a Bayer-Pattern CMOS RGB camera to enable the recording of two π/2 phase shifted images with a short delay compared to the camera exposure time. The proposed quadrature method enables surface phase retrieval with a standard deviation of ≈ [3 nm, · · ·, 5 nm], depending on phase noise and actuator precision. The applicability of the reconstructed phase data to unambiguity range extension algorithms based on the exact fraction method is considered. Experimental results demonstrate the feasibility of the setup to measure the topography of samples in motion or oscillating by mechanical vibrations.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. C. L. Koliopoulos, “Simultaneous phase-shift interferometer,” Proc. SPIE 1531, 119–128 (1992).
  2. S. Ma, C. Quan, R. Zhu, C. J. Tay, and L. Chen, “Surface profile measurement in white-light scanning interferometry using a three-chip color ccd,” Appl. Opt. 50, 2246–2254 (2011).
    [Crossref] [PubMed]
  3. J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 55310 (2004).
  4. A. Pförtner and J. Schwider, “Red-green-blue interferometer for the metrology of discontinuous structures,” Appl. Opt. 42, 667–673 (2003).
    [Crossref] [PubMed]
  5. S. Tereschenko, P. Lehmann, L. Zellmer, and A. Brueckner-Foit, “Passive vibration compensation in scanning white-light interferometry,” Appl. Opt. 55, 6172–6182 (2016).
    [Crossref] [PubMed]
  6. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [Crossref]
  7. K. Kitagawa, “Multi-wavelength single-shot interferometry,” in 2009 International Symposium on Optomechatronic Technologies, (2009), pp. 34–39.
    [Crossref]
  8. K. Kitagawa, “Fast surface profiling by multi-wavelength single-shot interferometry,” Int. J. Optomechatronics 4, 136–156 (2010).
    [Crossref]
  9. V. Srivastava, M. Inam, R. Kumar, and D. S. Mehta, “Single shot white light interference microscopy for 3d surface profilometry using single chip color camera,” J. Opt. Soc. Korea 20, 784–793 (2016).
    [Crossref]
  10. P. J. de Groot, “Extending the unambiguous range of two-color interferometers,” Appl. Opt. 33, 5948–5953 (1994).
    [Crossref] [PubMed]
  11. M. Schake and P. Lehmann, “Anwendungsorientiertes verfahren zur eindeutigkeitsbereichserweiterung eines fasergekoppelten zweiwellenlaengen-interferometers,” Tech. Messen 83, 192–200 (2016).
  12. K. Kitagawa, “Multiwavelength single-shot interferometry without carrier fringe introduction,” Proc. SPIE 8000, 80001 (2011).
  13. K. Kitagawa, “Single-shot surface profiling by multiwavelength interferometry without carrier fringe introduction,” J. Electron. Imaging 21, 021107 (2012).
    [Crossref]
  14. M. Schake and P. Lehmann, “Perturbation resistant rgb-interferometry with pulsed led illumination,” Proc. SPIE 10678, 1067805 (2018).
  15. A. Safrani and I. Abdulhalim, “High-speed 3d imaging using two-wavelength parallel-phase-shift interferometry,” Opt. Lett. 40, 4651–4654 (2015).
    [Crossref] [PubMed]
  16. M. Ney, A. Safrani, and I. Abdulhalim, “Three wavelengths parallel phase-shift interferometry for real-time focus tracking and vibration measurement,” Opt. Lett. 42, 719–722 (2017).
    [Crossref] [PubMed]
  17. I. Abdulhalim, M. Ney, A. Aizen, A. Nazarov, and A. Safrani, “Parallel phase shift microscopy, vibrometry and focus tracking systems (conference presentation),” Proc. SPIE 10678, 106780P (2018).
  18. H. Muhamedsalih, S. Al-Bashir, F. Gao, and X. Jiang, “Single-shot rgb polarising interferometer,” Proc. SPIE 10749, 107496 (2018).
  19. X. Tian, X. Tu, J. Zhang, O. Spires, N. Brock, S. Pau, and R. Liang, “Snapshot multi-wavelength interference microscope,” Opt. Express 26, 18279–18291 (2018).
    [Crossref] [PubMed]
  20. P. Zhu and K. Wang, “Single-shot two-dimensional surface measurement based on spectrally resolved white-light interferometry,” Appl. Opt. 51, 4971–4975 (2012).
    [Crossref] [PubMed]
  21. A. Butola, A. Ahmad, V. Dubey, V. Singh, T. Joshi, P. Senthilkumaran, and D. S. Mehta, “Quantitative phase imaging using spectrally resolved white light interferometry,” Proc. SPIE 10414, 104144 (2017).
  22. P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-d surface contouring,” Opt. Eng. 38, 38 (1999).
    [Crossref]
  23. M. Padilla, M. Servin, and G. Garnica, “Fourier analysis of rgb fringe-projection profilometry and robust phase-demodulation methods against crosstalk distortion,” Opt. Express 24, 15417–15428 (2016).
    [Crossref] [PubMed]
  24. Z. Zhang, C. E. Towers, and D. P. Towers, “Time efficient color fringe projection system for 3d shape and color using optimum 3-frequency selection,” Opt. Express 14, 6444–6455 (2006).
    [Crossref] [PubMed]
  25. M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).
    [Crossref]
  26. M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path,” Appl. Opt. 41, 7437–7444 (2002).
    [Crossref] [PubMed]
  27. M. Schulz and P. Lehmann, “Measurement of distance changes using a fibre-coupled common-path interferometer with mechanical path length modulation,” Meas. Sci. Technol. 24, 065202 (2013).
    [Crossref]
  28. HALLE Präzisions-Kalibriernormale GmbH, “Depth-setting standards with planar base grooves,” (2009).
  29. SiMETRICS GmbH, “Resolution standard type rs-m,” (2009).

2018 (4)

M. Schake and P. Lehmann, “Perturbation resistant rgb-interferometry with pulsed led illumination,” Proc. SPIE 10678, 1067805 (2018).

I. Abdulhalim, M. Ney, A. Aizen, A. Nazarov, and A. Safrani, “Parallel phase shift microscopy, vibrometry and focus tracking systems (conference presentation),” Proc. SPIE 10678, 106780P (2018).

H. Muhamedsalih, S. Al-Bashir, F. Gao, and X. Jiang, “Single-shot rgb polarising interferometer,” Proc. SPIE 10749, 107496 (2018).

X. Tian, X. Tu, J. Zhang, O. Spires, N. Brock, S. Pau, and R. Liang, “Snapshot multi-wavelength interference microscope,” Opt. Express 26, 18279–18291 (2018).
[Crossref] [PubMed]

2017 (2)

M. Ney, A. Safrani, and I. Abdulhalim, “Three wavelengths parallel phase-shift interferometry for real-time focus tracking and vibration measurement,” Opt. Lett. 42, 719–722 (2017).
[Crossref] [PubMed]

A. Butola, A. Ahmad, V. Dubey, V. Singh, T. Joshi, P. Senthilkumaran, and D. S. Mehta, “Quantitative phase imaging using spectrally resolved white light interferometry,” Proc. SPIE 10414, 104144 (2017).

2016 (4)

2015 (1)

2013 (1)

M. Schulz and P. Lehmann, “Measurement of distance changes using a fibre-coupled common-path interferometer with mechanical path length modulation,” Meas. Sci. Technol. 24, 065202 (2013).
[Crossref]

2012 (2)

K. Kitagawa, “Single-shot surface profiling by multiwavelength interferometry without carrier fringe introduction,” J. Electron. Imaging 21, 021107 (2012).
[Crossref]

P. Zhu and K. Wang, “Single-shot two-dimensional surface measurement based on spectrally resolved white-light interferometry,” Appl. Opt. 51, 4971–4975 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

K. Kitagawa, “Fast surface profiling by multi-wavelength single-shot interferometry,” Int. J. Optomechatronics 4, 136–156 (2010).
[Crossref]

2006 (1)

2004 (1)

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 55310 (2004).

2003 (1)

2002 (1)

1999 (1)

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-d surface contouring,” Opt. Eng. 38, 38 (1999).
[Crossref]

1994 (1)

1992 (1)

C. L. Koliopoulos, “Simultaneous phase-shift interferometer,” Proc. SPIE 1531, 119–128 (1992).

1982 (1)

Abdulhalim, I.

Ahmad, A.

A. Butola, A. Ahmad, V. Dubey, V. Singh, T. Joshi, P. Senthilkumaran, and D. S. Mehta, “Quantitative phase imaging using spectrally resolved white light interferometry,” Proc. SPIE 10414, 104144 (2017).

Aizen, A.

I. Abdulhalim, M. Ney, A. Aizen, A. Nazarov, and A. Safrani, “Parallel phase shift microscopy, vibrometry and focus tracking systems (conference presentation),” Proc. SPIE 10678, 106780P (2018).

Al-Bashir, S.

H. Muhamedsalih, S. Al-Bashir, F. Gao, and X. Jiang, “Single-shot rgb polarising interferometer,” Proc. SPIE 10749, 107496 (2018).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).
[Crossref]

Brock, N.

Brock, N. J.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 55310 (2004).

Brueckner-Foit, A.

Burton, D. R.

Butola, A.

A. Butola, A. Ahmad, V. Dubey, V. Singh, T. Joshi, P. Senthilkumaran, and D. S. Mehta, “Quantitative phase imaging using spectrally resolved white light interferometry,” Proc. SPIE 10414, 104144 (2017).

Chen, L.

Chiang, F.-P.

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-d surface contouring,” Opt. Eng. 38, 38 (1999).
[Crossref]

de Groot, P. J.

Dubey, V.

A. Butola, A. Ahmad, V. Dubey, V. Singh, T. Joshi, P. Senthilkumaran, and D. S. Mehta, “Quantitative phase imaging using spectrally resolved white light interferometry,” Proc. SPIE 10414, 104144 (2017).

Gao, F.

H. Muhamedsalih, S. Al-Bashir, F. Gao, and X. Jiang, “Single-shot rgb polarising interferometer,” Proc. SPIE 10749, 107496 (2018).

Garnica, G.

Gdeisat, M. A.

Hayes, J. B.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 55310 (2004).

Herráez, M. A.

Hu, Q.

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-d surface contouring,” Opt. Eng. 38, 38 (1999).
[Crossref]

Huang, P. S.

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-d surface contouring,” Opt. Eng. 38, 38 (1999).
[Crossref]

Ina, H.

Inam, M.

Jiang, X.

H. Muhamedsalih, S. Al-Bashir, F. Gao, and X. Jiang, “Single-shot rgb polarising interferometer,” Proc. SPIE 10749, 107496 (2018).

Jin, F.

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-d surface contouring,” Opt. Eng. 38, 38 (1999).
[Crossref]

Joshi, T.

A. Butola, A. Ahmad, V. Dubey, V. Singh, T. Joshi, P. Senthilkumaran, and D. S. Mehta, “Quantitative phase imaging using spectrally resolved white light interferometry,” Proc. SPIE 10414, 104144 (2017).

Kitagawa, K.

K. Kitagawa, “Single-shot surface profiling by multiwavelength interferometry without carrier fringe introduction,” J. Electron. Imaging 21, 021107 (2012).
[Crossref]

K. Kitagawa, “Multiwavelength single-shot interferometry without carrier fringe introduction,” Proc. SPIE 8000, 80001 (2011).

K. Kitagawa, “Fast surface profiling by multi-wavelength single-shot interferometry,” Int. J. Optomechatronics 4, 136–156 (2010).
[Crossref]

K. Kitagawa, “Multi-wavelength single-shot interferometry,” in 2009 International Symposium on Optomechatronic Technologies, (2009), pp. 34–39.
[Crossref]

Kobayashi, S.

Koliopoulos, C. L.

C. L. Koliopoulos, “Simultaneous phase-shift interferometer,” Proc. SPIE 1531, 119–128 (1992).

Kumar, R.

Lalor, M. J.

Lehmann, P.

M. Schake and P. Lehmann, “Perturbation resistant rgb-interferometry with pulsed led illumination,” Proc. SPIE 10678, 1067805 (2018).

M. Schake and P. Lehmann, “Anwendungsorientiertes verfahren zur eindeutigkeitsbereichserweiterung eines fasergekoppelten zweiwellenlaengen-interferometers,” Tech. Messen 83, 192–200 (2016).

S. Tereschenko, P. Lehmann, L. Zellmer, and A. Brueckner-Foit, “Passive vibration compensation in scanning white-light interferometry,” Appl. Opt. 55, 6172–6182 (2016).
[Crossref] [PubMed]

M. Schulz and P. Lehmann, “Measurement of distance changes using a fibre-coupled common-path interferometer with mechanical path length modulation,” Meas. Sci. Technol. 24, 065202 (2013).
[Crossref]

Liang, R.

Ma, S.

Mehta, D. S.

A. Butola, A. Ahmad, V. Dubey, V. Singh, T. Joshi, P. Senthilkumaran, and D. S. Mehta, “Quantitative phase imaging using spectrally resolved white light interferometry,” Proc. SPIE 10414, 104144 (2017).

V. Srivastava, M. Inam, R. Kumar, and D. S. Mehta, “Single shot white light interference microscopy for 3d surface profilometry using single chip color camera,” J. Opt. Soc. Korea 20, 784–793 (2016).
[Crossref]

Millerd, J. E.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 55310 (2004).

Muhamedsalih, H.

H. Muhamedsalih, S. Al-Bashir, F. Gao, and X. Jiang, “Single-shot rgb polarising interferometer,” Proc. SPIE 10749, 107496 (2018).

Nazarov, A.

I. Abdulhalim, M. Ney, A. Aizen, A. Nazarov, and A. Safrani, “Parallel phase shift microscopy, vibrometry and focus tracking systems (conference presentation),” Proc. SPIE 10678, 106780P (2018).

Ney, M.

I. Abdulhalim, M. Ney, A. Aizen, A. Nazarov, and A. Safrani, “Parallel phase shift microscopy, vibrometry and focus tracking systems (conference presentation),” Proc. SPIE 10678, 106780P (2018).

M. Ney, A. Safrani, and I. Abdulhalim, “Three wavelengths parallel phase-shift interferometry for real-time focus tracking and vibration measurement,” Opt. Lett. 42, 719–722 (2017).
[Crossref] [PubMed]

North-Morris, M. B.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 55310 (2004).

Novak, M.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 55310 (2004).

Padilla, M.

Pau, S.

Pförtner, A.

Quan, C.

Safrani, A.

Schake, M.

M. Schake and P. Lehmann, “Perturbation resistant rgb-interferometry with pulsed led illumination,” Proc. SPIE 10678, 1067805 (2018).

M. Schake and P. Lehmann, “Anwendungsorientiertes verfahren zur eindeutigkeitsbereichserweiterung eines fasergekoppelten zweiwellenlaengen-interferometers,” Tech. Messen 83, 192–200 (2016).

Schulz, M.

M. Schulz and P. Lehmann, “Measurement of distance changes using a fibre-coupled common-path interferometer with mechanical path length modulation,” Meas. Sci. Technol. 24, 065202 (2013).
[Crossref]

Schwider, J.

Senthilkumaran, P.

A. Butola, A. Ahmad, V. Dubey, V. Singh, T. Joshi, P. Senthilkumaran, and D. S. Mehta, “Quantitative phase imaging using spectrally resolved white light interferometry,” Proc. SPIE 10414, 104144 (2017).

Servin, M.

Singh, V.

A. Butola, A. Ahmad, V. Dubey, V. Singh, T. Joshi, P. Senthilkumaran, and D. S. Mehta, “Quantitative phase imaging using spectrally resolved white light interferometry,” Proc. SPIE 10414, 104144 (2017).

Spires, O.

Srivastava, V.

Takeda, M.

Tay, C. J.

Tereschenko, S.

Tian, X.

Towers, C. E.

Towers, D. P.

Tu, X.

Wang, K.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).
[Crossref]

Wyant, J. C.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 55310 (2004).

Zellmer, L.

Zhang, J.

Zhang, Z.

Zhu, P.

Zhu, R.

Appl. Opt. (6)

Int. J. Optomechatronics (1)

K. Kitagawa, “Fast surface profiling by multi-wavelength single-shot interferometry,” Int. J. Optomechatronics 4, 136–156 (2010).
[Crossref]

J. Electron. Imaging (1)

K. Kitagawa, “Single-shot surface profiling by multiwavelength interferometry without carrier fringe introduction,” J. Electron. Imaging 21, 021107 (2012).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Korea (1)

Meas. Sci. Technol. (1)

M. Schulz and P. Lehmann, “Measurement of distance changes using a fibre-coupled common-path interferometer with mechanical path length modulation,” Meas. Sci. Technol. 24, 065202 (2013).
[Crossref]

Opt. Eng. (1)

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-d surface contouring,” Opt. Eng. 38, 38 (1999).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Proc. SPIE (7)

I. Abdulhalim, M. Ney, A. Aizen, A. Nazarov, and A. Safrani, “Parallel phase shift microscopy, vibrometry and focus tracking systems (conference presentation),” Proc. SPIE 10678, 106780P (2018).

H. Muhamedsalih, S. Al-Bashir, F. Gao, and X. Jiang, “Single-shot rgb polarising interferometer,” Proc. SPIE 10749, 107496 (2018).

C. L. Koliopoulos, “Simultaneous phase-shift interferometer,” Proc. SPIE 1531, 119–128 (1992).

K. Kitagawa, “Multiwavelength single-shot interferometry without carrier fringe introduction,” Proc. SPIE 8000, 80001 (2011).

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 55310 (2004).

M. Schake and P. Lehmann, “Perturbation resistant rgb-interferometry with pulsed led illumination,” Proc. SPIE 10678, 1067805 (2018).

A. Butola, A. Ahmad, V. Dubey, V. Singh, T. Joshi, P. Senthilkumaran, and D. S. Mehta, “Quantitative phase imaging using spectrally resolved white light interferometry,” Proc. SPIE 10414, 104144 (2017).

Tech. Messen (1)

M. Schake and P. Lehmann, “Anwendungsorientiertes verfahren zur eindeutigkeitsbereichserweiterung eines fasergekoppelten zweiwellenlaengen-interferometers,” Tech. Messen 83, 192–200 (2016).

Other (4)

K. Kitagawa, “Multi-wavelength single-shot interferometry,” in 2009 International Symposium on Optomechatronic Technologies, (2009), pp. 34–39.
[Crossref]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).
[Crossref]

HALLE Präzisions-Kalibriernormale GmbH, “Depth-setting standards with planar base grooves,” (2009).

SiMETRICS GmbH, “Resolution standard type rs-m,” (2009).

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Figures (7)

Fig. 1
Fig. 1 Schematic drawing of the Michelson interferometer with RGB illumination and oscillating reference mirror, bandpass filter (BP), dichroic mirror (DM), collimator (C), beam splitter (BS) and long pass filter (LP).
Fig. 2
Fig. 2 (a) Photography of the employed Michelson interferometer setup. (b) Timing diagram visualizing the synchronization of the RG LED pulse timing to the camera exposure gap.
Fig. 3
Fig. 3 (a) Measured phase shift Δϕ21,k from multiple dualshot-images with a standard deviation std(eΔϕ) ≈ 2° for red illumination (red line) and green illumination (green dashed line). (b) Interference signal I 1 k ( x ) max ( I 1 k ( x ) ) of one line for a mirror surface and corresponding phase noise for red eh1(x) and green eh2(x) illumination using the quadrature based phase retrieval algorithm according to Eq. (7) and applying high pass filtering. The standard deviation is std(eh1(x)) ≈ 3.5 nm and std(eh2(x)) ≈ 5 nm.
Fig. 4
Fig. 4 (a) First recorded image showing the interferogram I 11 ( x , y ) max ( I 11 ( x , y ) ) for λ1 ≈ 632 nm at a 750 nm groove standard. (b) Second recorded image showing the ≈ π/2 phase shifted interferogram I 21 ( x , y ) max ( I 21 ( x , y ) ) for same wavelength at same position.
Fig. 5
Fig. 5 (a) 3D-topography of the measured 750 nm groove. (b) Cross section of the topography in x-direction, topography retrieved from the synthetic wavelength phase θΛ1 (black line), topography retrieved from the green wavelength phase θ2 in combination with the fringe order map obtained from θΛ1 (green dashed line).
Fig. 6
Fig. 6 (a) First recorded interferometric image I 11 ( x ) I max (black line), Hilbert transform of the first recorded interferometric image I 11 ( x ) I max e j π 2 (black dashed line), second recorded interferometric image I 21 ( x ) I max (red line), subplots α)-) refer to vd = [0, 10, 50, 100, 200] μ m s respectively. (b) Topography of the RS-M standard h1(x, y) with 90 nm nominal structure depth retrieved from the red interferogram by the quadrature based phase retrieval.
Fig. 7
Fig. 7 (a) Without mechanical perturbation: Section h1(y) of the rectangular structure of the RS-M standard for λ1 ≈ 632 nm (red line), section h2(y) of the rectangular structure for λ2 ≈ 532 nm (green line), median value of the upper and lower plateaus (black dashed line). (b) Mechanical perturbation of vd ≤ 10 μm/s in z-direction applied: Section h1(y) of the rectangular structure of the RS-M standard for λ1 ≈ 632 nm (red line), section h2(y) of the rectangular structure for λ2 ≈ 532 nm (green line), median value of the upper and lower plateaus (black dashed line).

Tables (1)

Tables Icon

Table 1 Evaluation of the phase difference Δϕ21,1 by its corresponding deviation eΔϕ and surface height error eh1(x,y) of the disturbed interference signals in Fig. 6(a), α)-).

Equations (9)

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

I m k ( x , y ) = A k ( x , y ) + B k ( x , y ) + 2 A k ( x , y ) B k ( x , y ) | C k ( x , y , h ) | cos ( 4 π λ k ( h k ( x , y ) + e m k ( x , y ) ) + ϕ m k )
I blue ( x , y ) = A blue ( x , y )
A k ( x , y ) = D k ( x , y ) I blue ( x , y )
D k ( x , y ) = A k , cal ( x , y ) I blue ( x , y )
D ¯ k = 1 ( N x N y ) x = 1 N x y = 1 N y D k ( x , y )
Δ τ r Δ τ g = λ 1 λ 2 Δ τ r = Δ τ g λ 1 λ 2
I ˜ 2 k ( x , y ) I ˜ 1 k ( x , y ) = sin ( 4 π λ k ( h k ( x , y ) + e 2 k ( x , y ) ) ) cos ( 4 π λ k ( h k ( x , y ) + e 1 k ( x , y ) ) ) h k ( x , y ) + e 12 k ( x , y ) = tan 1 ( I ˜ 2 k ( x , y ) I ˜ 1 k ( x , y ) ) λ k 4 π
e 12 k ( x , y ) tan 1 ( 4 π λ k e 2 k ( x , y ) ) λ k 4 π e 2 k ( x , y )
θ k ( x , y ) = 4 π h k ( x , y ) λ k

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