Phase imaging from defocus information in a light field

Abstract: Optical microscopy is without a doubt an essential component of life science research, but many objects of interest in biology are transparent. Chemical or immunological dyes, which can often be toxic, fluorescent transgenes, which require a protocol for transformation of exogenous DNA, and phase contrast, which inextricably combines phase information with amplitude, all serve to increase the contrast of transparent objects. Transparent objects of non-uniform refractive index and/or thickness are phase objects and phase can be extracted from defocus information above and below the object. The light microscopist will recognize this in that object contrast can vary as the stage is moved around an object's focal plane. This phase information can be quantitatively retrieved from a set of defocused images, but this has the disadvantage of decreasing temporal resolution, as the microscope stage has to be moved between image captures. By incorporating additional optics in the form of an array of pinholes or microlenses, the direction and position of all the rays can be recorded in a light field, a 4D function. By recording the light field, multiple planes of focus can be investigated, allowing for the capture of defocus information in real time. Here I discuss and investigate the use of the defocus information in a light field to obtain the transport of intensity equation, and use the fast Fourier transform method to solve this equation for phase.