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.