Hybrid height and slope figuring method for grazing-incidence reflective optics

Tianyi Wang, Lei Huang, Xiaolong Ke, Yi Zhu, Heejoo Choi, Weslin Pullen, Vipender Negi, Daewook Kim, Mourad Idir, U. Jeng

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Grazing-incidence reflective optics are commonly used in synchrotron radiation and free-electron laser facilities to transport and focus the emitted X-ray beams. To preserve the imaging capability at the diffraction limit, the fabrication of these optics requires precise control of both the residual height and slope errors. However, all the surface figuring methods are height based, lacking the explicit control of surface slopes. Although our preliminary work demonstrated a one-dimensional (1D) slope-based figuring model, its 2D extension is not straightforward. In this study, a novel 2D slope-based figuring method is proposed, which employs an alternating objective optimization on the slopes in the x- and y-directions directly. An analytical simulation revealed that the slope-based method achieved smaller residual slope errors than the height-based method, while the height-based method achieved smaller residual height errors than the slope-based method. Therefore, a hybrid height and slope figuring method was proposed to further enable explicit control of both the height and slopes according to the final mirror specifications. An experiment to finish an elliptical-cylindrical mirror using the hybrid method with ion beam figuring was then performed. Both the residual height and slope errors converged below the specified threshold values, which verified the feasibility and effectiveness of the proposed ideas.

Original languageEnglish (US)
Pages (from-to)65-75
Number of pages11
JournalJournal of Synchrotron Radiation
StatePublished - Jan 1 2023


  • ion beam figuring
  • surface slopes
  • synchrotron optics
  • two-dimensional

ASJC Scopus subject areas

  • Radiation
  • Nuclear and High Energy Physics
  • Instrumentation


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