B-X1 · Molecular energy from scattered light

Spontaneous Raman Spectrometer

Do molecular lines keep the same energy shift when the laser changes? Yes. A vibrational transition takes a fixed amount of photon energy, so changing the excitation moves the outgoing wavelength while preserving the Raman shift. Recovering it requires a calibrated spectral axis and enough resolution to separate nearby lines.

Calibrate a spectrometer, acquire weak scattered light and compare two excitation wavelengths. Separate a close pair of synthetic vibrational modes from fluorescence and counting noise.

Recorded photon counts $\text{—}$

Measured Raman shift $\text{—}$

Analysis $\text{—}$

Spontaneous light scattering

Measure a molecular shift

Choose a laser, measure a known reference, then record the specimen.

The spectrograph housing is open so you can follow the return arm to the CCD.

Prepare

Excitation laser

\lambda_0

532\,\mathrm{nm}

Exposure

t/\mathrm{s}

2

Instrumental response FWHM

\Gamma_{\rm inst}/\mathrm{cm}^{-1}

8

Spectral axis and background

Indicated wavelength offset

\delta\lambda/\mathrm{nm}

0.2

Fluorescence count rate per bin

b/\mathrm{s}^{-1}

15

Sampling seed

s_0

51

Changing the axis offset requires a new calibration. Existing records keep their own calibration.

Acquire

Calibration required for this laser

Ready for the first measurement.

Setup preview for the next acquisition.

This scalar teaching instrument assumes two nonresonant Stokes modes, a smooth fluorescence background and a Gaussian response. The mode positions and photon rates describe a synthetic material. They are not measured material data. The wavelength axis has an adjustable offset; a separately acquired reference at a known shift estimates that offset. Counts are seeded Poisson samples. The model omits polarization, resonance, damage, self-absorption, spatial mapping and anti-Stokes thermometry. Optical routing and magnification are schematic. Colors identify paths, including invisible infrared light.

Recorded measurements

From photons to a Raman shift

Record a sample to view its measurement and analysis here.

Physical assumptions and sources

Two synthetic modes are broadened and integrated over physical wavelength-bin edges. A separate known reference estimates the wavelength offset. Background is estimated from edge bins, so broad backgrounds or unresolved overlap limit peak recovery. Intensities and widths are assumed; the model does not identify a real substance. Apparatus sizes and ray angles are schematic. Physical CCD columns show the selected counts with logarithmic brightness; moving light markers are path guides.

HORIBA · MacroRAM educational laboratory
NIST · spectral intensity calibration

Start with the essentials

Focus question: Do molecular lines keep the same energy shift when the laser changes?
One-sentence intuition: A fixed vibrational energy gives a fixed reciprocal-wavelength difference, not a fixed wavelength difference.

Core mathematical model

Wavelength to Raman shift

\Delta\widetilde\nu=10^7\left(\frac1{\lambda_0}-\frac1{\lambda_s}\right)\;\mathrm{cm}^{-1}

Both wavelengths are inserted in nanometres. Positive shift means the photon left energy in the sample.

Energy transferred to the vibration

\Delta E=hc(100\Delta\widetilde\nu)

The factor of one hundred converts inverse centimetres into inverse metres. The mode energy is held fixed when the excitation changes.

Independent photon counts

N_i\sim\operatorname{Poisson}(\mu_i),\qquad\operatorname{Var}N_i=\mu_i

Each detector bin records its own signal and background photons. Subtracting an estimated background does not remove their counting noise.

Common difficulties

A smooth spectrum can hide two lines

Typical misconceptionEvery visible maximum is one molecular vibration, and smoothing can always recover a hidden pair.

Better mental modelFinite response blends nearby lines. The analysis requires two separated maxima with a resolved valley; otherwise it reports the pair as unresolved.

Run the experiment

01
Calibrate before acquiring the sample
Use Resolve the pair and Acquire calibration reference. Acquire the sample, then analyze stored samples.
What to observe: The known reference estimates the wavelength offset. The sample analysis uses the stored counts and that frozen calibration.
02
Change the laser
Select Change excitation, calibrate the second laser, and acquire another sample. Switch the graph between wavelength and Raman shift.
What to observe: The wavelength peaks move farther from the infrared source, but the recovered energy shifts agree within counting and calibration errors.
03
Test resolution and background
Acquire the Blurred doublet and Strong fluorescence presets.
What to observe: Broadening can merge the pair. More background increases fluctuations even when its smooth trend is subtracted.

Spontaneous Raman Spectrometer

From photons to a Raman shift

Light recorded by the CCD

Analyze

Which shifts can be resolved?

Read a molecular energy difference