Current interest in Fourier lightfield microscopy is increasing, due to its ability to acquire 3D images of thick dynamic samples. This technique is based on simultaneously capturing, in a single shot, and with a monocular setup, a number of orthographic perspective views of 3D microscopic samples. An essential feature of Fourier lightfield microscopy is that the number of acquired views is low, due to the trade-off relationship existing between the number of views and their corresponding lateral resolution. Therefore, it is important to have a tool for the generation of a high number of synthesized view images, without compromising their lateral resolution. In this context we investigate here the use of a neural radiance field view synthesis method, originally developed for its use with macroscopic scenes acquired with a moving (or an array of static) digital camera(s), for its application to the images acquired with a Fourier lightfield microscope. The results obtained and presented in this paper are analyzed in terms of lateral resolution and of continuous and realistic parallax. We show that, in terms of these requirements, the proposed technique works efficiently in the case of the epi-illumination microscopy mode.