Because of factors such as aberration, processing defects, and beam symmetry loss, the three important performances of traditional autocollimators in terms of measuring range, measurement accuracy and working distance cannot be improved at the same time. In this paper, the Risley prisms normal tracing angle measurement system is built according to the method of "normal tracing", and the angle measurement is realized by tracing the normal angle change of the mirror to be measured. When using this method for angle measurement, by rotating the Risley prisms, the measurement beam is incident on the mirror surface in the near-specular normal direction and reflected, so as to realize the trace measurement of the normal direction of the reflective mirror. The experiment shows that when the normal tracing method is used for angle measurement, the system error related to distance in the autocollimator system is greatly reduced. Within the precision range allowed by the experimental environment, the measured data of the normal tracing angle measurement system based on Risley prisms does not show obvious systematic error characteristics.
The normal tracing angle measurement system based on Risley prisms can eliminate the influence of aberrations other than the dispersion of Risley prisms on the angle measurement accuracy. Although the traditional dispersion optimization method based on the extreme point can make the beam directions of different wavelengths more consistent after passing through the Risley prisms, the light intensity distribution that deviates from the extreme point wavelength causes the spot centroid to deviate from the target position, thus introducing the angle measurement error. In this paper, we propose a highly symmetry-glued achromatic Risley prisms optimization method for the needs of a normal tracing angle measurement system. Our method not only realizes the beam direction as closely as possible after the deflection of the Risley prisms but also compensates for the centroid error caused by the beam deviating from the central wavelength. ZEMAX simulation shows that, in the normal tracing angle measurement system, within the angle measurement range of ±700 ″ and the light source wavelength range of 600 to 700 nm, the angle measurement error introduced by the dispersion of the optimized Risley prisms is not >0.01 ″ .
Pencil beam deflectometric profilers are common instruments for high-accuracy surface slope metrology of x-ray mirrors in synchrotron facilities. An f-theta optical system is a key optical component of the deflectometric profilers and is used to perform the linear angle-to-position conversion. Traditional optimization procedures of the f-theta systems are not directly related to the angle-to-position conversion relation and are performed with stops of large size and a fixed working distance, which means they may not be suitable for the design of f-theta systems working with a small-sized pencil beam within a working distance range for ultra-high-accuracy metrology. If an f-theta system is not well-designed, aberrations of the f-theta system will introduce many systematic errors into the measurement. A least-squares’ fitting procedure was used to optimize the configuration parameters of an f-theta system. Simulations using ZEMAX software showed that the optimized f-theta system significantly suppressed the angle-to-position conversion errors caused by aberrations. Any pencil-beam f-theta optical system can be optimized with the help of this optimization method.
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