Multiple-fluorophore-specie detection with a tapered Fabry-Perot fluorescence spectrometer

Multiple-fluorophore-specie detection with atapered Fabry–Perot fluorescence spectrometer

Jeremy A. Wahl, Jay S. Van Delden, and Sandip Tiwari

A novel fluorescence spectrometer and method for the simultaneous detection of multiple-fluorophorespecies in a no-moving-parts, instantaneous manner is described. In the reported embodiment of theinstrument, a tapered Fabry–Perot filter is used to spatially encode the fluorescence spectrum from amultiple-dye-containing test sample. Using a pseudoinverse reconstruction algorithm, we spectrallydecode the particle concentration for each dye specie in the test sample. Experimental results are reportedalong with a theoretical treatment of the method. © 2005 Optical Society of America

OCIS codes: 120.2230, 120.2440, 260.3160.

1. Introduction

As is well known in the field of fluorescence micros-copy, certain classes of polyaromatic molecule emitlight as a result of being illuminated by a pumpsource. These fluorescent dyes or fluorophores can bedesigned to selectively bind to various biological en-tities, thus providing an efficient optical means foridentifying and quantifying them.

Over the years, this notion of optically tagging bi-ological agents has inspired a diverse assortment ofinstruments. However, few approaches to date haveshown multiple-dye-specie identification and quanti-fication in a no-moving-parts, instantaneous manner.For example, in a clever embodiment first conceivedby Hirschfeld and Block,1,2 and later developed bySaaski and Jung,3 the surface of an optical waveguideis coated or infused with high-specificity capture an-tibodies that bind target analyte particles in closeproximity to the core. Subsequent introduction of re-porter (i.e., fluorescently labeled) antibodies allowsevanescent field excitation and detection of the targetanalyte particles.

Fundamental to nearly all fiber-optic evanescentfield fluorosensors is the need for near-critical-anglelight propagation within the core. Such propagation

maximizes the penetration depth of the evanescentfield into a liquid cladding test medium. This require-ment places severe restrictions on the size of thetarget analyte particles. Furthermore, this regime ofoperation generally precludes multiple-wavelengthexcitation, thus limiting the selection of availablefluorophores. Aside from numerous processing diffi-culties (filling, flushing, incubating, adsorbing, agi-tating, etc.) seemingly overcome by Jung et al.,4 thisapproach does not appear to be quantitative withregard to particle count.

A substantially different approach to fluorescencedetection, one that is more akin to the method de-scribed herein, has been proposed by Gouzman et al.5In their scheme, two linear interference filters [ta-pered Fabry–Perot (TFP) filters] replace the scanningmonochromators in a traditional double-beam fluo-rescence spectrometer. However, Gouzman utilizes asequential approach for measuring the data by me-chanically translating the filters relative to fixed di-aphragms. And like Jung, Gouzman makes noattempt to quantify the particle count that gives riseto the measured fluorescence signal.

Here we describe a novel single-beam fluorescencespectrometer that utilizes a TFP filter to spatiallyencode the polychromatic spectrum of a broadband-pumped, multiple-dye-containing test sample. Ourapproach secures all the data in a single image framewith no moving parts so that particle identificationand quantification occur in real time.

2. Experimental Setup

The TFP fluorescence spectrometer consists primar-ily of (1) a broadband excitation source with associ-ated pump optics, (2) a multiple-fluorophore-laden

The authors are with Cornell University, 115 Phillips Hall,Ithaca, New York 14853. J. A. Wahl ([email protected]) is withthe Department of Applied Physics; J. S. Van Delden and S. Tiwariare with the Department of Electrical and Computer Engineering.

Received 10 November 2004; revised manuscript received 12April 2005; accepted 13 April 2005.

0003-6935/05/255190-08$15.00/0© 2005 Optical Society of America

5190 APPLIED OPTICS � Vol. 44, No. 25 � 1 September 2005

sample cell, (3) collection optics, (4) a TFP filter, (5)relay optics, (6) an imaging detector, and (7) a com-puter program that performs the mathematical re-construction for recovering the particle concentrationfrom the spatially encoded spectrum. The instrumentis shown schematically in Fig. 1.

White light from a 6 W, 3100 K (color tempera-ture) tungsten–halogen lamp (Ocean Optics, LS-1) iscoupled into a 1 m length of 400 �m, step-index,silica-core fiber. The fiber isolates the test samplefrom any heat generated by the lamp. At the distalend of the fiber, a 19 mm focal length f�1.7 lens(Thermo-Oriel, 77646) excites a nominal 0.68 mm3

focal volume within the quartz sample cell (StarnaCells, 23-3.45-Q-3, inner dimensions of 3.0 mm� 3.0 mm). We collected the resulting polychromaticfluorescence using a long working distance (LWD)microscope objective [Mitutoyo, M Plan Apo 50X, 0.55numerical aperture (NA)]. The objective is positionedto overfill the nominal 20 mm � 40 mm aperture ofthe TFP filter, ensuring uniform illumination. TheTFP filter is a linear variable interference filter(Schott Corporation, Veril S 60) designed for use inthe 400–700 nm spectral region with a 14 nm FWHMbandwidth and a 7.0 nm�mm dispersion.

What makes the Veril filter and other TFP-likestructures6 useful in this particular system is theirability to spatially encode the incident spectrum.Only those wavelengths that are locally resonantwithin the aperture of the filter are allowed to pass.As a result, uniform illumination of the TFP filter bya polychromatic beam of light produces a discretearray of colored virtual slits. These slits are virtual inthe sense that they are not formed by any sharplyedged apertures in the optical system. Instead, theslits are formed because only a narrow, threadlikeregion of the TFP filter’s aperture satisfies the reso-nance (i.e., all-pass) condition.

Following the TFP filter is an anamorphic relaylens system that forms an image of the virtual slitsonto the detector array. The relay lens system con-sists of a 178 mm f�2.5 Kodak lens combined withtwo 100 mm f�2 cemented achromats (Edmund Op-tics, NT45-353) and a 250 mm plano–convex cylin-drical lens (Melles Griot, 01-LCP-017). The use of a

cylindrical lens in the relay system enables us tooptimally select the relay magnification in each plane(mrx

and mry) to further concentrate the signal seen by

the detector array.The image sensor deployed in the instrument is a

back-thinned, full-frame transfer, silicon CCD arraywith 512 � 122 active pixels (Hamamatsu, S7034-0907). With a pixel size of 24 �m � 24 �m, a full-wellcapacity of 300,000 electrons is typically achieved(before binning) with a dynamic range of �10,000.The image sensor is mounted into a multichanneldetector head (Hamamatsu, C7044) that allowssingle-stage thermoelectric cooling to �10 °C. Fi-nally, the detector head is interfaced to a controller(Hamamatsu, C7557), which further includes driverand amplifier circuitry, a power supply, and a 16 bitanalog-to-digital converter (ADC). Software is pro-vided by Hamamatsu for simple image acquisitionand manipulation. In practice, to increase the dy-namic range, we found the vertical binning facility tobe particularly useful.

As shown in Fig. 2, the TFP fluorescence spectrom-eter is assembled onto an optical breadboard that is

Fig. 1. Schematic of the TFP fluorescence spectrometer.

Fig. 2. Photo of the TFP fluorescence spectrometer on a2 ft �0.61 m� � 3 ft �0.91 m� optical breadboard.

1 September 2005 � Vol. 44, No. 25 � APPLIED OPTICS 5191

further housed within a lighttight box to reduce straylight aliasing of the recorded spectra.

3. Theory

A. Forward Problem: a Radiometric Approach

The physical size of a single dye molecule is extraor-dinarily small (of the order of 1 nm). As a result,optically we can treat each dye molecule as a pointemitter. Let us consider a multiple-specie ensemble ofdye molecules randomly distributed within a smallsample volume V. All the dye species are illuminatedwith the same broadband excitation source and eachemits a characteristic fluorescence signal that differsin wavelength.

For a denumerable ensemble of dye species �m �1, 2, . . . M�, the total spectral power (power per unitwavelength) emitted by all the dye particles is gov-erned by

�tot(�) ��0

�

d��0(��) �m�1

M

�m(�)�1

� exp[�m(��)leffcm]�, (1)

where �m�� is the spectral quantum yield (ratio ofradiative, light-producing transitions to the totalnumber of transitions per unit wavelength, nm�1),�0�� is the incident spectral power �watts�nm�contained in the pump beam, m�� is the molar ab-sorptivity (liter cm�1 mole�1), cm is the molar con-centration �moles�liter�, and leff is the effective pathlength traversed by the illuminating pump beam(cm). In our notation, we use � to describe the wave-length of the emitted fluorescence signal and �� todesignate the wavelength of the incident pump beam.

The usefulness of any given dye depends in part onthe efficiency with which it emits and absorbs pho-tons. Emission and absorption are quantified byquantum yield and molar absorptivity, respectively.In practice, the quantum yield is given by �m�� mFm

e��, where �m varies from 0.0 to 1.0, and Fme��

is the emission spectrum of dye m, normalized to unitarea (nm�1). The molar absorptivity (i.e., the proba-bility of absorption for an incident photon) is given bymFm

a��, where m, the molar extinction coefficient,typically varies from 5000 to 200,000 liters cm�1

mole�1 and Fma�� is the absorption spectrum of dye

m, normalized to a peak value of unity.It is common to define the sample volume or focal

volume �V � A0leff� as some small region whose trans-verse extent �A0� is determined by the focusing opticsand pump beam. As area A0 is reduced, for the sameamount of incident optical power, the irradiance inthe pump beam is sizably increased, thus leading to alarger fluorescence signal. Within this limit, the poly-chromatic fluorescence signal is directionally isotro-pic so that the spectral power intercepted by thecollection optics is given by �c�� 0.5c1 � �1 �NA2�1�2�tot��, where c and the NA are the average

transmission and numerical aperture, respectively,of the collection optics.

All the optical power intercepted by the collectionoptics, aside from transmission losses, is utilized toform an image of the focal volume on the entranceaperture of the TFP filter. We should commentbriefly on the distribution of light contained in thisimage. The fluorophores are too small to be resolvedby the collection optics. However, a portion of thelight they emit is captured by the lens to form animage of each pointlike object. For a highly cor-rected lens, each point emitter in the sample vol-ume will give rise to an Airy disk irradiancedistribution in the image plane. And, since the pointemitters emit temporally incoherent light, the dis-tribution of light in the image plane (i.e., TFP filter)is an incoherent superposition of randomly distrib-uted Airy disk functions. As a result, within thelimit of a large number of point emitters, the lightdistribution is assumed to be uniform. Under thisassumption, the spectral irradiance incident uponthe TFP filter can be approximated by Einc�� c��Ai, where Ai � leffmc

2�A0�1�2 is the area con-tained within the image formed by the collectionoptics. Experimentally, the object �z0� and image �zi�distances were selected to yield a collection-lensmagnification of mc � zi�z0 that overfills the20 mm � 40 mm rectangular aperture of the TFPfilter.

The spectral irradiance distribution immediatelyfollowing the TFP filter, ETFP�x, y, ��, is equal to theincident spectral irradiance, Einc��, times the trans-mission function of the filter, TTFP�x, y, ��, which canbe approximated by a weighted, shifted Lorentzianfunction of the form

TTFP(x, y, �) � f

�xlw

2 Lx � x0(�); 0.5xlw

� exp�� xxbw

2�rect� xwx

rect� ywy

,(2)

where x0�� 0.135� � 74.25 is the spatial location(mm) of peak transmittance for wavelength � �nm�,xbw � 40 mm is the spatial bandwidth, xlw �1.9 mm is the spatial linewidth for each wavelength,and f, �0.70, is the average transmission. The rectfunctions7 explicitly define the rectangular clear ap-erture of the TFP filter, outside of which there is nolight passage, and L�x; a� � �1��a��x2 � a2�. In thisway, the spectral irradiance distribution has pickedup an explicit spatial dependence that is due to thespatial-wavelength-encoding functionality of the TFPfilter. The spectral optical power contained withinthis light distribution is the spectral irradiance timesthe area of the filter so that �TFP�x, y, �� ETFP�x, y, ��ATFP, where ATFP � wxwy � 40 mm �20 mm.


In our experimental setup, light that leaves theTFP filter is optically relayed onto the surface of aback-thinned, Si CCD detector array by use of amultielement anamorphic lens system. Because thelength-to-width ratio of the TFP aperture �wx�wy� isdifferent from the active area of the detector array�lx�ly�, the relay system includes a cylindrical lens tomaximize the light-collection efficiency.

Now, let us image the light distribution that im-mediately follows the TFP filter onto the surface ofthe detector array. As the size of the virtual slitscreated by the TFP filter is large compared to theresolution capabilities of the relay lens system, wecan comfortably apply a first-order or geometricprojection of the TFP light distribution onto thesurface of the detector array. The spectral powercomprising the final image presented to the detectorarray is thus given by �d�x, y, �� r�TFP�x, y, ��,where r is the average transmission of lightthrough the relay lens system. The correspondingdetector spectral irradiance distribution is givenby

Ed(x, y, �) ��cfrxlw�1 � �1 � NA2�

4Aimry

L�x

� mrxx0(�); 0.5mrx

xlw�

� exp�� xmrx

xbw 2�rect� x

mrxwx

� rect� y

mrywy

�0

�

d��0(��)

� �m�1

M

�mFme(�)�1

� exp�mFma(��)leffcm�, (3)

where mrx� Nxpx�wx � 0.31 for Nx � 512 active pixels

in the x direction, mry� Nypy�wy � 0.15 for Ny � 1

vertically binned active pixels in the y direction, andAd � mrx

mryATFP.

If we were to select an infinitesimal region thatsurrounds point �x, y� on the surface of the detector,Eq. (3) would give the irradiance for that particularregion at a specific value of fluorescence wave-length. However, fluorescing dye particles exhibitfinite-bandwidth emission spectra. And the detectoritself will have some wavelength-dependent re-sponse, ��. As a result, our system must becharacterized by integration over all emissionwavelengths.

Also, included in the digital imaging process is thenotion of spatial integration. Point detectors gener-ally have some finite lateral extent over which theyspatially integrate the incident optical signal. Includ-ing both wavelength and spatial integration pro-cesses, the electrical photocurrent associated witheach vertically binned pixel i �i � 1, 2, 3 . . . Nx� isgiven by

gi ��cfrxlw�1 � �1 � NA2�

4Aimry

�0

�

d��0

�

d�

��

�

dxdy��pixi(x, y) �m�1

M

�mFme(�)�0(��)�1

� exp�mFma(��)leffcm�Lx

� mrxx0(�); 0.5mrx

xlwexp�� xmrx

xbw 2�

� rect� xmrx

wx rect� y

mrywy

, (4)

where pixi�x, y� is a piecewise-continuous two-dimensional window function that selects the indi-vidual pixel over which integration occurs. Thefunction pixi�x, y� is given by

pixi�x, y� � rect�x � xi

px rect� y

py , (5)

where px � 24 �m and py � 2.928 mm are the dimen-sions of a single vertically binned pixel in the x and ydirections, respectively and xi � ipx is the location ofthe ith horizontal pixel.

Now, if we consider the lateral extent of a singlepixel in the x direction compared with mrxxbw andmrxxlw, we find that integration over space can beapproximated such that

��

�

dxdy pixi(x, y)L[x � mrxx0(�); 0.5mrx

xlw]

� exp�� xmrx

xbw 2�� ApL�xi

� mrxx0(�); 0.5mrx

xlw�exp�� xi

mrxxbw

2�(6)

where, Ap � pxpy is the area of a single verticallybinned pixel. We refer to approximation (6) as theslowly varying pixel approximation, which indicatesthat the spatial variation of the TFP filter image onthe detector is small compared with the size of asingle pixel in the array. If we insert approximation(3) into Eq. (4) we find that pixel photocurrent gi isgiven by

gi ��cfr�mxlw�1 � �1 � NA2�Ap

4Aimry

��0

�

d��0

�

d�� m�1

M

Fme(�)�0(��)�1

� exp�mFma(��)leffcm�Lxi

� mrxx0(�); 0.5mrx

xlwexp�� xi

mrxxbw

2�. (7)


Further simplification of Eq. (7) occurs within thelimit of small concentrations such that 0 m��leffcm 0.02. This allows us to include only thefirst term of a MacLauren series expansion for theexponential function exp��x� � 1 � x. With thisapproximation we find

gi ��cfr�mleffxlw�1 � �1 � NA2�Ap

4Aimry

� exp�� xi

mrxxbw

2��0

�

d��0

�

d��0(��)L�xi

� mrxx0(�); 0.5mrx

xlw� �m�1

M

Fme(�)mFm

a(��)cm . (8)

Now, if we interchange the order of integration andsummation, we can rewrite approximation (8) so that

gi � �m�1

M

himcm, (9)

where

him ��cfr�mmxlw�1 � �1 � NA2�Ap

4mrymc

2A01�2

� exp�� xi

mrxxbw

2��0

�

d��Fma��

��0

�

d��Fme(�)L�xi � mrx

x0(�); 0.5mrxxlw�.

(10)

Equation (9) states that, for pixel i, the total gener-ated photocurrent gi �amps� is equal to the molarconcentration cm �moles�liter� times him summed overall reactive dye species in the test sample. This equa-tion is a discrete-to-discrete mapping operation fromconcentration to photocurrent and represents the for-ward problem.

B. Reverse Problem: a Pseudoinverse Reconstruction

In the reverse problem, we are given spectral data inthe form of pixel photocurrents gi, and we want toreconstruct the corresponding unknown dye concen-trations cm �m � 1, 2, 3 . . . M�. To solve the reverseproblem, one approximation or another must bemade. Thus far we have employed several approxi-mations to arrive at Eq. (9). For example, we haveassumed constant illumination, small concentra-tions, and the slowly varying pixel approximation. Inprinciple, Eq. (9) holds true for every pixel in thedetector array �i � 1, 2, 3 . . . Nx�. However, in prac-tice, this relation is best realized at those locations atwhich the signal-to-noise ratio is largest (i.e., the lo-cal maxima of the data). Consider a multiple-dyespectrum given by

gmaxp� �

m�1

M

hmaxpmcm, (11)

where gmaxpis the photocurrent that corresponds to

peak p in a multiple-peak response. If we assume thatthe individual spectral peaks for each dye specie arewell separated and uncorrelated, the number of indi-vidual peaks in spectral scan Np will be equal to thenumber of dye species in test sample M. In operatorform, we can rewrite Eq. (11) as

Gmax � Hmax · C, (12)

where Gmax and C are M-element column vectors andHmax is an M � M square matrix whose elements aredye-specie and instrument-parameter dependent.Hmax is a discrete-to-discrete mapping operator whoseelements, hmaxpm

, are a subset of him given by Eq. (10).Writing Eq. (12) explicitly we have

�gmax1

gmax2

É

gmaxM

� � �hmax11

hmax12. . . hmax1M

hmax21hmax22

. . . hmax2M

É É É É

hmaxM1hmaxM2

. . . hmaxMM

� �c1

c2

É

cM

�. (13)

To solve the reverse problem, both sides of Eq. (12)are multiplied on the left by Hmax

�1 so that

C � Hmax�1 · Gmax. (14)

Reconstructing the concentrations from the pho-tocurrents can be done either analytically or throughcalibration. The analytic approach requires knowl-edge of all dye characteristics, detector characteris-tics, and other instrument-dependent parameters togreat precision, so that the integrals that comprisethe elements of Hmax can be computed. Then the in-verse is computed by Gaussian reduction or someother conventional method and the resulting concen-trations, cm, are determined by use of Eq. (14). Theproblem with the analytic approach is that ourknowledge of the instrument and dye properties isnot that precise and this imprecision would causealiasing of the reconstructed concentration data. Abetter approach is to determine the elements of Hmaxthrough calibration.

By selecting a set of known concentrations andrecording the associated pixel photocurrents for eachset, we can determine the elements of Hmax in a min-imum least-squares (LS) manner using the Moore–Penrose pseudoinverse.8 Consider the situation whenwe have Nc separate concentrations for each dye spe-cie m � 1, 2, 3 . . . M (i.e., for each peak p �1, 2, 3 . . . Np) such that

�gmaxp

(1)

gmaxp

(2)

É

gmaxp

(Nc)� � �

c1(1) c2

(1) . . . cM(1)

c1(2) c2

(2) . . . cM(2)

É É É É

c1(Nc) c2

(Nc) . . . cM(Nc)

� �hmaxLSp1

hmaxLSp2

É

hmaxLSpM

�. (15)


In operator form, Eq. (15) can be written as G� C · HmaxLS, where G and HmaxLS are column vectorsand C is an Nc � M matrix whose elements are care-fully prepared calibration concentrations cm

�n�, wheren is the concentration number and m is the dye spe-cie. In other words, concentration matrix C is com-prised of Nc separately calibrated concentrations foreach of the M dye species. In general, C is not squareso its true inverse is not defined. However, we candefine a pseudoinverse such that

HmaxLS � C� · G, (16)

where the pseudoinverse C� is given by C� ��C† · C��1 · C† (C† is the transpose of C).

The calibration procedure is as follows: mix a set ofappropriate concentrations for each dye in the testsample, measure the spectrum for each individualconcentration, and find the maximum photocurrent,gmaxp

�n�. Then construct concentration matrix C andmeasurement vector G. From these photocurrentsand the pseudoinverse of C, we can solve for each rowof Hmax in a minimum LS manner by using Eq. (16).Once we know the elements of Hmax, we can numer-ically invert it to obtain Hmax

�1 and to solve for indi-vidual concentrations cm according to Eq. (14). Fromconcentrations cm one can then determine the particlecount for each dye specie according to

Nm(no. of particles) � 0.001 A0leffNAcm, (17)

where NA is Avogadro’s number �NA � 6.023 �1023 particles�mole� and A0leff �cm3� is the illumi-nated test sample volume.

4. Results

A. Single-Dye Reconstruction

Our mathematical treatment of the reconstructionprocess is completely general with regard to the num-ber of dye species found in the test sample. However,before considering the multiple-dye reconstruction,let us experimentally confirm that our treatment isworking satisfactorily for the single-dye case.

Six different mixtures of Sulforhodamine 101�SR 101, e � 105,700 cm�1 M�1, � � 1.0� and etha-nol were prepared in concentrations of 5, 10, 50, 500,1000 and 2000 nM, respectively. SR 101 (MolecularProbes) was selected because its peak emission wave-length �593 nm� is well within the useful range of theTFP filter deployed in our experimental setup. SR 101also has a peak absorption wavelength �578 nm� thatis efficiently pumped by the tungsten–halogen source.Experimental spectral scans for each of the concentra-tions are shown in Fig. 3 with a pure ethanol back-ground (i.e., dark) subtract and 25 ms exposures. Eachseparate curve is an average over 100 spectral scans.For each curve, the peak response (i.e., peak photocur-rent gmax) is extracted from the data and plotted as afunction of concentration in Fig. 4, along with a LSlinear fit to the experimental data (solid line). With a

coefficient of determination R2 of 0.99991, we find thatthe line is an excellent fit to the data.

Having determined the concentration matrix C, inthis case a six-element column matrix, we thenprepared a 100 nM text mixture of SR 101 and eth-anol and measured its corresponding spectral re-sponse (see Fig. 5). From the single-specie spectralpeak and C, we were able to compute HmaxLS fromEq. (16), which resulted precisely within the slope ofthe best-fit line in Fig. 4, as it should in the trivialsingle-dye case. Equation (14) then results in a con-centration of 98.3 nM with an impressive 1.7% ex-perimental error for the single-dye case.

B. Multiple-Dye Reconstruction

Emboldened by our successful reconstruction for asingle dye, we set out to verify experimentally our

Fig. 3. Measured spectra for six calibration concentrations of SR101 in pure ethanol for 25 ms exposures and 100 averaged frames.

Fig. 4. Maximum counts minus the background for each of the sixSR 101 calibration concentrations. The solid line is a LS linearfit.


theoretical treatment in the multiple-dye case. Manydifferent dye species are available for use in the vis-ible spectrum. However, multicolor labeling requiresthat we judiciously select those dyes whose emissionwavelengths are well separated and whose absorp-tion peaks do not lie within any of the emissionbands. Further exacerbating the dye selection pro-cess are (1) environmental factors (solvent polarity,pH, etc.), (2) fluorescence resonance energy transfer,(3) photobleaching, and (4) excimer formation effects.To mitigate some of these issues, we decided to usefluorophores that are encapsulated within polysty-rene spheres. These FluoSpheres (Molecular Probes)are available in several different sizes with a varietyof impregnated dyes.

For multiple-dye reconstruction, two carboxylate-modified FluoSpheres were selected � � 80,000cm�1 M�1, � � 1.0� to comprise the test sample. Thefirst was a yellow-green (YG) 2% solid suspension of21 nm beads in water with an absorption (emission)

peak of 505 nm �515 nm�, (Molecular Probes F-8787).The second was a crimson (CR) 2% solid suspensionof 24 nm beads in water with an absorption (emis-sion) peak of 625 nm �645 nm� (Molecular ProbesF-8782). The small size of the FluoSpheres was se-lected to reduce scattering effects that are due to arefractive-index mismatch between polystyrene �n� 1.59� and water �n � 1.33�.

For each of the two FluoSpheres, five serial dilu-tions in pure water were prepared in separate glasscuvettes (YG, 39.1, 19.6, 9.78, 4.89, 0.391 �1012 beads�ml; CR, 26.2, 5.24, 2.62, 0.524, 0.262� 1012 beads�ml). Each concentration was measuredwith a pure-water background subtract, and 100 msexposures were averaged over ten readings. The spec-tral scans are shown in Fig. 6 on a log-linear scale.For each curve, the peak spectral response, gmax, isextracted from the data and plotted as a function ofconcentration in Fig. 7, along with a LS linear fit tothe data (solid lines). With coefficients of determina-tion, RYG

2 � 0.9993 and RCR2 � 0.9997, we find that

both sets of data are highly linear.Having determined concentration matrix C, in this

case a ten-element rectangular matrix, we then pre-pared a 1:1 mixture (by volume) of YG and CR beadsin water and measured the corresponding dual-specie spectral scan (see Fig. 8). From these data Gwas determined and we then used C and G to deter-mine HmaxLS by using Eq. (16). Reconstructing theconcentrations according to Eq. (14) then results in3.82 � 1012 and 3.15 � 1012 beads�ml for the YG andCR FluoSpheres, respectively. After measuring theconstituent beads prior to mixing, we confirmed ac-tual concentrations of 5.06 � 1012 and 2.52 �1012 beads�ml for the YG and CR FluoSpheres, re-spectively, which yields a reconstruction error of theorder of 25% for each.

Clearly, systematic errors in the experimental re-construction process exist in the multiple-dye case.One such error occurs if the absorption spectrum of oneconstituent overlaps the emission spectrum of another.

Fig. 5. Measured spectrum for 100 nM SR 101 in pure ethanol for25 ms integration and 100 averages.

Fig. 6. Measured spectra of (a) YG FluoSpheres and (b) CR Fluospheres on a log-linear scale for 100 ms exposure and ten averagedframes.


In Fig. 8 we show the constituent spectral scans of thedual-specie test mixture. Because the absorptionspectrum is blueshifted from the emission spectrumfor both FluoSpheres, one can surmise that the CRabsorption spectrum will overlap the YG emissionspectrum, thus causing the reconstructed CR (YG) con-centration to be larger (smaller) than the actual value,as was seen in our experimental work. Inherent in ourreconstruction process is the requirement that thedyes be noninteracting with regard to their absorptionand emission energy levels. In theory, an energy bal-ance correction factor could be introduced into ourtreatment that takes into account such interactions.

5. Conclusion

The tapered Fabry–Perot fluorescence spectrometerprovides an elegant, no-moving-parts approach for

identifying and quantifying fluorescing particles inreal time. With higher NA collection optics, a morejudicious choice of relay lenses, dual pumping ofhigher-power beams, and a double-pass sample cell,we believe that the sensitivity of our instrumentcould be increased substantially. Especially intrigu-ing is the integration of photonics, electronics, andmicrofluidics into compact lab-on-chip systems withnanoliter sample volumes and increased sensitivity.These are research and development areas to be re-alized in future embodiments of this study.

The authors thank Barbara Leonard and AntjeBaeumner for the use of their laboratory.

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Fig. 7. Concentration versus gmax for (a) YG FluoSpheres and (b) CR FluoSpheres for 100 ms exposures and ten averaged frames withLS linear fits (solid lines).

Fig. 8. Measured spectra of 1:1 (by volume) mixture of YG and CRbeads along with the measured spectra of the constituent compo-nents. The exposure time was 100 ms and the spectra were aver-aged ten times.


Multiple-fluorophore-specie detection with a tapered Fabry-Perot fluorescence spectrometer

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