Abstract

We describe a simple, compact, low-cost spectrometer comprised of a broadband diffractive optic and a sensor array. The diffractive optic is designed to disperse incident collimated light onto the sensor array in a prescribed manner defined by its spatial-spectral point-spread function. By applying a novel nonlinear optimization method, we show that it is possible to reconstruct the unknown spectrum from the measured image on the sensor array. We experimentally reconstructed numerous spectra with resolution as small as ~1nm and bandwidths as large as 450nm. Furthermore, we readily resolved two spatially overlapping but spectrally distinct objects. The spectral resolution is determined by dispersion of the diffractive optic via a spectral correlation function, while the bandwidth is limited primarily by the quantum efficiency of the sensor array. Using simulations, we present a spectral extraction of solar radiation from 300nm to 2500nm with a resolution of ~0.11nm. Moreover, our technique utilizes almost all the incident photons owing to the high transmission efficiency of the broadband diffractive optic, which allows for fast spectroscopy with dim illumination. Due to its simple construction with no moving parts, our technique could have important applications in portable, low-cost spectroscopy.

© 2014 Optical Society of America

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P. Wang and R. Menon, “Optimization of generalized dielectric nanostructures for enhanced light trapping in thin-film photovoltaics via boosting the local density of optical states,” Opt. Express 22(S1), A99–A110 (2014).
[CrossRef]

P. Wang, C. G. Ebeling, J. Gerton, and R. Menon, “Hyper-spectral imaging in scanning-confocal-fluorescence microscopy using a novel broadband diffractive optic,” Opt. Commun. 324, 73–80 (2014).
[CrossRef]

2013 (4)

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[CrossRef]

P. Wang and R. Menon, “Optimization of periodic nanostructures for enhanced light-trapping in ultra-thin photovoltaics,” Opt. Express 21(5), 6274–6285 (2013).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

2012 (2)

2011 (1)

2010 (1)

2009 (2)

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science 324(5929), 917–921 (2009).
[CrossRef] [PubMed]

2008 (2)

2007 (3)

2006 (3)

2005 (2)

G. Fortin and N. McCarthy, “Chirped holographic grating used as the dispersive element in an optical spectrometer,” Appl. Opt. 44(23), 4874–4883 (2005).
[CrossRef] [PubMed]

T. Zimmermann, “Spectral imaging and linear unmixing in light microscopy,” Adv. Biochem. Eng. Biotechnol. 95, 245–265 (2005).
[CrossRef] [PubMed]

2004 (2)

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53(1), 197–202 (2004).
[CrossRef]

C. P. Bacon, Y. Mattley, and R. DeFrece, “Miniature spectroscopic instrumentation: applications to biology and chemistry,” Rev. Sci. Instrum. 75(1), 1–16 (2004).
[CrossRef]

2002 (1)

S. B. Utter, J. R. C. López-Urrutia, P. Beiersdorfer, and E. Träbert, “Design and implementation of a high-resolution, high-efficiency optical spectrometer,” Rev. Sci. Instrum. 73(11), 3737–3741 (2002).
[CrossRef]

2001 (1)

1997 (1)

K. Reimer, H. J. Quenzer, M. Juerss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
[CrossRef]

Adibi, A.

Andrew, T. L.

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science 324(5929), 917–921 (2009).
[CrossRef] [PubMed]

Auner, G.

Auner, G. W.

Avrutsky, I.

Babin, S.

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Bacon, C. P.

C. P. Bacon, Y. Mattley, and R. DeFrece, “Miniature spectroscopic instrumentation: applications to biology and chemistry,” Rev. Sci. Instrum. 75(1), 1–16 (2004).
[CrossRef]

Beiersdorfer, P.

S. B. Utter, J. R. C. López-Urrutia, P. Beiersdorfer, and E. Träbert, “Design and implementation of a high-resolution, high-efficiency optical spectrometer,” Rev. Sci. Instrum. 73(11), 3737–3741 (2002).
[CrossRef]

Brady, D. J.

Bugrov, A.

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Cabrini, S.

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Cao, H.

Caputo, R.

Chaganti, K.

Chamanzar, M.

Chen, H.

Chen, L.

De Sio, L.

DeFrece, R.

C. P. Bacon, Y. Mattley, and R. DeFrece, “Miniature spectroscopic instrumentation: applications to biology and chemistry,” Rev. Sci. Instrum. 75(1), 1–16 (2004).
[CrossRef]

Dhuey, S.

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Dominguez-Caballero, J. A.

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[CrossRef]

P. Wang, J. A. Dominguez-Caballero, D. J. Friedman, and R. Menon, “A new class of multi-bandgap high efficiency photovoltaics enabled by broadband diffractive optics,” Prog. Photovolt. Res. Appl., in press.

Domínguez-Caballero, J. A.

Ebeling, C. G.

P. Wang, C. G. Ebeling, J. Gerton, and R. Menon, “Hyper-spectral imaging in scanning-confocal-fluorescence microscopy using a novel broadband diffractive optic,” Opt. Commun. 324, 73–80 (2014).
[CrossRef]

Eftekhar, A. A.

Feller, S. D.

Fernandez, C.

Fortin, G.

Friedman, D. J.

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[CrossRef]

P. Wang, J. A. Dominguez-Caballero, D. J. Friedman, and R. Menon, “A new class of multi-bandgap high efficiency photovoltaics enabled by broadband diffractive optics,” Prog. Photovolt. Res. Appl., in press.

Gehm, M. E.

Gerton, J.

P. Wang, C. G. Ebeling, J. Gerton, and R. Menon, “Hyper-spectral imaging in scanning-confocal-fluorescence microscopy using a novel broadband diffractive optic,” Opt. Commun. 324, 73–80 (2014).
[CrossRef]

Goltsov, A.

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Guenther, B. D.

Guo, L. J.

L. J. Guo, “Nanoimprint lithography: methods and material requirements,” Adv. Mater. 19(4), 495–513 (2007).
[CrossRef]

Hsieh, C.

Ivonin, I.

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Juerss, M.

K. Reimer, H. J. Quenzer, M. Juerss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
[CrossRef]

Kim, G.

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[CrossRef]

G. Kim, J. A. Domínguez-Caballero, and R. Menon, “Design and analysis of multi-wavelength diffractive optics,” Opt. Express 20(3), 2814–2823 (2012).
[CrossRef] [PubMed]

Kley, E.-B.

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Kyotoku, B. B. C.

Lee, H.

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[CrossRef]

Li, Q.

Liew, S. F.

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[CrossRef]

Lipson, M.

López-Urrutia, J. R. C.

S. B. Utter, J. R. C. López-Urrutia, P. Beiersdorfer, and E. Träbert, “Design and implementation of a high-resolution, high-efficiency optical spectrometer,” Rev. Sci. Instrum. 73(11), 3737–3741 (2002).
[CrossRef]

Mattley, Y.

C. P. Bacon, Y. Mattley, and R. DeFrece, “Miniature spectroscopic instrumentation: applications to biology and chemistry,” Rev. Sci. Instrum. 75(1), 1–16 (2004).
[CrossRef]

McCain, S. T.

McCarthy, N.

Menon, R.

P. Wang, C. G. Ebeling, J. Gerton, and R. Menon, “Hyper-spectral imaging in scanning-confocal-fluorescence microscopy using a novel broadband diffractive optic,” Opt. Commun. 324, 73–80 (2014).
[CrossRef]

P. Wang and R. Menon, “Optimization of generalized dielectric nanostructures for enhanced light trapping in thin-film photovoltaics via boosting the local density of optical states,” Opt. Express 22(S1), A99–A110 (2014).
[CrossRef]

P. Wang and R. Menon, “Optimization of periodic nanostructures for enhanced light-trapping in ultra-thin photovoltaics,” Opt. Express 21(5), 6274–6285 (2013).
[CrossRef] [PubMed]

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[CrossRef]

G. Kim, J. A. Domínguez-Caballero, and R. Menon, “Design and analysis of multi-wavelength diffractive optics,” Opt. Express 20(3), 2814–2823 (2012).
[CrossRef] [PubMed]

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science 324(5929), 917–921 (2009).
[CrossRef] [PubMed]

P. Wang, J. A. Dominguez-Caballero, D. J. Friedman, and R. Menon, “A new class of multi-bandgap high efficiency photovoltaics enabled by broadband diffractive optics,” Prog. Photovolt. Res. Appl., in press.

Momeni, B.

Momtahan, O.

Nitkowski, A.

Peroz, C.

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Pitsianis, N. P.

Popoff, S. M.

Potuluri, P.

Prather, D. W.

Quenzer, H. J.

K. Reimer, H. J. Quenzer, M. Juerss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
[CrossRef]

Redding, B.

Reimer, K.

K. Reimer, H. J. Quenzer, M. Juerss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
[CrossRef]

Salakhutdinov, I.

Sarma, R.

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[CrossRef]

Schmidt, H.

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Sharkawy, A.

Shi, S.

Soltani, M.

Sullivan, M. E.

Tabiryan, N.

Träbert, E.

S. B. Utter, J. R. C. López-Urrutia, P. Beiersdorfer, and E. Träbert, “Design and implementation of a high-resolution, high-efficiency optical spectrometer,” Rev. Sci. Instrum. 73(11), 3737–3741 (2002).
[CrossRef]

Tsai, H. Y.

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science 324(5929), 917–921 (2009).
[CrossRef] [PubMed]

Umeton, C.

Utter, S. B.

S. B. Utter, J. R. C. López-Urrutia, P. Beiersdorfer, and E. Träbert, “Design and implementation of a high-resolution, high-efficiency optical spectrometer,” Rev. Sci. Instrum. 73(11), 3737–3741 (2002).
[CrossRef]

Veltri, A.

Wagner, B.

K. Reimer, H. J. Quenzer, M. Juerss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
[CrossRef]

Wang, P.

P. Wang, C. G. Ebeling, J. Gerton, and R. Menon, “Hyper-spectral imaging in scanning-confocal-fluorescence microscopy using a novel broadband diffractive optic,” Opt. Commun. 324, 73–80 (2014).
[CrossRef]

P. Wang and R. Menon, “Optimization of generalized dielectric nanostructures for enhanced light trapping in thin-film photovoltaics via boosting the local density of optical states,” Opt. Express 22(S1), A99–A110 (2014).
[CrossRef]

P. Wang and R. Menon, “Optimization of periodic nanostructures for enhanced light-trapping in ultra-thin photovoltaics,” Opt. Express 21(5), 6274–6285 (2013).
[CrossRef] [PubMed]

P. Wang, J. A. Dominguez-Caballero, D. J. Friedman, and R. Menon, “A new class of multi-bandgap high efficiency photovoltaics enabled by broadband diffractive optics,” Prog. Photovolt. Res. Appl., in press.

Wolffenbuttel, R. F.

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53(1), 197–202 (2004).
[CrossRef]

Xia, Z.

Yankov, V.

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Yegnanarayanan, S.

Zimmermann, T.

T. Zimmermann, “Spectral imaging and linear unmixing in light microscopy,” Adv. Biochem. Eng. Biotechnol. 95, 245–265 (2005).
[CrossRef] [PubMed]

Adv. Biochem. Eng. Biotechnol. (1)

T. Zimmermann, “Spectral imaging and linear unmixing in light microscopy,” Adv. Biochem. Eng. Biotechnol. 95, 245–265 (2005).
[CrossRef] [PubMed]

Adv. Mater. (1)

L. J. Guo, “Nanoimprint lithography: methods and material requirements,” Adv. Mater. 19(4), 495–513 (2007).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Instrum. Meas. (1)

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53(1), 197–202 (2004).
[CrossRef]

J. Vac. Sci. Technol. B (1)

S. Babin, C. Peroz, A. Bugrov, A. Goltsov, I. Ivonin, V. Yankov, S. Dhuey, S. Cabrini, E.-B. Kley, and H. Schmidt, “Fabrication of novel digital optical spectrometer on chip,” J. Vac. Sci. Technol. B 27(6), 3187–3191 (2009).
[CrossRef]

Nat. Photonics (1)

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[CrossRef]

Opt. Commun. (1)

P. Wang, C. G. Ebeling, J. Gerton, and R. Menon, “Hyper-spectral imaging in scanning-confocal-fluorescence microscopy using a novel broadband diffractive optic,” Opt. Commun. 324, 73–80 (2014).
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P. Wang and R. Menon, “Optimization of periodic nanostructures for enhanced light-trapping in ultra-thin photovoltaics,” Opt. Express 21(5), 6274–6285 (2013).
[CrossRef] [PubMed]

P. Wang and R. Menon, “Optimization of generalized dielectric nanostructures for enhanced light trapping in thin-film photovoltaics via boosting the local density of optical states,” Opt. Express 22(S1), A99–A110 (2014).
[CrossRef]

G. Kim, J. A. Domínguez-Caballero, and R. Menon, “Design and analysis of multi-wavelength diffractive optics,” Opt. Express 20(3), 2814–2823 (2012).
[CrossRef] [PubMed]

L. De Sio, N. Tabiryan, R. Caputo, A. Veltri, and C. Umeton, “POLICRYPS structures as switchable optical phase modulators,” Opt. Express 16(11), 7619–7624 (2008).
[CrossRef] [PubMed]

A. Nitkowski, L. Chen, and M. Lipson, “Cavity-enhanced on-chip absorption spectroscopy using microring resonators,” Opt. Express 16(16), 11930–11936 (2008).
[CrossRef] [PubMed]

B. B. C. Kyotoku, L. Chen, and M. Lipson, “Sub-nm resolution cavity enhanced micro-spectrometer,” Opt. Express 18(1), 102–107 (2010).
[CrossRef] [PubMed]

Z. Xia, A. A. Eftekhar, M. Soltani, B. Momeni, Q. Li, M. Chamanzar, S. Yegnanarayanan, and A. Adibi, “High resolution on-chip spectroscopy based on miniaturized microdonut resonators,” Opt. Express 19(13), 12356–12364 (2011).
[CrossRef] [PubMed]

S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Adibi, “Multiple order coded aperture spectrometer,” Opt. Express 15(9), 5625–5630 (2007).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

B. Redding, S. M. Popoff, and H. Cao, “All-fiber spectrometer based on speckle pattern reconstruction,” Opt. Express 21(5), 6584–6600 (2013).
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Opt. Lett. (1)

Phys. Rev. Lett. (1)

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
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Science (1)

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science 324(5929), 917–921 (2009).
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Other (9)

Andor Camera Model Clara specifications: http://www.andor.com/scientific-cameras/clara-interline-ccd-series/clara .

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American Society for Testing and Materials (ASTM) Terrestrial Reference Spectra for Photovoltaic Performance Evaluation, http://rredc.nrel.gov/solar/spectra/am1.5/ .

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P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms (SIAM Press, 2010).

P. Wang, J. A. Dominguez-Caballero, D. J. Friedman, and R. Menon, “A new class of multi-bandgap high efficiency photovoltaics enabled by broadband diffractive optics,” Prog. Photovolt. Res. Appl., in press.

P. Wang and R. Menon, “Three-dimensional lithography via digital holography,” in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper FTu3A.4.

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic explaining the principle of the proposed computational spectrometer. Incident light of unknown spectrum is dispersed by the polychromat onto the sensor. The image of each wavelength is unique and can be used to recover the unknown spectrum. (b) – (d) The first design (regular polychromat) is a high-efficiency spectrum splitter. (e) – (g) The second design (random polychromat) with a highly irregular spatial-spectral PSF. (b) and (e) Depth profile plots of the two polychromats with groove width of 3μm and maximum depth of 1.2μm (insets: magnified views of a 0.2mm-long segment (b) and a 0.15mm-long segment (e), enclosed by the black boxes). (c) and (f) Optical micrographs of a corner of the fabricated devices (insets: Atomic-force microscope measurements of a small region delimited by the white boxes). (d) and (g) Spatial-spectral point-spread-functions of the designed polychromats measured with spatial resolution of 6.45μm at the distances of d = 90mm (d) and d = 450mm (g). The spectral resolutions are 2nm (d) and 1nm (g), respectively. (h) Spectral correlation analysis of the polychromats with respect to wavelength spacing δλ. (inset: spectral resolution derived from the correlation function for the random polychromats as a function of image distance, d with spatial (size of sensor pixel) resolution of Δx’ = 3μm (magenta line) and Δx’ = 6.45μm (cyan line); the orange cross represents the resolution of the regular polychromat at d = 90mm). (i) Schematic of the experimental setup for capturing diffraction patterns of a variety of spectra by CCD array. Flip mirrors are used to select different sources. The recorded images are utilized to retrieve photon flux spectra.

Fig. 2
Fig. 2

Spectrum extraction results of coherent laser beams. The photon flux spectra obtained by a conventional spectrometer with resolution of 0.4nm are plotted by black lines for reference. (a) Experimental results for a 404nm solid state laser by using the regular polychromat (red lines) with spectrum from 380nm to 780nm and = 2nm. Top left inset: photograph of the dispersed image in the image plane (d = 90mm). Right inset: magnified view of the photon flux spectrum between 380nm and 440nm. Bottom left inset: evolution of the relative image error ε versus iteration number. (b) Experimental results for a 532nm solid state laser. Red lines: using the regular polychromat with spectrum from 400nm to 800nm and = 2nm. Blue lines: using the random polychromat with spectrum from 450nm to 900nm and = 1nm. Left inset: photograph of the dispersed image in the image plane of the regular polychromat (d = 90mm). Right inset: magnified view of the photon flux spectrum between 525nm and 555nm. All the plots in (a) and (b) are normalized and interpolated to 0.2nm wavelength spacing. The peak wavelengths λ0 and FWHMs Δλ are denoted by the same colors as the corresponding plots.

Fig. 3
Fig. 3

Spectrum extraction results for LEDs. The photon flux spectra obtained by a conventional spectrometer with resolution of 0.4nm are shown by black lines for reference. Insets: normalized CCD images representing intensity distributions of the output electric signals. (a) – (d) Experimental results (red lines) using the regular polychromat at d = 90mm with spectrum from 400nm to 800nm and = 2nm. (e) – (h) Experimental results (blue lines) using the random polychromat at d = 450mm with spectrum from 450nm to 900nm and = 1nm. (a) and (e) are of a blue LED. (b) and (f) are of a green LED. (c) and (g) are of a yellow LED. (d) and (h) are of red LED. (i) Spectrum extraction results of two spectrally distinct but spatially overlapping LEDs (a blue LED and a green LED). (j) A magnified plot of (i) from 450nm to 550nm. All the plots are normalized and interpolated to 0.2nm wavelength spacing. The peak wavelengths λ0 and FWHMs Δλ of the LED spectra are labeled using the same color codes.

Fig. 4
Fig. 4

Spectrum extraction results of broadband sources and validation of spectral resolution. The photon flux spectra measured by a conventional spectrometer with resolution of 0.4nm are plotted with black lines for reference. Insets: normalized sensor images representing intensity distributions of the output electric signals. (a) – (d) Experimental results (red lines) using a Xenon lamp and the regular polychromat at d = 90mm with spectrum from 400nm to 800nm and = 2nm. (e) – (h) Experimental results (blue lines) using a super-continuum source and the random polychromat at d = 450mm with spectrum from 450nm to 900nm and = 1nm. (a) is the Xenon lamp spectrum and (b) – (d) are the transmitted spectra through various samples when illuminated by collimated light from the Xenon lamp. (e) is the super-continuum source spectrum and (f) – (h) are the transmitted spectra through various samples when illuminated by collimated light from the super-continuum source. The samples are a pink ruler ((b) and (f)), a pair of laser glasses ((c) and (g)), an organic chromophore (BTE) on a glass slide ((d) and (h)). All the plots are normalized and interpolated to 0.2nm. (I) Magnified view of the measured (black line) and the extracted (blue line) spectra of the super-continuum source in (e). Two shallow peaks separated by 1.1nm are properly resolved while the other two separated by 0.6nm are not. (j) and (k) Extracted spectra (blue lines) by the image numerically constructed by the measured SS-PSF of the random polychromat at d = 450nm. The original spectra (black lines) are synthesized by the 532nm laser spectrum and the same but red-shifted by 0.8nm (j) and by 1.2nm (k), respectively.

Fig. 5
Fig. 5

Simulated spectral resolution (a) versus groove width with d = 450mm, N = 2000 and H = 1.2µm; and (b) versus number of grooves with d = 450mm, Δx = 3µm and H = 1.2µm.

Fig. 6
Fig. 6

Analysis of parameters in the DBS-based extraction algorithm. They are derived from the Xenon lamp experiment with the regular polychromat. The reference spectrum was collected by Ocean Optics Jaz Spectrometer (black solid lines) with resolution of 0.4nm. And the extraction results are plotted in red solid lines. (a) – (e) Results of changing spectral sampling rate . Unit perturbation is kept at 0.005 and the initial solution is a Gaussian function. (f) – (j) Results of changing unit perturbation . is kept at 2nm and the initial solution is a Gaussian function. Results of using different initial solutions: (k) started from a uniform spectrum, (l) started from a random spectrum, (m) started from a Gaussian function with central wavelength of 600nm and FWHM of 50nm. = 2nm and = 0.005.

Fig. 7
Fig. 7

Spectrum extraction results of an ultra-broadband spectrum (AM1.5 solar spectrum from 300nm to 2500nm).The black line is the standard spectrum and the green line is the spectrum extracted by using the simulated random polychromat at d = 500mm and the DBS method with spectral sampling rate of ~0.11nm. (b) Error between the reference and the extracted spectra. (c) Zoom-in plot of the reference and extracted spectra between 900nm and 1000nm. (d) Simulated SS-PSF with spatial range from X’ = −4.5mm to X’ = 4.5mm and spectral range from 300nm to 2500nm. (e) Zoom-in plot of the simulated SS-PSF enclosed by the cyan block in (d). Both (d) and (e) are normalized. (f) Spectral correlation analysis of the simulated polychromat with the predicted resolution of ~0.112nm (inset: calculated resolution spectrum of the design).

Tables (1)

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Table 1 Geometric parameters of the random polychromat for ultra-broadband spectrum extraction

Equations (4)

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S=PSFQEΦ ,
ε= 1 N ( Err ) 2 ,
PSF(λ,x')= I(λ,x') I dark (λ) I ref (λ) I dark (λ) ,
C(δλ,x')= <PSF(λ,x')PSF(λ+δλ,x')> <PSF(λ,x')><PSF(λ+δλ,x')> 1,

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