Abstract
In this paper, we propose a scheme for measuring the focal length of a collimating optical instrument. First, a mathematical model for measuring the focal length of a collimator with double gratings is derived based on the moiré fringe formula and the principles of geometric optics. Mathematical simulation shows that a slight difference in the focal length of two collimators has an important influence on the imaging law of moiré fringes. Our solution has a good resolution ability for focal length differences within 5‰, especially in the small angle range below 4°. Thus, the focal length of collimators can be measured by the amplification of the slight difference. Further, owing to the relative reference measurement, the measurement resolution at the symmetrical position of focal length is poor. Then, in the designed experiment, a corresponding moiré image at different angles is acquired using collimators with known focal length. The experimental results indicate that the root mean square error (RMSE) of the collimator corresponding to grating angles of 2°–4° is better than 4.7‰, indicating an ideal measurement accuracy of the proposed scheme. This work demonstrates that our proposed scheme can achieve an ideal accuracy in the measurement of a symmetrical optical path.
Highlights
The grating measurement system commonly uses the grating pitch as the reference
The error source of this setup mainly comes from two parts, of which one is the charge coupled device (CCD) fringe fitting error, and the other is the beam drift caused by vibration and airstream in the optical system
This paper focuses on the scheme of measuring the focal length of a collimating optical system with two gratings
Summary
The grating measurement system commonly uses the grating pitch as the reference. When the grating pitch is below 10 μm, it is a grating precision measurement system that follows the principles of diffraction interference of light. When the grating pitch is in the range from 10 to 200 μm, the grating line distance is much larger than the source wavelength and the diffraction phenomenon can be neglected. The grating measurement can be analyzed by the occlusion effect of geometric optics [1]. At present, grating measurement technologies based on the principles of geometric optics, such as grating rulers, encoders, and roll angle measurement, have been widely used [2,3]. Moiré fringes are generated when two gratings are rotated relative to each other, and the displacement measurement can be realized by counting and subdividing the moiré fringes. The common collimating optical system is often referred to as a collimator, which can simulate the beam from infinity
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