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Virtual Journal for Biomedical Optics

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  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 11 — Oct. 31, 2012
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Narrowband multispectral filter set for visible band

K. Walls, Q. Chen, J. Grant, S. Collins, D.R.S. Cumming, and T.D. Drysdale  »View Author Affiliations


Optics Express, Vol. 20, Issue 20, pp. 21917-21923 (2012)
http://dx.doi.org/10.1364/OE.20.021917


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Abstract

We design, fabricate and characterise a narrowband Fabry-Pérot multispectral filter set for the visible range (400–750nm) that is suitable for integration onto complementary-metal oxide-semiconductor image sensors. We reduce the fabrication steps by fixing the physical cavity length and altering the effective optical length instead. Using electron-beam lithography, a sub-wavelength hole array is patterned in a silicon nitride cavity layer, backfilled with poly(methyl methacrylate), and bounded by aluminium mirrors to create 23 filters with full-width half-maximums of 22–46nm. Additionally, for colourmetric reproduction applications, using as few as 10 filters gives a colour difference (CIEDE2000) of 0.072, better than trichromatic filters.

© 2012 OSA

1. Introduction

Multispectral imaging systems are increasingly in demand for applications including agricultural monitoring systems [1

1. A. K. Tilling, G. O’Leary, J. G. Ferwerda, S. D. Jones, G. Fitzgerald, and R. Belford, “Remote sensing to detect nitrogen and water stress in wheat,” in Proc. 13th ASA Conference. N. C. Turner, T. Acuna, and R. C. Johnson, eds. (2006) pp.10–14.

], quality control [2

2. A. A. Gowen, C. P. O’Donnell, P. J. Cullen, G. Downey, and J. M. Frias, “Hyperspectral imaging - an emerging process analytical tool for food quality and safety control,” Trends in Food Sci. and Tech. 18, 590–598 (2007). [CrossRef]

], art conservation [3

3. H. Liang, “Advances in multispectral and hyperspectral imaging for archaeology and art conservation,” Appl. Phys. A: Material Sci. and Process. 106, 309–323 (2012). [CrossRef]

] and medical [4

4. I. Kuzmina, I. Diebele, D. Jakovels, J. Spigulis, L. Valeine, J. Kapostinsh, and A. Berzina, “Towards noncontact skin melanoma selection by multispectral imaging analysis,” J. of Biomedical Optics Let. 16, 1–3 (2011).

] and scientific imaging [5

5. R. M. Levenson, D. T. Lynch, H. Kobayashi, J. M. Backer, and M. V. Backer, “Multiplexing with multispectral imaging: from mice to microscopy,” ILAR Journal 49, 78–88 (2008). [PubMed]

]. Contemporary multispectral imaging technologies typically exploit dispersion (prisms, gratings) or interference (etalons). Dispersive methods offer fine resolution but are difficult to intergrate with an array of photodetectors so are often best for single point measurements. Interference-based imagers that use filter wheels in front of the camera are too bulky for the smallest satellites and unmanned aerial vehicles and their speed can be limited by their mechanical nature. Faster systems can be made with electronically tuneable filters but the fabrication of multiple filter and polariser stages is not trivial [6

6. S. Zhi-Xue, L. Jian-Feng, Z. Da-Yong, L. Yong-Quan, L. Yan, H. Li-Xian, L. Hai-Tao, and L. Fei, “Research on LC-based spectral imaging system for visible band,” Proc. SPIE 8181, 1–7 (2011).

], and multiple exposures are still required as for filter wheels. An emerging approach is the integration of filters directly on top of the image sensor’s pixel array, providing multispectral imaging in a single exposure. For example two multispectral filters were demonstrated at 1500nm using 41 layer photonic crystals [7

7. A. Mehta, R. C. Rumpf, Z. Roth, and E. G. Johnson, “Nanofabrication of a space-variant optical transmission filter, ” Opt. Lett. 31, 2903–2905 (2006) [CrossRef] [PubMed]

], but in the visible range only trichromatic (RGB) filters have been realised [8

8. L. Frey, P. Parrein, J. Raby, C. Pelle, D. Herault, M. Marty, and J. Michailos “Color filters including infrared cut-off integrated on CMOS image sensor,” Opt. Express 19, 13073 – 13080 (2011). [CrossRef] [PubMed]

]. In comparison Fabry-Pérot (FP) filters are much thinner, and so can be expected to have less crosstalk when arrayed.

Conventionally, the passband of a FP filter is determined by the cavity length. Each additional passband that is desired in a planar array of FP filters costs additional fabrication steps. It would be preferable to fix the cavity length and tune the optical length instead. This concept has been validated in [9

9. A. Mitra, H. Harutyunyan, S. Palomba, and L. Novotnyo, “Tuning the cavity modes of a fabry-perot resonator using gold nanoparticles,” Opt. Lett. 35, 953 – 955 (2010). [CrossRef] [PubMed]

], where gold nanoparticles doped a poly(methyl methacrylate) (PMMA) filled cavity to good effect but in an uncontrolled manner. We present here a technique that provides controlled tuning via lithographic means. We select the effective refractive index of each FP cavity by choosing the fill ratio of its two dielectrics. The remainder of the paper describes the design of a full set of narrowband filters for the visible range that is compatible with CMOS image sensors, the fabrication and characterisation of an example set, and an evaluation of the colourimetric imaging performance.

2. Design

Our FP cavity contains two dielectrics bounded by optically thin aluminium (Al) mirrors. We control the dielectric filling ratio lithographically, by etching holes into a deposited layer of silicon nitride (SiN) and backfilling with PMMA. PMMA is spin castable and hardens on baking. A fully intact upper mirror layer can then be deposited. A further layer of PMMA is spin-cast on top to act as an anti-reflection layer (ARL), both increasing transmission and preventing the mirror oxidising. A schematic of the proposed filter structure is shown in Fig. 1(a), where holes of diameter d and period Λ are etched into the SiN, and assuming planarisation after backfilling. The inverse structure, where the etch leaves SiN pillars, is not shown. Neglecting dispersion, for a fixed physical length cavity comprising two dielectrics of refractive index n1, n2 the maximum tuning range is 1 : n2/n1 where n2 > n1, or 38% for SiN (n2 = 2.05) and PMMA (n1 = 1.49).

Fig. 1 (a) Schematic of the filter vertical cross section. (b) A plot of the cavity neff using Eq.1, with d=60nm (solid), 100nm (– –) and 180nm (···) for Λ=200nm. This is compared to the neff calculated from FDTD simulation for tSiN =800nm (black), 500nm (green), 200nm (blue). With d=60nm (square), 100nm (diamond) and 180nm (cross).

We studied the behaviour of the hole structure (fill ratio f=π(d2)2/Λ2) in detail using a commercial finite-difference time-domain (FDTD) tool (Lumerical) to account for the expected dispersion. The effective refractive index (neff) of the cavity was extracted from the calculated transmission spectra and was shown to depend only on the ratio of the hole-size to the period of the hole array and not on the cavity length tSiN, for practical structures of interest to us. The results were well fitted by the average of the second order transverse electric ( εTE(2)) and transverse magnetic ( εTM(2)) effective medium theory (EMT) [10

10. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Soviet Physics JETP 2, 466–475 (1956).

]:
neff(λ)=εTE(2)(λ)+εTM(2)(λ)2ε0
(1)
A subset of the results showing typical levels of agreement is plotted in Fig. 1(b), for a representative range of hole sizes and cavity lengths, with FDTD results as markers and Eq. 1 as lines.

In order to ensure sufficient free spectral range that each filter has only one transmission peak in the visible range, careful selection of the physical cavity length (tSiN) was required, as well as optimisation of the mirror thickness, hole/pillar diameter, array period and ARL thickness. We studied an extensive parameter range using an adapted version of the FDTD tool TEMPEST [11

11. A. Wong and A. R. Neureuther, “Rigorous three-dimensional time-domain finite-difference electromagnetic simulation for photolithographic applications,” IEEE Trans. Semicond. Manuf. 8, 419–431 (1995). [CrossRef]

]. Aluminium was modelled by the Drude + 2 critical points model [12

12. A. Vial and T. Laroche, “Description of the dispersion properties of metals by means of the critical points model and the application to the study of resonant structures using the FDTD method,” J. Phys. D: Appl. Phys 40, 7152–7158 (2007). [CrossRef]

]. The chosen design parameters were tSiN=150nm (first resonance) and tSiN=240nm (second resonance) for the long and short wavelength halves of the band respectively, 20nm mirrors and 100nm ARL, Λ=200nm and both pillar and hole structures with 60 ≤ d ≤ 180 nm. The use of two cavity lengths is consistent with the expected maximum tuning range of a single cavity. The transmission of the filters is plotted in Fig. 2. Full-width half-maximums (FWHM) of 13–36nm were achieved corresponding to finesse of 10–30, or mirror reflectivity of 0.7–0.9. The transmission and FWHM is typically better at shorter wavelengths due to dispersion in the aluminium.

Fig. 2 The FDTD simulated spectral response of a filter set with Λ=200nm. 3D sketches identify structure type and thickness. Taller sketches (see legend) represent tSiN =240nm; shorter, tSiN =150nm.

3. Fabrication

We fabricated a subset of the structures in Fig. 1, selecting a single physical cavity length. The bottom Al mirror and the SiN cavity were deposited onto a microscope slide by a Plassys MEB 400S Electron Beam Evaporator and an Oxford Instruments PECVD tool respectively. Spin-coated ZEP520A electron beam (EB) resist was exposed using a Vistec VB6 UHR EWF lithography tool. The holes were etched using CHF3/O2 in a Plasmalab 80 Plus. After resist removal, PMMA was spin-coated as backfill and baked. We did not polish away the slight overfill. The upper Al mirror was deposited. PMMA was spin-coated on top of the whole stack to form the ARL. An array of 6 filter subsets, each with a different mask hole size, was fabricated simultaneously. Different filter passbands were produced in each of the sets by altering the EB dosage (237–2000 μC/cm2) to achieve fine variation of the hole size.

4. Results

The transmission was measured using a TFProbe MSP300 spectrometer, and is plotted in Fig. 3 for a selection of 23 filters that cover the whole visible range. The insert shows white light transmission microscope images. The measured results are in good agreement with the simulations, with transmission highest and FWHM narrowest at the shorter wavelengths as expected. Quantitatively the measured transmission is 4–13% (8–17% simulated) and the measured FWHM is 22–46nm (13–36nm simulated) both in reasonable agreement with the FDTD simulations in Fig. 2. The reduced transmission compared to a trichromatic dye filter can be compensated for once in use, by opening the aperture of the imaging system’s lens by 2–3 stops. We attribute the small discrepancies to the unexpectedly wide tuning range we demonstrated with this hole-only, single physical cavity length set. We have introduced an external filter (High-pass, λc=525nm) to eliminate any unwanted second resonances for clarity in Fig. 3 although it does not completely block the second resonance in the green of the two longest wavelength filters. Note that a FP filter set using two cavity lengths does not need the additional filter because the unwanted resonances lie outside the visible band. We have already demonstrated that aluminium-based filters can be integrated on a CMOS imager [13

13. Q. Chen, D. Das, D. Chitnis, K. Walls, T. D. Drysdale, S. Collins, and D. R. S. Cumming, “A CMOS image sensor integrated with plasmonic colour filters,” Plasmonics 7, [CrossRef] (2012). [PubMed]

].

Fig. 3 The measured spectral response of the filters. Line colours indicate nominal hole diameter in mask before EB dosage adjustment. A montage of the white-light microscope images of the filters is shown (Insert).

A focused ion beam (FIB) was used to mill a hole so that a scanning electron microscope (SEM) could examine the cross-section; see Fig. 4(a). The Al and SiN thickness was uniform across all filters (approximately 15nm and 200nm respectively). The overfill layer thickness varied with hole size as expected (15–90nm) giving a slight red shift. After careful study of the dimensions, overfill, materials and spectrometer set-up, we attribute the widely extended tuning range to the unexpected dispersion in the SiN. In our machine, a significant increase in silicon (Si) content arises if the SiH4 flow rate increases during deposition [14

14. H. Zhou, C. Sim, A. Glidle, C. Hodson, R. Kinsey, and C. D. W. Wilkinson, Properties of Silicon Nitride by Room-temperature Inductively Coupled Plasma Deposition (Wiley-VCH Verlag GmbH and Co. KGaA, 2005) 77–86.

]. The resulting mixture of Si and SiN is more dispersive and lossy than stoichiometric Si3N4. The impact on device performance can be illustrated by estimating the average refractive index of the Si/SiN mixture using zeroth-order EMT. Substituting this index for that of stoichiometric Si3N4 in Eq. 1 and using the T-matrix method [15

15. J. H. Davies, The Physics of Low-dimensional Semiconductors : An Introduction (Cambridge University Press, 1998).

] to rapidly calculate the overall transmission, we replicated the measured performance. We plot the measured response of the filter in Fig. 4(b), along with two simulated responses, one using stoichiometric Si3N4, the other the Si-rich SixNy obtained during deposition. We simulated the remainder of the filters using the Si-rich SixNy model and the results are plotted in Fig. 4(c), obtaining transmission between 2–7% and FWHM 22–40nm. The simulated FWHM are in excellent agreement with the measured results (22–46nm) and the reduction in transmission from 4–13% is equivalent to overestimating the Al layer thickness by a few nanometres. This experimental result suggests non-standard materials can be usefully exploited.

Fig. 4 Analysis of the fabricated structure (a) scanning electron micrograph of cross section, (b) measured (without additional filter) and simulated transmission for both PMMA-Si3N4 and PMMA-Si-rich(60%) SixNy (40%) cavities. The dimensions used are as measured from (a); Al 15nm, tSiN 200nm, overfill 90nm, d 140nm and ARL 85nm. Simulations at non-normal incidence also shown. (c) T-matrix simulations of all 23 measured filters using the Si-rich SixNy model. The effect of the additional filter used in Fig. 3 is included for clarity.

The performance of the filters under non-normal incident illumination, as occurs at the pixel-array edges, was investigated by simulation assuming two standard camera configurations. First a telephoto lens (e.g. for surveillance or long-focus microscopy) with ±20° field of view and second, a single lens reflex (SLR) camera objective with up to a ±50° field of view [16

16. E. Hecht, Optics (Addison-Wesley, 2002).

]. For sake of space we show the results superimposed in Fig. 4(b) for the stoichiometric Si3N4 case, for incidence at ±0° and ±25°. There is little change for the moderate incidence angle (telephoto lens) but a small blue shift of 11nm at ±25° (SLR lens). An analysis of the Poynting vector of the transmitted light over a plane 200nm below a typical filter shows a maximum variation in angle of 0.01% (0.1%) and in magnitude of 0.03% (0.2%) from the expected direction for illumination incident at an angle of 0° (25°) to the normal. This negligible degree of scattering is consistent with the subwavelength nature of the structure.

In addition to detecting narrow spectral bands, multispectral filters offer improved colour reproduction as measured by the CIEDE2000 formula [17

17. G. Sharma, W. Wu, and E. N. Dalal, “The CIEDE2000 color-difference formula: implementation notes, supplementary test data and mathematical observations,” Color Res. Appl. 30, 21–30 (2005). [CrossRef]

]. We used 24 patches of the Gretag-Macbeth colour checker as training data, then simulated a test of the filter set by multiplying their measured transmission spectra by the spectra of 1269 patches from the Munsell colour book under D65 illumination. For all 23 filters we obtain ΔE2000=0.0474, nearly 60 times better than a representative tricolour filter that achieves 2.711 [18

18. R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Signal Process. Mag. 22, 34–34 (2005). [CrossRef]

]. We studied the relationship between ΔE2000 and number of filters by using a genetic algorithm to select optimal members of the set. The colour difference linearly increases to 0.072 for 10 filters (0.005/filter), but from 10 to 6 filters the additional colour difference per filter removed increases to 0.070/filter, giving ΔE2000=0.35 for 6 filters.

5. Conclusion

The fabrication of a set of 23 narrowband filters, with FWHM of 22–46nm, covering the full visible band (400–750nm) has been demonstrated, with better CIEDE2000 colour difference performance than trichromatic filters. The structures use holes etched into the dielectric layer (SiN) of a FP cavity that is then backfilled with a second dielectric (PMMA) to act as a tuning mechanism. The fabrication cost and complexity is reduced compared to varying the physical cavity length alone. We used only CMOS compatible materials to illustrate that our approach is suitable for direct integration onto CMOS image sensors in industrial foundries. The application of such narrowband filters across a sensor array will enable the simultaneous detection of the full visible spectrum at high resolution in a compact system. We expect this approach will enable multispectral imaging in CubeSats and small unmanned aerial vehicles.

Acknowledgments

This work was supported by the Engineering and Physical Sciences Research Council ( EP/G008329/1). Damien McGrouther operated the FIB milling machine.

References and links

1.

A. K. Tilling, G. O’Leary, J. G. Ferwerda, S. D. Jones, G. Fitzgerald, and R. Belford, “Remote sensing to detect nitrogen and water stress in wheat,” in Proc. 13th ASA Conference. N. C. Turner, T. Acuna, and R. C. Johnson, eds. (2006) pp.10–14.

2.

A. A. Gowen, C. P. O’Donnell, P. J. Cullen, G. Downey, and J. M. Frias, “Hyperspectral imaging - an emerging process analytical tool for food quality and safety control,” Trends in Food Sci. and Tech. 18, 590–598 (2007). [CrossRef]

3.

H. Liang, “Advances in multispectral and hyperspectral imaging for archaeology and art conservation,” Appl. Phys. A: Material Sci. and Process. 106, 309–323 (2012). [CrossRef]

4.

I. Kuzmina, I. Diebele, D. Jakovels, J. Spigulis, L. Valeine, J. Kapostinsh, and A. Berzina, “Towards noncontact skin melanoma selection by multispectral imaging analysis,” J. of Biomedical Optics Let. 16, 1–3 (2011).

5.

R. M. Levenson, D. T. Lynch, H. Kobayashi, J. M. Backer, and M. V. Backer, “Multiplexing with multispectral imaging: from mice to microscopy,” ILAR Journal 49, 78–88 (2008). [PubMed]

6.

S. Zhi-Xue, L. Jian-Feng, Z. Da-Yong, L. Yong-Quan, L. Yan, H. Li-Xian, L. Hai-Tao, and L. Fei, “Research on LC-based spectral imaging system for visible band,” Proc. SPIE 8181, 1–7 (2011).

7.

A. Mehta, R. C. Rumpf, Z. Roth, and E. G. Johnson, “Nanofabrication of a space-variant optical transmission filter, ” Opt. Lett. 31, 2903–2905 (2006) [CrossRef] [PubMed]

8.

L. Frey, P. Parrein, J. Raby, C. Pelle, D. Herault, M. Marty, and J. Michailos “Color filters including infrared cut-off integrated on CMOS image sensor,” Opt. Express 19, 13073 – 13080 (2011). [CrossRef] [PubMed]

9.

A. Mitra, H. Harutyunyan, S. Palomba, and L. Novotnyo, “Tuning the cavity modes of a fabry-perot resonator using gold nanoparticles,” Opt. Lett. 35, 953 – 955 (2010). [CrossRef] [PubMed]

10.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Soviet Physics JETP 2, 466–475 (1956).

11.

A. Wong and A. R. Neureuther, “Rigorous three-dimensional time-domain finite-difference electromagnetic simulation for photolithographic applications,” IEEE Trans. Semicond. Manuf. 8, 419–431 (1995). [CrossRef]

12.

A. Vial and T. Laroche, “Description of the dispersion properties of metals by means of the critical points model and the application to the study of resonant structures using the FDTD method,” J. Phys. D: Appl. Phys 40, 7152–7158 (2007). [CrossRef]

13.

Q. Chen, D. Das, D. Chitnis, K. Walls, T. D. Drysdale, S. Collins, and D. R. S. Cumming, “A CMOS image sensor integrated with plasmonic colour filters,” Plasmonics 7, [CrossRef] (2012). [PubMed]

14.

H. Zhou, C. Sim, A. Glidle, C. Hodson, R. Kinsey, and C. D. W. Wilkinson, Properties of Silicon Nitride by Room-temperature Inductively Coupled Plasma Deposition (Wiley-VCH Verlag GmbH and Co. KGaA, 2005) 77–86.

15.

J. H. Davies, The Physics of Low-dimensional Semiconductors : An Introduction (Cambridge University Press, 1998).

16.

E. Hecht, Optics (Addison-Wesley, 2002).

17.

G. Sharma, W. Wu, and E. N. Dalal, “The CIEDE2000 color-difference formula: implementation notes, supplementary test data and mathematical observations,” Color Res. Appl. 30, 21–30 (2005). [CrossRef]

18.

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Signal Process. Mag. 22, 34–34 (2005). [CrossRef]

OCIS Codes
(050.2230) Diffraction and gratings : Fabry-Perot
(330.1730) Vision, color, and visual optics : Colorimetry
(050.2065) Diffraction and gratings : Effective medium theory
(110.4234) Imaging systems : Multispectral and hyperspectral imaging
(220.4241) Optical design and fabrication : Nanostructure fabrication

ToC Category:
Diffraction and Gratings

History
Original Manuscript: June 13, 2012
Revised Manuscript: September 3, 2012
Manuscript Accepted: September 4, 2012
Published: September 10, 2012

Virtual Issues
Vol. 7, Iss. 11 Virtual Journal for Biomedical Optics

Citation
K. Walls, Q. Chen, J. Grant, S. Collins, D.R.S. Cumming, and T.D. Drysdale, "Narrowband multispectral filter set for visible band," Opt. Express 20, 21917-21923 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-20-21917


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References

  1. A. K. Tilling, G. O’Leary, J. G. Ferwerda, S. D. Jones, G. Fitzgerald, and R. Belford, “Remote sensing to detect nitrogen and water stress in wheat,” in Proc. 13th ASA Conference. N. C. Turner, T. Acuna, and R. C. Johnson, eds. (2006) pp.10–14.
  2. A. A. Gowen, C. P. O’Donnell, P. J. Cullen, G. Downey, and J. M. Frias, “Hyperspectral imaging - an emerging process analytical tool for food quality and safety control,” Trends in Food Sci. and Tech.18, 590–598 (2007). [CrossRef]
  3. H. Liang, “Advances in multispectral and hyperspectral imaging for archaeology and art conservation,” Appl. Phys. A: Material Sci. and Process.106, 309–323 (2012). [CrossRef]
  4. I. Kuzmina, I. Diebele, D. Jakovels, J. Spigulis, L. Valeine, J. Kapostinsh, and A. Berzina, “Towards noncontact skin melanoma selection by multispectral imaging analysis,” J. of Biomedical Optics Let.16, 1–3 (2011).
  5. R. M. Levenson, D. T. Lynch, H. Kobayashi, J. M. Backer, and M. V. Backer, “Multiplexing with multispectral imaging: from mice to microscopy,” ILAR Journal49, 78–88 (2008). [PubMed]
  6. S. Zhi-Xue, L. Jian-Feng, Z. Da-Yong, L. Yong-Quan, L. Yan, H. Li-Xian, L. Hai-Tao, and L. Fei, “Research on LC-based spectral imaging system for visible band,” Proc. SPIE8181, 1–7 (2011).
  7. A. Mehta, R. C. Rumpf, Z. Roth, and E. G. Johnson, “Nanofabrication of a space-variant optical transmission filter, ” Opt. Lett.31, 2903–2905 (2006) [CrossRef] [PubMed]
  8. L. Frey, P. Parrein, J. Raby, C. Pelle, D. Herault, M. Marty, and J. Michailos “Color filters including infrared cut-off integrated on CMOS image sensor,” Opt. Express19, 13073 – 13080 (2011). [CrossRef] [PubMed]
  9. A. Mitra, H. Harutyunyan, S. Palomba, and L. Novotnyo, “Tuning the cavity modes of a fabry-perot resonator using gold nanoparticles,” Opt. Lett.35, 953 – 955 (2010). [CrossRef] [PubMed]
  10. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Soviet Physics JETP2, 466–475 (1956).
  11. A. Wong and A. R. Neureuther, “Rigorous three-dimensional time-domain finite-difference electromagnetic simulation for photolithographic applications,” IEEE Trans. Semicond. Manuf.8, 419–431 (1995). [CrossRef]
  12. A. Vial and T. Laroche, “Description of the dispersion properties of metals by means of the critical points model and the application to the study of resonant structures using the FDTD method,” J. Phys. D: Appl. Phys40, 7152–7158 (2007). [CrossRef]
  13. Q. Chen, D. Das, D. Chitnis, K. Walls, T. D. Drysdale, S. Collins, and D. R. S. Cumming, “A CMOS image sensor integrated with plasmonic colour filters,” Plasmonics7, (2012). [CrossRef] [PubMed]
  14. H. Zhou, C. Sim, A. Glidle, C. Hodson, R. Kinsey, and C. D. W. Wilkinson, Properties of Silicon Nitride by Room-temperature Inductively Coupled Plasma Deposition (Wiley-VCH Verlag GmbH and Co. KGaA, 2005) 77–86.
  15. J. H. Davies, The Physics of Low-dimensional Semiconductors : An Introduction (Cambridge University Press, 1998).
  16. E. Hecht, Optics (Addison-Wesley, 2002).
  17. G. Sharma, W. Wu, and E. N. Dalal, “The CIEDE2000 color-difference formula: implementation notes, supplementary test data and mathematical observations,” Color Res. Appl.30, 21–30 (2005). [CrossRef]
  18. R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Signal Process. Mag.22, 34–34 (2005). [CrossRef]

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