Optimal algorithm for fluorescence suppression of modulated Raman spectroscopy

Optimal algorithm for fluorescencesuppression of modulated Raman

spectroscopy

Michael Mazilu1,∗, Anna Chiara De Luca1, Andrew Riches2, C. SimonHerrington2, and Kishan Dholakia1

1SUPA-School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews,Fife, KY16 9SS, UK

2Bute Medical School, University of St Andrews St. Andrews, Fife, KY16 9TS, UK

*[email protected]

http://www.st-andrews.ac.uk/∼atomtrap/

Abstract: Raman spectroscopy permits probing of the molecular andchemical properties of the analyzed sample. However, its applicability hasbeen seriously limited to specific applications by the presence of a strongfluorescence background. In our recent paper [Anal. Chem. 82, 738 (2010)],we reported a new modulation method for separating Raman scatteringfrom fluorescence. By continuously changing the excitation wavelength,we demonstrated that it is possible to continuously shift the Raman peakswhile the fluorescence background remains essentially constant. In thisway, our method allows separation of the modulated Raman peaks from thestatic fluorescence background with important advantages when comparedto previous work using only two [Appl. Spectrosc. 46, 707 (1992)] or afew shifted excitation wavelengths [Opt. Express 16, 10975 (2008)]. Thepurpose of the present work is to demonstrate a significant improvementof the efficacy of the modulated method by using different processingalgorithms. The merits of each algorithm (Standard Deviation analysis,Fourier Filtering, Least-Squares fitting and Principal Component Analysis)are discussed and the dependence of the modulated Raman signal onseveral parameters, such as the amplitude and the modulation rate of theRaman excitation wavelength, is analyzed. The results of both simulationand experimental data demonstrate that Principal Component Analysis isthe best processing algorithm. It improves the signal-to-noise ratio in thetreated Raman spectra, reducing required acquisition times. Additionally,this approach does not require any synchronization procedure, reduces userintervention and renders it suitable for real-time applications.

© 2010 Optical Society of America

OCIS codes: (300.6450) Spectroscopy, Raman; (300.6380) Spectroscopy, modulation.

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#124453 - $15.00 USD Received 22 Feb 2010; revised 30 Apr 2010; accepted 6 May 2010; published 14 May 2010(C) 2010 OSA 24 May 2010 / Vol. 18, No. 11 / OPTICS EXPRESS 11382

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1. Introduction

Raman spectroscopy is a powerful analytical and research tool currently available for biochem-ical characterization of samples. This spectroscopic technique is based on the inelastic scatte-ring of monochromatic radiation when it interacts with matter. During this process, energy isexchanged between the photon and the molecule so that the scattered photon is of higher orlower energy than the incident photon. The difference in energy between incident and scatteredphoton depends on the change in the rotational and vibrational energies of the interrogatedmolecule. As vibrational modes have energies that are highly specific to the chemical consti-tution of the molecule, the identity and structure of the molecule can be deduced. Therefore, a


Raman spectrum obtained, for example, from a cell is an intrinsic molecular fingerprint of thesample, revealing detailed information about its DNA, protein, and lipid content in a rapid andnoninvasive way [1-3]. The great benefits of this technique render it suitable for a wide varietyof substance characterizations in many research areas, including chemical [4, 5], physical [6, 7],biological [8, 9], pharmaceutical [10, 11] and medical [12-14] fields.

The main challenges in Raman microscopy arise from the fact that typically only 1 in 106-108 photons incident on a sample are Raman scattered. In fact, the detection of such weakRaman peaks is often precluded by the presence of the much more intense fluorescence signals.Although Raman spectroscopy has important advantages as a diagnostic and analytical tool forbiomedical applications, its use has been severely limited by the presence of such fluorescence,which unfortunately occurs in the same spectral window. Raman spectra from biological sam-ples can often be masked by autofluorescence which, while much broader than the sharp Ramanbands, can dominate the spectrum and obscure the Raman signal. Therefore, such autofluores-cence often needs to be removed. Recently different methods have been developed to isolatethe Raman features from the fluorescence background [15–20].

In our recent paper, we demonstrated a simple fluorescence-rejection method, modulatedRaman spectroscopy, based on the continuous modulation of the Raman excitation wavelengthand on the use of the principle of multi-channel lock-in detection [21]. Once the synchro-nization and calibration procedure is performed, the fluorescence-free Raman spectrum is ob-tained online by applying the least-squares fitting algorithm. While this approach is concep-tually similar to Shifted Excitation Raman Difference Spectroscopy (SERDS) [15, 17, 22, 23]or single-channel wavelength modulation techniques [24], it offers important advantages andimprovements. First, both scattering and fluorescence from the sample and spurious stray lightare completely suppressed thanks to the modulation of the Raman excitation wavelength andto the multi-channel lock-in detection. The use of continuously modulated wavelength in ourmethod as opposed to the use of only two (or few) excitation wavelengths in SERDS [16] helpsfurther in the reconstruction of the Raman signal. Additionally, the SNR is further improvedby increasing the modulation frequency, which is a consequence of the decreased 1/f noise.Another important advantage of our method is that this gives on-line access to the fluores-cence free Raman spectra with a minimal required user intervention making the method morepractical and less time-consuming with respect to the standard SERDS methods. Addition-ally, multi-channel lock-in detection, compared with single-channel detection, requires muchshorter signal accumulation times rendering the method suitable for real-time static backgroundremoval, especially in the presence of biological samples, which are normally photochemicallylabile.

In this paper, we present a powerful improvement of the modulated Raman method for fluo-rescence rejection by comparing different processing algorithms used to analyze the raw data:Standard Deviation analysis (SD), Fourier Filtering (FF), Least-Squares fitting (LSQ) and Prin-cipal Component Analysis (PCA). A suspension of polystyrene beads (2μm in size) in a nearinfrared (NIR) dye which gives a high fluorescence signal in the Raman spectra was chosen as atest sample to illustrate the potential of these approaches. We perform a systematic study of theRaman spectrum of polystyrene using these different processing algorithms, and its dependenceon several parameters, such as the amplitude and the Raman excitation wavelength modulation.Our results demonstrate that the PCA processing algorithm significantly enhances the efficacyof the modulation Raman method for fluorescence background removal, revealing importantadvantages. Firstly, this approach, compared with the previously reported LSQ method [21],does not require any wavelength calibration and synchronization procedure, reducing comput-ing time. Additionally, it improves the signal-to-noise ratio of the Raman spectra, reducing therequired accumulation time and favoring real-time applications.


Fig. 1. Experimental set-up. Except for the laser (tunable in this instance), the setup usedfor the modulation technique is identical to the standard Raman set-up. It is composed ofan inverted microscope that images the biological cells, focuses the Raman excitation beamonto the sample and collects the Raman scattering. Abbreviation: L, lens; BS, beam splitter;DBS, dichroic beam splitter; BPF, bandpass filter, M, mirror.

2. Experimental set-up

The basic principle of our modulated Raman spectroscopy has been described elsewhere [21].The main parts of the modulated Raman setup are shown in Fig. 1. A tunable diode laser(Sacher, Tiger Series, maximum power 1 W and total tuning range 200 GHz) centered at 785nm was directed into a home-made inverted microscope equipped with a 100x objective lens(Olympus, oil immersion, infinity corrected, 1.4 NA) to excite the Raman spectra. The laserbeam was passed through a bandpass filter (Semrock optic, Max line 785), to remove any spon-taneous emission from the laser source. To fill the objective back aperture, the infrared (IR)beam was expanded through a telescopic system: the final beam diameter was 8 mm. The ob-jective lens used to focus the laser onto the sample was also used to collect the back-scatteredphotons. By going back along the incoming path, this scattered light passes through a Ra-zorEdge Dichroic beamsplitter (Semrock), which reflects the Rayleigh scattered light incidentat 45◦ while efficiently passing the longer wavelength shifted Raman photons. The resultingfiltered radiation is focused onto the spectrometer entrance slit; this was an Andor spectrom-eter (Shamrock), equipped with a 300 lines/mm grating (785-nm blaze wavelength). Finally,the Raman radiation was detected by using an Andor CCD camera (iDus, 1024 x 256 pixels),thermoelectrically cooled at -80 ◦C and placed at the spectrometer exit. To allow observation,the light from a LED, was focused onto the sample by a 20X objective, which was then imagedonto a CCD camera.

3. Method and experimental results

3.1. Standard Raman spectroscopy

A typical standard Raman spectrum of a 2 μm polystyrene sphere suspended in a NIR-dye(Fluorescent Red NIR, Sigma) at a concentration 10−7M is reported in Fig. 2(a). The laser


Fig. 2. Standard Raman spectrum of a polystyrene bead (2 μm sized) in a solution 10−7Mof NIR-dye, showing the polymer Raman peaks on top of a broad fluorescence signal (a).The laser power on the sample was 5 mW and the integration time 10s. The SERDS spec-trum is obtained by acquiring only two spectra with an integration time of 5s each at twoslightly different laser wavenumbers (Δν ∼40 GHz) (b). Comparison of the modulatedRaman spectra obtained by using different mathematical approaches: Standard Deviationanalysis (c), Fourier Filtering (d), Least-Squares fitting (e) and Principal Component Anal-ysis (f). The spectra are obtained by modulating the Raman excitation wavelength witha frequency of f ∼1Hz and an amplitude A ∼40 GHz. 100 spectra are acquired with anintegration time of 0.1s each. The inserts show an expanded view of the spectral windowbetween 1700-1750 cm−1.

Table 1. Polystyrene Raman bands [25].

Polystyrene bands Assignmentcm−1

621 ring deformation mode795 C-H out-of-plane deformation1001 ring breathing mode1031 C-H in-plane deformation1155 C-C stretch1450 CH2 scissoring1583 C=C stretch1602 ring-skeletal stretch

power on the sample was ∼5mW and the integration time was 10s. Polystyrene has a relativelysimple Raman spectrum and Table 1 reports its principal Raman bands. The acquired spectrum


shows several Raman peaks due to the polymer on top of a broad fluorescence signal. Thefluorescence signal is essentially due to the dye in which the beads are diluted. Under theseconditions, the biochemical characterization of the sample is difficult. In particular, we candistinguish the peaks at 621, 1001, 1031 and 1602 cm−1, despite the fluorescence background,while the peaks at 795, 1155, 1450 cm−1 are more difficult to detect. Therefore, this spectrumis an ideal candidate to demonstrate and compare the effectiveness of the different algorithms(SD analysis, FF, LSQ fit and PCA) in extracting the modulated Raman information from thestatic fluorescence background.

3.2. Modulated Raman spectroscopy

Wavelength modulated Raman spectroscopy is based on the difference in spectral behaviour offluorescence and Raman scattering. In this section, we present multiple methods to use this dif-ference in order to distinguish and extract the Raman spectra from the background fluorescencespectra. We start this section by defining the data acquired in the modulated Raman spectra andthen we describe the different methods used to treat this data.

In the following section, we consider the measured spectra to be defined by the continuousfunction S(ν). The spectrum is measured N times for a duration of Δt, each, and a total ac-quisition time T = NΔt. Each individual spectrum is indexed by the parameter j and measuredat the discrete wavenumber set νi. Altogether, the wavenumber modulated spectra are definedby S j(νi) and Δν j corresponds to the wavenumber shift of the Raman excitation laser for theindividual spectra S j. For molecules with both Raman and fluorescence emission, this can beconsidered as the superposition of two parts: the fluorescent part SF(νi + Δν j)and the Ramanpeaks SR(νi + Δν j). For small Δν j, SF(νi + Δν j) ≈ SF(νi). Therefore, the individual Ramanspectrum can be represented as:

S j(νi) = SF(νi +Δν j)+SR(νi +Δν j)= SF(νi)+SR(νi +Δν j) (1)

Once this is known there are multiple algorithms that can be used to extrapolate the modulatedRaman information from the static fluorescence background. To be able to compare the differ-ent approaches, all the experimental parameters, total integration time and laser power on thesample, are kept constant. More precisely, 100 Raman spectra (with an integration time of 0.1s,each) were acquired by modulating the Raman excitation wavenumber ( f ∼ 1Hz, Δν ∼ 40Gz).

Shifted Excitation Raman Difference Spectroscopy (SERDS) To obtain a referencefluorescence-free Raman spectrum we used Shifted Excitation Raman Difference Spectroscopy(SERDS). In this case, we consider the acquisition of two spectra S1(νi) and S2(νi). The differ-ence between these two spectra is then computed, D(νi) = S1(νi)−S2(νi). For small symmetricwavenumber shifts Δν1 = Δν/2 and Δν2 = −Δν/2, the difference in the spectra is essentiallyproportional to the first order derivative of the Raman spectra SR(ν). Indeed, we have:

D(νi) = S1(νi)−S2(νi)= SR(νi +Δν/2)−SR(νi −Δν/2)≈ Δν∂νSR(νi) (2)

where we rely on the Taylor expansion of the continuous Raman spectra around each wavenum-ber of interest νi. In Fig. 2(b) we report the acquired differential SERDS spectrum (2). Thisspectrum is free from any fluorescence contribution, but not all the weak Raman bands are vis-ible due to the low signal-to-noise ratio inherent in this approach, as explained in our previouspaper [21]. Indeed, the noise level is additive when subtracting the two acquired spectra.


Standard Deviation (SD) When acquiring a full set of N spectra each with differentwavenumber shifts Δν j it is possible to calculate the average S and the standard deviation σof the spectral signal for each wavenumber component νi

S(νi) =1N

N

∑j=1

S j(νi) (3)

σ(νi) =

√√√√

1N

N

∑j=1

(S j(νi)− S(νi))2. (4)

In the absence of any noise, the standard deviation as defined by Eq. (4) is non zero only forthe wavenumber components νi where the Raman signal SR is present. Indeed, the fluorescencebackground cancels out in Eq. (4). The magnitude of the standard deviation spectra depends onthe distribution of the wavenumber shift Δν j and the shape of the Raman peak. This implies thatthis approach removes the fluorescence background but does not necessarily conserve relativeintensity of the Raman peaks with respect to each other. In Fig. 2(c), we show the derivativeof the measured standard deviation Eq. (4). We observe that the retrieved spectrum does notdetect the weaker Raman peaks, between 1100-1500 cm−1, which are buried in the residualbackground. In addition, comparing Fig. 2(c) with the standard Raman spectrum in Fig. 2(a)shows that, for the standard deviation method, the ratio between different Raman peaks is notconstant, demonstrating the non-linearity of the method.

Fig. 3. Trends of the ratio between two polystyrene Raman peaks, R = I1001/I1031, as afunction of the amplitude A (GHz) of the laser modulation. The different sets of data cor-respond to the different algorithms used to treat the acquired spectra.

In order to better investigate the linearity of the standard deviation approach in reconstructingthe Raman signal, we have studied the ratio between two Raman peaks (R = I1001/I1031) as afunction of the laser modulation amplitude (A), see Fig. 3. For the SD approach to deliver auseful Raman spectrum, this ratio needs to be constant regardless of the modulation amplitudeor frequency. In this case, the experimental results reported in Fig. 3 clearly demonstrate that


the SD method distorts the reconstructed Raman signal as the ratio R is not constant.

Fig. 4. (a): Plot of the temporal behaviour of the Raman spectra as the Raman excitationwavenumber is modulated. We can clearly see the periodical modulation of the Ramanpeaks with increasing acquisition numbers. (b): The signal intensity of a single selectedpixel as a function of the acquisition number.

Fourier Filtering (FF) Another approach applicable in the case of modulated Raman spec-troscopy is Fourier Filtering (FF). Here, we consider the periodic wavenumber modulation ofthe Raman excitation laser. From Fig. 4(a), we can see the periodic modulation behavior of theRaman peaks as the excitation wavenumber is modulated. The movement of the Raman peaksessentially appears as periodic fluctuation on each CCD pixel. Figure 4(b) shows the associatedintensity modulation of a single wavenumber component corresponding to the signal measuredby a single CCD pixel. Any pixels giving a stable intensity or an intensity not varying at thecorrect modulation rate have their signal rejected as being noise and not Raman signal. TheRaman signal after Fourier Filtering SFF is defined by:

SFF(νi) =N

∑j=1

sin( j2π/np)S j(νi). (5)

where np is the period of the wavenumber modulation in number of acquisitions. In practice,by using Fourier filtering we can select only the modulated part of the signal (Raman peaks)and any noise and fluorescence is rejected as neither of these will vary with the same frequencyas the modulation of the Raman excitation wavenumber [see Fig. 2(d)]. This mathematicalalgorithm mimics the function of a lock-in amplifier. Again, the FF retrieved Raman spectrumpresents an improved signal-to-noise ratio when compared to the classic SERDS method and itnow reveals the weak Raman bands between 1100 and 1500 cm−1.

Unfortunately, while the apparent signal-to-noise ratio improves, the ratio between the Ra-man peaks is not maintained and the peaks shape is not exactly symmetric. These effects can beexplained by analyzing the behavior of the signal intensity detected by a single CCD pixel (see


Fig. 5. Signal intensity of a single CCD pixel as a function of the acquisition number fortwo different amplitudes of the laser modulation. Higher amplitudes result in a change ofthe sinusoidal behavior.

Fig. 5). Indeed, a large amplitude compared to the spectral widths of a Raman peak, inducesa change from the simple sinusoidal behavior to additionally including higher harmonics. Thisissue could be fixed either by reducing the modulation amplitude or by taking into account thehigher harmonic oscillations when Fourier Filtering.

Least-Squares fit (LSQ) The application of the Least-Squares fit method to separate themodulated Raman peaks from the fluorescence background is based on determining the bestpossible decomposition of the Raman spectra into static and shifting components [21]. Thisapproach requires the laser wavenumber to be precisely assigned for each acquired spectrum(calibration and synchronization steps). In this case, the single acquired spectrum can be repre-sented as follows:

S j(νi) = SF(νi)+SR(νk)Mik(Δν j) (6)

where we implied summation over repeating indices and where the shift matrix Mik(Δν j) isgiven by:

Mik(Δν j) = (Δν j −Δν j)δi+Δν j ,k+(Δν j −Δν j)δi+Δν j ,k (7)

where Δν j and Δν j correspond respectively to the next smallest and next largest integer withrespect to Δν j.

Knowledge of the excitation wavenumber shift allows us to count 2n unknowns (SF(νi) andSR(νk)) where n is the number of pixels or wavenumbers acquired on the CCD camera (i,k=1...n). Acquiring more than two spectra, each giving n equations, defines an over determinedlinear system that we solve using the least square procedure and retrieve at the same time theRaman and the fluorescence spectra. Conceptually, the least square fit corresponds to a lock-inprocedure where the modulation reference is given by the fractional wavenumber shift opera-tor Mik. From this retrieved Raman spectra we deduce the modulated Raman spectra through


Dk = SR(νk)−SR(νk+1) [21]. The retrieved derivative-like Raman spectrum free from any flu-orescence contribution, is reported in Fig. 2(e). This result clearly shows the polystyrene bandsat 795, 1155, 1450 cm−1 due to C-H out-of-plane deformation, C-C stretching vibration andCH2 scissoring, respectively. These are not clearly observed in the standard Raman spectrumof Fig. 2(a).

Principal component analysis (PCA) The standard deviation method presented above isbased on the observation that the Raman spectrum varies during wavenumber modulation whilethe fluorescence background does not. Here, we use Principal Component Analysis (PCA) toextract the precise maximal variation between the set of N spectra. This maximal variation spec-tra is given by the first principal component [26] and is directly associated with the derivative-like Raman spectra. Indeed, the variation of the measured spectra is induced by the continuousshift of the Raman peaks. We define the derivative-like Raman signal SPCA as the eigenvectorwith the largest eigenvalue μ of the covariance matrix Cik:

μSPCA(νi) = CikSPCA(νk) (8)

where the covariance matrix is:

Cik =N

∑j=1

(S j(νi)− S(νi))(S j(νk)− S(νk)). (9)

S(νi) and S(νk) are the average of the spectral signals for the wavenumber components νi andνk, respectively. In the case of only two shift wavenumbers, the first eigenvector of matrix Cik isequal to the SERDS spectra. In a mechanical context, the principal decomposition correspondsto determining the major axis of rotation of a multidimentional object made of scattered points,where each point corresponds to a spectrum in an n−dimensional space where n is the numberof measured wavenumbers νi.

Better results are obtained by plotting the eigenvector SPCA of the covariance matrix with thelargest eigenvalue, as shown in Fig. 2(f). Obviously, Fig. 2(f) is much better in visual appear-ance than the raw spectra of Fig. 2(a). All of the details are revealed and there is also an increasein the signal-to-noise ratio with respect to all the other spectra reported in Fig. 2, reducing therequired accumulation time. In addition, the processing algorithm does not need any wavenum-ber calibration and synchronization procedures, reducing user intervention and rendering themethod useful for real-time applications.

3.3. Discussion

Using the experimental setup and conditions described above, the best fluorescence-free signalis obtained by using the PCA method. Figure 6 directly compares the standard polystyreneRaman spectrum and the modulated Raman spectrum derived by PCA analysis. In this figure,the fluorescence background is completely eliminated and we can also clearly see the smallRaman bands due to the vibrational modes of the analyzed polymer.

To compare directly the effects of the different mathematical algorithms employed in terms ofsignal-to-noise ratio, we have analyzed the modulated Raman spectra of the same polystyrenebead acquired at different modulation frequencies f of the laser wavenumber (see Fig. 7). Theacquisition time of the single spectrum and the total number of the acquired spectra are chosento keep the total acquisition time (T ) and the number of the spectral acquisitions per modulationperiod (np) constant.

We estimate the signal-to-noise ratio by measuring the intensity of the polystyrene Ramanpeak at 1001cm−1 with respect to the standard deviation of the surrounding background. A


Fig. 6. (a)The standard Raman spectrum of a 2 μm polystyrene bead in a 10−7M solutionof a NIR dye. The spectrum was acquired with an integration time of 10s and the laserpower was approximately 5mW at the sample. (b) The corresponding modulated Ramanspectrum obtained by analyzing the spectra, acquired by continuously shifting the Ramanexcitation wavenumber ( f =1Hz), with the PCA algorithm. In this case, the total integrationtime was also 10s.

common feature for all the experimental curves in Fig. 7 is the presence of three regions. Inthe first region, the SNR increases almost linearly and then reaches a plateau. This trend canbe easily understood: as the modulation rate increases, the signal-to-noise ratio increases as aconsequence of the decrease in the 1/ f noise. By further increasing f , the signal-to-noise ratioreaches a saturation plateau. This last trend can be attributed to the fact that at higher lasermodulation frequencies the acquisition time of the single spectrum is reduced (Δt < 50ms)rendering the read-out-noise level almost comparable to the peak intensity and consequentlyaffecting the measurements. Finally, when the peak intensity is hindered by the read-out-noiselevel, the signal-to-noise ratio decreases again.

At all the modulation rates for the experimental conditions used in Fig. 7, we can observethat the modulated Raman spectra, obtained by analyzing the first PC in PCA analysis, showsthe best signal-to-noise ratio. More precisely, by using a wavenumber modulation rate of 1Hzthe PCA modulated spectrum presents an improvement of the signal-to-noise ratio with respectto the previously reported LSQ method of about 30%, and with respect to the ”static” SERDSmethod of about 70%. Generally, the precise signal-to-noise ratio improvements delivered bythe various methods depend on the experimental limitations such as the readout noise, acquisi-tion duty cycle and reliable acquisition rates.

To better understand the relationship between the modulation rate and the efficacy of thedifferent processing algorithms used, we have also performed numerical simulations. In thiscase, a model spectrum is generated by overlapping a broad polynomial function (mimickingthe fluorescence background), a small number of Gaussian peaks (Raman signals) with randomheights and widths. Additionally, we took into account also the different noise contributionsconsisting of read-out noise, 1/ f noise and shot noise. The relative intensities of the fluores-


Fig. 7. Signal-to-noise ratio (SNR) of the polystyrene Raman peak at 1001cm−1 as a func-tion of the laser wavenumber modulation rate ( f ). The different sets of data correspond tothe different algorithms (PCA, LSQ fit, FF and SD) used to treat the acquired spectra.

Fig. 8. Signal-to-noise ratio (SNR) of a simulated Raman peak as a function of the laserwavenumber modulation rate ( f ). Additionally, the height and width of the Raman peaksand the noise level selected for the simulations are quite close to the measured experimentalparameters. The different sets of data correspond to the different algorithms (PCA, LSQ fit,FF and SD) used to treat the simulated spectra.

cence and Raman signals were varied to demonstrate the impact of the different approaches on


the reconstruction performance. The simulations performed, as shown in Fig. 8, confirm theexperimental results: there is a clear advantage in using the PCA algorithm to analyze the rawspectra.

These important experimental and simulated results identify the PCA approach as the bestprocess algorithm for the online suppression of fluorescence background from modulated Ra-man spectra. In fact, the PCA method improves the signal-to-noise ratio in the treated Ramanspectra, reducing the accumulation time. Importantly, this approach does not require any syn-chronization procedure, further reducing user intervention and rendering modulation Ramanspectroscopy useful for real-time applications.

4. Conclusion

In conclusion, we have demonstrated improvement in the efficacy of the modulated Ramanspectroscopy for fluorescence background suppression using continuous modulation of the Ra-man excitation wavelength combined with different mathematical approaches. The work hasbeen mainly devoted to a systematic characterization and comparison of the modulated Ramanspectra obtained using the following mathematical approaches: Least-Squares fit (LSQ), Prin-cipal Component Analysis (PCA), Fourier filtering (FF) and Standard Deviation (SD) analysis.All the algorithms presented can substantially suppress the fluorescence background and im-prove the spectral quality of the data. The FF method is quite adept at fluorescence rejectionbut it induces some artifacts or peak shape distortions, especially for high modulation ampli-tudes of the Raman excitation wavelength. The SD Raman spectrum is much noisier and mostof the weak Raman peaks are buried in the residual background. In addition, this procedure isnot linear and hence introduces artifacts in the final spectrum. The LSQ fit, as reported in ourprevious work [21], powerfully removes the fixed pattern noise associated with the fluorescencebackground and renders visible the hidden weak Raman features: however it requires two pre-liminary steps; the calibration and synchronization procedures. The best signal-to-noise ratio inthe modulated Raman spectra is obtained by using the PCA approach. More precisely, the mod-ulated Raman spectrum obtained by using the PCA method and a wavelength modulation rateof 1Hz presents an improvement in the signal-to-noise ratio with respect to the previously re-ported LSQ method of about 30%, and with respect to the SERDS method of about 70%. Thisimprovement is also confirmed by numerical simulations. This algorithm is linear and hencedoes not induce artifacts in the retrieved spectra. Additionally the PCA approach does not re-quire any calibration or synchronization procedure. Therefore, the use of the PCA approachin modulated Raman spectroscopy markedly reduces the accumulation time required as wellas the noise of the Raman signal. This is a robust technique that can be implemented withincurrent Raman systems and significantly reduces user intervention, rendering the method morepractical for real-time applications.

The results obtained are promising. They should expand the use of Raman spectroscopy tomany types of samples that are difficult to analyze due to fluorescence interference. Because ofthe simplicity and robustness of our modulation method combined with the PCA approach, weexpect that it will see wide applicability in the field of clinical diagnostics. In fact, modulatedRaman spectroscopy, with consequent rejection of the fluorescence background and reductionof signal acquisition times with respect to SERDS or previous wavelength modulation tech-niques [15, 16, 24], for example, should improve biochemical characterization and the discrim-ination between cancer and non-cancer cells.

Acknowledgments

We acknowledge the Cancer Research UK and the Engineering and Physical Sciences ResearchCouncil (EPSRC), in association with the Medical Research Council (MRC), for funding this


research. KD is a Royal Society-Wolfson Merit Award Holder.


Documents

Optimal algorithm for fluorescence suppression of modulated Raman spectroscopy