Research on Focal Length Measurement Scheme of Self-Collimating Optical Instrument Based on Double Grating

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.

Method for determining uncertainty and error in the process of ophthalmic lens calibration

“…This article presented a procedure for calibrating ophthalmic lenses. Additionally, it proposed a mathematical model for estimating uncertainty based on a non-stochastic methodology such as the Guide for the Expression of Measurement Uncertainty (GUM) [11] and the application of dimensional metrology concepts. This study also identified sources of uncertainty that had not been previously observed or analyzed in most research papers in the literature.…”

“…Applying the expression above to the function of ophthalmic lens calibration and considering the sources of uncertainty established in ( 1) and ( 4), the output variable is given by ( 10): 𝑃 = 𝑓(𝑑 𝑗 , 𝐶 𝑃 , 𝐶 𝐴 , 𝐶 𝑇 , 𝐶 𝐷𝐸 ) (10) Applying ( 8) in ( 1) and (3), we obtain (11):…”

“…The k coverage factor can be obtained using this equation, which is derived from a table of values and based on a Student's t-distribution evaluated for a coverage probability of 95.45 %. A coverage factor of k = 2.0 is used in this study, which must be multiplied by the combined uncertainty, 𝑢 𝑐 , to find the expanded uncertainty, 𝑈 𝑒 , using (10) and (11) with the result shown in (13). For negative lenses, we obtain ( 14):…”

Research on Dynamic Modeling Measurement and Control of Cable Traction Devices for Electro-Optical Unmanned Systems

“…The electro-optical unmanned system driven by the cable frequently will suffer from mechanical wear and fracture of the cable. To solve this problem, the rope pulley interaction of the cable traction device is analyzed, and the scientific method for the rational design of the cable traction system is studied [12][13] . As shown in Figure 3, when the human does not exert external traction torque, under the effect of preload 𝑇 𝑝𝑟𝑒𝑙𝑜𝑎𝑑 , the tension 𝑇 1 at the rope inlet end, and the tension 𝑇 2 at the rope outlet end is (8).…”

Design of a Roll Angle Measuring Sensor

“…6(a) is a captured moiré image, an image processing series, i.e., filtering, contrast enhancement, threshold segmentation, corrosion, and thinning, converts these stripes into single-pixel lines as shown in Fig. 6(b) [24]. If the average horizontal spacing between these lines is denoted as x and vertical spacing as y, the width W of moiré fringe can be calculated as follows:…”