Bent elliptical mirrors are often used as X-ray microfocus device in synchrotron radiation beamlines.In this paper
the theory of width-variable bent elliptical microfocus mirror was reviewed.The formula for calculating the required bending moments and residual slope error when the working condition(source distance
grazing incident angle and image distance) of the mirror differed from the designed values was deduced.The microfocus mirror of the SSRF X-ray microfocus beamline was calculated as an example.The results show that
by adjusting the bending moments
a large range of the grazing incident angles and source-to-mirror distances can be of choice
and the resulted additional slope error can be negligible.However
a relatively small change of image distance will result in large slope error.