The efficiency of a diffraction grating was measured near normal incidence in the 125–225-Å wavelength range with synchrotron radiation. The grating pattern had 2400 grooves/mm and was recorded on a concave fused-silica blank by a holographic technique. The grooves were shaped by ion-beam etching to provide a facet with a blaze angle of 2.5° as determined by atomic force microscopy. Because of the characteristics of the etching process the groove profile was approximately triangular, with the other facet inclined at an angle of 5.5° to the surface. The measured efficiency was compared with the efficiency calculated by a computer program, small enough to run on a personal computer, that solved the periodic boundary-value problem corresponding to electromagnetic radiation incident on a diffraction grating with finite conductivity. The calculation was based on the nominal groove profile that was determined by atomic force microscopy. The measured and the calculated efficiencies were in good agreement. This investigation indicates that the diffraction efficiency of a normal-incidence grating can be calculated in the soft-x-ray region with a personal computer.
© 1997 Optical Society of America
Original Manuscript: May 15, 1997
Revised Manuscript: July 11, 1997
Published: December 1, 1997
M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, and J. C. Rife, "Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range," Appl. Opt. 36, 8939-8943 (1997)