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Dispersion multiplexing with broadband filtering forminiature spectrometers

E. C. Cull, M. E. Gehm, D. J. Brady, C. R. Hsieh, O. Momtahan, and A. Adibi

We replace the traditional grating used in a dispersive spectrometer with a multiplex holographic gratingto increase the spectral range sensed by the instrument. The multiplexed grating allows us to measurethree different, overlapping spectral bands on a color digital focal plane. The detector’s broadband colorfilters, along with a computational inversion algorithm, let us disambiguate measurements made fromthe three bands. The overlapping spectral bands allow us to measure a greater spectral bandwidth thana traditional spectrometer with the same sized detector. Additionally, our spectrometer uses a staticcoded aperture mask in the place of a slit. The aperture mask allows increased light throughput,offsetting the photon loss at the broadband filters. We present our proof-of-concept dispersion multiplex-ing spectrometer design with experimental measurements to verify its operation. © 2007 OpticalSociety of America

OCIS codes: 120.620, 090.1970.

1. Introduction

Current environmental sensing, defense, and re-search applications demand compact and inexpensivespectrometers that maintain a high level of perfor-mance. We have designed a spectrometer to meet thisgoal by using aperture coding and dispersion multi-plexing with broadband filtering.

A traditional dispersive spectrometer is com-posed of three primary elements: an input aperture,a digital focal plane, and a dispersive element.Other optics are usually present, optimized to relaylight between the primary elements while minimiz-ing optical aberrations. This spectrometer is oper-ated under the assumption that uniform, spatiallyincoherent light fully fills the aperture. To achievereasonable spectral resolution, this requires the ap-erture to be a spatial filter (typically a slit) to limitthe angular extent of the source input to the spec-trometer. When examining a diffuse source, the slitblocks the majority of the photons incident on the

instrument, limiting light throughput to the spec-trometer. This is one of the major trade-offs inslit-based dispersion spectrometer design: spectralresolution versus light throughput. Increasing lightthroughput in a slit spectrometer while maintain-ing spectral resolution requires a taller slit anddetector, effectively increasing the size and cost ofthe system. One solution to this problem is to re-place the slit with a coded mask with many timesthe open area of a single slit.

The most expensive single part of a dispersion spec-trometer is typically the detector array. The primaryreason for this is the demand for spectrometers withthe sensitivity to measure low-intensity samples.This challenge is exacerbated by the resolution-throughput trade-off in a slit-based device. A sec-ondary reason for the high cost of spectroscopydetector arrays is their nonstandard aspect ratio.Detector arrays produced in high volume typicallyuse an aspect ratio of 4:3 or 16:9, to be used inconsumer imaging devices. Many spectrometers usea noncommodity detector with an aspect ratio of 4:1or more to increase the number of detector elementsalong the dispersion axis, thereby increasing spectralresolution. Dispersion multiplexing allows us to use astandard aspect-ratio focal plane by overlaying sev-eral spectral ranges across the dispersion axis ofthe detector. One commercial system uses a form ofdispersion multiplexing by dispersing two spectralranges along discrete stripes, separated along thenondispersion axis of the CCD.1 (They do, however,

E. C. Cull, M. E. Gehm, and D. J. Brady ([email protected]) arewith the Duke University Fitzpatrick Institute for Photonics, Box90291, Durham, North Carolina 27708. C. R. Hsieh, O. Mom-tahan, and A. Adibi ([email protected]) are with the GeorgiaInstitute of Technology, Atlanta, Georgia 30332-0250.

Received 27 March 2006; revised 8 September 2006; accepted 25September 2006; posted 28 September 2006 (Doc. ID 69352); pub-lished 4 January 2007.

0003-6935/07/030365-10$15.00/0© 2007 Optical Society of America

20 January 2007 � Vol. 46, No. 3 � APPLIED OPTICS 365

use a standard spectroscopy detector array.) Ourtechnique uses a transmissive holographic gratingwith multiple grating periods recorded in it to simul-taneously disperse three spectral ranges across theentire extent of the detector.

This paper describes a doubly multiplexed spec-trometer, using both aperture coding and disper-sion multiplexing. This system does not directlymeasure the spectrum such as a traditional disper-sive spectrometer. Our multiplex spectrometer is acomputational sensor that measures a combinationof components of the input spectrum at each pixellocation, which can be processed to provide a spectralmeasurement. In this paper, we discuss the designand implementation of this dispersion multiplexingspectrometer. The next section describes the theoryand inversion procedure used with our Hadamard-coded aperture. Section 3 contains the central point ofthis manuscript, a description of dispersion multi-plexing with broadband filtering for spectrometerminiaturization, followed by a section on our specificsystem design. We discuss the experimental perfor-mance of our device in the fifth section and concludein the sixth.

2. Coded Aperture Spectroscopy

Replacing the slit used in the aperture of a traditionaldispersion-based spectrometer with a two-dimensionalcoded aperture with many openings allows us to over-come the trade-off between spectral resolution andlight throughput faced by spectrometer designers.This is particularly advantageous for systems used tomeasure the spectra of diffuse sources, since the con-stant radiance theorem states that light from a dif-fuse, incoherent source cannot be focused or haveits intensity increased through (de)magnification.2Other techniques used in spectroscopic instrumentsto overcome the resolution-throughput trade-off in-clude the use of a structured fiber bundle for lightcollection or interferometric-based (nondispersive)techniques.3,4 Neither of these techniques are usefulfor a low cost spectrometer. The fiber bundle cancollect light over a large aperture on one end, but onthe other, the bundle must be stacked to imitate theshape of a slit, requiring large optics and a detectorfor a large collection area. The design stability andtolerances for interferometric spectrometers makethem prohibitively expensive when compared to adispersion-based device.

Coded aperture spectrometers, introduced as mul-tislit spectrometers, were initially implemented withsingle-channel detectors and moving masks.5–7 Thesedevices were used to increase light throughput with-out loss of spectral resolution. Eventually, an entireclass of spectrometer was developed known as theHadamard transform spectrometer (HTS).8 The ba-sis for the HTS was a moving mask (or set of masks)with a series of openings based on the Hadamardmatrix. The primary disadvantage of the HTS sys-tems using a single-channel detector is the time re-quired to take the measurement—each spectralmeasurement requires a full set of detector measure-

ments for each position of the moveable mask. Sincemultichannel detectors have become widely avail-able, coded aperture spectrometers have been imple-mented with spatial light modulators (SLM) andmicroelectromechanical mirror (MEM) arrays to sim-ulate the moving masks.9,10 With a two-dimensionalaperture code and a two-dimensional array detector,it is possible to measure the spectrum with singleshot. Our design uses a static coded aperture madeof a two-dimensional chrome pattern deposited onglass, a simpler and more cost effective solution thanthe MEM- and SLM-based designs. Below, we discussthe theory behind our coding scheme. A more detaileddiscussion can be found in a prior publication.11

Figure 1 shows a simple schematic of a coded ap-erture spectrometer and defines the coordinate sys-tems used in this section. Light incident on thedetector plane can be represented by

I�x�, y�� x � �x� � �� c��y � y��

� T�x, y�S�x, y; ��dxdyd�. (1)

Here, ��x � �x� � �� c�� is the propagation kernelfor a dispersive spectrometer with no internal mag-nification and with linear dispersion of � along the xaxis and center wavelength of �c at x � 0 for all y.T�x, y� represents the transmittance function of atwo-dimensional aperture mask, and S�x, y; �� repre-sents the spectral density as a function of position inthe aperture. Since this paper focuses on a spectrom-eter and not a hyperspectral imager, we assume thatthere is no spatial structure in the input spectrum ofthe aperture. This means that S�x, y; �� is constant inx and y, reducing the spectral density to S��. Thisreduces Eq. (1) to

I�x�, y�� T�x, y��S�� x � x�

�� c�dx. (2)

This means that the intensity measured at the detec-tor is a one-dimensional convolution between thespectrum of the source and the transmittance func-tion of the aperture measured along the dispersionaxis of the detector. For a slit-based dispersive spec-trometer with the slit at x � x0, T�x, y� can be approx-imated by a delta function, ��x � x0�, so that oneposition in x= on the detector corresponds to the in-tensity at a single wavelength:

Fig. 1. System diagram showing coordinate systems.

366 APPLIED OPTICS � Vol. 46, No. 3 � 20 January 2007

I�x�, y�� S�� x0 � x�

�� c�. (3)

Using a coded transmittance pattern for T�x, y�causes the instrument to become a multiplex devicesuch that one position on the detector in �x�, y�� mea-sures the sum of the intensities at several wave-lengths. This T�x, y� must be properly designed toyield an accurate estimation of the source spectrum.

Previously, we have shown that mask transmit-tance patterns based on families of orthogonal func-tions are sufficient for the design requirements of asystem based on a coded aperture mask.11 Tradition-ally, the Hadamard matrix has been used as the basisfor coded aperture spectrometers. The order-p Had-amard matrix is an orthogonal matrix with p rows,originally derived as an optimal solution for makinga multiplex measure of several weights in the pres-ence of noise.8,12 A mask based on an order-12 Had-amard matrix is shown in Fig. 2. While the order-12Hadamard matrix has 12 rows, this mask has beenconstructed according to a previously published row-doubling procedure, yielding the 24 rows shown inthe figure.11

In a dispersive spectrometer, a coded aperturesystem decouples spectral resolution from lightthroughput. For a traditional slit-based spectrome-ter, a required minimum spectral resolution specifiesa maximum slit width, w. A system based on a codedaperture achieves the same spectral resolution byusing a feature size of w, where feature size refers tothe size of one of the open elements in the aperturemask. Since the coded aperture is constructed of anumber of these open elements, it has a larger en-trance aperture area and therefore higher lightthroughput versus the slit. For an aperture based onthe order-p Hadamard matrix, there is a 50% loss oflight because half of the mask features are opaque.This means that the Hadamard-code-based systemachieves p�2 times the light throughput of the tradi-tional system when considering a diffuse source thatfully fills the input aperture. Further, a finer-pitched

mask pattern covering the same aperture area as theoriginal pattern maintains the same light throughputbut increases the spectral resolution of the coded ap-erture spectrometer.

To recover the target spectrum, we take the datafrom the detector, subtract a dark image to reduce thepattern noise, and then slightly shift each row tocorrect for the “smile” distortion present in gratingspectrometers.13 The smile distortion can be easilycharacterized by looking at a target with distinctspectral features such as a gas discharge lamp. It isalso possible to reduce smile distortion by introducinga “negative” curvature to the aperture pattern whenfabricating the mask, a technique currently used insome slit spectrometers. Generally, we design ouraperture mask such that a single mask element cov-ers several pixels on the detector. The last step beforeinversion is to average the set of pixel rows (along thenondispersion axis of the spectrometer) that make upa single mask feature. The result for a mask with rrows is a set of r data vectors with length correspond-ing to the number of pixels along the dispersion axisof the detector. A mathematical formulation of this isshown in the following equation, where the rows of Mare the data vectors from the detector, the rows of Ware spectral estimates formed for each row of inputdata, and H is the matrix representation of the ap-erture code.

H · W � M. (4)

A nonnegative least-squares inversion algorithm isused to calculate the spectra in W. (Typically, we usethe LSQNONNEG function built into MATLAB.) We thenaverage these r spectral estimates to determine thespectrum of the target. A more detailed discussion ofthe coded aperture spectral reconstruction algorithmcan be found in a prior publication by our group.14

3. Dispersion Multiplexing

In a traditional slit-based dispersion spectrometer, thesource spectrum is spread across the detector. A one-dimensional detector is sufficient to record the entirespectrum, though a two-dimensional detector is fre-quently used to increase the signal-to-noise ratio. For afixed size detector and a target spectral range, thistraditional spectrometer system design is completelyspecified—the maximum spectral resolution is set bythe number of pixels on the detector along the disper-sion axis. (Aberrations in the relay optics and a slitwidth not optimized for maximum spectral resolutioncan, however, reduce the spectral resolution.) To in-crease spectral resolution, one must either decreasethe spectral range of interest or replace the detectorwith a higher resolution (and more expensive) model.Assuming the use of a two-dimensional detector, dis-persion multiplexing provides an alternative that canincrease spectral resolution with the same detectorand the same spectral range.

Holographic gratings are useful for dispersionmultiplexing spectrometers due to their flexibilityin implementing different dispersion patterns. One

Fig. 2. Diagram of a row-doubled Hadamard aperture maskbased on an order-12 Hadamard matrix. White areas indicate lighttransmission, and black areas indicate where light is blocked.


commercial system, the Kaiser Holoplex, dispersestwo separate spectral bands on the detector, eachcovering a different spectral range.15 The spectralbands are separated along the nondispersion axisof the detector. Our system uses a multiplex holo-graphic grating with three different grating periods.The Bragg wavelength selectivity of the hologram istuned so that each of the gratings responds to a differ-ent spectral band, as shown in Fig. 3. The gratingperiods are set to disperse the spectral range of eachband fully across the detector.

This results in three spectral bands incident on thesame detector pixels. To disambiguate these overlap-ping bands, we use broadband filters that match thespectral range for each band. While it is possible toimplement this type of dispersion multiplexing spec-trometer with a set of disambiguation filters externalto the detector, we chose to use a simpler and morecost effective color CCD. This combines the broad-band filters and detector into a single component. Atypical color digital focal plane records data in threespectral bands by using an array of red, green, andblue (RGB) per-pixel filters. The standard pattern ofRGB filters used on a color focal plane is known as theBayer pattern, as shown in Fig. 4.16 This filter pat-tern provides one sample of green in each column ofthe detector and one sample of red and blue in alter-nating columns of the detector. For a detector with N

pixels along the dispersion axis of the detector, thisyields N samples of the green spectral band and N�2samples for each of the red and blue spectral bandsfor our system.

The spectral responses of the Bayer pattern filtersused in our system are shown in Fig. 5. These re-sponses are typical of filters used in RGB color imag-ing. The red-filtered pixels provide an estimate of thespectrum within the red spectral band. Similarly, thegreen- and blue-filtered pixels estimate their respec-tive spectral bands. As shown in Fig. 5, the RGB filterresponses overlap. This causes the three spectralranges sensed by our dispersion multiplexing spec-trometer to overlap. It is necessary to correct for thisoverlap to eliminate spurious spectral features fromour final spectral estimate.

If we assume, in a traditional dispersion spectrom-eter, that the dispersion direction of the instrumentcorresponds to the horizontal axis of the detector, theneach column of the detector represents a specific ele-ment of spectral resolution. A single column of thedetector in our dispersion multiplexing spectrometercorresponds to three elements of spectral resolution—one for each of the spectral bands on the detector. Sincethe per-pixel filter functions are smooth, we can labela column’s spectral resolution elements for a columnits center wavelength: �r, �g, and �b. In our system wetreat every two columns on the detector as one col-umn of output data, giving us one sample of red andblue and two of green for each element of spectralresolution. If we record the values �R, G, B� for oneeffective column of the detector then we can calculatethe proper values, accounting for overlap in the spec-tral bands, �r, g, b� by solving Eq. (5). The Fcolor��represents the value of the R, G, or B filter functionsat the wavelength corresponding to the particularcolumn of the detector.

R � rFred��r� � gFred��g� � bFred��b�,

G � rFgreen��r� � gFgreen��g� � bFgreen��b�,

B � rFblue��r� � gFblue��g� � bFblue��b�. (5)

Fig. 3. (Color online) Spectral responses of each grating recordedin the hologram due to Bragg selectivity.

Fig. 4. (Color online) Bayer filter pattern. Each square representsa pixel, and each letter represents either a red, green, or blue filter.

Fig. 5. (Color online) Spectral response of Bayer filters.


We use a nonnegative least-squares solving algo-rithm to recover �r, g, b� from �R, G, B�.

4. System Design

The layout of the dispersion multiplexing spectrom-eter (DMS) is shown in Fig. 6. The optical componentsfrom input to output are the coded aperture (CA), thefirst set of relay lenses (L1), the multiplex hologram(MH), the second set of relay lenses (L2), and theCCD. The coded aperture is based on a Hadamardmatrix of order p � 12 as shown in Fig. 2. An indi-vidual element within this mask is a square, sized78 � 78 �m. The aperture is implemented as a pat-tern in chrome on a glass substrate, manufactured byApplied Image Group. The two sets of relay lensesform a 4-f system. Each set is composed of a pair ofoff-the-shelf 9 mm diameter lenses (Edmund OpticsNT45-091 and NT45-092) in a Petzval configurationcomputationally optimized for low distortion withZEMAX optical design software.

The multiplex hologram is a custom-designed three-grating diffractive element as described in Section 3.The three spectral bands defined by the gratings arespecified in Table 1. The holograms are recorded usingthe angular multiplexing method.17 The model that isused to design the holograms is based on Kogelnik’smethod.18 We record the three holograms at wave-length �rec with proper incident angles for the record-ing beams ri, for i � 1, 2, or 3. All the parameters arecalculated inside the material with refractive index n,if it is not otherwise mentioned. We find the diffrac-tion efficiency for one of the holographic gratings, and

the result can be extended to all three multiplexedholograms.

We use two beams with equal incident angles of r1to record the hologram. This produces a grating vec-tor, Kg1, with magnitude described by

Kg1 �4 sin�r1�

�rec. (6)

The hologram is then read with a collimated beam atwavelength � with an incident angle of �. We assumethe reading beam has an arbitrary polarization. We,therefore, must calculate the response for both theTE (electric field perpendicular to the plane of in-cidence) and the TM (magnetic field perpendicularto the plane of incidence) polarizations. Kogelnik’smethod calculates the exact solution for the first-order diffraction from a volume grating.18 Thismethod is valid for the holograms recorded in sam-ples of a few micrometers thickness, such as thiscase. The diffraction efficiency, �, from each holo-gram is

� � �2sin2�� 2 � �2�

2 � �2 , (7)

where � and � are defined as

� �n1LZ

� cos��PF, (8)

� ��B � ��Kg1

2LZ

8n cos��. (9)

In these equations PF, �B, LZ, and n1 are polarizationfactor, Bragg wavelength, hologram thickness, andrefractive index modulation of the hologram, respec-tively. The polarization factor is defined as

PF ��1 for TE polarization

cos2 arcsin�� sin�r1��rec

� for TM polarization.

(10)

The Bragg wavelength, �B, is defined as the wave-length that is perfectly Bragg matched to the holo-gram with the incident angle �, therefore

�B ��rec sin��sin�r1�

. (11)

The measured diffraction efficiency ��r1� at the re-cording wavelength ��rec� and at the Bragg angle �r1�is used to find n1 from

n1 �arcsin��r1��rec cos�r1�

LZ, (12)

Fig. 6. (Color online) Optical component layout of the dispersionmultiplexing spectrometer.

Table 1. Spectral Band Data

CenterWavelength

(nm)

SpectralBandwidth(1�e FullWidth)(nm)

PeakDiffractionEfficiency

(%)

GratingPeriod

(lines�mm)

Red band 634 330 10.2 1150Green band 531 222 9.27 1400Blue band 452 155 14.6 1670


where we assumed the measurement was performedusing a beam with TE polarization.

To complete the model, we consider the effect of thepolarization of the input beam. We assume we haveequal power in TE and TM polarizations. Let us callthe diffraction efficiency calculated for TE polarization�TE and for TM polarization �TM. Also, the total trans-mission from the interfaces between the air to thematerial and the material to air are considered as TTE

for TE polarization and TTM TM polarization. There-fore the total diffraction efficiency ��Tot� is

�Tot ��TETTE � �TMTTM

LZ, (13)

where TTE and TTM can be found from

TTE � 1 �sin2� � ��sin2� � ��

, (14)

TTM � 1 �tan2� � ��tan2� � ��

, (15)

with � referring to the angle measured in the air.For this derivation, we assumed that each holo-

gram diffracts the input beam independently of theother holograms. This is a valid assumption when thediffraction efficiency of each hologram is not high (forexample, less than 25%). When the diffraction effi-ciency of each hologram is high, all the diffractioncomponents should be considered simultaneouslyusing numerical methods such as rigorous coupled-wave analysis.

For the miniature spectrometer, the three holo-grams are recorded at �rec � 532 nm wavelength(measured in the air) in VRP-M holographic materialfrom Integraf with an emulsion thickness of 6–7 �m.The holograms are designed to be used with an inci-dent angle, �, of 22.86°. This results in the total an-gles between the recording beams of 52.78°, 43.73°,and 35.66°. These correspond to Bragg wavelengthsof 465, 555, and 675 nm, respectively. (Again, allwavelengths are measured in air.) Since the � in Eq.(7) is a function of wavelength, the maximum diffrac-tion efficiency is obtained at 452, 531, and 632 nm(for TE polarization) as listed in Table 1. The band-width three spectral bands defined by the gratingsare also specified in Table 1.

Our detector is a color CCD (Unibrain Fire-i BoardCamera with a Sony ICX-098BQ detector) with 5.6 �mpixels and a 640 � 480 resolution. The CCD is typicalof the inexpensive detectors used in consumer gradedevices like webcams, with standard Bayer color fil-ters on the pixels, a maximum exposure time of32 ms, and an 8-bit dynamic range. The optical com-ponents are assembled with a rigid polymer structureprinted on a rapid prototyping system. Figure 7shows a photograph of the assembled system.

The data recorded by the DMS must be processedin two steps to form a spectral estimation of the input

source. The first step forms a spectral estimate foreach of the three spectral bands. The second stepcombines the three estimates into a single spectral

Fig. 8. Original 550 nm data captured by CCD (top) and unproc-essed data separated into the RGB color channels (lower images).

Fig. 7. (Color online) A: Photograph of the dispersion multiplex-ing spectrometer’s internal structure. B: Photograph of the spec-trometer with keys to show approximate size.


estimate. For the first step, we assume that the cam-era records three separate images of the aperture-coded spectrum in RGB. We perform the datainversion procedure described in Section 2 of the pa-per to calculate the spectrum corresponding to eachof these images. We then apply the dispersion mul-tiplexing correction algorithm described in Section 3to these three spectra. Care is taken to preservethe spatial relation between reconstructed spectral

bands so that the kth sample in one spectral bandcorresponds to the kth sample in another, which areboth related to a specific column on the detector. Todetermine the relationship between the columns ofthe detector and wavelength, we record a set of databy sweeping a monochromator input to the spectrom-eter over the visible wavelength range. This gives usthe ��r, �g, �b� values to evaluate the filter functionsin Eq. (5). Solving the system of equations in Eq. (5)

Fig. 9. (Color online) Spectra for 550 nm input, RGB color channels separated by rows. Results from coded aperture inversion appear inthe left column, and the results after applying the dispersion multiplexing correction appear in the right column. Note the differing scaleof the y axis for the different color channels.


yields the corrected RGB spectra, which are thencombined to form the complete spectral estimate.

The spectral resolution of the DMS is different forthe three spectral bands. The system model devel-oped in the ZEMAX software package provides valuesfor the linear dispersion of the three gratings at thedetector plane. For the DMS prototype, the limitingfactor for the spectral resolution is the 78 �m size ofthe mask elements of the coded aperture, rather thanthe optical spot size or the pixel size on the detector.With the linear dispersion values and the feature sizeof the aperture mask, it is possible to calculate theresolutions of the three spectral bands. Resolution�� for a single band is calculated with Eq. (16)—theproduct of the linear dispersion of the grating at thedetector �d��dx� with the feature size of the mask (�).

�� d�

dx �. (16)

Values for linear dispersion of the RGB bands fromour ZEMAX model are 43.3, 36.3, and 30.7 nm�mm.With a 78 �m feature size, the RGB resolutions are3.37, 2.83, and 2.39 nm. A reduction in the featuresize, combined with a increase in mask complexity(basing it on a higher-order Hadamard matrix) wouldincrease both spectral resolution and light through-put of the instrument.

5. Experimental Data

To demonstrate the data processing procedure, a mono-chromatic source of wavelength 550 nm and FWHMwidth of 4.5 nm was measured with the DMS system.The light source was a monochromator with spectralbandwidth verified by an Ocean Optics USB 2000spectrometer. Figure 8 shows the original data re-corded by the CCD as well as the three images formedby separating the RGB pixels into individual images.The patched look of the original image is due to theresponse of the Bayer pattern filters on the CCDpixels. The green channel image in Fig. 8 clearlyshows the response of all three grating periods to themonochromatic input. The Hadamard-type pattern

in the center is the response of the green grating,while the partial pattern at the right is due to theblue grating, and the partial pattern at the left isthe red grating—each near the edge of their respec-tive spectral ranges. The Hadamard patterns are vis-ible in all the color channel images because 550 nmfalls within the combined spectral response of theirrespective Bayer filters and grating diffraction effi-ciencies. Figure 9 shows the result of the coded aper-ture inversion procedure applied to the RGB imagesin the left column and the spectra after correcting forthe dispersion multiplexing overlap on the right col-umn. The scale of the y axes is adjusted to show thealiasing caused by Bayer filter responses. The greenchannel in the right column shows the response to the550 nm input, while the red and blue channels in theright column show the noise floor of the system. Fig-ure 10 shows the spectral estimate of the 550 nminput, a combination of the three spectra in the rightcolumn of Fig. 9. Analysis of the data plotted in Fig.10 shows a full width of 4.7 nm at half of the maxi-mum intensity value.

A fluorescent ceiling lamp was used as a dem-onstration spectral source with features across the

Fig. 10. Fully processed spectrum measured from a 550 nmsource.

Fig. 11. Original fluorescent light data captured by a CCD (top)and unprocessed data separated into the RGB color channels(lower images).


entire spectral range of the DMS. The original imageas well as the separated RGB color channel imagesappear in Fig. 11. The separated RGB channel im-ages show the system response to spectral featureswithin the different spectral regions. Figure 12 showsthe Hadamard-reconstructed spectra in the left col-umn and the spectra corrected for dispersion multi-plexing in the right column. Again, the spectra for the

individual RGB color channels are separated acrossthe rows of Fig. 12. The fully processed fluorescentlight spectrum appears in Fig. 13, above a spectrumof the same lamp measured with an Ocean OpticsUSB 2000 spectrometer. Both instruments havevarying spectral intensity responses due to the char-acteristics of the individual diffractive elements anddetectors used. Neither of the spectra in Fig. 13 are

Fig. 12. (Color online) DMS spectra for a fluorescent lamp. Results from coded aperture inversion (left column) and dispersion multi-plexing correction (right column). The rows show the separate RGB color channels.


intensity corrected, so the relative heights of thepeaks in the spectra are different.

6. Summary

We have presented a spectrometer design, which im-plements two different multiplexing techniques, allow-ing us to miniaturize the system versus a traditionalspectrometer design. One multiplexing technique isimplemented in the aperture, utilizing an aperturemask to provide high light throughput without sacri-ficing spectral resolution. This allows us to collect asufficient signal with small diameter optics and asmall detector. The other multiplexing technique isimplemented in the dispersive element, utilizing a ho-logram with three grating periods recorded in it. Withdispersion multiplexing, we measure three differentspectral bands simultaneously, each dispersed across

the full extent of the detector. This allows us to in-crease the total spectral range measured with a smalldetector. Both of these techniques can be used inde-pendently in spectrometer design, though they do com-pliment each other in our design.

This work was performed with the support of grantN01-AA-23013 from the National Institute of Alco-holism and Alcohol Abuse and grant W911NF-04-1-0319 from DARPA-MTO and ARL-SEDD.

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Fig. 13. Fully processed spectrum of a fluorescent lamp from theDMS (top) compared with a measurement made with a commercialspectrometer (bottom).


dispersion multiplexing with broadband ﬁltering for ...gehm/pubs/applopt.46.365.pdfone commercial...

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