Zero-method scanning-probe profilometer for steeply curved aspheric x-ray mirrors

Advances in x-ray free-electron laser and ultra-low-emittance synchrotron radiation facilities have enabled high-intensity, highly coherent x rays, driving significant progress in x-ray analytical techniques. To fully exploit these sources, reflective optics with sub-nanometer figure accuracy, capable of preserving both wavefront quality and beam intensity, are essential. Achieving such accuracy while accommodating increasingly steep and aspheric surface profiles required for next-generation optics poses substantial challenges in surface figure metrology. This study introduces a non-contact scanning profilometer that overcomes cumulative errors typically observed in conventional stitching interferometry. The instrument, referred to as the ZSP (Zero-method Scanning-probe Profilometer), integrates a chromatic confocal sensor with a measurement technique based on the zero method, effectively eliminating linearity errors in the sensor output. The ZSP achieves a root-mean-square reproducibility of 1.3 nm when measuring a steeply curved elliptical-cylindrical mirror with a sag of 105 μm and a grazing-incident angle distribution of 11 mrad. Furthermore, it was employed in the fabrication of the x-ray nanofocusing mirror, validating its designed focusing performance. The proposed approach is inherently applicable to the measurement of increasingly complex two-dimensional aspheric surfaces, thereby contributing to the advancement of ultra-precision metrology.