Abstract

An optical standing-wave interferometer based on the detection of scattered light is proposed in this study. By inserting an ultra-thin scattering plate into the optical standing-wave field and detecting the scattered light, the intensity of the optical standing-wave field can be observed. The phase quadrature detection technique using two scattering plates is developed for measuring the displacement. The experimental results demonstrate that the measurement resolution and range can reach nanometer and micrometer levels, respectively.

© 2017 Optical Society of America

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References

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    [PubMed]
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  4. M. Sasaki, X. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Appl. Phys. Lett. 75(14), 2008–2010 (1999).
  5. Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode type optical interferometers,” Meas. Sci. Technol. 14, 479–483 (2003).
  6. H. Stiebig, H. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing-wave interferometer,” Appl. Phys. Lett. 83(1), 12–14 (2003).
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    [PubMed]

2017 (1)

2011 (1)

2010 (1)

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

2009 (2)

M. S. Kim, B. J. Kim, H. H. Lim, and M. Cha, “Observation of standing light wave by using fluorescence from a polymer thin film and diffuse reflection from a glass surface: Revisiting Wiener’s experiment,” Am. J. Phys. 77(8), 761–764 (2009).

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

2005 (2)

K. H. Jun, E. Bunte, and H. Stiebig, “Optimization of phase-sensitive transparent detector for length measurements,” IEEE Trans. Electron Dev. 52(7), 1656–1661 (2005).

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).

2004 (3)

H. Stiebig, V. Mandryka, E. Bunte, H.-J. Büchner, and K. H. Jun, “Novel micro interferometer for length measurements,” J. N. Crystal. S. 338–340, 793–796 (2004).

C. M. Wu, “Heterodyne interferometric system with subnanometer accuracy for measurement of straightness,” Appl. Opt. 43(19), 3812–3816 (2004).
[PubMed]

E. Bunte, V. Mandryka, K. H. Jun, H.-J. Büchner, G. Jäger, and H. Stiebig, “Thin transparent pin-photodiodes for length measurements,” Sensor Actuat. A Phys. 113(3), 334–337 (2004).

2003 (4)

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, and D. Knipp, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1–2), 152–156 (2003).

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode type optical interferometers,” Meas. Sci. Technol. 14, 479–483 (2003).

H. Stiebig, H. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing-wave interferometer,” Appl. Phys. Lett. 83(1), 12–14 (2003).

H.-J. Büchner, H. Stiebig, V. Mandryka, E. Bunte, and G. Jäger, “An optical standing-wave interferometer for displacement measurements,” Meas. Sci. Technol. 14, 311–316 (2003).

2002 (1)

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE J. Sel. Top. Quantum Electron. 8, 98–105 (2002).

1999 (1)

M. Sasaki, X. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Appl. Phys. Lett. 75(14), 2008–2010 (1999).

1998 (1)

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).

1994 (1)

D. A. B. Miller, “Laser tuners and wavelength-sensitive detectors based on absorbers in standing waves,” IEEE J. Quantum Electron. 30, 732–749 (1994).

1988 (1)

R. J. Moffat, “Describing the uncertainties in experimental results,” Exp. Therm. Fluid Sci. 1(1), 3–17 (1988).

Ayraud, M.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Barbier, D.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Bhalotra, S. R.

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE J. Sel. Top. Quantum Electron. 8, 98–105 (2002).

Blaize, S.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Bonneville, C.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Boussey, J.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Büchner, H.

H. Stiebig, H. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing-wave interferometer,” Appl. Phys. Lett. 83(1), 12–14 (2003).

Büchner, H.-J.

E. Bunte, V. Mandryka, K. H. Jun, H.-J. Büchner, G. Jäger, and H. Stiebig, “Thin transparent pin-photodiodes for length measurements,” Sensor Actuat. A Phys. 113(3), 334–337 (2004).

H. Stiebig, V. Mandryka, E. Bunte, H.-J. Büchner, and K. H. Jun, “Novel micro interferometer for length measurements,” J. N. Crystal. S. 338–340, 793–796 (2004).

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, and D. Knipp, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1–2), 152–156 (2003).

H.-J. Büchner, H. Stiebig, V. Mandryka, E. Bunte, and G. Jäger, “An optical standing-wave interferometer for displacement measurements,” Meas. Sci. Technol. 14, 311–316 (2003).

Bunte, E.

V. Jovanov, E. Bunte, H. Stiebig, and D. Knipp, “Transparent Fourier transform spectrometer,” Opt. Lett. 36(2), 274–276 (2011).
[PubMed]

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).

K. H. Jun, E. Bunte, and H. Stiebig, “Optimization of phase-sensitive transparent detector for length measurements,” IEEE Trans. Electron Dev. 52(7), 1656–1661 (2005).

H. Stiebig, V. Mandryka, E. Bunte, H.-J. Büchner, and K. H. Jun, “Novel micro interferometer for length measurements,” J. N. Crystal. S. 338–340, 793–796 (2004).

E. Bunte, V. Mandryka, K. H. Jun, H.-J. Büchner, G. Jäger, and H. Stiebig, “Thin transparent pin-photodiodes for length measurements,” Sensor Actuat. A Phys. 113(3), 334–337 (2004).

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, and D. Knipp, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1–2), 152–156 (2003).

H. Stiebig, H. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing-wave interferometer,” Appl. Phys. Lett. 83(1), 12–14 (2003).

H.-J. Büchner, H. Stiebig, V. Mandryka, E. Bunte, and G. Jäger, “An optical standing-wave interferometer for displacement measurements,” Meas. Sci. Technol. 14, 311–316 (2003).

Cai, D. P.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

Cha, M.

M. S. Kim, B. J. Kim, H. H. Lim, and M. Cha, “Observation of standing light wave by using fluorescence from a polymer thin film and diffuse reflection from a glass surface: Revisiting Wiener’s experiment,” Am. J. Phys. 77(8), 761–764 (2009).

Chan, C. H.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

Chen, C. C.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

Chen, T. J.

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

Chien, H. T.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

Demarest, F. C.

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).

Demonte, B.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Ferrand, J.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Fischer, A.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

Fu, H.

Gonthiez, T.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Hane, K.

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode type optical interferometers,” Meas. Sci. Technol. 14, 479–483 (2003).

M. Sasaki, X. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Appl. Phys. Lett. 75(14), 2008–2010 (1999).

Harris, J. S.

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE J. Sel. Top. Quantum Electron. 8, 98–105 (2002).

Hou, C. H.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

Hsiao, F. L.

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

Hsu, K. C.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

Hu, P.

Jäger, G.

E. Bunte, V. Mandryka, K. H. Jun, H.-J. Büchner, G. Jäger, and H. Stiebig, “Thin transparent pin-photodiodes for length measurements,” Sensor Actuat. A Phys. 113(3), 334–337 (2004).

H. Stiebig, H. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing-wave interferometer,” Appl. Phys. Lett. 83(1), 12–14 (2003).

H.-J. Büchner, H. Stiebig, V. Mandryka, E. Bunte, and G. Jäger, “An optical standing-wave interferometer for displacement measurements,” Meas. Sci. Technol. 14, 311–316 (2003).

Jovanov, V.

Jun, K. H.

K. H. Jun, E. Bunte, and H. Stiebig, “Optimization of phase-sensitive transparent detector for length measurements,” IEEE Trans. Electron Dev. 52(7), 1656–1661 (2005).

E. Bunte, V. Mandryka, K. H. Jun, H.-J. Büchner, G. Jäger, and H. Stiebig, “Thin transparent pin-photodiodes for length measurements,” Sensor Actuat. A Phys. 113(3), 334–337 (2004).

H. Stiebig, V. Mandryka, E. Bunte, H.-J. Büchner, and K. H. Jun, “Novel micro interferometer for length measurements,” J. N. Crystal. S. 338–340, 793–796 (2004).

Kern, P.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Kim, B. J.

M. S. Kim, B. J. Kim, H. H. Lim, and M. Cha, “Observation of standing light wave by using fluorescence from a polymer thin film and diffuse reflection from a glass surface: Revisiting Wiener’s experiment,” Am. J. Phys. 77(8), 761–764 (2009).

Kim, M. S.

M. S. Kim, B. J. Kim, H. H. Lim, and M. Cha, “Observation of standing light wave by using fluorescence from a polymer thin film and diffuse reflection from a glass surface: Revisiting Wiener’s experiment,” Am. J. Phys. 77(8), 761–764 (2009).

Knipp, D.

V. Jovanov, E. Bunte, H. Stiebig, and D. Knipp, “Transparent Fourier transform spectrometer,” Opt. Lett. 36(2), 274–276 (2011).
[PubMed]

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, and D. Knipp, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1–2), 152–156 (2003).

H. Stiebig, H. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing-wave interferometer,” Appl. Phys. Lett. 83(1), 12–14 (2003).

Kung, H. L.

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE J. Sel. Top. Quantum Electron. 8, 98–105 (2002).

Le Coarer, E.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Lee, C. C.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

Li, Y.

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode type optical interferometers,” Meas. Sci. Technol. 14, 479–483 (2003).

Lim, H. H.

M. S. Kim, B. J. Kim, H. H. Lim, and M. Cha, “Observation of standing light wave by using fluorescence from a polymer thin film and diffuse reflection from a glass surface: Revisiting Wiener’s experiment,” Am. J. Phys. 77(8), 761–764 (2009).

Mandryka, V.

H. Stiebig, V. Mandryka, E. Bunte, H.-J. Büchner, and K. H. Jun, “Novel micro interferometer for length measurements,” J. N. Crystal. S. 338–340, 793–796 (2004).

E. Bunte, V. Mandryka, K. H. Jun, H.-J. Büchner, G. Jäger, and H. Stiebig, “Thin transparent pin-photodiodes for length measurements,” Sensor Actuat. A Phys. 113(3), 334–337 (2004).

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, and D. Knipp, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1–2), 152–156 (2003).

H.-J. Büchner, H. Stiebig, V. Mandryka, E. Bunte, and G. Jäger, “An optical standing-wave interferometer for displacement measurements,” Meas. Sci. Technol. 14, 311–316 (2003).

H. Stiebig, H. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing-wave interferometer,” Appl. Phys. Lett. 83(1), 12–14 (2003).

Mansell, J. D.

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE J. Sel. Top. Quantum Electron. 8, 98–105 (2002).

Martinez-Gil, A.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

Mi, X.

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode type optical interferometers,” Meas. Sci. Technol. 14, 479–483 (2003).

M. Sasaki, X. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Appl. Phys. Lett. 75(14), 2008–2010 (1999).

Miller, D. A. B.

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE J. Sel. Top. Quantum Electron. 8, 98–105 (2002).

D. A. B. Miller, “Laser tuners and wavelength-sensitive detectors based on absorbers in standing waves,” IEEE J. Quantum Electron. 30, 732–749 (1994).

Moffat, R. J.

R. J. Moffat, “Describing the uncertainties in experimental results,” Exp. Therm. Fluid Sci. 1(1), 3–17 (1988).

Morand, A.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Puget, P.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Sasaki, M.

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode type optical interferometers,” Meas. Sci. Technol. 14, 479–483 (2003).

M. Sasaki, X. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Appl. Phys. Lett. 75(14), 2008–2010 (1999).

Stiebig, H.

V. Jovanov, E. Bunte, H. Stiebig, and D. Knipp, “Transparent Fourier transform spectrometer,” Opt. Lett. 36(2), 274–276 (2011).
[PubMed]

K. H. Jun, E. Bunte, and H. Stiebig, “Optimization of phase-sensitive transparent detector for length measurements,” IEEE Trans. Electron Dev. 52(7), 1656–1661 (2005).

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).

H. Stiebig, V. Mandryka, E. Bunte, H.-J. Büchner, and K. H. Jun, “Novel micro interferometer for length measurements,” J. N. Crystal. S. 338–340, 793–796 (2004).

E. Bunte, V. Mandryka, K. H. Jun, H.-J. Büchner, G. Jäger, and H. Stiebig, “Thin transparent pin-photodiodes for length measurements,” Sensor Actuat. A Phys. 113(3), 334–337 (2004).

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, and D. Knipp, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1–2), 152–156 (2003).

H. Stiebig, H. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing-wave interferometer,” Appl. Phys. Lett. 83(1), 12–14 (2003).

H.-J. Büchner, H. Stiebig, V. Mandryka, E. Bunte, and G. Jäger, “An optical standing-wave interferometer for displacement measurements,” Meas. Sci. Technol. 14, 311–316 (2003).

Taillepierre, P.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

Tan, J.

Tsai, Y. L.

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

Tseng, S. Z.

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

Venancio, L. G.

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

Wang, Y.

Wu, C. M.

Yang, S. L.

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

Zhu, J.

Am. J. Phys. (1)

M. S. Kim, B. J. Kim, H. H. Lim, and M. Cha, “Observation of standing light wave by using fluorescence from a polymer thin film and diffuse reflection from a glass surface: Revisiting Wiener’s experiment,” Am. J. Phys. 77(8), 761–764 (2009).

Appl. Opt. (1)

Appl. Phys. B (1)

C. H. Chan, A. Fischer, A. Martinez-Gil, P. Taillepierre, C. C. Lee, S. L. Yang, C. H. Hou, H. T. Chien, D. P. Cai, K. C. Hsu, and C. C. Chen, “Anti-reflection layer formed by monolayer of microspheres,” Appl. Phys. B 100, 547–551 (2010).

Appl. Phys. Lett. (3)

C. H. Chan, C. H. Hou, S. Z. Tseng, T. J. Chen, H. T. Chien, F. L. Hsiao, C. C. Lee, Y. L. Tsai, and C. C. Chen, “Improved output power of GaN-based light-emitting diodes grown on a nanopatterned sapphire substrate,” Appl. Phys. Lett. 95, 011110 (2009).

M. Sasaki, X. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Appl. Phys. Lett. 75(14), 2008–2010 (1999).

H. Stiebig, H. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing-wave interferometer,” Appl. Phys. Lett. 83(1), 12–14 (2003).

Exp. Therm. Fluid Sci. (1)

R. J. Moffat, “Describing the uncertainties in experimental results,” Exp. Therm. Fluid Sci. 1(1), 3–17 (1988).

IEEE J. Quantum Electron. (1)

D. A. B. Miller, “Laser tuners and wavelength-sensitive detectors based on absorbers in standing waves,” IEEE J. Quantum Electron. 30, 732–749 (1994).

IEEE J. Sel. Top. Quantum Electron. (1)

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE J. Sel. Top. Quantum Electron. 8, 98–105 (2002).

IEEE Trans. Electron Dev. (2)

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).

K. H. Jun, E. Bunte, and H. Stiebig, “Optimization of phase-sensitive transparent detector for length measurements,” IEEE Trans. Electron Dev. 52(7), 1656–1661 (2005).

J. N. Crystal. S. (1)

H. Stiebig, V. Mandryka, E. Bunte, H.-J. Büchner, and K. H. Jun, “Novel micro interferometer for length measurements,” J. N. Crystal. S. 338–340, 793–796 (2004).

Meas. Sci. Technol. (3)

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode type optical interferometers,” Meas. Sci. Technol. 14, 479–483 (2003).

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).

H.-J. Büchner, H. Stiebig, V. Mandryka, E. Bunte, and G. Jäger, “An optical standing-wave interferometer for displacement measurements,” Meas. Sci. Technol. 14, 311–316 (2003).

Opt. Express (1)

Opt. Lett. (1)

Sensor Actuat. A Phys. (1)

E. Bunte, V. Mandryka, K. H. Jun, H.-J. Büchner, G. Jäger, and H. Stiebig, “Thin transparent pin-photodiodes for length measurements,” Sensor Actuat. A Phys. 113(3), 334–337 (2004).

Thin Solid Films (1)

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, and D. Knipp, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1–2), 152–156 (2003).

Other (2)

E. Le Coarer, L. G. Venancio, P. Kern, J. Ferrand, P. Puget, M. Ayraud, C. Bonneville, B. Demonte, A. Morand, J. Boussey, D. Barbier, S. Blaize, and T. Gonthiez, “SWIFTS: On-chip very high spectral resolution spectrometer,” in Int. Conference on Space Opt. (2010).

S. O. Schönberg, O. Dietrich, and M. F. Reiser, Parallel Imaging in Clinical MR Applications (Springer, 2007), Chap. 4.

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Figures (9)

Fig. 1
Fig. 1 Observation of the optical standing wave by scattering plate S. OI: Optical isolator, L: Lens, PD: photodetector, M: Mirror.
Fig. 2
Fig. 2 Schematic of the quadrature detection system. OI: Optical isolator, PZT: Piezoelectric actuator, DAQ: Data acquisition card, PC: Personal computer.
Fig. 3
Fig. 3 Intensity of the interference signals from the scattering plate.
Fig. 4
Fig. 4 (a) Optical image of the glass substrate covered with 300 nm SiO2 spheres. (b) SEM image of the cross-sectional view of the monolayer of 300-nm SiO` spheres on glass substrates. Inset: Top view of the monolayer spheres arrangement.
Fig. 5
Fig. 5 Measurement results for forward and backward displacement with micrometer scales.
Fig. 6
Fig. 6 Measurement results for the nanometer scale step motion.
Fig. 7
Fig. 7 (a) Light scattered by the small element layer of the scattering plate. (b) Relationship between the contrast of the scattered light and the ratio of nZ to λ.
Fig. 8
Fig. 8 Noise level of the measured displacement.
Fig. 9
Fig. 9 (a) Difference between the measured displacement using our method and that measured using the strain gauge sensor, and (b) Lissajous patterns of the calibrated (I'sa and I'sb) signals.

Equations (20)

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E 1 = E 10 exp( i 2π λ z 1 iωt ),
E 2 = E 20 exp( i 2π λ z 1 +i 2π λ 2 z 2 iωt+iπ ),
I= I 0 [ 1γcos( 4π λ ( z 1 z 2 ) ) ],
I s = I s0 [ 1 γ s cos( 4π λ ( z 1 z 2 )+ ϕ s ) ],
I sa = I sa0 [ 1 γ sa cos( 4π λ ( z 1a z 2 )+ ϕ sa ) ]
I sb = I sb0 [ 1 γ sb cos( 4π λ ( z 1b z 2 )+ ϕ sb ) ],
z 1b = z 1a +( 2πm+π/2 ) λ 4π +( ϕ sa ϕ sb ) λ 4π ,
I sb = I sb0 [ 1 γ sb sin( 4π λ ( z 1a z 2 )+ ϕ sa ) ].
D C sa = ( I saM + I sam )/2 = I sa0
A C sa = ( I saM I sam )/2 = I sa0 γ sa .
D C sb = ( I sbM + I sbm )/2 = I sb0
A C sb = ( I sbM I sbm )/2 = I sb0 γ sb .
I sa = I sa D C sa A C sa =cos( 4π λ ( z 1a z 2 )+ ϕ sa )
I sb = I sb D C sb A C sb =sin( 4π λ ( z 1a z 2 )+ ϕ sa ).
z 2 = λ 4π tan 1 I sb I sa + z 1a + λ 4π ϕ 0a = λ 4π tan 1 I sb I sa +C.
d I s = I s0 nZ [ 1γcos( 4π λ ( z 1 + z ) 4π λ z 2 ) ]d z ,
I s = z =0 z =nZ d I s = I s0 [ 1 sin( 2πnZ/λ ) 2πnZ/λ γcos( 4π λ ( z 1 z 2 )+ 2πnZ λ ) ].
γ s = sin( 2πnZ/λ ) 2πnZ/λ γ.
Δ z 2 = ( z 2 I sa Δ I sa ) 2 + ( z 2 I sb Δ I sb ) 2 = λ 4π Δ I I sa 2 + I sb 2 .
ε k = λ 4π Γ k Γ 1 sin[ ( k1 )φ ],

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