---
title: "Synchrotron Beamline Interactive Lab | Sandbox Physics"
description: "Why can a bright source deliver very little light to a sample? A beamline selects the directions and energies that reach a sample."
canonical_url: "https://sandboxphysics.com/labs/synchrotron-beamline/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/synchrotron-beamline/"
last_modified: "2026-11-13"
---

# Synchrotron Beamline

**Why can a bright source deliver very little light to a sample?** A beamline selects the directions and energies that reach a sample. Slits and crystals remove part of the light; mirrors focus what survives. Independent counter calibration supports flux and transmission measurements.

Follow an undulator beam through a slit, two crystals and two focusing mirrors. Compare energy selection, focus and transmission using screen pixels and side-counter readouts.

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

### Select, focus, measure

Six computed cases can be acquired. Other settings produce a model preview; drag a gold dial to explore.

Compare a case Selected energy / keV 10 Slit opening / mm 0.8 Second-crystal pitch / µrad 0 Aluminium thickness / µm 100

Source strength and focal position

Undulator strength K 1.3411 Sample offset from focus / mm 0

Preparing the default measurement…

Model assumptions

Teaching model of a finite planar undulator driven by a given 6 GeV, 0.2 A electron beam with assumed size and divergence. Photon budgets cover 8–36 keV and the ±100 µrad filament-angle integration domain, convolved with the supplied electron phase space. Finite crystals and elliptical KB mirrors use actual first-contact surfaces and complex polarization-preserving amplitudes. The retractable screen is a separate exposure, not a simultaneous transmission measurement. Independent whole-path references calibrate Rayleigh and Compton counts from a weak carbon sampling foil; side counts alone are not sample photon flux. Each detector cell has its own timing gate and rate domain. Inference consumes only raw readouts and independent references, retaining shared standard errors and limits from unidentified reflection order, clipping, invalid references and insufficient numerical precision. The counter cannot resolve the monochromator's narrow bandwidth. This model omits a complete storage ring, thermal deformation, measured mirror figure and beamline vibration. Spot profiles use geometrical rays convolved with the given electron phase space rather than coherent propagation through the complete line. Readout standard uncertainties do not cover the discrepancy between this approximation and wave optics. Absolute subpixel alignment has no established model-accuracy guarantee. Paths are slowed and transverse dimensions enlarged; neither depicts actual light speed or a uniformly scaled instrument.

## Delivering light to a sample

**Background** A slit, crystals and mirrors pass only the part of a source accepted by the beamline. The photon rate at the sample depends on every element along that path.

**Why it matters** Selecting a narrower range or a smaller spot often costs photons. Following the path alongside the readouts reveals where delivery is lost.

- **Focus question**: Why can a bright source leave the sample short of light?
- **One-sentence intuition**: Slits select directions, crystals select energy, and mirrors set the focus. Independent response standards convert side counts into flux.

### Core mathematical model

#### A crystal selects wavelength

$$
2d\sin\theta=n\lambda
$$

Lattice-plane spacing d and glancing angle θ select constructive reflection at wavelength λ and order n. Independent angle and energy readouts together identify the order.

#### Bracket the sample with open measurements

$$
T=\frac{\Phi_{\mathrm{sample}}}{(\Phi_{\mathrm{before}}+\Phi_{\mathrm{after}})/2}
$$

The numerator is calibrated flux with the sample; the denominator comes from independent open exposures before and after it. An unstable bracket withholds transmission. Shared calibration errors retain their correlation.

#### Thickness for a given material

$$
t=-\frac{\ln T}{\mu(E)}
$$

The total attenuation coefficient μ belongs to the given aluminium family. The central ray is normal to the sample; oblique rays use their actual path length. Total attenuation includes scattering out of the primary beam and is not a heat-deposition measurement.

### Common difficulties

#### Side counts and flux

**Typical misconception** The number counted each second equals the photons delivered to the sample.

**Better mental model** A weak foil scatters a tiny fraction into a finite detector with its own response. Independent whole-path references support the conversion.

#### Brightness and coherence

**Typical misconception** More photons in a smaller spot directly reveal coherence.

**Better mental model** Flux describes the arrival rate. Coherence concerns stable relationships in the light field and needs suitable field or interference information.

### Run the experiment

1. 01

   #### Follow the whole path

   Open the crystal, mirror and sample views, then inspect the default screen and counter spectrum.

   **What to observe:** Two crystal reflections return the beam to a direction parallel to its entrance. The two mirrors focus in different transverse planes.

2. 02

   #### Narrow the doorway

   Choose A narrower doorway and compare its saved measurement with the default.

   **What to observe:** The slit removes some directions and changes delivered flux. A narrower profile does not directly identify coherence.

3. 03

   #### Turn the second crystal

   Choose The second crystal turns. Inspect endpoints, side counts and screen edges.

   **What to observe:** The second reflection changes both acceptance and direction. Clipped pixels are retained while unsupported full-profile widths are withheld.

4. 04

   #### Move beyond focus

   Choose Beyond the focus and compare the separate screen exposures.

   **What to observe:** Moving the sample plane broadens the spot. Independent camera references supply pixel scale and point-spread width.

5. 05

   #### Thicken the sample

   Choose Few photons get through and inspect individual cell counts and transmission uncertainty.

   **What to observe:** Fewer counts increase statistical uncertainty. Insufficient references or signal withhold the affected thickness inference and retain the raw observations.

Physical conclusion

A beamline turns part of a source into the energy, direction and spot needed by an experiment.

## 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 **Getting synchrotron light onto a sample**](https://sandboxphysics.com/stories/instruments/synchrotron-beamline/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

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