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In any measurement, the precision of the measuring tool is an essential factor. An ordinary ruler, for example, can measure length to the closest millimeter; a caliper, on the other hand, can measure length to the nearest 0.01 mm. As a result, the caliper is a more precise measurement tool because it can measure extremely minute changes in length. The measurements will be more accurate if the measuring tool is more precise.
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Related Experiment Video

Updated: Jan 20, 2026

A Random-displacement Measurement by Combining a Magnetic Scale and Two Fiber Bragg Gratings
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Focal shift induced by source displacements and optical figure errors.

Michele Manfredda1, Lorenzo Raimondi1, Nicola Mahne2

  • 1Elettra-Sincrotrone Trieste SCpA, SS 14 - km 163.5, 34149 Basovizza, Trieste Italy.

Journal of Synchrotron Radiation
|September 7, 2019
PubMed
Summary
This summary is machine-generated.

Investigating focal shifts in ellipsoidal mirrors reveals how source position and mirror errors impact focus. Wavelength and pointing angle also influence focal shifts, crucial for free-electron laser (FEL) light sources.

Keywords:
FELGaussian beamsX-ray opticselliptical mirrorsfree-electron laserswavefront sensing

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Area of Science:

  • Optics and Photonics
  • X-ray Optics
  • Free-Electron Laser Technology

Background:

  • Ellipsoidal mirrors are critical components in focusing light, particularly in advanced light sources like free-electron lasers (FELs).
  • Understanding focal plane shifts is essential for maintaining optimal performance and resolution in optical systems.
  • Source position, mirror imperfections, wavelength, and pointing angle can all affect focal stability.

Purpose of the Study:

  • To investigate the longitudinal focal plane shifts in ellipsoidal mirrors.
  • To analyze the impact of source position and mirror figure errors on focal shifts.
  • To determine the influence of wavelength and source pointing angle on focal shifts, especially in the XUV spectral range.

Main Methods:

  • Derived an analytical formula for source-to-focus shift in ideal mirrors illuminated by Gaussian beams.
  • Employed numerical solutions of the Huygens-Fresnel integral, incorporating metrological data for realistic mirror defects.
  • Conducted numerical computations to analyze wavelength and pointing angle dependencies.

Main Results:

  • An analytical formula was developed for predicting focal shifts in ideal ellipsoidal mirrors.
  • Numerical simulations quantified focal shifts caused by surface shape defects, comparing them with analytical predictions.
  • Identified and quantified additional focal shifts dependent on wavelength and source pointing angle.

Conclusions:

  • Source position and mirror figure errors are significant contributors to focal plane shifts.
  • Wavelength and source pointing angle introduce further dependencies on focal shifts, particularly relevant for FELs.
  • The developed methods are applicable to various optical elements and sources, including parabolic reflectors and lenses.