Abstract

Integration of phase manipulation and polarization multiplexing was introduced to self-mixing interferometry (SMI) for high-sensitive measurement. Light polarizations were used to increase measuring path number and predict manifold merits for potential applications. Laser source was studied as a microwave-photonic resonator optically-injected by double reflected lights on a two-feedback-factor analytical model. Independent external paths exploited magnesium-oxide doped lithium niobate crystals at perpendicular polarizations to transfer interferometric phases into amplitudes of harmonics. Theoretical resolutions reached angstrom level. By integrating two techniques, this SMI outperformed the conventional single-path SMIs by simultaneous dual-targets measurement on single laser tube with high sensitivity and low speckle noise. In experimental demonstration, by nonlinear filtering method, a custom-made phase-resolved algorithm real-time figured out instantaneous two-dimensional displacements with nanometer resolution. Experimental comparisons to lock-in technique and a commercial Ploytec-5000 laser Doppler velocity meter validated this two-path SMI in micron range without optical cross-talk. Moreover, accuracy subjected to slewing rates of crystals could be flexibly adjusted.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (1)

Y. Tao, M. Wang, and W. Xia, “Carrier-separating demodulation of phase shifting self-mixing interferometry,” Opt. Laser Technol. 89, 75–85 (2017).
[Crossref]

2016 (7)

O. D. Bernal, H. C. Seat, U. Zabit, F. Surre, and T. Bosch, “Robust detection of non-regular interferometric fringes from a self-mixing displacement sensor using Bi-Wavelet transform,” IEEE Sens. J. 16(22), 7903–7910 (2016).
[Crossref]

M. Wienold, T. Hagelschuer, N. Rothbart, L. Schrottke, K. Biermann, H. T. Grahn, and H. W. Hubers, “Real-time terahertz imaging through self-mixing in a quantum-cascade laser,” Appl. Phys. Lett. 109(1), 011102 (2016).
[Crossref]

R. Verma and R. Mehra, “PSO algorithm based adaptive median filter for noise removal in image processing application,” International Journal of advanced computer science and applications 7(7), 92–98 (2016).
[Crossref]

E. Nikahd, P. Behnam, and R. Sameni, “High-speed hardware implementation of fixed and runtime variable window length 1-D median filters,” IEEE Trans. Circuits Sys. II-express briefs 63(5), 478–482 (2016).
[Crossref]

S. Zhang, S. Zhang, Y. Tan, and L. Sun, “Self-mixing interferometry with mutual independent orthogonal polarized light,” Opt. Lett. 41(4), 844–846 (2016).
[Crossref] [PubMed]

V. Contreras, J. Lönnqvist, and J. Toivonen, “Detection of single microparticles in airflows by edge-filter enhanced self-mixing interferometry,” Opt. Express 24(8), 8886–8894 (2016).
[Crossref] [PubMed]

H. Xia, S. Montresor, R. Guo, J. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24(25), 28713–28730 (2016).
[Crossref] [PubMed]

2015 (4)

Y. Huang, Q. Zhao, L. Kamyab, A. Rostami, F. Capolino, and O. Boyraz, “Sub-micron silicon nitride waveguide fabrication using conventional optical lithography,” Opt. Express 23(5), 6780–6786 (2015).
[Crossref] [PubMed]

V. Contreras, J. Lonnqvist, and J. Toivonen, “Edge filter enhanced self-mixing interferometry,” Opt. Lett. 40(12), 2814–2817 (2015).
[Crossref] [PubMed]

H. Wang, J. Shen, and X. Cai, “Online measurement of nanoparticle size distribution in flowing Brownian motion system using laser diode self-mixing interferometry,” Appl. Phys. B 120(1), 129–139 (2015).
[Crossref]

Y. Tao, M. Wang, D. M. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340(340), 141–150 (2015).
[Crossref]

2014 (3)

S. Donati and M. Norgia, “Self-Mixing interferometry for biomedical signals sensing,” IEEE J. Quantum Electron. 20(2), 6900108 (2014).

D. Reusch and J. Strydom, “Understanding the effect of PCB layout on circuit performance in a high-frequency Gallium-Nitride-Based point of load converter,” IEEE Trans. Power Electron. 29(4), 2008–2015 (2014).
[Crossref]

S. Donati and G. Martini, “Systematic and random errors in self-mixing measurements: effect of the developing speckle statistics,” Appl. Opt. 53(22), 4873–4880 (2014).
[Crossref] [PubMed]

2013 (3)

F. Azcona, R. Atashkhooei, S. Royo, J. Mendez Astudillo, and A. Jha, “A nanometric displacement measurement system using differential optical feedback interferometry,” IEEE Photonics Technol. Lett. 25(21), 2074–2077 (2013).
[Crossref]

S. Donati, G. Martini, and T. Tambosso, “Speckle pattern errors in self-mixing interferometry,” IEEE J. Quantum Electron. 49(9), 798–806 (2013).
[Crossref]

Y. Kanamori, M. Okochi, and K. Hane, “Fabrication of antireflection subwavelength gratings at the tips of optical fibers using UV nanoimprint lithography,” Opt. Express 21(1), 322–328 (2013).
[Crossref] [PubMed]

2012 (1)

T. Ansbæk, C. H. Nielsen, S. Dohn, D. Larsson, I. Chung, and K. Yvind, “Vertical-cavity surface-emitting laser vapor sensor using swelling polymer reflection modulation,” Appl. Phys. Lett. 101(14), 143505 (2012).
[Crossref]

2011 (1)

2010 (2)

M. T. Fathi and S. Donati, “Thickness measurement of transparent plates by a self-mixing interferometer,” Opt. Lett. 35(11), 1844–1846 (2010).
[Crossref] [PubMed]

S. L. Zhang, W. H. Du, and G. Liu, “Orthogonal linear polarized lasers (III)—applications in self-sensing,” Prog. Nat. Sci. 15(11), 961–971 (2010).

2009 (1)

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

2007 (1)

J. Capmany and D. Novak, “Microwave photonic combines two words,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

2006 (1)

2005 (3)

2004 (2)

2001 (2)

H. L. Eng and K. K. Ma, “Noise adaptive soft-switching median filter,” IEEE Trans. Image Process. 10(2), 242–251 (2001).
[Crossref] [PubMed]

M. Norgia, S. Donati, and D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37(6), 800–806 (2001).
[Crossref]

2000 (1)

N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electro optic modulator,” IEEE J. Sel. Top. Quantum Electron. 6(5), 798–802 (2000).
[Crossref]

1998 (1)

1994 (1)

L. Weiss, “Wavelets and wideband correlation processing,” IEEE Trans. Signal Process. Mag. 11(1), 13–32 (1994).
[Crossref]

1992 (1)

S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38(2), 617–643 (1992).
[Crossref]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

1964 (2)

W. M. Doyle and M. B. White, “White frequency splitting and mode competition in a dual-polarization He-Ne gas laser,” Appl. Phys. Lett. 5(10), 193–195 (1964).
[Crossref]

W. E. Lamb, “Theory of an optical Maser,” Phys. Rev. 134(6A), A1429–A1450 (1964).
[Crossref]

Ancona, A.

Andrews, J. H.

Ansbæk, T.

T. Ansbæk, C. H. Nielsen, S. Dohn, D. Larsson, I. Chung, and K. Yvind, “Vertical-cavity surface-emitting laser vapor sensor using swelling polymer reflection modulation,” Appl. Phys. Lett. 101(14), 143505 (2012).
[Crossref]

Atashkhooei, R.

F. Azcona, R. Atashkhooei, S. Royo, J. Mendez Astudillo, and A. Jha, “A nanometric displacement measurement system using differential optical feedback interferometry,” IEEE Photonics Technol. Lett. 25(21), 2074–2077 (2013).
[Crossref]

Azcona, F.

F. Azcona, R. Atashkhooei, S. Royo, J. Mendez Astudillo, and A. Jha, “A nanometric displacement measurement system using differential optical feedback interferometry,” IEEE Photonics Technol. Lett. 25(21), 2074–2077 (2013).
[Crossref]

Bargiel, S.

Behnam, P.

E. Nikahd, P. Behnam, and R. Sameni, “High-speed hardware implementation of fixed and runtime variable window length 1-D median filters,” IEEE Trans. Circuits Sys. II-express briefs 63(5), 478–482 (2016).
[Crossref]

Bernal, O. D.

O. D. Bernal, H. C. Seat, U. Zabit, F. Surre, and T. Bosch, “Robust detection of non-regular interferometric fringes from a self-mixing displacement sensor using Bi-Wavelet transform,” IEEE Sens. J. 16(22), 7903–7910 (2016).
[Crossref]

Biermann, K.

M. Wienold, T. Hagelschuer, N. Rothbart, L. Schrottke, K. Biermann, H. T. Grahn, and H. W. Hubers, “Real-time terahertz imaging through self-mixing in a quantum-cascade laser,” Appl. Phys. Lett. 109(1), 011102 (2016).
[Crossref]

Boisen, A.

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

Bosch, T.

O. D. Bernal, H. C. Seat, U. Zabit, F. Surre, and T. Bosch, “Robust detection of non-regular interferometric fringes from a self-mixing displacement sensor using Bi-Wavelet transform,” IEEE Sens. J. 16(22), 7903–7910 (2016).
[Crossref]

N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electro optic modulator,” IEEE J. Sel. Top. Quantum Electron. 6(5), 798–802 (2000).
[Crossref]

Boyraz, O.

Cai, X.

H. Wang, J. Shen, and X. Cai, “Online measurement of nanoparticle size distribution in flowing Brownian motion system using laser diode self-mixing interferometry,” Appl. Phys. B 120(1), 129–139 (2015).
[Crossref]

Capmany, J.

J. Capmany and D. Novak, “Microwave photonic combines two words,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Capolino, F.

Cheng, H.

Chung, I.

T. Ansbæk, C. H. Nielsen, S. Dohn, D. Larsson, I. Chung, and K. Yvind, “Vertical-cavity surface-emitting laser vapor sensor using swelling polymer reflection modulation,” Appl. Phys. Lett. 101(14), 143505 (2012).
[Crossref]

Contreras, V.

Cretin, B.

Cui, L.

D’Alessandro, D.

M. Norgia, S. Donati, and D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37(6), 800–806 (2001).
[Crossref]

Dabbicco, M.

De Lucia, F.

Dohn, S.

T. Ansbæk, C. H. Nielsen, S. Dohn, D. Larsson, I. Chung, and K. Yvind, “Vertical-cavity surface-emitting laser vapor sensor using swelling polymer reflection modulation,” Appl. Phys. Lett. 101(14), 143505 (2012).
[Crossref]

Donati, S.

S. Donati and M. Norgia, “Self-Mixing interferometry for biomedical signals sensing,” IEEE J. Quantum Electron. 20(2), 6900108 (2014).

S. Donati and G. Martini, “Systematic and random errors in self-mixing measurements: effect of the developing speckle statistics,” Appl. Opt. 53(22), 4873–4880 (2014).
[Crossref] [PubMed]

S. Donati, G. Martini, and T. Tambosso, “Speckle pattern errors in self-mixing interferometry,” IEEE J. Quantum Electron. 49(9), 798–806 (2013).
[Crossref]

M. T. Fathi and S. Donati, “Thickness measurement of transparent plates by a self-mixing interferometer,” Opt. Lett. 35(11), 1844–1846 (2010).
[Crossref] [PubMed]

M. Norgia, S. Donati, and D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37(6), 800–806 (2001).
[Crossref]

Doyle, W. M.

W. M. Doyle and M. B. White, “White frequency splitting and mode competition in a dual-polarization He-Ne gas laser,” Appl. Phys. Lett. 5(10), 193–195 (1964).
[Crossref]

Du, W. H.

S. L. Zhang, W. H. Du, and G. Liu, “Orthogonal linear polarized lasers (III)—applications in self-sensing,” Prog. Nat. Sci. 15(11), 961–971 (2010).

Eng, H. L.

H. L. Eng and K. K. Ma, “Noise adaptive soft-switching median filter,” IEEE Trans. Image Process. 10(2), 242–251 (2001).
[Crossref] [PubMed]

Fainman, Y.

Fathi, M. T.

Fei, L.

Gorecki, C.

Grahn, H. T.

M. Wienold, T. Hagelschuer, N. Rothbart, L. Schrottke, K. Biermann, H. T. Grahn, and H. W. Hubers, “Real-time terahertz imaging through self-mixing in a quantum-cascade laser,” Appl. Phys. Lett. 109(1), 011102 (2016).
[Crossref]

Greve, A.

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

Guo, D.

Guo, D. M.

Y. Tao, M. Wang, D. M. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340(340), 141–150 (2015).
[Crossref]

Guo, R.

Hagelschuer, T.

M. Wienold, T. Hagelschuer, N. Rothbart, L. Schrottke, K. Biermann, H. T. Grahn, and H. W. Hubers, “Real-time terahertz imaging through self-mixing in a quantum-cascade laser,” Appl. Phys. Lett. 109(1), 011102 (2016).
[Crossref]

Hane, K.

Hao, H.

Y. Tao, M. Wang, D. M. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340(340), 141–150 (2015).
[Crossref]

Heinis, D.

Huang, Y.

Hubers, H. W.

M. Wienold, T. Hagelschuer, N. Rothbart, L. Schrottke, K. Biermann, H. T. Grahn, and H. W. Hubers, “Real-time terahertz imaging through self-mixing in a quantum-cascade laser,” Appl. Phys. Lett. 109(1), 011102 (2016).
[Crossref]

Hvam, J. M.

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

Hwang, W. L.

S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38(2), 617–643 (1992).
[Crossref]

Jha, A.

F. Azcona, R. Atashkhooei, S. Royo, J. Mendez Astudillo, and A. Jha, “A nanometric displacement measurement system using differential optical feedback interferometry,” IEEE Photonics Technol. Lett. 25(21), 2074–2077 (2013).
[Crossref]

Kamyab, L.

Kanamori, Y.

Kesab, B.

K. G. Tarun, C. Sivaji, B. Kesab, and C. Saibal, “Wavelet analysis of optical signal extracted form a non-contact fibre-optic vibration sensor using an extrinsic Fabry-Perot interferometer,” Meas. Sci. Technol. 16(5), 1075–1082 (2005).
[Crossref]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Lamb, W. E.

W. E. Lamb, “Theory of an optical Maser,” Phys. Rev. 134(6A), A1429–A1450 (1964).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Larsson, D.

T. Ansbæk, C. H. Nielsen, S. Dohn, D. Larsson, I. Chung, and K. Yvind, “Vertical-cavity surface-emitting laser vapor sensor using swelling polymer reflection modulation,” Appl. Phys. Lett. 101(14), 143505 (2012).
[Crossref]

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

Lescure, M.

N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electro optic modulator,” IEEE J. Sel. Top. Quantum Electron. 6(5), 798–802 (2000).
[Crossref]

Li, J.

Liu, G.

S. L. Zhang, W. H. Du, and G. Liu, “Orthogonal linear polarized lasers (III)—applications in self-sensing,” Prog. Nat. Sci. 15(11), 961–971 (2010).

Liu, Q.

Y. Tao, M. Wang, D. M. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340(340), 141–150 (2015).
[Crossref]

Lonnqvist, J.

Lönnqvist, J.

Lugarà, P. M.

Ma, K. K.

H. L. Eng and K. K. Ma, “Noise adaptive soft-switching median filter,” IEEE Trans. Image Process. 10(2), 242–251 (2001).
[Crossref] [PubMed]

Mallat, S.

S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38(2), 617–643 (1992).
[Crossref]

Martini, G.

S. Donati and G. Martini, “Systematic and random errors in self-mixing measurements: effect of the developing speckle statistics,” Appl. Opt. 53(22), 4873–4880 (2014).
[Crossref] [PubMed]

S. Donati, G. Martini, and T. Tambosso, “Speckle pattern errors in self-mixing interferometry,” IEEE J. Quantum Electron. 49(9), 798–806 (2013).
[Crossref]

Mehra, R.

R. Verma and R. Mehra, “PSO algorithm based adaptive median filter for noise removal in image processing application,” International Journal of advanced computer science and applications 7(7), 92–98 (2016).
[Crossref]

Mendez Astudillo, J.

F. Azcona, R. Atashkhooei, S. Royo, J. Mendez Astudillo, and A. Jha, “A nanometric displacement measurement system using differential optical feedback interferometry,” IEEE Photonics Technol. Lett. 25(21), 2074–2077 (2013).
[Crossref]

Mezzapesa, F. P.

Montresor, S.

Nielsen, C. H.

T. Ansbæk, C. H. Nielsen, S. Dohn, D. Larsson, I. Chung, and K. Yvind, “Vertical-cavity surface-emitting laser vapor sensor using swelling polymer reflection modulation,” Appl. Phys. Lett. 101(14), 143505 (2012).
[Crossref]

Nikahd, E.

E. Nikahd, P. Behnam, and R. Sameni, “High-speed hardware implementation of fixed and runtime variable window length 1-D median filters,” IEEE Trans. Circuits Sys. II-express briefs 63(5), 478–482 (2016).
[Crossref]

Norgia, M.

S. Donati and M. Norgia, “Self-Mixing interferometry for biomedical signals sensing,” IEEE J. Quantum Electron. 20(2), 6900108 (2014).

M. Norgia, S. Donati, and D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37(6), 800–806 (2001).
[Crossref]

Novak, D.

J. Capmany and D. Novak, “Microwave photonic combines two words,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Okochi, M.

Ovryn, B.

Panasenko, D.

Picart, P.

Reusch, D.

D. Reusch and J. Strydom, “Understanding the effect of PCB layout on circuit performance in a high-frequency Gallium-Nitride-Based point of load converter,” IEEE Trans. Power Electron. 29(4), 2008–2015 (2014).
[Crossref]

Rostami, A.

Rothbart, N.

M. Wienold, T. Hagelschuer, N. Rothbart, L. Schrottke, K. Biermann, H. T. Grahn, and H. W. Hubers, “Real-time terahertz imaging through self-mixing in a quantum-cascade laser,” Appl. Phys. Lett. 109(1), 011102 (2016).
[Crossref]

Royo, S.

F. Azcona, R. Atashkhooei, S. Royo, J. Mendez Astudillo, and A. Jha, “A nanometric displacement measurement system using differential optical feedback interferometry,” IEEE Photonics Technol. Lett. 25(21), 2074–2077 (2013).
[Crossref]

Saibal, C.

K. G. Tarun, C. Sivaji, B. Kesab, and C. Saibal, “Wavelet analysis of optical signal extracted form a non-contact fibre-optic vibration sensor using an extrinsic Fabry-Perot interferometer,” Meas. Sci. Technol. 16(5), 1075–1082 (2005).
[Crossref]

Sameni, R.

E. Nikahd, P. Behnam, and R. Sameni, “High-speed hardware implementation of fixed and runtime variable window length 1-D median filters,” IEEE Trans. Circuits Sys. II-express briefs 63(5), 478–482 (2016).
[Crossref]

Saperstein, R. E.

Scamarcio, G.

Schrottke, L.

M. Wienold, T. Hagelschuer, N. Rothbart, L. Schrottke, K. Biermann, H. T. Grahn, and H. W. Hubers, “Real-time terahertz imaging through self-mixing in a quantum-cascade laser,” Appl. Phys. Lett. 109(1), 011102 (2016).
[Crossref]

Seat, H. C.

O. D. Bernal, H. C. Seat, U. Zabit, F. Surre, and T. Bosch, “Robust detection of non-regular interferometric fringes from a self-mixing displacement sensor using Bi-Wavelet transform,” IEEE Sens. J. 16(22), 7903–7910 (2016).
[Crossref]

Servagent, N.

N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electro optic modulator,” IEEE J. Sel. Top. Quantum Electron. 6(5), 798–802 (2000).
[Crossref]

Shen, J.

H. Wang, J. Shen, and X. Cai, “Online measurement of nanoparticle size distribution in flowing Brownian motion system using laser diode self-mixing interferometry,” Appl. Phys. B 120(1), 129–139 (2015).
[Crossref]

Sibillano, T.

Sivaji, C.

K. G. Tarun, C. Sivaji, B. Kesab, and C. Saibal, “Wavelet analysis of optical signal extracted form a non-contact fibre-optic vibration sensor using an extrinsic Fabry-Perot interferometer,” Meas. Sci. Technol. 16(5), 1075–1082 (2005).
[Crossref]

Strydom, J.

D. Reusch and J. Strydom, “Understanding the effect of PCB layout on circuit performance in a high-frequency Gallium-Nitride-Based point of load converter,” IEEE Trans. Power Electron. 29(4), 2008–2015 (2014).
[Crossref]

Sun, L.

Surre, F.

O. D. Bernal, H. C. Seat, U. Zabit, F. Surre, and T. Bosch, “Robust detection of non-regular interferometric fringes from a self-mixing displacement sensor using Bi-Wavelet transform,” IEEE Sens. J. 16(22), 7903–7910 (2016).
[Crossref]

Tambosso, T.

S. Donati, G. Martini, and T. Tambosso, “Speckle pattern errors in self-mixing interferometry,” IEEE J. Quantum Electron. 49(9), 798–806 (2013).
[Crossref]

Tan, S.

Tan, Y.

Tao, Y.

Y. Tao, M. Wang, and W. Xia, “Carrier-separating demodulation of phase shifting self-mixing interferometry,” Opt. Laser Technol. 89, 75–85 (2017).
[Crossref]

Y. Tao, M. Wang, D. M. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340(340), 141–150 (2015).
[Crossref]

Tarun, K. G.

K. G. Tarun, C. Sivaji, B. Kesab, and C. Saibal, “Wavelet analysis of optical signal extracted form a non-contact fibre-optic vibration sensor using an extrinsic Fabry-Perot interferometer,” Meas. Sci. Technol. 16(5), 1075–1082 (2005).
[Crossref]

Toivonen, J.

Verma, R.

R. Verma and R. Mehra, “PSO algorithm based adaptive median filter for noise removal in image processing application,” International Journal of advanced computer science and applications 7(7), 92–98 (2016).
[Crossref]

Wang, H.

H. Wang, J. Shen, and X. Cai, “Online measurement of nanoparticle size distribution in flowing Brownian motion system using laser diode self-mixing interferometry,” Appl. Phys. B 120(1), 129–139 (2015).
[Crossref]

Wang, M.

Y. Tao, M. Wang, and W. Xia, “Carrier-separating demodulation of phase shifting self-mixing interferometry,” Opt. Laser Technol. 89, 75–85 (2017).
[Crossref]

Y. Tao, M. Wang, D. M. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340(340), 141–150 (2015).
[Crossref]

D. Guo, M. Wang, and S. Tan, “Self-mixing interferometer based on sinusoidal phase modulating technique,” Opt. Express 13(5), 1537–1543 (2005).
[Crossref] [PubMed]

Weiss, L.

L. Weiss, “Wavelets and wideband correlation processing,” IEEE Trans. Signal Process. Mag. 11(1), 13–32 (1994).
[Crossref]

White, M. B.

W. M. Doyle and M. B. White, “White frequency splitting and mode competition in a dual-polarization He-Ne gas laser,” Appl. Phys. Lett. 5(10), 193–195 (1964).
[Crossref]

Wienold, M.

M. Wienold, T. Hagelschuer, N. Rothbart, L. Schrottke, K. Biermann, H. T. Grahn, and H. W. Hubers, “Real-time terahertz imaging through self-mixing in a quantum-cascade laser,” Appl. Phys. Lett. 109(1), 011102 (2016).
[Crossref]

Xia, H.

Xia, W.

Y. Tao, M. Wang, and W. Xia, “Carrier-separating demodulation of phase shifting self-mixing interferometry,” Opt. Laser Technol. 89, 75–85 (2017).
[Crossref]

Yan, F.

Yvind, K.

T. Ansbæk, C. H. Nielsen, S. Dohn, D. Larsson, I. Chung, and K. Yvind, “Vertical-cavity surface-emitting laser vapor sensor using swelling polymer reflection modulation,” Appl. Phys. Lett. 101(14), 143505 (2012).
[Crossref]

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

Zabit, U.

O. D. Bernal, H. C. Seat, U. Zabit, F. Surre, and T. Bosch, “Robust detection of non-regular interferometric fringes from a self-mixing displacement sensor using Bi-Wavelet transform,” IEEE Sens. J. 16(22), 7903–7910 (2016).
[Crossref]

Zhang, S.

Zhang, S. L.

S. L. Zhang, W. H. Du, and G. Liu, “Orthogonal linear polarized lasers (III)—applications in self-sensing,” Prog. Nat. Sci. 15(11), 961–971 (2010).

Zhao, Q.

Appl. Opt. (1)

Appl. Phys. B (1)

H. Wang, J. Shen, and X. Cai, “Online measurement of nanoparticle size distribution in flowing Brownian motion system using laser diode self-mixing interferometry,” Appl. Phys. B 120(1), 129–139 (2015).
[Crossref]

Appl. Phys. Lett. (4)

T. Ansbæk, C. H. Nielsen, S. Dohn, D. Larsson, I. Chung, and K. Yvind, “Vertical-cavity surface-emitting laser vapor sensor using swelling polymer reflection modulation,” Appl. Phys. Lett. 101(14), 143505 (2012).
[Crossref]

M. Wienold, T. Hagelschuer, N. Rothbart, L. Schrottke, K. Biermann, H. T. Grahn, and H. W. Hubers, “Real-time terahertz imaging through self-mixing in a quantum-cascade laser,” Appl. Phys. Lett. 109(1), 011102 (2016).
[Crossref]

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009).
[Crossref]

W. M. Doyle and M. B. White, “White frequency splitting and mode competition in a dual-polarization He-Ne gas laser,” Appl. Phys. Lett. 5(10), 193–195 (1964).
[Crossref]

IEEE J. Quantum Electron. (4)

S. Donati and M. Norgia, “Self-Mixing interferometry for biomedical signals sensing,” IEEE J. Quantum Electron. 20(2), 6900108 (2014).

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

S. Donati, G. Martini, and T. Tambosso, “Speckle pattern errors in self-mixing interferometry,” IEEE J. Quantum Electron. 49(9), 798–806 (2013).
[Crossref]

M. Norgia, S. Donati, and D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37(6), 800–806 (2001).
[Crossref]

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

N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electro optic modulator,” IEEE J. Sel. Top. Quantum Electron. 6(5), 798–802 (2000).
[Crossref]

IEEE Photonics Technol. Lett. (1)

F. Azcona, R. Atashkhooei, S. Royo, J. Mendez Astudillo, and A. Jha, “A nanometric displacement measurement system using differential optical feedback interferometry,” IEEE Photonics Technol. Lett. 25(21), 2074–2077 (2013).
[Crossref]

IEEE Sens. J. (1)

O. D. Bernal, H. C. Seat, U. Zabit, F. Surre, and T. Bosch, “Robust detection of non-regular interferometric fringes from a self-mixing displacement sensor using Bi-Wavelet transform,” IEEE Sens. J. 16(22), 7903–7910 (2016).
[Crossref]

IEEE Trans. Circuits Sys. II-express briefs (1)

E. Nikahd, P. Behnam, and R. Sameni, “High-speed hardware implementation of fixed and runtime variable window length 1-D median filters,” IEEE Trans. Circuits Sys. II-express briefs 63(5), 478–482 (2016).
[Crossref]

IEEE Trans. Image Process. (1)

H. L. Eng and K. K. Ma, “Noise adaptive soft-switching median filter,” IEEE Trans. Image Process. 10(2), 242–251 (2001).
[Crossref] [PubMed]

IEEE Trans. Inf. Theory (1)

S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38(2), 617–643 (1992).
[Crossref]

IEEE Trans. Power Electron. (1)

D. Reusch and J. Strydom, “Understanding the effect of PCB layout on circuit performance in a high-frequency Gallium-Nitride-Based point of load converter,” IEEE Trans. Power Electron. 29(4), 2008–2015 (2014).
[Crossref]

IEEE Trans. Signal Process. Mag. (1)

L. Weiss, “Wavelets and wideband correlation processing,” IEEE Trans. Signal Process. Mag. 11(1), 13–32 (1994).
[Crossref]

International Journal of advanced computer science and applications (1)

R. Verma and R. Mehra, “PSO algorithm based adaptive median filter for noise removal in image processing application,” International Journal of advanced computer science and applications 7(7), 92–98 (2016).
[Crossref]

Meas. Sci. Technol. (1)

K. G. Tarun, C. Sivaji, B. Kesab, and C. Saibal, “Wavelet analysis of optical signal extracted form a non-contact fibre-optic vibration sensor using an extrinsic Fabry-Perot interferometer,” Meas. Sci. Technol. 16(5), 1075–1082 (2005).
[Crossref]

Nat. Photonics (1)

J. Capmany and D. Novak, “Microwave photonic combines two words,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Opt. Commun. (1)

Y. Tao, M. Wang, D. M. Guo, H. Hao, and Q. Liu, “Self-mixing vibration measurement using emission frequency sinusoidal modulation,” Opt. Commun. 340(340), 141–150 (2015).
[Crossref]

Opt. Express (8)

L. Cui and S. Zhang, “Semi-Classical theory model for feedback effect of orthogonally polarized dual frequency He-Ne laser,” Opt. Express 13(17), 6558–6563 (2005).
[Crossref] [PubMed]

L. Fei and S. Zhang, “Self-mixing interference effects of orthogonally polarized dual frequency laser,” Opt. Express 12(25), 6100–6105 (2004).
[Crossref] [PubMed]

H. Xia, S. Montresor, R. Guo, J. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24(25), 28713–28730 (2016).
[Crossref] [PubMed]

D. Guo, M. Wang, and S. Tan, “Self-mixing interferometer based on sinusoidal phase modulating technique,” Opt. Express 13(5), 1537–1543 (2005).
[Crossref] [PubMed]

Y. Kanamori, M. Okochi, and K. Hane, “Fabrication of antireflection subwavelength gratings at the tips of optical fibers using UV nanoimprint lithography,” Opt. Express 21(1), 322–328 (2013).
[Crossref] [PubMed]

Y. Huang, Q. Zhao, L. Kamyab, A. Rostami, F. Capolino, and O. Boyraz, “Sub-micron silicon nitride waveguide fabrication using conventional optical lithography,” Opt. Express 23(5), 6780–6786 (2015).
[Crossref] [PubMed]

V. Contreras, J. Lönnqvist, and J. Toivonen, “Detection of single microparticles in airflows by edge-filter enhanced self-mixing interferometry,” Opt. Express 24(8), 8886–8894 (2016).
[Crossref] [PubMed]

D. Heinis, C. Gorecki, S. Bargiel, and B. Cretin, “Feedback-induced voltage change of a Vertical-Cavity Surface-Emitting Laser as an active detection system for miniature optical scanning probe microscopes,” Opt. Express 14(8), 3396–3405 (2006).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

Y. Tao, M. Wang, and W. Xia, “Carrier-separating demodulation of phase shifting self-mixing interferometry,” Opt. Laser Technol. 89, 75–85 (2017).
[Crossref]

Opt. Lett. (6)

Phys. Rev. (1)

W. E. Lamb, “Theory of an optical Maser,” Phys. Rev. 134(6A), A1429–A1450 (1964).
[Crossref]

Prog. Nat. Sci. (1)

S. L. Zhang, W. H. Du, and G. Liu, “Orthogonal linear polarized lasers (III)—applications in self-sensing,” Prog. Nat. Sci. 15(11), 961–971 (2010).

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Figures (9)

Fig. 1
Fig. 1 Schematic of this lensless, phase shifting, polarization multiplexing SMI in absence of sophisticated electronics, which is consisted of a dual-output dual-longitudinal mode He-Ne laser, electro-optic modulators at perpendicular polarizations, polarization beam splitter (PBS) and targets at different directions. Two linearly polarizations by PBS are defined as o and e respectively. VTs (VT1, Thorlabs) denote adjustable resistors for converting photo-currents into voltages. PC denotes computer for signal processing. Generator provides alternating voltages to oscillate targete (loudspeaker), targeto (precision piezoelectric ceramics transducer, PZT) is driven by a closed-loop controller connected to PC. PD is Si-based photo electric detector (DET36A/M, Thorlabs). DAQ is data acquisition device (USB6361, NI). Because one mode light intensity already mirror status of two targets in following analysis, the dotted PDe and VTe can be removed for system simplicity.
Fig. 2
Fig. 2 SMI signals of o-path and e-path detected by PDo and PDe respectively in time domain (a) and frequency domain (b). Two insets are zoom-in view of signals. Among multi-harmonics of Fig. 2(b), the narrower-width harmonics with 39.5KHz spacing are o-harmonics, the wider-width harmonics with 98KHz spacing are e-harmonics.
Fig. 3
Fig. 3 One batch of SMI spectra with unchanged displacement, fo varies 39KHz→74KHz→ 110KHz→100KHz and fe varies 100KHz→45KHz→36KHz→98KHz.When slewing rates are very close, two kinds of harmonics will overlap and become difficult to distinguish.
Fig. 4
Fig. 4 Another batch of SMI spectra with unchanged slewing rates (fo = 39.5KHz, fe = 98KHz) but amplitude of targete varies 5μm→1.5μm→1μm→12μm, amplitude of targeto varies 3.5μm →10μm→15μm→20μm at 100Hz. Widths of harmonics gradually broaden until cause the overlapping as Fig. 3.
Fig. 5
Fig. 5 Signal processing with nonlinear filtering: 1. LPF and amplification. 2. 1-st and 2-nd harmonic extraction. 3. Nonlinear filtering on harmonics amplitudes. 4. Phase unwrapping, where CWT is programmed using VI provided by software toolkit of Labview2014.
Fig. 6
Fig. 6 Implementation of lock-in technique on simulated frequency modulated SMI and sinusoidal frequency driven voltages, where the dotted frame denotes the necessary functions inside a lock-in amplifier(notch filters are omitted), which outputs phase information displayed in an digital oscilloscope (OSC) and be sent to computer (PC) for phase unwrapping. PLL denotes a phase lock loop, BPF is a band-pass filter realized by (SR560, Stanford).
Fig. 7
Fig. 7 (a). Discrete phase of targeto outputted from arc-tangent calculation on our SMI, the inset is detailed phase points (b). The retrieved displacements of targeto using proposed phase algorithm (blue color) and lock-in technique (red color) respectively, where red-arrow pointed inset on left is detailed phase curves, the other inset on right is the yielded deviation between two results with a maximum error less than 3.5nm.
Fig. 8
Fig. 8 (a). Amplitudes of targeto increasing from 0.8μm to 0.91μm(PZT step size is 10nm) are measured by two instruments with residuals < 3nm. (b). Amplitudes of targete increasing from 0.85μm to 0.96μm are measured by two instruments with residuals < 2nm.
Fig. 9
Fig. 9 2D vibrations retrieved by SMI and LDV. (a). Electrocardiogram trajectory (ECG) and damping harmonic vibration lasting 8 seconds. (b). Zoom-in electrocardiogram trajectory of targete with result of LDV. (c). Zoom-in damping vibration of targeto with LDV result.

Equations (15)

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

P o/e = 1 D ( α o/e β e/o α e/o θ oe/eo )
α o/e = α o/e ' f o/e / Q o/e
D= β o β e θ oe θ eo
Q o/e = φ o/e 2 R 1 R o/e
P o/e = Ecos( φ o/e )Fcos( φ e/o ) [1+ C o cos( φ o/e )]×[1+ C e cos( φ e/o )]
P o × P e 0
P o/e Ecos( φ o/e ')Fcos( φ e/o ')
P o/e =...+E J 1 ( α o/e )sin( φ o/e )cos( ω o/e t)+E J 2 ( α o/e )cos( φ o/e )cos(2 ω o/e t) F J 1 ( α e/o )sin( φ e/o )cos( ω e/o t)F J 2 ( α e/o )cos( φ e/o )cos(2 ω e/o t)+...
I o/e1 ( ω o ,t)=(E/F) J 1 ( α o/e )sin( φ o/e )cos( ω o/e t)
I o/e2 (2 ω o/e ,t)=(E/F) J 2 ( α o/e )cos( φ o/e )cos(2 ω o/e t)
{ A o/e1 (t)= P o/e1 /cos( ω o/e t) A o/e2 (t)= P o/e1 /cos(2 ω o/e t)
φ o/e (t)= tan 1 [ A o/e1 (t) A o/e2 (t) ]
Δ L o/e (t)= λ o/e 4π unwrap[angle( φ o/e (t))]
R o/e (t)= λ o/e f φ o/e (t) 2π f o/e (t)
A o/e (i)=med[ A o/e (iN),... A o/e (i),... A o/e (i+N)]

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