In the present study, we proposed a new type of autocollimator for high-accuracy angular measurement within a large angle range. The new system comprises a traditional autocollimator and Risley prisms, and it employs the normal tracing method to measure the angle. By rotating the Risley prisms, the outgoing beam of the autocollimator can be deflected close to the normal direction of the reflecting mirror and then reflected back to the system by the mirror along the near normal direction to realize normal tracing. Based on the angle measured by the autocollimator and the rotation angles of Risley prisms, we can calculate the tilt angle of the mirror. Since the beam returns to the system close to the original path, the angle error caused by aberration, optical component processing defects, nonuniform refractive index, and so on, can be ignored. Due to the normal tracing measurement method, theoretically, the angle error is not affected by the working distance. ZEMAX non-sequential simulation shows that the angle error caused by aberration in the new system can be significantly reduced.

A new straightforward method was proposed to measure the local roughness exponent of a scanning tunnelling microscopy (STM) image. Its reliability was tested against some ideal self-affine surfaces. Taking the mean value of a number of local roughness exponents for the STM images, which were randomly recorded on a fracture surface, as the roughness exponent of the fracture surface, we quantitatively assessed the experimental error of the measured roughness exponent by statistical analysis. The experimental results for two different fracture surfaces showed that the difference between the two roughness exponents was not produced by their experimental errors to a 90% probability.

A modified method for measuring the absolute figure of a large optical flat surface in synchrotron radiation by a small aperture interferometer is presented. The method consists of two procedures: the first step is oblique incidence measurement; the second is multiple rotating measurements. This simple method is described in terms of functions that are symmetric or antisymmetric with respect to reflections at the vertical axis. Absolute deviations of a large flat surface could be obtained when mirror antisymmetric errors are removed by N-position rotational averaging. Formulas are derived for measuring the absolute surface errors of a rectangle flat, and experiments on high-accuracy rectangle flats are performed to verify the method. Finally, uncertainty analysis is carried out in detail.