The curved light-emitting diode (LED) array has so many advantages over conventional planar micro LED array such as wider viewing angles, and convenience in its actual applications:curved mobile phone screen, curved smart watch screen, and wide-angle communication illumination light source, etc. Irradiance uniformity is considered to be one of the momentous parameters for evaluating the degree of display or communication lighting devices. In order to improve the untilization of micro-curved LED array in display illumination, we focus on uniform irradiance of cylindrical and spherical micro-LED array by the method of ray-tracing. The calculation results show that the curved radius R and LED radiation parameter m are main factors affecting the uniform irradiance of the cylindrical array. We can improve the energy utilization efficiency by arranging the array pixel positions rationally. The simulation of 1010 cylindrical array with bending radius R=5 cm shows that the uniformity of maximum irradiance can reach 90.5% when detection distance z=300 cm and the detection area is defined as {(x, y)|-100 x 100, -100 y 100}. Furthermore, the irradiance distribution of spherical array is calculated and the results show that the irradiance uniformity of the single spherical array is unrelated to the number of pixels when it surpasses three. The main factors that affect the irradiance distribution of the multi-ring LED array are the ring distribution coefficient K, the normal angle 0, and the luminous flux ratio of each ring . Also the two-ring LED array model is calculated when the pixel number of the first ring is set to be 6 and the second ring is assumed to be 12. And the simulation results show that the maximum irradiance uniformity of the two-ring LED array can reach 94.8% in which the value of 0 is set to be 20, the ring distribution coefficient K=0.5 and the two ring pixel unit luminous flux ratio =20. Experimentally, we adopt the approach of the two micro LEDs to confirm the accuracy of the theory. And the results show that the irradiance distributions of two LEDs with the values of angle =13, 15 and 17 are consistent with the theoretical calculations. Thus, the theoretical and the experimental results in the paper can offer references for curved-LED display and multi-mode intelligent illumination.

To achieve the miniaturization and the static state of the Fourier transform spectrometer, two stepped mirror arrays are introduced into the time-modulation Fourier transform spectrometer to replace of the plane mirrors. The two stepped mirrors can sample the interferogram data in two-dimensional space, which can reduce the size of the instrument and increase the stability of the system. Due to the precision restriction on the stepped mirrors in the fabrication process, the various sub-mirrors of the stepped mirrors may contain various thickness errors and angle errors, which can affect the distribution of the interferogram and the quality of the spectrum. We regard the thickness error and the angle error of all the sub-mirrors as random variables, and synthesize all the error terms into a Fourier transform integration function using Monte Carlo method. By means of statistic analysis on the spectrum error factor, we can appraise the recovered spectrum affected by the thickness error and the angle error of the sub-mirror. The statistical result indicates that the statistical mean of the spectrum error factor increases with thickness standard deviation and angle standard deviation increasing. According to the statistical analysis on spectrum error factor, the tolerances of the thickness standard deviation and the angle standard deviation of the sub-mirror can be determined in the fabrication process of the stepped mirrors.

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