Thus, as a unit-amplitude plane wave with a wave vector is normally incident onto the sample, its reflection from and transmission into the sample is described by ray optics. Then, the transmitted field with amplitude is scattered from RI fluctuations inside the sample as described by the Born approximation: the far-zone scattering amplitude of the scattered field with wave vector is , where is the scattering wave vector (inside the sample).36 When the scattered field leaves the sample, its transmission amplitude through the top interface is described again by ray optics . Finally, the field that reaches the image plane of an epi-illumination bright-field microscope is a result of optical interference between (i) the field reflected from the sample’s top surface [referred to as reference arm , amplitude ] and (ii) the field scattered from its internal fluctuations [sample arm , Fig. 1], with only the waves propagating at solid angles within the NA of the objective being collected. Thus, for a microscope with magnification , moderate NA (), focused at a point () in the image plane is38Display Formula
(4)where is the microscope’s pupil function—a cone in the spatial-frequency space with a radius [Fig. 3(a)]. As seen in Eq. (4), the objective performs low-pass transverse-plane spatial frequency filtering, with the cutoff corresponding to the spatial coherence length.