An approximate three-dimensional analytical formula for flattened Gaussian beams passing through an off-axis and defocused expanding optical system are deduced by using the theory of matrix optics and expanding the aperture function into a finite sum of complex Gaussian functions. By numerical computation, the laws governing the variation of the intensity distribution of the output beam with the off-axis size and focal shift are given. It is revealed that the intensity distribution at the export of the expanding optical system has large asymmetric aberrance because of the off-axis of the expanding optical system. But a good focus ability of the intensity distribution can be gotten in the far-field. What’s more, it is shown that a suitable choice of the focal shift would lead to a higher peak intensity and a better focus ability at the far-field than that of no focal shift. The analytical formula has practical reference significance for the design of the laser expanding optical system.
This paper presents a method of detecting high-speed moving targets with single light source and dual frequency laser coherence.Due to the influence of cutoff response frequency of detector, the dynamic range of velocity measurement in traditional single-frequency coherent detection system is limited, and the velocity measurement of high-speed moving target cannot be realized. In this paper, six signal components are generated by four-light coherent mixing, one of which is the difference between the fixed frequency shift and the doppler frequency shift. The simulation verifies the feasibility of the method proposed in this paper, which has the characteristics of small data collection, large dynamic range, high precision and good real-time performance of the system, and improves the theoretical guidance of the method for further high-speed target detection research.
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