Raman hyperspectral line map

A Raman line scan across the edge of an exfoliated 2-D flake: a full spectrum is recorded at every position, so the raw data is intensity against Raman shift and position. Peak positions identify the material, and their ratios and widths report layer number and strain.

Raman is a weak effect sitting on a strong fluorescence background, and the peaks span a wide intensity range – the graphene G and 2D bands here are two orders above the silicon substrate line’s tail. PowerNorm with an exponent below one lifts the weak bands into view without clipping the strong ones or resorting to a log scale, which the near-zero background between peaks would not survive.

The flake edge is a genuine discontinuity: the substrate peak appears and the carbon bands vanish within one step of the stage. Interpolating across it would invent a gradient where the physics has a step.

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import numpy as np
import polars as pl
import plotpress

rng = np.random.default_rng(67)
shift = np.linspace(1200.0, 2900.0, 420)     # cm^-1
position = np.linspace(0.0, 12.0, 300)       # micrometres
S, P = np.meshgrid(shift, position)

# The flake covers x < 7.2 um; bare substrate beyond it.
on_flake = P < 7.2
# Layer number steps up across the flake, changing the 2D/G ratio.
bilayer = (P > 3.4) & on_flake


def band(centre, width, amplitude):
    return amplitude * width ** 2 / ((S - centre) ** 2 + width ** 2)


intensity = 0.02 + 0.10 * np.exp(-((S - 2100.0) ** 2) / 9.0e5)   # fluorescence
intensity += band(1580.0, 9.0, np.where(on_flake, 1.0, 0.0))     # G band
intensity += band(1350.0, 14.0, np.where(on_flake, 0.16, 0.0))   # D (defects)
intensity += band(2690.0, 16.0, np.where(bilayer, 0.9, np.where(on_flake, 2.4, 0.0)))
intensity += band(1450.0, 6.0, np.where(on_flake, 0.0, 0.55))    # substrate line
intensity += rng.normal(0.0, 0.006, intensity.shape)
intensity = np.clip(intensity, 0.0, None)

# One row per spectrum sample -- the shape a Raman spectrometer's own line
# scan export is in, before it is gridded for the mesh.
scan = pl.DataFrame({"shift": S.ravel(), "position": P.ravel(), "intensity": intensity.ravel()}) \
    .sort(["position", "shift"])
shift = scan["shift"].unique().sort().to_numpy()
position = scan["position"].unique().sort().to_numpy()
intensity = scan["intensity"].to_numpy().reshape(position.size, shift.size)

fig, axes = plotpress.subplots(1, 2, figsize=(12.0, 4.4))
lin = axes[0].pcolormesh(shift, position, intensity, cmap="magma")
axes[0].set_title("linear norm")
fig.colorbar(lin, ax=axes[0]).set_title("counts\n(norm.)")

gamma = axes[1].pcolormesh(shift, position, intensity, cmap="magma",
                           norm=plotpress.PowerNorm(0.40))
axes[1].set_title("PowerNorm(0.40)")
fig.colorbar(gamma, ax=axes[1]).set_title("counts\n(norm.)")

for ax in axes:
    ax.set_xlabel("Raman shift (1/cm)")
    ax.set_ylabel("position (um)")
fig.suptitle("Raman line scan across a flake edge at 7.2 um")
fig.tight_layout()