Abstract

Digital micromirror device (DMD) based optical filters provide a new avenue for spectral modulation in many research applications. Traditional sequential channel scanning method for the calibration of such filters may suffer from compromised spectral tuning accuracy due to the signal to noise ratio restriction on the minimum pixel number of each channel. In this work, we propose a Hadamard transform based calibration method to address this issue. A DMD-based programmable optical filter is constructed and calibrated using both the sequential scanning method and the proposed method for the subsequent synthesis of three representative filters (i.e., the bandpass filter, Gaussian filter, and principal component based filter). The spectral tuning accuracy is evaluated by calculating the relative root mean square error (RMSE) between the synthesized transmittance spectrum and the target spectrum. The results show that when calibrated with the proposed method, the programmable filter exhibits a consistent decrease in the relative RMSE with an increasing channel number for all filters. The smallest relative RMSE values are therefore achieved when each channel contains only one DMD pixel. In contrast, for the sequential scanning method, the relative RMSE increases dramatically when each channel contains three or fewer DMD pixels. This suggests that our method is superior to the sequential scanning method in spectral tuning accuracy when the signal level is low.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  21. D. Luo, M. Taphanel, T. Längle, and J. Beyerer, “Programmable light source based on an echellogram of a supercontinuum laser,” Appl. Opt. 56(8), 2359–2367 (2017).
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  26. S. Chen, Y. H. Ong, X. Lin, and Q. Liu, “Optimization of advanced Wiener estimation methods for Raman reconstruction from narrow-band measurements in the presence of fluorescence background,” Biomed. Opt. Express 6(7), 2633–2648 (2015).
    [Crossref] [PubMed]

2018 (1)

Y. Li, L. Gao, T. Zhu, Y. Cao, M. Liu, D. Qu, F. Qiu, and X. Huang, “Graphene-assisted all-fiber optical-controllable laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 0901709 (2018).
[Crossref]

2017 (2)

2016 (1)

2015 (3)

2014 (1)

D. L. Graff and S. P. Love, “Toward real-time spectral imaging for chemical detection with a digital micro-mirror device-based programmable spectral filter,” J. Micro/Nanolith. MEMS MOEMS 13(1), 011111 (2014).
[Crossref]

2013 (4)

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, O. G. Rehrauer, P. Wang, and D. Ben-Amotz, “Digital compressive chemical quantitation and hyperspectral imaging,” Analyst (Lond.) 138(17), 4982–4990 (2013).
[Crossref] [PubMed]

Y. August and A. Stern, “Compressive sensing spectrometry based on liquid crystal devices,” Opt. Lett. 38(23), 4996–4999 (2013).
[Crossref] [PubMed]

S. Chen, Y. H. Ong, and Q. Liu, “Fast reconstruction of Raman spectra from narrow-band measurements based on Wiener estimation,” J. Raman Spectrosc. 44(6), 875–881 (2013).
[Crossref]

V. Bansal and P. Saggau, “Digital micromirror devices: principles and applications in imaging,” Cold Spring Harb. Protoc. 2013(5), 404–411 (2013).
[Crossref] [PubMed]

2012 (3)

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012).
[Crossref] [PubMed]

S. Chen and Q. Liu, “Modified Wiener estimation of diffuse reflectance spectra from RGB values by the synthesis of new colors for tissue measurements,” J. Biomed. Opt. 17(3), 030501 (2012).
[Crossref] [PubMed]

A. Santos, V. S. Balderrama, M. Alba, P. Formentín, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Tunable Fabry-Pérot interferometer based on nanoporous anodic alumina for optical biosensing purposes,” Nanoscale Res. Lett. 7(1), 370 (2012).
[Crossref] [PubMed]

2010 (1)

M. Blomberg, H. Kattelus, and A. Miranto, “Electrically tunable surface micromachined Fabry-Perot interferometer for visible light,” Sens. Actuators A Phys. 162(2), 184–188 (2010).
[Crossref]

2006 (1)

2004 (1)

L. Bei, G. I. Dennis, H. M. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis techniques,” Prog. Quantum Electron. 28(2), 67–87 (2004).
[Crossref]

2003 (2)

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003).
[Crossref]

N. Riza and M. J. Mughal, “Broadband optical equalizer using fault tolerant digital micromirrors,” Opt. Express 11(13), 1559–1565 (2003).
[Crossref] [PubMed]

2002 (1)

J. Sapriel, D. Charissoux, V. Voloshinov, and V. Molchanov, “Tunable acoustooptic filters and equalizers for wdm applications,” J. Lightwave Technol. 20(5), 892–899 (2002).
[Crossref]

1999 (1)

1998 (1)

1996 (1)

S. H. Huang, X. Y. Zou, S. M. Hwang, A. E. Willner, Z. Bao, and D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5-Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8(9), 1243–1245 (1996).
[Crossref]

1991 (1)

J. S. Pater and M. W. Maeda, “Tunable polarization diversity liquid-crystal wavelength filter,” IEEE Photonics Technol. Lett. 3(8), 739–740 (1991).
[Crossref]

Abed, F. M.

Alba, M.

A. Santos, V. S. Balderrama, M. Alba, P. Formentín, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Tunable Fabry-Pérot interferometer based on nanoporous anodic alumina for optical biosensing purposes,” Nanoscale Res. Lett. 7(1), 370 (2012).
[Crossref] [PubMed]

Arce, G. R.

Arguello, H.

August, I.

August, Y.

Balderrama, V. S.

A. Santos, V. S. Balderrama, M. Alba, P. Formentín, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Tunable Fabry-Pérot interferometer based on nanoporous anodic alumina for optical biosensing purposes,” Nanoscale Res. Lett. 7(1), 370 (2012).
[Crossref] [PubMed]

Bansal, V.

V. Bansal and P. Saggau, “Digital micromirror devices: principles and applications in imaging,” Cold Spring Harb. Protoc. 2013(5), 404–411 (2013).
[Crossref] [PubMed]

Bao, Z.

S. H. Huang, X. Y. Zou, S. M. Hwang, A. E. Willner, Z. Bao, and D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5-Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8(9), 1243–1245 (1996).
[Crossref]

Bei, L.

L. Bei, G. I. Dennis, H. M. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis techniques,” Prog. Quantum Electron. 28(2), 67–87 (2004).
[Crossref]

Ben-Amotz, D.

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, O. G. Rehrauer, P. Wang, and D. Ben-Amotz, “Digital compressive chemical quantitation and hyperspectral imaging,” Analyst (Lond.) 138(17), 4982–4990 (2013).
[Crossref] [PubMed]

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012).
[Crossref] [PubMed]

Berns, R. S.

Beyerer, J.

Blomberg, M.

M. Blomberg, H. Kattelus, and A. Miranto, “Electrically tunable surface micromachined Fabry-Perot interferometer for visible light,” Sens. Actuators A Phys. 162(2), 184–188 (2010).
[Crossref]

Buzzard, G. T.

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, O. G. Rehrauer, P. Wang, and D. Ben-Amotz, “Digital compressive chemical quantitation and hyperspectral imaging,” Analyst (Lond.) 138(17), 4982–4990 (2013).
[Crossref] [PubMed]

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012).
[Crossref] [PubMed]

Cao, Y.

Y. Li, L. Gao, T. Zhu, Y. Cao, M. Liu, D. Qu, F. Qiu, and X. Huang, “Graphene-assisted all-fiber optical-controllable laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 0901709 (2018).
[Crossref]

Carnahan, J. W.

L. Bei, G. I. Dennis, H. M. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis techniques,” Prog. Quantum Electron. 28(2), 67–87 (2004).
[Crossref]

Charissoux, D.

J. Sapriel, D. Charissoux, V. Voloshinov, and V. Molchanov, “Tunable acoustooptic filters and equalizers for wdm applications,” J. Lightwave Technol. 20(5), 892–899 (2002).
[Crossref]

Chen, S.

S. Chen, Y. H. Ong, X. Lin, and Q. Liu, “Optimization of advanced Wiener estimation methods for Raman reconstruction from narrow-band measurements in the presence of fluorescence background,” Biomed. Opt. Express 6(7), 2633–2648 (2015).
[Crossref] [PubMed]

S. Chen, Y. H. Ong, and Q. Liu, “Fast reconstruction of Raman spectra from narrow-band measurements based on Wiener estimation,” J. Raman Spectrosc. 44(6), 875–881 (2013).
[Crossref]

S. Chen and Q. Liu, “Modified Wiener estimation of diffuse reflectance spectra from RGB values by the synthesis of new colors for tissue measurements,” J. Biomed. Opt. 17(3), 030501 (2012).
[Crossref] [PubMed]

Chi, M.

Cohen, A. D.

Cox, B. D.

Dennis, G. I.

L. Bei, G. I. Dennis, H. M. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis techniques,” Prog. Quantum Electron. 28(2), 67–87 (2004).
[Crossref]

Dudley, D.

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003).
[Crossref]

Duncan, W. M.

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003).
[Crossref]

Ferré-Borrull, J.

A. Santos, V. S. Balderrama, M. Alba, P. Formentín, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Tunable Fabry-Pérot interferometer based on nanoporous anodic alumina for optical biosensing purposes,” Nanoscale Res. Lett. 7(1), 370 (2012).
[Crossref] [PubMed]

Formentín, P.

A. Santos, V. S. Balderrama, M. Alba, P. Formentín, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Tunable Fabry-Pérot interferometer based on nanoporous anodic alumina for optical biosensing purposes,” Nanoscale Res. Lett. 7(1), 370 (2012).
[Crossref] [PubMed]

Gao, L.

Y. Li, L. Gao, T. Zhu, Y. Cao, M. Liu, D. Qu, F. Qiu, and X. Huang, “Graphene-assisted all-fiber optical-controllable laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 0901709 (2018).
[Crossref]

Graff, D. L.

D. L. Graff and S. P. Love, “Toward real-time spectral imaging for chemical detection with a digital micro-mirror device-based programmable spectral filter,” J. Micro/Nanolith. MEMS MOEMS 13(1), 011111 (2014).
[Crossref]

Hao, P.

Huang, S. H.

S. H. Huang, X. Y. Zou, S. M. Hwang, A. E. Willner, Z. Bao, and D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5-Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8(9), 1243–1245 (1996).
[Crossref]

Huang, X.

Y. Li, L. Gao, T. Zhu, Y. Cao, M. Liu, D. Qu, F. Qiu, and X. Huang, “Graphene-assisted all-fiber optical-controllable laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 0901709 (2018).
[Crossref]

Hwang, S. M.

S. H. Huang, X. Y. Zou, S. M. Hwang, A. E. Willner, Z. Bao, and D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5-Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8(9), 1243–1245 (1996).
[Crossref]

Kattelus, H.

M. Blomberg, H. Kattelus, and A. Miranto, “Electrically tunable surface micromachined Fabry-Perot interferometer for visible light,” Sens. Actuators A Phys. 162(2), 184–188 (2010).
[Crossref]

Kim, P.

Längle, T.

Lee, D.

Li, Y.

Y. Li, L. Gao, T. Zhu, Y. Cao, M. Liu, D. Qu, F. Qiu, and X. Huang, “Graphene-assisted all-fiber optical-controllable laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 0901709 (2018).
[Crossref]

Lin, X.

Liu, M.

Y. Li, L. Gao, T. Zhu, Y. Cao, M. Liu, D. Qu, F. Qiu, and X. Huang, “Graphene-assisted all-fiber optical-controllable laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 0901709 (2018).
[Crossref]

Liu, Q.

S. Chen, Y. H. Ong, X. Lin, and Q. Liu, “Optimization of advanced Wiener estimation methods for Raman reconstruction from narrow-band measurements in the presence of fluorescence background,” Biomed. Opt. Express 6(7), 2633–2648 (2015).
[Crossref] [PubMed]

S. Chen, Y. H. Ong, and Q. Liu, “Fast reconstruction of Raman spectra from narrow-band measurements based on Wiener estimation,” J. Raman Spectrosc. 44(6), 875–881 (2013).
[Crossref]

S. Chen and Q. Liu, “Modified Wiener estimation of diffuse reflectance spectra from RGB values by the synthesis of new colors for tissue measurements,” J. Biomed. Opt. 17(3), 030501 (2012).
[Crossref] [PubMed]

Liu, Y.

Love, S. P.

D. L. Graff and S. P. Love, “Toward real-time spectral imaging for chemical detection with a digital micro-mirror device-based programmable spectral filter,” J. Micro/Nanolith. MEMS MOEMS 13(1), 011111 (2014).
[Crossref]

Lucier, B. J.

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, O. G. Rehrauer, P. Wang, and D. Ben-Amotz, “Digital compressive chemical quantitation and hyperspectral imaging,” Analyst (Lond.) 138(17), 4982–4990 (2013).
[Crossref] [PubMed]

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012).
[Crossref] [PubMed]

Luo, D.

Maeda, M. W.

J. S. Pater and M. W. Maeda, “Tunable polarization diversity liquid-crystal wavelength filter,” IEEE Photonics Technol. Lett. 3(8), 739–740 (1991).
[Crossref]

Marsal, L. F.

A. Santos, V. S. Balderrama, M. Alba, P. Formentín, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Tunable Fabry-Pérot interferometer based on nanoporous anodic alumina for optical biosensing purposes,” Nanoscale Res. Lett. 7(1), 370 (2012).
[Crossref] [PubMed]

Mears, R. J.

Miller, H. M.

L. Bei, G. I. Dennis, H. M. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis techniques,” Prog. Quantum Electron. 28(2), 67–87 (2004).
[Crossref]

Miranto, A.

M. Blomberg, H. Kattelus, and A. Miranto, “Electrically tunable surface micromachined Fabry-Perot interferometer for visible light,” Sens. Actuators A Phys. 162(2), 184–188 (2010).
[Crossref]

Molchanov, V.

J. Sapriel, D. Charissoux, V. Voloshinov, and V. Molchanov, “Tunable acoustooptic filters and equalizers for wdm applications,” J. Lightwave Technol. 20(5), 892–899 (2002).
[Crossref]

Mughal, M. J.

Oiknine, Y.

Ong, Y. H.

Pallarès, J.

A. Santos, V. S. Balderrama, M. Alba, P. Formentín, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Tunable Fabry-Pérot interferometer based on nanoporous anodic alumina for optical biosensing purposes,” Nanoscale Res. Lett. 7(1), 370 (2012).
[Crossref] [PubMed]

Park, J.

Park, N.

Parker, M. C.

Pater, J. S.

J. S. Pater and M. W. Maeda, “Tunable polarization diversity liquid-crystal wavelength filter,” IEEE Photonics Technol. Lett. 3(8), 739–740 (1991).
[Crossref]

Qian, F.

Qiu, F.

Y. Li, L. Gao, T. Zhu, Y. Cao, M. Liu, D. Qu, F. Qiu, and X. Huang, “Graphene-assisted all-fiber optical-controllable laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 0901709 (2018).
[Crossref]

Qu, D.

Y. Li, L. Gao, T. Zhu, Y. Cao, M. Liu, D. Qu, F. Qiu, and X. Huang, “Graphene-assisted all-fiber optical-controllable laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 0901709 (2018).
[Crossref]

Rehrauer, O. G.

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, O. G. Rehrauer, P. Wang, and D. Ben-Amotz, “Digital compressive chemical quantitation and hyperspectral imaging,” Analyst (Lond.) 138(17), 4982–4990 (2013).
[Crossref] [PubMed]

Riza, N.

Riza, N. A.

Rueda, H.

Saggau, P.

V. Bansal and P. Saggau, “Digital micromirror devices: principles and applications in imaging,” Cold Spring Harb. Protoc. 2013(5), 404–411 (2013).
[Crossref] [PubMed]

Santos, A.

A. Santos, V. S. Balderrama, M. Alba, P. Formentín, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Tunable Fabry-Pérot interferometer based on nanoporous anodic alumina for optical biosensing purposes,” Nanoscale Res. Lett. 7(1), 370 (2012).
[Crossref] [PubMed]

Sapriel, J.

J. Sapriel, D. Charissoux, V. Voloshinov, and V. Molchanov, “Tunable acoustooptic filters and equalizers for wdm applications,” J. Lightwave Technol. 20(5), 892–899 (2002).
[Crossref]

Slaughter, J.

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003).
[Crossref]

Smith, D. A.

S. H. Huang, X. Y. Zou, S. M. Hwang, A. E. Willner, Z. Bao, and D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5-Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8(9), 1243–1245 (1996).
[Crossref]

Spaine, T. W.

L. Bei, G. I. Dennis, H. M. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis techniques,” Prog. Quantum Electron. 28(2), 67–87 (2004).
[Crossref]

Stern, A.

Sumriddetchkajorn, S.

Taphanel, M.

Voloshinov, V.

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Figures (7)
Fig. 1
Fig. 1 Schematic layout of the experimental setup for implementing and evaluating the programmable optical filter. Note that the module inside the dashed box is the programmable optical filter and the rest is for evaluating it.

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Fig. 2
Fig. 2 (a) The 11th order S matrix and (b) a checkerboard-like illustration of the corresponding DMD pattern sequence with 11 channels. Each row of the checkerboard represents a DMD pattern and each column represents a DMD channel. White and black squares stand for the ‘on’, i.e. value 1 in the S matrix, and ‘off’, i.e. value 0 in the S matrix, status of the channels, respectively.

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Fig. 3
Fig. 3 Target transmittance spectrum after scaling down.

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Fig. 4
Fig. 4 Performance of the programmable filter in terms of relative RMSE for the synthesis of three different types of filters as a function of channel number used for both the sequential scanning calibration method and the Hadamard transform based method. Note that both the x and y axes are in the log-10 scale.

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Fig. 5
Fig. 5 Transmittance spectrum of a Gaussian filter synthesized using the Hadamard transform-based calibration method with 1123 channels and the target spectrum. The red curve and the blue curve represent the target transmittance spectrum and the synthesized transmittance spectrum, respectively.

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Fig. 6
Fig. 6 Transmittance spectrum of a bandpass filter synthesized using the Hadamard transform-based calibration method with 1123 channels and the target spectrum. The red curve and the blue curve stand for the target transmittance spectrum and the synthesized transmittance spectrum, respectively.

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Fig. 7
Fig. 7 Transmittance spectrum of a principal component based filter synthesized using the Hadamard transform-based calibration method with 1123 channels and the target spectrum. The red curve and the blue curve stand for the target transmittance spectrum and the synthesized transmittance spectrum, respectively.

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Equations (8)

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

M=[ T 1 T 2 ... T n ],
S −1 = 2 n+1 (2 S T − J ),
H i = S i,1 T 1 + S i,2 T 2 +...+ S i,n T n =M S i T ,
H=[ H 1 , H 2 ,..., H n ]=M S T .
M=H ( S T ) −1 = 2 n+1 H(2S−J).
F= d 1 T 1 + d 2 T 2 +...+ d n T n =MD.
D= M −1 F,
relativ e RMSE= ( ∑ i=1 m [ F synthesized ( λ i )− F target ( λ i ) ] 2 N×max [ F target ( λ i )] 2 ) 1/2 ×100%.

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