Fraunhofer diffraction at the two-dimensional quadratically distorted (QD) grating

A two-dimensional (2D) mathematical model of quadratically distorted (QD) grating is established with the principles of Fraunhofer diffraction and Fourier optics. A discrete sampling method is applied for finding a numerical solution of the diffraction pattern of QD grating. An optimized working phase term, which determines the balanced energies and high efficiency of multi-plane images, can be obtained by the bisection algorithm. To confirm the analytical approach described above, the results have been compared with those obtained using a classical numerical model based on Fraunhofer diffraction theory and a fast Fourier transform (FFT) algorithm. The results show that our analytical approach allows the precise design of QD grating and improves the optical performance of simultaneous multi-plane imaging system. An optical setup based on our well-designed QD grating has been appended to the camera port of a commercial microscope, and some preliminary microscopy images have been successfully obtained. Further upgrade of our analytical model is in progress to improve the image quality and promote the applications.