Significance: Fourier ptychography microscopy (FPM) is a computational optical imaging technology that employs angularly varying illuminations and a phase retrieval algorithm to achieve a wide field of view and high-resolution imaging simultaneously. In the FPM, LED position error will reduce the quality of the reconstructed high-resolution image. To correct the LED positions, current methods consider each of the LED positions as independent and use an optimization algorithm to get each of the positions. When the positional misalignment is large or the search position falls into a local optimal value, the current methods may lack stability and accuracy. Aim: We improve the model of the LED position and propose an accurate and stable two-step correction scheme (tcFPM) to calibrate the LED position error. Approach: The improved LED positions model combines the overall offset, which represents the relative deviation of the LED array and the optical axis, with the slight deviation of each LED’s independent position. In the tcFPM, the overall offset of the LED array is corrected at first, which obtains an approximate value of the overall offset of the LED array. Then the position of each LED is precisely adjusted, which obtains the slight offset of each LED. Results: This LED position error model is more in line with the actual situation. The simulation and experimental results show that the method has high accuracy in correcting the LED position. Furthermore, the reconstruction process of tcFPM is more stable and significantly improves the quality of the reconstruction results, which is compared with some LED position error correction methods. Conclusions: An LED position error correction technology is proposed, which has a stable iterative process and improves the reconstruction accuracy of complex amplitude.

中文翻译：

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用于傅里叶 ptychographic 显微镜的准确稳定的两步 LED 位置校准方法

意义：傅立叶 ptychography 显微镜 (FPM) 是一种计算光学成像技术，它采用角度变化的照明和相位检索算法，同时实现宽视野和高分辨率成像。在 FPM 中，LED 位置误差会降低重建的高分辨率图像的质量。为了校正 LED 位置，当前的方法将每个 LED 位置视为独立的，并使用优化算法来获得每个位置。当位置错位较大或搜索位置落入局部最优值时，现有方法可能缺乏稳定性和准确性。目的：我们改进了 LED 位置的模型，并提出了一种准确稳定的两步校正方案 (tcFPM) 来校准 LED 位置误差。方法：改进后的 LED 位置模型结合了整体偏移，代表 LED 阵列和光轴的相对偏差，以及每个 LED 独立位置的轻微偏差。在 tcFPM 中，首先校正 LED 阵列的整体偏移，从而获得 LED 阵列整体偏移的近似值。然后精确调整每个 LED 的位置，从而获得每个 LED 的轻微偏移。结果：该LED位置误差模型更符合实际情况。仿真和实验结果表明，该方法对LED位置的校正具有较高的精度。此外，与一些 LED 位置误差校正方法相比，tcFPM 的重建过程更加稳定，并显着提高了重建结果的质量。结论：