---
title: "Brillouin Microscope Interactive Lab | Sandbox Physics"
description: "Why does a shifted light peak not tell us directly how much stiffer a sample became? The shift depends on sound speed, refractive index and scattering angle."
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  zh-CN: "https://sandboxphysics.com/zh/labs/brillouin-microscope/"
last_modified: "2026-11-03"
---

IN23 · Light listens to sound

# Brillouin Microscope

**Why does a shifted light peak not tell us directly how much stiffer a sample became?** The shift depends on sound speed, refractive index and scattering angle. Converting it to a longitudinal modulus also needs density. This response occurs at gigahertz frequencies and differs from the slow stretching measured by a Young modulus. A focal spot crossing two materials can collect both responses at once.

Scan two materials with a focused beam. Fit calibrated photon spectra, then test how refractive index and density change a longitudinal-modulus estimate.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Drag the bright focal volume across the boundary, then save a scan to compare the spectra.

Angle between the rays Focus across the boundary $-2.5\,\mu\mathrm{m}$ Focal spot width $0.7\,\mu\mathrm{m}$

A complete simulated scan and independent standards are loaded.

Material, counting and conversion assumptions

Specimen and bath index $1.333$ Both sound speeds $1$ Nominal response width $0.35\,\mathrm{GHz}$ Left reference speed / m/s $1482.36$ Right reference speed / m/s $2200$ Left backscatter width / GHz $0.35$ Right backscatter width / GHz $0.65$ Signal exposure / s $0.5$ Accepted scattered photons / s $12000$ Background per bin / s $1.5$ Assumed conversion index $1.333$ Assumed left density / kilograms per cubic metre $998$ Assumed right density / kilograms per cubic metre $1100$ Declared calibration sideband / GHz $12$ Random seed $196$ Photon counting noise

Conversion assumptions are saved separately from the optical specimen. The real calibration sidebands are at twelve gigahertz; a changed declaration must pass the independent six-gigahertz check.

Model assumptions

Two uniform isotropic teaching regions share an index-matched bath. A prescribed Gaussian confocal weighting samples their incoherent spectra; equal integrated scattering strength is assumed. Central rays set one internal scattering angle; finite numerical-aperture broadening, refraction mismatch, multiple scattering, anisotropy, heating and chemical identification are omitted. The quasi-elastic longitudinal relation neglects optical recoil below twenty parts per million in the supported parameter range. Weakly damped Lorentzian material lines convolve with a Lorentzian instrument response; an ideal post-dispersion stop rejects the central band. Photon counts, separate backgrounds and sequential midpoint clocks are retained. Known modulation sidebands calibrate frequency and response width, with independent withheld sidebands. Two raw homogeneous-region spectra supply fitted endmembers for the scan; this two-region decomposition is not general spectral unmixing. Intrinsic widths below a conservative counting-resolution diagnostic are withheld. Assumed refractive index and density convert a resolved frequency shift to a GHz longitudinal modulus, not a static Young modulus or a diagnosis. No single modulus is assigned to a mixed focal volume. Specimen size, scan travel, beam width, false colours, point size and replay speed are schematic; pixel illumination is the live expected signal and the data row contains retained simulated counts.

Retained simulated photons

## The spectrum before the modulus

Saved scan

Saved component shift $7.43\,\mathrm{GHz}$

Intrinsic component width $0.367\,\mathrm{GHz}$

Conditional longitudinal modulus $2.20\,\mathrm{GPa}$

Right spectral contribution $0.238\,\%$

Both measured components and calibration

| Region | Shift / GHz | Intrinsic width / GHz | Conditional modulus / GPa |
| --- | --- | --- | --- |

The two homogeneous-region spectra are measured in this saved scan. Their fitted shapes are shared across the line; only their contributions and each separately measured background vary. Fractions describe accepted spectral photons. Equal scattering strength is needed to interpret them as focal-volume fractions. Narrow-width rejection uses a conservative count-scale diagnostic, not a calibrated confidence statement.

Model, optical scale and interpretation

Both synthetic isotropic regions and the surrounding bath have the same adjustable refractive index. The Gaussian spot is prescribed; one central scattering wavevector omits finite-aperture broadening. The excitation linewidth is neglected; independently supplied calibration light has a known twenty-megahertz intrinsic width. Weakly damped Lorentzian doublets convolve with a Lorentzian response. A post-dispersion stop removes the central band. Poisson low counts use exact draws; means of at least fifty use a rounded normal shot-noise approximation. Sixteen-bit photon counters retain clipping flags. The ideal frequency mapper replaces a full VIPA design. Its actual receiving pixels use the same bin coordinates as the count model. Specimen and scan travel are enlarged relative to hardware; beam width, colours, light-particle size and speed are schematic. The physical array displays current expected illumination; all plotted spectra come from saved counts.

The conditional result is a longitudinal storage modulus at gigahertz acoustic frequency. Density, optical index, geometry, water content and frequency dependence matter; it is not a static Young modulus or a medical diagnosis. A mixed spot has separate fitted responses and no single assigned modulus.

$$
M'=\rho\left[\frac{\lambda_0\nu_B}{2n\sin(\theta/2)}\right]^2
$$

[Chan, Bevilacqua and Prevedel (2021): modulus, ambiguity and instrumental broadening](https://www.nature.com/articles/s42003-021-02662-5) [Antonacci and Braakman (2016): confocal geometry and longitudinal response](https://www.nature.com/articles/srep37217)

Physics tutorial

## A frequency shift with several causes

**Background** Thermal motion produces tiny travelling compressions inside a material. Light scattered by those fluctuations can leave with a slightly different frequency.

**Why it matters** A changed peak may reflect sound speed, optical index or collection geometry. Measuring the spectrum comes before choosing a mechanical interpretation.

Start with the essentials

- **Focus question**: Why does a shifted light peak not tell us directly how much stiffer a sample became?
- **One-sentence intuition**: The spectrum measures a frequency response; refractive index, density and a material model are needed to turn that response into a modulus.

### Core mathematical model

#### Momentum selects an acoustic wavelength

$$
q=\frac{4\pi n}{\lambda_0}\sin\frac{\theta}{2},\qquad \nu_B=\frac{vq}{2\pi}
$$

The angle is between incoming and outgoing propagation directions inside the index-matched medium. Vacuum wavelength and refractive index set the optical wavevector. This is the quasi-elastic longitudinal approximation.

#### Conditional longitudinal storage modulus

$$
M'=\rho\left[\frac{\lambda_0\nu_B}{2n\sin(\theta/2)}\right]^2
$$

Density and refractive index are independently declared assumptions. The result describes the longitudinal response at the measured acoustic frequency, not a quasi-static Young modulus.

#### A Lorentzian response adds widths

$$
\Gamma_{\mathrm{observed}}=\Gamma_B+\Gamma_{\mathrm{instrument}}
$$

Both functions must be Lorentzian for direct width subtraction. The known optical sideband width is removed when estimating the instrument response. Unsupported narrow residual widths are withheld.

### Common difficulties

#### Fast compression versus slow stretching

**Typical misconception** A larger Brillouin shift means the same percentage increase in Young modulus.

**Better mental model** The conversion also depends on optical index and density, and probes a different frequency and deformation. Viscoelastic materials can respond differently to slow stretching and fast compression.

#### One line does not prove uniformity

**Typical misconception** One broad peak means there is only one material response.

**Better mental model** Close spectra can be indistinguishable at finite resolution. The two-region fractions are withheld when the measured reference shapes become too similar.

### Run the experiment

1. 01

   #### Move the illuminated volume

   Drag the bright spot in the specimen view, then save a scan.

   **What to observe:** The same physical position chooses a raw spectrum. Near the boundary the finite spot receives photons from both regions.

2. 02

   #### Change collection direction

   Drag the gold collection grip or choose a different angle.

   **What to observe:** The source and collection wavevectors change their difference. A right-angle arrangement gives a smaller shift than backscatter at the same sound speed.

3. 03

   #### Calibrate before subtracting widths

   Change Nominal response width, acquire standards and save a new scan.

   **What to observe:** The measured line broadens. Known sidebands independently determine the instrument width before a material width is reported.

4. 04

   #### Separate optical and mechanical assumptions

   Compare Index changes with the default and inspect the declared conversion assumptions.

   **What to observe:** The peak moves at the same configured sound speed. Keeping the old assumed index changes the inferred modulus.

5. 05

   #### Look at a mixed volume

   Choose A spot across the boundary.

   **What to observe:** Two measured endmember spectra explain the signal. The table keeps their separate responses; one modulus for the combined volume is withheld.

Physical conclusion

Keep the fitted frequency and width separate from the assumptions used for modulus. A mixed focal volume can contain two resolved responses.

## Related experiments and articles

How physics instruments measure · Reading path

### How physics instruments measure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Brillouin Microscopy Listens to Sound with Light**](https://sandboxphysics.com/stories/instruments/brillouin-microscope/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)