The various theories of specular x-ray reflection at small grazing angles are briefly examined and compared with the reflectance of several very smooth mirror surfaces. Particular emphasis is given to examining the peak reflection efficiency and the harmonic rejection capability of x-ray mirrors operating in the hard x-ray domain. The graded index of refraction model of Croce and Nevot most closely matches the experimental curves. In this model the surface roughness is treated as a local variation in the refractive index. In experimental tests, platinum coated and float glass mirrors were observed to reflect x-rays with high efficiency up to 38 keV. The measured harmonic rejection capability of a float glass mirror and of a platinum coated mirror were found to be virtually identical. In particular, for a raw float glass mirror at a 3.5 milliradian angle of incidence, the mirror reflected with 85% efficiency at 8 keV and only 8% at 16 keV. For a platinum mirror at a 8 milli-radian angle, the corresponding reflectivities were 70% at 8 keV and 6% at 16 keV, Fresnel theory for a smooth platinum surface coating overestimates the reflectivity by a factor of about 30 for the 16 keV x-rays. Therefore, real platinum coated mirrors may be better harmonic rejectors than previously realized. In other experiments, changing the surface roughness of float glass by chemical etching altered the falloff rate beyond the knee of the reflection curve by factors as large as 2.5.
D. H. Bilderback,
"Reflectance Of X-Ray Mirrors From 3.8 To 50 keV (3.3 To 0.25Å)", Proc. SPIE 0315, Reflecting Optics for Synchrotron Radiation, (3 May 1982); doi: 10.1117/12.932994; https://doi.org/10.1117/12.932994