Planar double-grating microspectrometer

Planar double-gratingmicrospectrometer

S. Grabarnik1∗, R. Wolffenbuttel1, A. Emadi1, M. Loktev1,E. Sokolova2 and G. Vdovin1

1Electronic Instrumentation Laboratory, Delft University of TechnologyMekelweg 4, 2628 CD Delft, The Netherlands

2TNO Institute of Science and TechnologyStieltjesweg 1, 2628 CK Delft, The Netherlands

∗[email protected]

Abstract: We report on a miniature spectrometer with a volume of0.135 cm3 and dimensions of 3x3x11 mm, mounted directly on the surfaceof a CCD sensor. The spectrometer is formed by two flat diffraction gratingsthat are designed to perform both the dispersion and imaging functions,eliminating the need for any spherical optics. Two separate parts of thedevice were fabricated with the single-mask 1 μm lithography on a singleglass wafer. The wafer was diced and the device was assembled and directlymounted onto a CCD sensor. The resolution of 3 nm, spectral range of 450to 750 nm and the optical throughput of ∼9% were measured to be in acomplete agreement with the model used for the development of the device.

© 2007 Optical Society of America

OCIS codes: (300.6190) Spectrometers; (050.1950) Diffraction gratings; (350.3950) Micro-optics; (080.2740) Geometrical optics, optical design.

References and links1. R. F. Wolffenbuttel,”MEMS-based optical mini- and microspectrometers for the visible and infrared spectral

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lamellar grating interferometer based on silicon technology,” Opt. Lett. 29, 1437–1439 (2004)6. G. Boer, P. Ruffieux, T. Scharf, P. Seitz, and R. Dndliker, ”Compact Liquid-Crystal-Polymer Fourier-Transform

Spectrometer,” Appl. Opt. 43, 2201-2208 (2004)7. S. Ura,F. Okayama, K. Shiroshita, K. Nishio, T. Sasaki, H. Nishihara, T. Yotsuya, M. Okano, and K. Satoh,

”Planar Reflection Grating Lens for Compact Spectroscopic Imaging System ,” Appl. Opt. 42, 175–180 (2003).8. K. Chaganti, I.Salakhutdinov, I. Avrutsky, and G. W. Auner, ”A simple miniature optical spectrometer with a

planar waveguide grating coupler in combination with a plano-convex lens,” Opt. Express 14, 4064–4072 (2006).9. S. Ura, T. Sasaki and H. Nishihara, ”Combination of Grating Lenses for Color Splitting and Imaging ,” Appl.

Opt. 40, 5819–5824 (2001).10. J. F. James and R. S. Sternberg ”The Design Of Optical Spectrometers”, Chapman and Hall, London 196911. H. Noda, T. Namioka, and M. Seya, ”Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031–1036 (1974).12. Cristopher Palmer, Wayne R. McKinney, ”Imaging theory of plane-symmetric varied line-space grating systems,”

Opt. Eng., 33, 820–829 (1994).

#79414 - $15.00 USD Received 25 January 2007; revised 4 March 2007; accepted 4 March 2007

(C) 2007 OSA 19 March 2007 / Vol. 15, No. 6 / OPTICS EXPRESS 3581

13. ZEMAX Optical Design Program, User’s Guide, Version 9.0 (Focus Software, Inc., Tucson, Ariz., 2000).14. http://www.videologyinc.com

1. Introduction

Spectroscopic devices have applications in practically all industries [1]. The cheaper and thesmaller the spectrometer is, the more applications it can have. Small and cheap spectrometersare in demand.

Different approaches to the design of an inexpensive compact spectrometer have been pre-sented during the last two decades [2] – [8]. One of the early works describes a Rowlandspectrometer implemented in a planar waveguide [2]. The device was capable to separate twochannels with the 10 nm wavelength difference. The recent progress in integrated optics andMEMS technology brought new possibilities for design of the compact spectrometers usingvery small integrated optical and opto-mechanical components. For example in [4] a planarwaveguide spectrometer with the largest dimension of about 2 cm and spectral resolution of9 nm within the 300 nm operating range is reported. A small Fourier Transform (FT) spec-trometer with moving micro parts based on a 5 mm x 5 mm lamellar diffraction grating withvariable depth was presented in [5] and demonstrated 1.6 nm resolution at a wavelength of 400nm and 5.5 nm resolution at 800 nm. Static FT spectrometer with the 10 nm resolution at awavelength of 570 nm based on a polarization interferometer realized with liquid-crystal mate-rials was described in [6]. MEMS technology was used in [7] for the fabrication of an imagingdiffraction grating used in a spectrometer as small as 1 cm3. The reported spectroscopic devicedemonstrated 5 nm resolution within 100 nm range. A promising result was obtained recentlyemploying integrated optics in [8], describing a spectrometer having the largest dimension ofthe optical part of about 1.2 cm and having resolution varying from 0.3 to 4.6 nm in the 150 nmwavelength range.

In this article we report on an imaging spectrometer that combines wide operating spectralbandwidth of 300 nm with a good spectral resolution (3 nm) in a very small overall dimensions(3x3x11 mm3). The fabrication technology of the device is extremely simple – all parts of thedevice can be fabricated with a single lithographic step on a planar surface with a consequentbatch assembling including wafer-to-wafer bonding through a spacer structure. Thus our de-sign avoids difficulties with the alignment of different parts of the device common to classicalspectrometers and complicated processing specific to integrated optics.

2. Theoretical considerations for a two-grating spectrometer

The concept of a general spectroscopic device is presented on Fig. 1. It includes an entrance slit,

entrance slit

photosensordispersiveelementcollimator

focusingelement

Fig. 1. General spectroscopic device

a dispersive element, a focusing element and an image sensor or – depending on the function –the exit slit [10].



Our decision to design a spectrometer with flat optics only, leaded to a grating that mustprovide both focusing and dispersion functions. Such a combination does not allow for highresolution in a wide spectral range, therefore we decided to use two gratings. The second grat-ing provides additional compensation of the aberrations introduced by the first grating thusincreasing the operating bandwidth considerably. A similar configuration was described in [9]for separate three-color imaging.

The theory of imaging gratings is well developed [11, 12] and various techniques includingmechanical ruling, holography and lithography have been successfully used for their fabrica-tion. Figure 2(a) presents the geometry of a diffraction grating which images point A into pointB. Plane yoz of the coordinate system oxyz lies in the grating plane and the origin of the coor-dinate system o coincides with the point O.

a bA

B

PO

x

yz

r

r‘

αβ

A

B

O1

P1

PO

x

yy1z

z1

Fig. 2. The grating imaging geometry. Point source A is imaged to an image point B.Single-grating (a) and double-grating (b) systems.

Consider the grating central point O and a point P somewhere in the grating plain. Then theoptical pass difference between light beams passing from A to B via the point P and the pointO is:

ψ(λ ,y,z) = APB−AOB+mλN(y,z), (1)

where N(y,z) is a function equal to the groove number at the point (y,z), m is a diffractionorder and λ is a wavelength. Equation (1) could be decomposed into power series and take theform:

ψ(λ ,y,z) =∞

∑i=0

∞

∑j=0

Fi jyiz j =

∞

∑i=0

∞

∑j=0

(Mi j +mλNi j)yiz j (2)

The coefficients Mi j in Eq. (2) depend on the system configuration and the coefficients N i j

are determined by the grating groove pattern [12]. The path difference equal to zero ψ = 0corresponds to a spherical wavefront convergent to an image point B. Since the value of thecoefficient Fi j determines the deviation of the diffracted wavefront from the spherical one pro-portional to yiz j the coefficients Fi j in Eq. (2) can be interpreted as the aberration coefficients[12]. From the formal mathematical point of view Eq. (1) could also be decomposed in toMcLoren series keeping λ as a parameter:



ψ(λ ,y,z) =∞

∑n=0

1n!

[y

(∂∂y

)0,0

+ z

(∂∂ z

)0,0

]n

ψ(λ ,y,z) (3)

We can impose a requirement for the aberration coefficients Fi j in equation 2 to be zero, thusobtaining an aberration reduced image of a point A for the wavelength λ . From 3 we can obtainthe formulation for the coefficients Ni j of an abberation reduced grating:

Ni j = −Mi j

mλ= − 1

i! j!mλ

[∂ i+ j(APB−AOB)

∂yi∂ z j

](0,0)

(4)

Equation (4) allows calculation of the grating coefficients from the system geometry. Exactformulas for Mi j are listed for example in [12]. Suppose we eliminated aberrations for onewavelength λ0 having calculated grating coefficients according to Eq. (4). The image of thepoint A produced by this grating for some another wavelength λ 1 would be different fromthe point B, the image of the point A for the wavelength λ 0 (see Fig. 2(a)). It means that thecoefficients Mi j in Eq. (2) change with the wavelength. However the product λN i j change muchfaster than Mi j . That is why aberrations eliminated for one wavelength appear again for anotherone. It could be shown that in case of two diffraction gratings as Fig. 2(b) presents, the Eq. (2)takes the form:

ψ(λ ,y,z) =∞

∑i=0

∞

∑j=0

(Mi j +mλNi j + mλ Ni j

)yiz j (5)

In Eq. (5) the coefficients Mi j are defined by the system geometry, Ni j and Ni j are dependenton the groove pattern of the first and second gratings respectively.

Consider two light beams having the wavelength λ1 and λ2 emitted from a source point Aand diffracted from the grating 1. Light beam having the wavelength λ 1 is imaged into pointB1 and second beam - into point B2. The grating 1 can compensate aberrations for one of thesebeams, for example the beam 1. However, according to Eq. (2), it is impossible to compensateaberrations for the beam 2 with the same grating. Since the light beams under considerationbecome spatially separated after being diffracted, we can use grating 2 to compensate aberra-tions for the second beam. It can be achieved by an appropriate choice of the coefficients Ni j

in Eq. (5). This approach has been demonstrated in [9] for a system that operates with threewavelengths and uses a three segments grating to compensate aberrations. However in casewhen the wavelengths λ1 and λ2 are close to each other the diffracted beams could run a longdistance in space before they become separated. We used a single grating to reduce aberrationsof the diffracted beams partially overlapped in space and tried to optimize it to provide suffi-cient compensation of aberrations for all wavelengths within the specified operating bandwidth.Using this approach, we were able to keep compact dimensions of the optical design. We alsotried to avoid the problem of the alignment of different optical components: we proposed a pla-nar configuration where all optical components are made on a single wafer using lithographytechnique.

3. Spectrometer design

Figure 3 presents schematics of our design.The spectrometer consists of two pieces of glass aligned parallel to each other. All spectrom-

eter optical components, including the input slit and the diffraction gratings, work in reflection.The light from a source is reflected from a stripe mirror, acting as a slit and then diffracts on thegrating 1, redirected by the second mirror to the grating 2 and finally goes to the photodetector



glass wafer

glass wafer

incominglight

non-diffracted light



grating 1 grating 2

mirror (slit) mirror

photodetector

Fig. 3. The design of a compact planar spectrometer.

through the glass plate. Both gratings operate in the −1 diffraction order. The size of the grat-ing 1 defines the input aperture of the spectrometer since the non-diffracted light escapes thesystem through the glass plate as designated by the dashed arrows on the Fig. 3. The trajectoryof light in the spectrometer is determined by the geometry and the position of the input slitfabricated as a mirror stripe, and the geometries of the two gratings. Higher incident angles andhigher grating spatial frequencies allow to obtain a better performance. In practice, there arelimits to these parameters. The available lithographic technology limited the maximum gratingfrequency to ∼1000 lines per millimeter. As the incident angle is being increased the amountof light reflected from the glass surfaces due to Fresnel reflections is also increasing. Such par-asitic reflections contribute to the stray light as will be discussed below. Finally we had chosenthe incident angle of the input light to be 60 degrees. The distance between glass plates waschosen to be 3 mm and the size of each peace was 3x11 mm 2. Grating 1 and grating 2 had ellip-tical shape with axes of ellipses equal to 1 mm by 0.6 mm and 2.5 mm by 1 mm, respectively,defining the input numerical aperture to be equal to ∼0.05. We used Zemax [13] to calculate theparameters of the gratings via numerical optimization, since analytical calculations in case oftwo gratings require a huge amount of algebraic work. ZEMAX uses a polynomial representa-tion of a diffractive surface similar to Eq. (2). A plane grating can be described by the functionN(y,z) (see Eq. (1)) which equals to the number of the groove passing through the point (y,z).It follows from Eq. (1) that the number of the groove passing through the point (0,0) is zero.Suppose we can decompose function N into series as was done in Eq. (2). Then we can write:

N(y,z) =∞

∑n=0

ci jyiz j (6)

Our numerical experiment has shown that 20 coefficients of the Eq. (6) are enough to describeour gratings and a larger number of coefficients does not improve the performance. We canchoose orientation of the coordinate system so that the grating is symmetrical relative to z axis.Then all members of Eq. (6) with j odd are equal to zero and we have only 11 coefficients tooptimize. So, for two gratings, our design task was an optimization problem with 22 parameters.With ZEMAX optimization engine we obtained the optimal values of grating coefficients whichwere then used in conjunction with Eq. (6) for mask design. Using Eq. (6) for each of thegrating grooves we determined a set of points (y,z) belonging to the groove and describing its



position in the grating plane. This procedure enabled drawing of the grating structure on themask. The period of each of the gratings varied from 1 μ to 4 μ which was within the limitsof the available lithography resolution. The lithographic technique did not allow fabricationof the blazed gratings, the only physical parameter we were able to optimize was the depthof the grating grooves which was chosen to be equal to 230 nm for Al-coated grating. Themaximum diffraction efficiency for a single grating did not exceed 30%. An improvement ofthe diffraction efficiency would involve more complicated fabrication technology (for exampleholography) which is out of scope of our work.

4. Fabrication and testing of the spectrometer

All elements of the spectrometer including the slit and the gratings were fabricated on a singleAl-coated glass wafer. The waver was covered with 650 nm of aluminum and then severalprocess steps followed. First, the grating patterns were etched by plasma, to form 230 nm deepgrooves. Then aluminum was patterned to define the input slit, the gratings and the intermediatemirror. Finally the wafer was diced and the two parts of the spectrometer were aligned in aspresented in the Fig. 4 with the Videology 21K137 CCD board camera [14] that was used as aphoto-detector.

Fig. 4. The experimental setup. The spectrometer is visible as two transparent rectanglesmounted over the image sensor. The light is fed to the spectrograph from the fiber tip visiblein the left top corner.

5. Spectrometer characterization

A multi-mode optical fiber was used to feed the spectrometer. One of the cleaved fiber tips wasexposed to a light source under test and the second fiber tip illuminated the input slit of thespectrometer. As an example of the device performance, Fig. 5 represents the spectrum of a Nelamp captured with the device CCD in the range 550 to 750 nm.

The presence of stray light is clearly visible in Fig. 5. Stray light represents a serious problembecause of the two features of the device. First, glass surface around the input slit reflects about9% of the incoming light to the grating 1 (see Fig. 3) due to Fresnel reflection. Thus spectralimage presented in Fig. 5 is actually a superposition of the dispersed images of the entrance



Fig. 5. The spectrum of a Neon lamp produced with the planar spectrograph and registeredwith a CCD chip.

slit and the fiber tip that was used for illumination of the slit. Such elliptical images of thefiber tip are also visible on the Fig. 5. The minor contribution to the stray light is due to lowtotal diffraction efficiency of less than 10%, which means that approximately 90% of all inputlight is scattered. Most of this light leaves the device through transparent glass surfaces, butsome light returns after parasitic reflections. Thus the elimination of Fresnel reflections wouldsubstantially decrease the level of stray light. It could be achieved by depositing an appropriatecoating on the unused surfaces. The coating process would involve additional lithography step:the deposition of a light absorbing material on top of a wafer followed by the patterning of thismaterial to open aluminum gratings and mirrors and that part of the glass plate which the lightgoes through to reach the photosensor. Implementation of such a coating is the scope of ourfuture work.

Figure 6 presents the spectrum of Ne, obtained with our spectrometer. The major lines aremarked to identify them with the Ne spectral lines. Judging from the Fig. 6, the resolution ofour spectrometer is approximately 3 nm, while the relative positions of spectral lines can bedetermined with a precision of better than 1 nm.

580 600 620 640 660 680 700 720 7400

0.2

0.4

0.6

0.8

585.2

703.2

724.6

693.2

639.2

614.1 650.5

Wavelength, nm

Inta

ncity

, a.u

.

Fig. 6. Graphic representation of the registered spectrum of a Neon lamp.

In spite of its low diffraction efficiency, the device appeared to be sensitive enough to reg-ister spectra of different sources, such as lamps, LEDs, and groups of pixels on a computerscreen. For example, Fig. 7 demonstrates the spectra of red, yellow and white pixels of theLCD computer screen. In this experiment the fiber tip was placed in front of the computer



450 500 550 600 650

0.1

0.2

0.3

0.4

490

546

611

Wavelength, nm

Inte

ncity

, a. u

.

redgreenwhite

Fig. 7. Spectra of different pixel groups of a color LCD screen.

screen displaying a three-color image. These spectra were recorded at the lowest shutter speed(1/50 sec.) and automatic electronic gain control of the CCD camera. That is why they ex-hibit a periodic modulation which is a fixed pattern camera noise in a high sensitivity regime.The overall sensitivity of the spectrometer depends on the throughput of the optical part of thedevice and the sensitivity of the photo-detector. An optical throughput is:

L = S∗NA∗P (7)

In the Eq. (7) S is the input slit area, NA is the input aperture and P is the efficiency of theoptical scheme. In our design we have NA = 0.05 and P = 0.065. The relatively small value ofthe NA is a compromise between the throughput and the spectral resolution. A small value of Pis the consequence of low diffraction grating efficiency ( 30%). The second grating decrease thedevice throughput further, so that less than 9% of the incoming light goes to the photo-detector.Relatively low throughput of our design is a disadvantage which is, however, not critical forapplications requiring very low-cost high-resolution spectrometer coupled to a bright source.

6. Conclusion

We designed, fabricated and tested a new planar miniature spectrometer. Using a design withtwo planar gratings, we were able to obtain a 3 nm resolution within ∼300 nm bandwidth withthe small 3x3x11 mm3 dimensions. All spectrometer components were fabricated lithographi-cally on a single wafer. Planar miniature design of the spectrometer allows its integration withvarious types of photodetectors including low-cost CMOS sensors.

Acknowledgment

The authors acknowledge the financial support from STW The Dutch Technical Foundation,grant DET.6667. We appreciate the help from Dr. Lina Sarro, Jan Groeneweg, Jan CornelisWolff and Charles de Boer with the mask design and wafer processing and useful discussionswith Dr. A. Simonov.



Planar double-grating microspectrometer

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