The source of LED has been widely used in our daily life. The intensity angle distribution of single LED is lambert distribution, which does not satisfy the requirement of people. Therefore, we need to distribute light and change the LED’s intensity angle distribution. The most commonly method to change its intensity angle distribution is the free surface. Generally, using ordinary differential equations to calculate free surface can only be applied in a point source, but it will lead to a big error for the expand light. This paper proposes a LED collimating lens based on the ordinary differential equation, combined with the LED's light distribution curve, and adopt the method of calculating the center gravity of the extended light to get the normal vector. According to the law of Snell, the ordinary differential equations are constructed. Using the runge-kutta method for solution of ordinary differential equation solution, the curve point coordinates are gotten. Meanwhile, the edge point data of lens are imported into the optical simulation software TracePro. Based on 1mm×1mm single lambert body for light conditions, The degrees of collimating light can be close to ±3. Furthermore, the energy utilization rate is higher than 85%. In this paper, the point light source is used to calculate partial differential equation method and compared with the simulation of the lens, which improve the effect of 1 degree of collimation.
The atmospheric coherence length which reflects the intensity of atmospheric turbulence is a very important parameter of laser atmospheric propagation and adaptive optics. It has been used as the modern definition of atmospheric seeing in astronomical observations. Day-night atmospheric coherence length monitor is a conventional instrument which can measure the atmospheric coherence length. It uses the two aperture differential imaging motion method (DIMM) to measure the atmospheric coherence length r<sub>0</sub> based on continuous observation of stars. When there are clouds in the sky especially for cloudy weather, the starlight are often obscured by clouds and the SNR of image is very low for only faint starlight received by Day-night atmospheric coherence length monitor. This would cause unacceptable measurement error. Therefore, there are fewer atmospheric coherent length data in the cloudy weather. The paper analyzes the measurement errors and tracking errors under the low SNR condition. Based on the experimental data, the characteristics of night cloudy sky background are analyzed. According to the fact that the sky background obeys Gauss distribution, we present an improved method of Gaussian spot extraction fitting method to extract the optical spot region. The processing method includes the following steps: first, the mean intensity of the image is calculated by Gauss fitting, then, divide the image into the background and the suspected target with the threshold of the half width of the Gauss distribution above the mean intensity. The largest area of the suspected target will be taken as the optical spot area. After that, a sliding window of 5 multiply 5 scale is used to scan the optical spot area to carry out gauss fitting for the center pixel x<sub>ij</sub> at the angle of 0degree,45degree,90degree and 135degree. A comparison is taken between x<sub>ij</sub> and the average values of the four fitting results, if the difference exceeds the threshold value, the pixel x<sub>ij</sub> will be taken as the noise pixel, and the mean value of the fitting result is used to replace the pixel intensity. In order to verify the accuracy of the method, the turbulence phase screen has been used in numerical simulation. The result shows that this barycenter extraction method can accurately extract the centroid of optical spot under low contrast situation. Even when the SNR is 1.25db, the measurement error of r<sub>0</sub> is still less than 10%. We believe that this method may be useful in improving the adaptability of Day-night atmospheric coherence length monitor to more kinds of weather.