Methods guide

What each RNSpectraX step does to your data, why it works (the physics), how it is computed (the mathematics), when to use it, and how to read what it shows. The full derivations are in METHODS.md; button-by-button instructions are in the user manual.

The processing order

A measured Raman spectrum is the sum of several things: the Raman bands you want, a broad fluorescence background, random noise, occasional cosmic-ray spikes, and a small error in the wavenumber axis. Each processing step removes one of these, so the order matters. RNSpectraX always applies them in this order:

Why this order? Spikes are removed before anything else because a 3000-count spike would drag a fitted baseline upwards and be smeared out by smoothing. The baseline is removed before normalising, otherwise "divide by the maximum" would divide by the fluorescence rather than by your band. Smoothing comes after the baseline so the filter acts on the bands, not on a steep background slope. The derivative is last because it amplifies noise and is only meaningful on a clean spectrum.

The Stage-by-Stage Data export (Export ▾) writes every one of these intermediate spectra for each file, so you — or a reviewer — can see exactly what each step did.

Which method should I use?

Shift calibration

What it does

Adds a constant $\delta$ to every Raman shift: $\tilde\nu' = \tilde\nu + \delta$. It corrects a spectrometer whose axis has drifted, so band positions can be compared between days, instruments and published values.

The physics

The Raman shift is the difference between the laser and the scattered photon energies, $\tilde\nu = 1/\lambda_\text{laser} - 1/\lambda_\text{scattered}$ (in cm⁻¹). A small error in the assumed laser wavelength, or a slight movement of the grating, shifts every band by nearly the same amount. Some materials have one very sharp band at a precisely known position: crystalline silicon (optical phonon, 520.7 cm⁻¹), polystyrene (ring breathing, 1001.4 cm⁻¹) and diamond (1332 cm⁻¹). Measuring one of them with the same settings tells you how far the axis is off.

The mathematics

Inside ±w of the reference position the highest point is found and refined with a parabola through the seven points around it, $y = c_0 + c_1 t + c_2 t^2$, whose vertex $t^* = -c_1/2c_2$ gives a sub-pixel band position $\tilde\nu_\text{meas}$. Then $\delta = \tilde\nu_\text{ref} - \tilde\nu_\text{meas}$.

When to use it · how to read it

Use it whenever you report band positions to better than a few cm⁻¹, or combine spectra from different sessions. Load the silicon (or polystyrene) spectrum with your samples, choose it as the Reference spectrum and press 🎯 Measure shift. The toast reports the measured position and the correction (e.g. "+2.48 cm⁻¹"). A correction of more than ~5 cm⁻¹ usually means the wrong laser wavelength was set in the acquisition software.

Excluded regions

What it does: removes the points inside the ranges you type (e.g. 1540-1560; 2320-2340) before any other processing.

Why: some features are not from your sample: a substrate band (Si at 520 or 950 cm⁻¹ on a silicon chip), atmospheric O₂/N₂ (1556/2331 cm⁻¹), a notch-filter edge near 0 cm⁻¹ or a detector artefact. Left in, they distort the baseline fit, normalisation and PCA (which would happily "separate" samples by how much substrate they show).

Mathematics: none — those points are simply not used. The line on the plot joins across the gap.

Despiking (cosmic-ray removal)

The physics

High-energy cosmic-ray particles hit the CCD and deposit charge in one or two pixels. They appear as extremely narrow, very tall spikes at random positions that do not repeat between acquisitions. A genuine Raman band is at least several pixels wide, because its width is set by the vibrational lifetime and the spectrometer resolution.

The mathematics

Spikes are detected on the first difference $\Delta y_i = y_i - y_{i-1}$, which turns a narrow spike into a huge jump while a smooth band stays small. A modified z-score uses the median and the median absolute deviation (MAD), which a few spikes cannot inflate:

Points with $|z_i|$ above the threshold (default 6) are flagged. Modified Z-score repairs them by linear interpolation between the nearest good neighbours; Whitaker–Hayes replaces them with the mean of the good points inside the repair window.

Settings

Threshold 6 is a safe start; lower it (4–5) if spikes survive, raise it (8–10) if a sharp real band is being cut. Keep the repair window small (2–3 points).

Baseline correction

The baseline (dashed) is estimated underneath the bands and subtracted.

The physics

Raman scattering is weak — roughly one photon in 10⁶–10⁸. Many samples (cells, tissue, bacteria, dyes, SERS substrates) also fluoresce: they absorb the laser and re-emit a broad continuum thousands of times stronger. It appears as a smooth, curved background tens to hundreds of cm⁻¹ wide, under bands only ~5–40 cm⁻¹ wide. Because fluorescence varies with focus, photobleaching and sample, it must be removed before intensities are compared. Every method below exploits the same idea: the background is much smoother than the bands.

The methods

Asymmetric least squares (ALS) in detail

ALS finds the baseline $z$ that balances two wishes: stay close to the data, and be smooth. It minimises

The second term penalises curvature: λ is the stiffness (entered as log₁₀ λ; 5 means 10⁵). The trick is the asymmetric weight: points above the current baseline (bands) get the small weight $p$, points below get $1-p$. After each solution the weights are updated and the system is solved again, so the curve sinks under the bands and hugs the bottom of the noise. p (typically 0.001–0.05) sets how tightly it hugs the bottom; smaller = lower.

Smoothing

The same noisy band smoothed two ways. A filter wider than the band flattens and broadens it.

The physics

Photon counting is a Poisson process: a pixel that collects N photons fluctuates by about $\sqrt N$ (shot noise), plus detector read noise. Neighbouring pixels are independent, so averaging m of them reduces the noise by about $\sqrt m$. But a band is spread over only a few pixels, so averaging too many also averages the band away. Every filter trades noise against distortion; the rule is:

Why Savitzky–Golay keeps bands: a band top is curved. A moving average fits a flat line (order 0) to it and so cuts the top off; a quadratic fit (order 2) follows the curvature, so the top survives while the random wiggles, which no low-order polynomial can follow, are removed.

Normalisation

Why normalise?

The absolute Raman intensity depends on laser power, focus, integration time, sample thickness and (in SERS) the number of hot spots — none of which is chemistry. Normalising divides each spectrum by a quantity that carries these factors, so the relative band intensities, which reflect composition, can be compared.

In XY mode, Scale normalized Y to multiplies the result, e.g. 100 for a 0–100 % scale.

Derivative spectra

Two overlapping bands (1628 and 1658 cm⁻¹) give one peak with a shoulder; the second derivative shows a separate minimum for each.

What it does

Replaces the spectrum by its first ($dy/dx$) or second ($d^2y/dx^2$) derivative, computed with a Savitzky–Golay filter.

The physics and mathematics

A band is a peaked function; its second derivative is negative and sharpest exactly at the band centre and roughly 2–3× narrower than the band itself. So overlapping bands whose envelope shows a single maximum, or only a shoulder, give separate minima in the second derivative. Differentiation also removes backgrounds: a constant disappears in the first derivative and a straight line in the second.

Numerically, a polynomial $\sum_k c_k t^k$ is fitted to the points in the window with $t = x_j - x_i$ (the true spacing), and $dy/dx = c_1$, $d^2y/dx^2 = 2c_2$. The window smooths at the same time, because differentiation amplifies noise strongly (by roughly $1/\Delta x$ per order).

When to use it · how to read it

• Use the 2nd derivative to count bands and read their positions in a crowded region (Amide I, CH stretches) — e.g. before choosing start positions for peak fitting.
• Read minima (not maxima) of the 2nd derivative as band positions. The 1st derivative crosses zero at each band maximum.
• Use a window of 9–15 points; a narrow window gives a very noisy derivative.
• Derivative spectra are not intensities — don't compare their heights between methods. Identify always uses the spectrum before the derivative.

Averaging, SD and SEM

Replicate spectra of one sample (or one group) are averaged point by point after all processing. Two different error measures can be shown:

• SD describes the spread of individual spectra — sample heterogeneity and measurement variation. Use it to show how variable your samples are.
• SEM describes how precisely the mean is known; it shrinks with more replicates. Use it when comparing means between groups. Always state which one you show and the number n (shown in the legend).

Spectra are averaged only over the X range they all share; if their X values differ, they are linearly interpolated onto the first spectrum's points.

Peak detection & assignment

A local maximum is kept as a band when its topographic prominence — how far it rises above the higher of the two lowest points separating it from any taller signal — is at least the chosen percentage of the intensity range. Prominence ignores baseline level and offsets, so a small band on a high shoulder is judged by its own height.

Detected bands are matched against a built-in table of common Raman assignments (proteins, nucleic acids, lipids, carotenoids, silicon). These are suggestions from the literature, not identifications: the same position can belong to different molecules. Edit the table freely before exporting.

Band Library (under Peak Detection) chooses where the suggestions come from: Biological tissue (default; Movasaghi et al. 2007, Talari et al. 2015), Human cell organelles — the marker bands of the nucleus and nucleoli, perinuclear area (ER), mitochondria, lipid droplets and cytoplasm from Table 1 of A. M. Nowakowska et al., “The Raman Map of the Human Cell”, Anal. Chem. 97, 16374–16382 (2025), doi:10.1021/acs.analchem.5c02035 (CC BY 4.0) — or Both. The organelle library was measured on living human endothelial cells with 532 nm excitation, so the cytochrome bands (605, 753, 1131, 1307, 1584 cm⁻¹) are resonance-enhanced; at longer wavelengths they are much weaker. The citation of the selected library appears under the peak table and in the exported reports.

Identify (library match)

Compares your processed spectrum with 202 reference spectra (RamanBiolib) over their common range. Both are min–max scaled, then scored:

• Correlation HQI $=100\,r^2$, with $r$ the Pearson correlation of the two spectra. Sensitive to the whole shape, including leftover background.
• Derivative HQI — the same on first derivatives; tolerant of residual background, more sensitive to noise.
• Peak match — bands of your spectrum and of the reference that agree within ± tolerance: $100\,m/(N_\text{query}+N_\text{ref}-m)$ for m matched bands (the share of all bands that are shared). Best for sharp-band spectra.

A high score with a clear lead over the second-best match is good evidence; a crowd of similar scores means "a protein-like spectrum", not a specific protein. SERS, mixtures and a different laser change relative intensities — confirm with a measured standard.

Peak fitting (deconvolution)

What it does

Explains a region of the spectrum as a sum of N individual bands on a background, and adjusts every band's height, centre and width until that sum matches the data as closely as possible. It turns one broad envelope into separate bands with numbers attached — position, width, area — each with an uncertainty.

How to read the plot

The band shapes — and the physics behind them

• Lorentzian $L(x) = \dfrac{A}{1+4(x-c)^2/w^2}$. A vibration that decays exponentially in time (finite lifetime τ) gives a Lorentzian in frequency, with FWHM $= 1/(\pi c\,\tau)$. This is the natural, homogeneous line shape — sharp top, long tails.
• Gaussian $G(x) = A\,e^{-4\ln 2\,(x-c)^2/w^2}$. When molecules sit in many slightly different environments (disorder, amorphous solids, hydrogen-bond networks, the instrument's slit function) their centres are spread normally: inhomogeneous broadening.
• Pseudo-Voigt $= \eta L + (1-\eta) G$, with the Lorentzian fraction $\eta$ fitted (0–1). Real bands usually have both kinds of broadening, so this is the best default. η near 1: lifetime-dominated; η near 0: disorder- or instrument-dominated.

The mathematics

The parameters $\theta$ (A, c, w [, η] per band, plus background) minimise the sum of squared residuals $S(\theta)=\sum_i (y_i - f(x_i;\theta))^2$ by the Levenberg–Marquardt algorithm, which moves smoothly between gradient descent (far from the answer) and Gauss–Newton steps (near it). Start values come from your typed positions, or from the minima of the second derivative. Uncertainties come from the curvature of $S$ at the minimum: the covariance matrix $(J^\top J)^{-1}\,s^2$ with $s^2 = S/(n-p)$; the ± value is one standard error. Areas are $1.0645\,A w$ (Gaussian) and $\tfrac\pi2 A w$ (Lorentzian), and their errors are propagated through the full covariance matrix.

Reading the table

• Centre — band position (cm⁻¹); compare with assignments.
• FWHM — full width at half maximum; narrower = more ordered / longer-lived vibration.
• Area and Area % — integrated intensity and its share of the region. For Amide I the area % of the components is the usual estimate of secondary-structure fractions (α-helix ≈ 1650–1658, β-sheet ≈ 1610–1640, turns / random coil ≈ 1660–1690 cm⁻¹).
• R² close to 1 and a noise-like residual mean the model describes the data.

Band ratio & statistics

What it does: measures one number per spectrum — the height or area of band A, or the ratio A/B — and compares groups.

Why ratios: a ratio of two bands from the same spectrum cancels laser power, focus and acquisition time, so it reflects composition (e.g. 1004/1450 ≈ phenylalanine relative to total CH₂, i.e. protein vs lipid).

Height is the maximum inside the band window; area is the trapezoidal integral $\sum \tfrac12 (x_{k+1}-x_k)(y_{k+1}+y_k)$. With Local baseline, a straight line joining the window ends is subtracted first — use it only if no baseline correction was applied, and make the window cover the whole band.

The statistics

• Two groups → Welch's t-test. $t = (\bar a - \bar b)\big/\sqrt{s_a^2/n_a + s_b^2/n_b}$, which does not assume equal variances. The p-value is the probability of a difference at least this large if the groups were really the same.
• Three or more → one-way ANOVA. $F$ = variance between group means ÷ variance within groups. A small p says some groups differ; the pairwise tests say which (they are not corrected for multiple comparisons — be conservative).
• Stars: * p < 0.05, ** p < 0.01, *** p < 0.001; n.s. not significant.

The bar chart shows mean ± SD (or SEM) with every individual spectrum as a dot — look at the dots: a "significant" difference driven by one outlier is not convincing.

PCA (principal component analysis)

Left: scores — each dot is one spectrum, ellipses are 95 % regions per group. Right: the PC1 loading shows which bands separate them.

What it does

A spectrum with 1400 points is a point in a 1400-dimensional space. PCA finds the few directions in which the spectra differ the most, and describes each spectrum by its coordinates along them (the scores). It uses no group labels, so if the groups separate in the score plot, the difference is the dominant variation in the data — strong, unbiased evidence.

The mathematics

The spectra (rows of $X$) are mean-centred (and, if autoscaled, divided by the SD at each point). PCA is the eigen-decomposition of their covariance: the first component $\mathbf p_1$ is the direction of maximum variance, the second the maximum of what is left and orthogonal to the first, and so on. Scores $t_{ik} = (\mathbf x_i - \bar{\mathbf x})\cdot\mathbf p_k$; explained variance of PC k $=\lambda_k/\sum\lambda$.

How to read it

• Score plot: groups that form separate clouds differ systematically. The axis label gives how much of the total variation that PC explains.
• Ellipses: the 95 % confidence region of each group's scores (needs ≥ 3 spectra per group). Non-overlapping ellipses = clear separation.
• Loadings: a spectrum-like curve per PC. A positive peak at 1004 cm⁻¹ in the PC1 loading means spectra with high PC1 scores have more intensity at 1004; a negative peak means less. Read the loading together with the scores to say which group has more of which band.

Difference spectrum

$\Delta(x) = \bar y_A(x) - \bar y_B(x)$, with B interpolated onto A's points. Positive bands are stronger in A, negative bands stronger in B. The shaded band is the uncertainty of the difference, $\sqrt{e_A^2+e_B^2}$ (SD or SEM). A feature well outside that band (marked * when larger than twice it) is a real difference; wiggles inside it are noise. Use the same normalisation for both groups, otherwise the difference mostly shows the normalisation.

Curve fitting models (XY mode)

Linear and polynomial models are solved exactly; the others by Levenberg–Marquardt from an automatic start. If your data have a Y-error column, each point is weighted by $1/\sigma_i^2$, so precise points count more.

R², χ² and the ± errors

• R² $= 1 - \sum(y-\hat y)^2/\sum(y-\bar y)^2$: the fraction of the variation the model explains. Adjusted R² penalises extra parameters — use it to compare models with different numbers of parameters.
• Reduced χ² (weighted fits) $=\frac{1}{n-p}\sum (y-\hat y)^2/\sigma^2$: ≈ 1 means the model fits within the stated errors; ≫ 1 means the model is wrong or the errors are underestimated; ≪ 1 means the errors are overestimated.
• ± values are one standard error from the parameter covariance matrix. Roughly, the true value lies within ±1 SE with 68 % and within ±2 SE with 95 % confidence.
• Always look at the plot as well: a high R² with a systematic misfit means the wrong model.

Resonance tracking (SPR / LSPR sensors)

The physics

In surface plasmon resonance, light couples to collective electron oscillations at a metal surface when the wavevectors match; that coupling removes light at one wavelength, giving a dip in reflectance (or a peak in extinction for nanoparticles, LSPR). The resonance condition depends on the refractive index next to the metal, so when analyte binds, the dip moves (typically to longer wavelength). The shift Δλ against concentration is the sensor's calibration curve.

Finding the dip

• Parabola fit (default): a parabola through the points within ± half-width of the lowest point; its vertex gives a sub-pixel position, far more precise than the pixel spacing.
• Centroid: the intensity-weighted centre of the part deeper than half the depth; robust for asymmetric dips.
• Lowest point: simplest, limited to the pixel spacing.

The dip is found in every replicate and then averaged per group — so the error bar is the real scatter of positions, not of the averaged curve.

Line shape: FWHM, Q and depth

Depth is measured from the mean level at the two ends of the search window to the minimum; FWHM is the width at half that depth; Q = λ_res/FWHM is the quality factor. A sharper resonance (higher Q) means a smaller shift can be resolved. Changes in FWHM or depth with concentration can reveal non-specific adsorption or damping. Set the window to include flat signal on both sides of the dip.

Sensitivity, LOD and LOQ

With a linear calibration $\Delta\lambda = a + S c$, the slope S is the sensitivity (e.g. nm per µg/mL; with the concentration unit RIU it is the bulk sensitivity in nm/RIU).

σ_blank is the SD of the blank replicates (≥ 2 needed, more is better). The LOD is the smallest concentration distinguishable from the blank; the LOQ the smallest that can be measured with acceptable precision. The ICH Q2 alternative uses the scatter of the calibration points about the line, $s_{y/x}=\sqrt{\sum(y-\hat y)^2/(n-2)}$: $\text{LOD} = 3.3\,s_{y/x}/|S|$, $\text{LOQ} = 10\,s_{y/x}/|S|$. Report which definition you use.

How to cite

If RNSpectraX contributes to your work, please cite:

In the app, File ▾ → Methods text writes a Methods paragraph with the exact settings you used and the references for each method.