Surface Gradient Integrated Profiler for X-ray and EUV Optics—Calibration of the rotational angle error of the rotary encoders.

A new ultraprecision profiler has been developed to measure for example asymmetric and aspheric profiles. The principle of our measuring method is that the normal vector at each point on the surface is determined by making the incident light beam on the mirror surface and the reflected beam at that point coincident. The gradient at each point is calculated from the normal vector, and the surface profile is then obtained by integrating the gradients. The measuring instrument was designed in accordance with the above principle for the measuring method and is called Surface Gradient Integrated Profiler (SGIP). In the design, four ultraprecision goniometers were applied to adjust the light axis for the normal vector measurement. These goniostages make it possible to attain an angular resolution of 0.018 μ radian by electrically dividing a pulse of the rotary encoder. The surface gradients are determined only by the rotational angle of goniometers. Thus in the measuring instrument, the most important factor is the accuracy of the normal vectors measured by the goniometers. To attain an accuracy of 0.1 μ radian, we developed a system for correcting the rotational angle error of the goniometers in which the trigonometric measuring method is utilized for geometrical angle determination. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]