1. Introduction

Raman spectroscopy is a powerful analytical and research tool currently available for biochemical characterization of samples. This spectroscopic technique is based on the inelastic scattering of monochromatic radiation when it interacts with matter. During this process, energy is exchanged between the photon and the molecule so that the scattered photon is of higher or lower energy than the incident photon. The difference in energy between incident and scattered photon depends on the change in the rotational and vibrational energies of the interrogated molecule. As vibrational modes have energies that are highly specific to the chemical constitution 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 the sample, revealing detailed information about its DNA, protein, and lipid content in a rapid and noninvasive way [1–3]. The great benefits of this technique render it suitable for a wide variety of 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 weak Raman 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 for biomedical 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 samples can often be masked by autofluorescence which, while much broader than the sharp Raman bands, can dominate the spectrum and obscure the Raman signal. Therefore, such autofluorescence often needs to be removed. Recently different methods have been developed to isolate the Raman features from the fluorescence background [15–20].

In our recent paper, we demonstrated a simple fluorescence-rejection method, modulated Raman spectroscopy, based on the continuous modulation of the Raman excitation wavelength and on the use of the principle of multi-channel lock-in detection [21]. Once the synchronization and calibration procedure is performed, the fluorescence-free Raman spectrum is obtained online by applying the least-squares fitting algorithm. While this approach is conceptually similar to Shifted Excitation Raman Difference Spectroscopy (SERDS) [15, 17, 22, 23] or single-channel wavelength modulation techniques [24], it offers important advantages and improvements. First, both scattering and fluorescence from the sample and spurious stray light are completely suppressed thanks to the modulation of the Raman excitation wavelength and to the multi-channel lock-in detection. The use of continuously modulated wavelength in our method as opposed to the use of only two (or few) excitation wavelengths in SERDS [16] helps further in the reconstruction of the Raman signal. Additionally, the SNR is further improved by 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 fluorescence free Raman spectra with a minimal required user intervention making the method more practical and less time-consuming with respect to the standard SERDS methods. Additionally, multi-channel lock-in detection, compared with single-channel detection, requires much shorter signal accumulation times rendering the method suitable for real-time static background removal, especially in the presence of biological samples, which are normally photochemically labile.

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

 

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

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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 785 nm 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 laser beam was passed through a bandpass filter (Semrock optic, Max line 785), to remove any spontaneous 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 objective lens used to focus the laser onto the sample was also used to collect the back-scattered photons. By going back along the incoming path, this scattered light passes through a RazorEdge Dichroic beamsplitter (Semrock), which reflects the Rayleigh scattered light incident at 45° while efficiently passing the longer wavelength shifted Raman photons. The resulting filtered radiation is focused onto the spectrometer entrance slit; this was an Andor spectrometer (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 × 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 imaged onto 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 power on the sample was ~5mW and the integration time was 10s. Polystyrene has a relatively simple 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. The fluorescence signal is essentially due to the dye in which the beads are diluted. Under these conditions, the biochemical characterization of the sample is difficult. In particular, we can distinguish 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 spectrum is 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 the static fluorescence background.

 

Fig. 2. Standard Raman spectrum of a polystyrene bead (2 μm sized) in a solution 10⁻⁷ M of 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 spectrum is obtained by acquiring only two spectra with an integration time of 5s each at two slightly different laser wavenumbers (Δν ~40 GHz) (b). Comparison of the modulated Raman spectra obtained by using different mathematical approaches: Standard Deviation analysis (c), Fourier Filtering (d), Least-Squares fitting (e) and Principal Component Analysis (f). The spectra are obtained by modulating the Raman excitation wavelength with a frequency of f ~1Hz and an amplitude A ~40 GHz. 100 spectra are acquired with an integration time of 0.1s each. The inserts show an expanded view of the spectral window between 1700–1750 cm⁻¹.

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Table 1. Polystyrene Raman bands [25].

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3.2. Modulated Raman spectroscopy

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

In the following section, we consider the measured spectra to be defined by the continuous function S(ν). The spectrum is measured N times for a duration of Δt, each, and a total acquisition time T = NΔt. Each individual spectrum is indexed by the parameter j and measured at the discrete wavenumber set ν_i. Altogether, the wavenumber modulated spectra are defined by S_j(ν_i) and Δν_j corresponds to the wavenumber shift of the Raman excitation laser for the individual spectra S_j. For molecules with both Raman and fluorescence emission, this can be considered as the superposition of two parts: the fluorescent part S_F(ν_i + Δν_j) and the Raman peaks S_R(ν_i + Δν_j). For small Δν_j, S_F(ν_i + Δν_j) ≈ S_F(ν_i). Therefore, the individual Raman spectrum can be represented as:

Once this is known there are multiple algorithms that can be used to extrapolate the modulated Raman information from the static fluorescence background. To be able to compare the different approaches, all the experimental parameters, total integration time and laser power on the sample, 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 reference fluorescence-free Raman spectrum we used Shifted Excitation Raman Difference Spectroscopy (SERDS). In this case, we consider the acquisition of two spectra S ₁(ν_i) and S ₂(ν_i). The difference between these two spectra is then computed, D(ν_i) = S ₁(ν_i)-S ₂(ν_i). For small symmetric wavenumber shifts Δν ₁ = Δν/2 and Δν₂ = -Δν/2, the difference in the spectra is essentially proportional to the first order derivative of the Raman spectra S_R(ν). Indeed, we have:

where we rely on the Taylor expansion of the continuous Raman spectra around each wavenumber of interest ν_i. In Fig. 2(b) we report the acquired differential SERDS spectrum (2). This spectrum is free from any fluorescence contribution, but not all the weak Raman bands are visible due to the low signal-to-noise ratio inherent in this approach, as explained in our previous paper [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 different wavenumber shifts Δν_j it is possible to calculate the average Ŝ and the standard deviation σ of the spectral signal for each wavenumber component ν_i

In the absence of any noise, the standard deviation as defined by Eq. (4) is non zero only for the wavenumber components ν_i where the Raman signal S_R is present. Indeed, the fluorescence background cancels out in Eq. (4). The magnitude of the standard deviation spectra depends on the distribution of the wavenumber shift Δν_j and the shape of the Raman peak. This implies that this approach removes the fluorescence background but does not necessarily conserve relative intensity of the Raman peaks with respect to each other. In Fig. 2(c), we show the derivative of the measured standard deviation Eq. (4). We observe that the retrieved spectrum does not detect the weaker Raman peaks, between 1100–1500 cm⁻¹, which are buried in the residual background. 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 not constant, demonstrating the non-linearity of the method.

 

Fig. 3. Trends of the ratio between two polystyrene Raman peaks, R = I ₁₀₀₁/I ₁₀₃₁, as a function of the amplitude A (GHz) of the laser modulation. The different sets of data correspond to the different algorithms used to treat the acquired spectra.

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In order to better investigate the linearity of the standard deviation approach in reconstructing the Raman signal, we have studied the ratio between two Raman peaks (R = I ₁₀₀₁/I ₁₀₃₁) as a function of the laser modulation amplitude (A), see Fig. 3. For the SD approach to deliver a useful Raman spectrum, this ratio needs to be constant regardless of the modulation amplitude or 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 excitation wavenumber is modulated. We can clearly see the periodical modulation of the Raman peaks with increasing acquisition numbers. (b): The signal intensity of a single selected pixel as a function of the acquisition number.

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

where n_p 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 frequency as the modulation of the Raman excitation wavenumber [see Fig. 2(d)]. This mathematical algorithm mimics the function of a lock-in amplifier. Again, the FF retrieved Raman spectrum presents an improved signal-to-noise ratio when compared to the classic SERDS method and it now reveals the weak Raman bands between 1100 and 1500 cm⁻¹.

Unfortunately, while the apparent signal-to-noise ratio improves, the ratio between the Raman peaks is not maintained and the peaks shape is not exactly symmetric. These effects can be explained by analyzing the behavior of the signal intensity detected by a single CCD pixel (see Fig. 5). Indeed, a large amplitude compared to the spectral widths of a Raman peak, induces a change from the simple sinusoidal behavior to additionally including higher harmonics. This issue could be fixed either by reducing the modulation amplitude or by taking into account the higher harmonic oscillations when Fourier Filtering.

 

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

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Least-Squares fit (LSQ) The application of the Least-Squares fit method to separate the modulated Raman peaks from the fluorescence background is based on determining the best possible decomposition of the Raman spectra into static and shifting components [21]. This approach 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 represented as follows:

where we implied summation over repeating indices and where the shift matrix M_ik(Δν_j) is given by:

where $\underline{\Delta {\nu }_j}$ and $\stackrel{̲}{\Delta {\nu }_j}$ correspond respectively to the next smallest and next largest integer with respect to Δν_j.

Knowledge of the excitation wavenumber shift allows us to count 2n unknowns (S_F(ν_i) and S_R(ν_k)) 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 determined linear system that we solve using the least square procedure and retrieve at the same time the Raman and the fluorescence spectra. Conceptually, the least square fit corresponds to a lock-in procedure where the modulation reference is given by the fractional wavenumber shift operator M_ik. From this retrieved Raman spectra we deduce the modulated Raman spectra through D_k = S_R(ν_k)-S_R(ν _k+1) [21]. The retrieved derivative-like Raman spectrum free from any fluorescence contribution, is reported in Fig. 2(e). This result clearly shows the polystyrene bands at 795, 1155, 1450 cm ⁻¹ due to C-H out-of-plane deformation, C-C stretching vibration and CH₂ scissoring, respectively. These are not clearly observed in the standard Raman spectrum of Fig. 2(a).

Principal component analysis (PCA) The standard deviation method presented above is based on the observation that the Raman spectrum varies during wavenumber modulation while the fluorescence background does not. Here, we use Principal Component Analysis (PCA) to extract the precise maximal variation between the set of N spectra. This maximal variation spectra is given by the first principal component [26] and is directly associated with the derivativelike Raman spectra. Indeed, the variation of the measured spectra is induced by the continuous shift of the Raman peaks. We define the derivative-like Raman signal S_PCA as the eigenvector with the largest eigenvalue μ of the covariance matrix C_ik:

where the covariance matrix is:

Ŝ(ν_i) and Ŝ(ν_k) are the average of the spectral signals for the wavenumber components ν_i and ν_k, respectively. In the case of only two shift wavenumbers, the first eigenvector of matrix C_ik is equal to the SERDS spectra. In a mechanical context, the principal decomposition corresponds to 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 number of measured wavenumbers ν_i.

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

3.3. Discussion

Using the experimental setup and conditions described above, the best fluorescence-free signal is obtained by using the PCA method. Figure 6 directly compares the standard polystyrene Raman 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 small Raman bands due to the vibrational modes of the analyzed polymer.

To compare directly the effects of the different mathematical algorithms employed in terms of signal-to-noise ratio, we have analyzed the modulated Raman spectra of the same polystyrene bead acquired at different modulation frequencies f of the laser wavenumber (see Fig. 7). The acquisition time of the single spectrum and the total number of the acquired spectra are chosen to keep the total acquisition time (T) and the number of the spectral acquisitions per modulation period (n_p) constant.

We estimate the signal-to-noise ratio by measuring the intensity of the polystyrene Raman peak at 1001 cm ⁻¹ with respect to the standard deviation of the surrounding background. A common feature for all the experimental curves in Fig. 7 is the presence of three regions. In the first region, the SNR increases almost linearly and then reaches a plateau. This trend can be easily understood: as the modulation rate increases, the signal-to-noise ratio increases as a consequence of the decrease in the 1/f noise. By further increasing f , the signal-to-noise ratio reaches a saturation plateau. This last trend can be attributed to the fact that at higher laser modulation frequencies the acquisition time of the single spectrum is reduced (Δt < 50 ms) rendering the read-out-noise level almost comparable to the peak intensity and consequently affecting the measurements. Finally, when the peak intensity is hindered by the read-out-noise level, the signal-to-noise ratio decreases again.

 

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

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

To better understand the relationship between the modulation rate and the efficacy of the different processing algorithms used, we have also performed numerical simulations. In this case, a model spectrum is generated by overlapping a broad polynomial function (mimicking the fluorescence background), a small number of Gaussian peaks (Raman signals) with random heights and widths. Additionally, we took into account also the different noise contributions consisting of read-out noise, 1/f noise and shot noise. The relative intensities of the fluorescence 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 the experimental results: there is a clear advantage in using the PCA algorithm to analyze the raw spectra.

 

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

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

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

4. Conclusion

In conclusion, we have demonstrated improvement in the efficacy of the modulated Raman spectroscopy for fluorescence background suppression using continuous modulation of the Raman excitation wavelength combined with different mathematical approaches. The work has been mainly devoted to a systematic characterization and comparison of the modulated Raman spectra obtained using the following mathematical approaches: Least-Squares fit (LSQ), Principal Component Analysis (PCA), Fourier filtering (FF) and Standard Deviation (SD) analysis. All the algorithms presented can substantially suppress the fluorescence background and improve the spectral quality of the data. The FF method is quite adept at fluorescence rejection but it induces some artifacts or peak shape distortions, especially for high modulation amplitudes of the Raman excitation wavelength. The SD Raman spectrum is much noisier and most of the weak Raman peaks are buried in the residual background. In addition, this procedure is not linear and hence introduces artifacts in the final spectrum. The LSQ fit, as reported in our previous work [21], powerfully removes the fixed pattern noise associated with the fluorescence background and renders visible the hidden weak Raman features: however it requires two preliminary steps; the calibration and synchronization procedures. The best signal-to-noise ratio in the modulated Raman spectra is obtained by using the PCA approach. More precisely, the modulated Raman spectrum obtained by using the PCA method and a wavelength modulation rate of 1Hz presents an improvement in the signal-to-noise ratio with respect to the previously reported LSQ method of about 30%, and with respect to the SERDS method of about 70%. This improvement is also confirmed by numerical simulations. This algorithm is linear and hence does not induce artifacts in the retrieved spectra. Additionally the PCA approach does not require any calibration or synchronization procedure. Therefore, the use of the PCA approach in modulated Raman spectroscopy markedly reduces the accumulation time required as well as the noise of the Raman signal. This is a robust technique that can be implemented within current Raman systems and significantly reduces user intervention, rendering the method more practical for real-time applications.

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