Fast wavelength calibration method for spectrometers based on waveguide comb optical filter Zhengang Yu, Meizhen Huang, Yang Wang, Ye Zou, Zhenhua Sun, and Zhuangqi Cao Citation: Review of Scientific Instruments 86, 043103 (2015); doi: 10.1063/1.4914026 View online: http://dx.doi.org/10.1063/1.4914026 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/86/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Surface plasmon resonance based integrable micro spectrometer Appl. Phys. Lett. 106, 101106 (2015); 10.1063/1.4914893 Straightforward correction for the astigmatism of a Czerny–Turner spectrometer Rev. Sci. Instrum. 81, 023503 (2010); 10.1063/1.3309792 Configurable-bandwidth imaging spectrometer based on an acousto-optic tunable filter Rev. Sci. Instrum. 77, 073108 (2006); 10.1063/1.2221542 Precision spectrometer for measurement of specular reflectance Rev. Sci. Instrum. 73, 2237 (2002); 10.1063/1.1477607 A simple, low-cost, versatile charge-coupled device spectrometer for plasma spectroscopy Rev. Sci. Instrum. 68, 1036 (1997); 10.1063/1.1147781

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REVIEW OF SCIENTIFIC INSTRUMENTS 86, 043103 (2015)

Fast wavelength calibration method for spectrometers based on waveguide comb optical filter Zhengang Yu,1,2 Meizhen Huang,1,a) Yang Wang,2 Ye Zou,1 Zhenhua Sun,2 and Zhuangqi Cao2 1 2

Department of Instrument Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

(Received 31 October 2014; accepted 20 February 2015; published online 2 April 2015) A novel fast wavelength calibration method for spectrometers based on a standard spectrometer and a double metal-cladding waveguide comb optical filter (WCOF) is proposed and demonstrated. By using the WCOF device, a wide-spectrum beam is comb-filtered, which is very suitable for spectrometer wavelength calibration. The influence of waveguide filter’s structural parameters and the beam incident angle on the comb absorption peaks’ wavelength and its bandwidth are also discussed. The verification experiments were carried out in the wavelength range of 200–1100 nm with satisfactory results. Comparing with the traditional wavelength calibration method based on discrete sparse atomic emission or absorption lines, the new method has some advantages: sufficient calibration data, high accuracy, short calibration time, fit for produce process, stability, etc. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4914026]

I. INTRODUCTION

Spectrometers are widely used in biochemical analysis, food and drug safety monitoring, material properties research, and so on.1–4 However, in order to obtain reliable detection or analysis result, the wavelength calibration for spectrometers needs to be done regularly, which is of great importance. So the standard lamp having characteristic emission spectrum is often chosen for calibration, such as mercury argon lamp, neon lamp, etc.;5–7 the alternative approach is using standard substances having characteristic absorption spectrum, such as holmium oxide solution, holmium glass, etc.8–10 The essence of wavelength calibration for CCD-based spectrometer is to find the corresponding relationship between pixel index and wavelengths. A common approach is the polynomial fitting method based on a few reference atomic lines.5 Although the atomic lines are able to provide absolute reference at discrete wavelengths, the corresponding wavelengths of pixels are only calculated accordingly, which highly depends on the structure and design of each spectrometer. There are some problems confronted by spectrometer designers and producers: the accuracy of calibration depends greatly on the number of lamp’s characteristic peaks which are insufficient in some wavelength range, the distribution of peaks is uneven, and the calibrating process is slow. Perret et al. utilized a Fabry-Perot multilayer structure filter, which provides multiple sharp calibration peaks over the full range to realize high precision wavelength calibration.11,12 When a standard spectrometer is available, a sufficiently dense frequency comb like wavelength reference source or any device to produce such a spectrum from a continuous wide-spectrum one would solve these problems.

a)Author to whom correspondence should be addressed. Electronic mail:

[email protected].

In this paper, a fast high accuracy wavelength calibration method for spectrometers based on waveguide comb optical filter (WCOF) is proposed. A double metal-cladding optical waveguide is designed as the comb optical filter, which can convert wide-spectrum of ordinary lamp into a comb like spectrum. What is more, the comb characteristic spectrum is tunable. With a standard spectrometer, it solves the problem of insufficient reference lines for calibration and uneven distribution of characteristic peaks.

II. THEORETICAL ANALYSIS OF WCOF

The structure of the WCOF is shown in Fig. 1. The layers from top to bottom are coupling prism, metal coating layer, waveguide layer, and metal substrate layer, of which the dielectric constants are ε 1, ε 2, ε 3, and ε 4, respectively. The waveguide is a double metal-cladding optical waveguide, also called symmetrical metal-cladding optical waveguide (SMCW). Fig. 1 shows, beam A1 with wavelength λ emission at the interface x = 0 at the angle of θ 1. After being coupled by the waveguide, the beam A1 turns to reflection beam B1. According to distributing function and boundary conditions of the electromagnetic field inside the waveguide, reflectivity is related to the waveguide’s parameters and the incident light’s wavelength, and can be expressed as13 R = f (θ 1, ε 1, ε 2, ε 3, d 1, d 2, λ),

(1)

where θ 1, ε 1, ε 2, ε 3, d 1, and d 2 maintains the same, the reflectivity of light in different wavelengths can be obtained, of which the reflection spectrum has comb shape. The eigen-equations of WCOF (ε 2 = ε 4) modes are14–16 for mode TE, ( ) α2 κ 3d 2 = mπ + 2 arctan , (2) κ3

0034-6748/2015/86(4)/043103/6/$30.00 86, 043103-1 © 2015 AIP Publishing LLC This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 149.150.51.237 On: Fri, 03 Apr 2015 09:36:13

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FIG. 1. Schematic of the structure of WCOF.

for mode TM, ) ε 3α 2 κ 3d 2 = mπ + 2 arctan , ε2 κ3 (

(3)

 where κ i = k 02ε i − β 2, is the horizontal wave vector of the √ √ ε 1 sin θ 1 is the longitudinal ith layer, β = k0 ε 1 sin θ 1 = 2π λ wave vector, α = −iκ . When m is i ( ) i (aεlarge ) value, then mπ ≫ α 2 arctan ακ 2 and mπ ≫ 2 arctan ε3 κ 2 , the TE and TM 3 2 3 modes are degenerate. Equations (2) and (3) can be simplified as κ 3d 2 = mπ.

(4)

Considering two adjacent modes (∆κ 3d 2 = π), the wavenumber interval of them is 1 ∆ν = . (5)  2d 2 ε 3 − ε 1 sin2 θ 1 According to Eq. (5), the wavenumber interval ∆ν relates to the incident angle θ 1, the thickness of waveguide layer d 2, the dielectric constant of waveguide layer and coupling layer ε 3, ε 1. It is irrelevant to the cladding structure. So for a designed and produced waveguide device, the wavenumber interval ∆ν also can be tuned by changing θ 1, means the comb spectrum is tunable.

be large, the dielectric constant ε 3 of the waveguide layer’s material should be large, and the dielectric constant ε 1 of the coupling layer’s material should be small. For example, setting d 1 = 40 nm, d 2 = 50 nm, selecting N-SF11(SCHOTT,ε3) as the waveguide layer and FK1 (SCHOTT, ε 1) as the coupling layer, and metal gold as the cladding layer, of which the dielectric constant ε relates to wavelength λ.17 Based on the above data and the expression R = f (θ1,ε1,ε2,ε3, d1, d2, λ), the reflecting spectrum can be obtained based on Eq. (1). Under the assumption that the incident light’s spectrum range covers the spectrometer spectral range, when the incident angle θ 1 = 5◦, reflectivity R will change with the wavenumber, as is shown in Fig. 2. Under this condition, it is known from Eq. (5) that the wavenumber’s interval period of the comb spectrum ∆ν ≈ 50 cm−1, and the total measuring wavenumber of the spectrometer is 2500 cm−1, so the number of spectral peaks in Fig. 2 can reach up to approximately 50. By measuring these absorption peaks, we can obtain the correspondence between CCD pixels and wavelengths (or wavenumbers). According to Eq. (5), we can change the number and distribution of peaks by changing d 2, ε 3, ε 1, and θ 1. As is shown that filtering by this waveguide filter, a large number of characteristic peaks can be obtained from a widespectrum lamp, so it provides more data for calibration, and the distribution of peaks is quite even, which improves the accuracy and reliability of the spectrometer’s calibration in the full spectrum. B. The bandwidth of the comb peak

When getting the spectrum for calibration, the main factor in identifying the exact position of the peak accurately is whether the spectral bandwidth of the peak is small enough. In Fig. 2, the full width at half-maximum (FWHM) of the waveguide comb spectrum optical filter is 1.5 cm−1. However, the thickness and flatness of the metal coating layer will affect the bandwidth of the peak.

III. DESIGN OF WAVEGUIDE COMB FILTER FOR CALIBRATION A. Regulation for comb peaks’ number

Facilitating the problem, we take a Raman spectrometer for example, of which the excitation laser wavelength is 785 nm. The measuring Raman spectrum wavenumbers range is 200–2700 cm−1, so the corresponding measuring spectrum wavelengths range approximately from 795 to 996 nm. In order to obtain sufficient data of the characteristic spectrum, the parameter ∆ν is supposed to be as small as possible. According to the expression of wavenumber’s interval period [Eq. (5)], the incident angle θ 1 of light coupling into the filter should be small, the thickness of the waveguide layer d 2 should

FIG. 2. The reflectivity spectrum of the waveguide comb optical filter (θ 1 = 5◦). This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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Except for the design of the waveguide filter, the divergence angle of incident light is another important factor affecting the FWHM of the spectrum. Considering the changes in emergent light’s wavelength and incident angle, from Eq. (4), we can get   d d 22 k02ε 3 − β 2 = d m2π 2 = 0. (6) Thus, dλ =

λ dd 2 − ( ε 3 d2 ε × 1

λ 2 sin(2θ 1)

− tan θ 1

) dθ 1,

(7)

where d 2 is a constant, and it is further simplified as dλ = − ( ε

3 ε1

λ ×

2 sin(2θ 1)

− tan θ 1

) dθ 1.

(8)

According to Eq. (7), considering the wavelength λ = 996 nm, the incident angle θ 1 = 5◦, when the incident angle deviation ε ∆θ 1 is a constant, according to Eq. (8), the larger ε3 and d 2 1 are, the smaller the spectrum drift ∆λ will be. And that is consistent with the requirement of making ∆ν small enough to obtain sufficient data of correspondence between detector’s pixels and wavelengths. Actually, the incident light has a certain divergence angle, which may be considered as a collection of a plurality of parallel light beams. In this way, the reflectivity of the incident light having a divergent angle may be simulated by the reflectivity’s superposition from the parallel lights in different angles within the range of divergence angle, as shown in Fig. 3. The central incident angle is θ 1, and due to the deviation of the incident angle dθ1, the bandwidth will broaden. For the spectrometer mentioned above, if the resolution is 3–4 cm−1, the FWHM of corresponding wavelength can be about 0.2 nm, ∆λ = 0.2 nm. Substituting ε 1, ε 3, and λ into Eq. (8), we can get the allowed divergent angle of the incident light as follows: (ε ) 2 3 ε 1 × sin(2θ 1) − tan θ 1 ∆θ 1 = − ∆λ ≈ 0.25◦. (9) λ

C. The identifiability of the comb peak

An important part in wavelength calibration is the identification of peak location. There are many methods for calculating the central peak position, such as peak to peak method, curve-fitting method, and centroid method.18 In these methods, the noise of the spectrometer should be considered. The noise might cover weak peaks. When the peak is wide or not sharp enough, and the noise is large, it may also cause some fake peaks. These circumstances will result in inaccuracy of distinguishing peaks. Comparing the intensity difference between the peak pixel and adjacent pixels with dark noise, we can estimate the influence of noise. The dynamic range of spectrometer also represents the noise level. The dynamic range of our test spectrometer is 300:1. Correspondingly, the normalized noise is 1/300. By taking the divergence angle in Eq. (9) into consideration, the reflectivity is obtained as shown in Fig. 4, where the central incident angle θ 1 is 5◦ and ∆θ 1 = 0.25◦. In Fig. 4, the ratio of reflectivity difference between peak pixel and adjacent pixels to the peak height is about 1:5.5, which is larger than the normalized noise. So the influence of noise in searching the peak location can be ignored. In Fig. 5(a), we add a random noise (−1/600 to 1/600) to signals received by the detector. The peak is sharp enough. And the abscissa of the peak is distinguished clearly and not changed, while the ordinate has a small fluctuation caused by noise. In this condition, the interference of noise can be ignored and the peak location can be identified clearly. Similarly, the other peaks can also be distinguished, so that the collimating light with a divergence angle of ∆θ 1 = 0.25◦ can be used in spectrometer’s calibration. When ∆θ 1 increases, the ratio of reflectivity difference between peak pixel and adjacent pixels to the peak height decreases. If this ratio approaches the normalized noise, the influence of noise can no longer be ignored. So we can find an acceptable maximum divergence angle by simulation according to the normalized noise (or dynamic range). This acceptable divergence angle ∆θ 1 is about 1.6◦, and the corresponding bandwidth is about 12 cm−1; Fig. 5(b) gives a result with a

FIG. 3. Reflectivity of the comb filter at different parallel incident angles and FIG. 4. The reflectivity R of the comb filter at allowable divergence angle, the corresponding superimposed effect. when θ 1 = 5◦. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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FIG. 5. (a) The impact of simulation noise on the identifiability of peak when ∆θ 1 = 0.25◦. (b) The impact of noise simulation on the identifiability of peak when ∆θ 1′ = 1.6◦.

divergence angle of 1.6◦. The peak location jumps between A and B, which may result in errors in calibration.

range, the spectral wavelength (or wavenumber) is stable, the calibration date can be obtained in a short time, etc.

D. The setup of wavelength calibration system

The setup of calibration system based on WCOF is shown in Fig. 6. The lamp for calibration supplied a continuous wide spectrum. The light was coupled into a fiber through an appropriate lens and collimated at the other end. Then the quasiparallel beam was coupled into the double metal-cladding optical waveguide. The reflected light was collected by an objective lens and coupled into another fiber. This fiber was a 1–N fiber. One of the outputs was connected to a standard spectrometer, the rest were connected to the spectrometers to be calibrated. In this way, the calibration for multiple spectrometers can be done simultaneously. The computer receives data from different spectrometers. And after calculating, the coefficient of calibration will be sent to corresponding spectrometers’ hardware or cloud computing services. It is proved that this calibration system is reliable due to the following figures of merit: data of the correspondence between pixels and wavelengths obtained from this calibration system has a uniform distribution within the measurement

IV. EXPERIMENT AND DISCUSSION

In order to verify the spectrum characteristic of the WCOF and the feasibility of the new wavelength calibration method, a wavelength calibration experiment system is setup as Fig. 6. The structure and parameter of the WCOF from top to bottom is as follows: (1) Prism coupling layer: an isosceles right triangle structure, refractive index N = 1.51; (2) gold coating layer: d 1 = 35 nm; (3) waveguide layer of air (also can be filled with liquid): d 2 = 10 µm; (4) gold substrate: d 3 = 110 nm; and (5) thick glass basement. Figure 7(a) shows an actual photograph of the WCOF sample, and the working region of the waveguide is in the black areas as marked. A halogen tungsten lamp was used as the calibration light source. The designed comb spectrum ranges from 10 450 to 24 200 cm−1. Based on this structure, a spectrometer with measurement ranging from 200 to 1100 nm is used to detect the spectral signals. Set θ 1 = 5◦, the spectrum measured is shown in Fig. 7(b).

FIG. 6. The setup of calibration system based on waveguide comb filter—1: lamp, 2: waveguide comb filter system (including WCOF, the collimation lens and focus lens), 3: optical fiber, 4: standard spectrometer and spectrometers for calibrating, and 5: computer. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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FIG. 7. (a) The actual photo of waveguide (top view) and (b) the halogen tungsten lamp spectrum before and after waveguide filter.

As is shown in Fig. 7(b), there are 21 peaks in the spectral range [410–910 nm]. And the peak is periodic with a period ∆ν ≈ 595 cm−1. According to Eq. (5), combining with the waveguide structural parameters given before and the relevant experimental data, we can get the theoretical ∆ν ≈ 600 cm−1. Therefore, Eq. (5) can be used as guidance for designing the comb spectrum filter. When the incident angle θ 1 ≈ 5◦ changes to θ 1 ± ∆θ 1 ◦ ≈ 5 ± 0.32◦, the new comb spectrums are shown as Fig. 8. From Fig. 8, we can see that a slight variation of the incident angle θ 1 will cause small shift in the comb spectrum distribution. When θ 1 increases, the whole spectrum moves towards the direction of large wavenumber (small wavelength). But the periodic intervals are almost unchanged. So we can change the comb peak distribution by changing the incident angle slightly. In this way, more calibration data can be obtained when the number of peaks is not enough.

V. CONCLUSION

In conclusion, a spectrometer calibration system based on a standard spectrometer and waveguide comb filter has been demonstrated. We analyzed the influence of waveguide filter’s structural parameters and the incident angle on a fiber optic spectrometer’s calibration. Comparing with the traditional wavelength calibration method based on discrete sparse atomic emission or absorption lines, the new spectrometer calibration method and system have the following advantages: sufficient calibration data, high accuracy, and fast calibration, especially suitable for spectrometers produce process.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (No. 61178083), the National Special

FIG. 8. (a) The comb spectrum of different incident angle and (b) partially enlarged drawing of (a). This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 149.150.51.237 On: Fri, 03 Apr 2015 09:36:13

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Fund for the Development of Major Research Equipment and Instruments of China (No. 2012YQ180132), and the Key Program of National Natural Science Foundation of China (No. 51235008). 1J. Dong, Y. Han,

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Fast wavelength calibration method for spectrometers based on waveguide comb optical filter.

A novel fast wavelength calibration method for spectrometers based on a standard spectrometer and a double metal-cladding waveguide comb optical filte...
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