Vignetting effect in Fourier ptychographic microscopy

Abstract

In the usual model of Fourier ptychographic microscopy (FPM), the coherent microscopic system is approximated by being taken as linear space-invariant (LSI) with transfer function determined by a complex pupil function of the objective. However, in real experimental conditions, several unexpected “semi-bright and semi-dark” images with strong vignetting effect can be observed when the sample is illuminated by the LEDs within the “transition zone” between bright field and dark field. These imperfect images, apparently, are not coincident with the LSI model and could deteriorate the reconstruction quality severely. Herein, we investigate the cause and the impact of model misfit based on ray-based and rigorous wave optics-based analysis. Our analysis shows that for a practical FPM microscope with a low magnification objective and a large field-of-view (FOV), the LSI model breaks down as a result of diffraction at other stops or apertures associated with different lens elements. A modified version of the linear space-variant (LSV) model is derived for quantitative analysis. The spectrum of the object will be modulated unexpectedly by a quadratic phase term relatively if assuming the shape of pupil function is invariable. Two countermeasures are also presented and experimentally verified to bypass or alleviate the vignetting-induced reconstruction artifacts. An adaptive update order and initial guess strategy is proposed and demonstrated for better reconstructions. Our work gives a deeper insight into the vignetting effect on wide-FOV imaging and provides a useful guide for easily achieving improved FPM reconstructions that bypass the adverse effect.