The interferometer consists of a polarizing beam splitter followed by two Koesters prisms. The polarizing beam splitter divides the incoming unpolarized light into two plane polarized beams with orthogonal polarizations, each having roughly half the incident intensity. The splitter then directs each beam to a Koesters prism and its associated optics, field stops, and photomultiplier tubes. The first figure below illustrates the light path between the Koesters prism and the PMTs.
The Koesters prisms are constructed of two halves of fused silica joined together along a coated surface which acts as a dielectric beam splitter. The dielectric layer performs an equal intensity division of the beam, reflecting half and transmitting half, imparting a 90 degree phase lag in the transmitted beam. This division and phase shift gives the Koesters prism its interferometric properties: the beam reflected from one side of the prism interferes constructively or destructively with the beam transmitted from the other side. The degree of interference between the two beams is directly related to the angle, or tilt, between the incoming wavefront's propagation vector and the plane of the dielectric surface.
Each Koesters prism emits two exit beams whose relative intensities depend on the tilt of the incident wavefront. Each beam is focussed by a positive doublet onto a field stop assembly (which narrows the IFOV to 5 x 5 arcsec). The focussed beams are recollimated by field lenses (after the field stop) and illuminate the photomultiplier tubes (PMT). The PMT electronics integrate the photon counts over 25 millisecond intervals.
The Koesters prism is sensitive to the angle of the incoming wavefront as projected onto its dielectric surface. To measure the true (non-projected) direction of the source, each FGS has two Koesters prisms oriented perpendicular to one another (and therefore a total of 4 PMTs).
Figure 1. Light Path from Koesters Prisms to the PMTs:
Small rotations of the star selector A and B assemblies alter the direction of the target's collimated beam, and hence the tilt of the incident wavefront with respect to the Koesters prisms. The figure below is a simplified illustration of Koesters prism interferometry. As the wavefront rotates about point b, the relative phase of the transmitted and reflected beams change as a function of angle 
. When the wavefront's propagation vector is parallel to the plane of the dielectric surface (b-d) a condition of interferometric null results, and the relative intensities of the two emergent beams will ideally be equal. When is not zero, the intensities of the left and right output beams will be unequal and the PMTs will record different photon counts.
Figure 2. The Koesters Prism - Constructive and Destructive Interference:
This case shows the interference within the Koesters Prism for a wavefront with a tilt such that the ray entering the prism at point a is advanced by 
/4 with respect to the ray entering at point c. The rays a' and c' are transmitted though the dielectric surface and are retarded by /4 in the process. Rays c" and a" are reflected by the dielectric and suffer no change in phase. Rays c' and a" are interferometrically recombined and exit the prism on the right hand side. Similarly, rays a' and c" are recombined and exit to the left. The intensity of each exit ray depends upon the phase difference of recombined reflected and transmitted rays.
The rays exiting the prism at its apex will always consist of components with 90 degree phase difference (because the reflected and transmitted components initially had zero phase difference, but the dielectric retarded the transmitted wave by /4). Therefore, at the apex, constructive and destructive interference occur at the same rate and the two exit rays have equal intensity. In the ex-ample shown here, the intensity of the rays exiting the left face of the prism increases as one moves along the face, away from the apex, in the direction of increasing constructive interference (the recombined beams a' and c" have zero phase difference). On the right face of the prism, destructive interference increases away from the apex (a" and c' are out of phase by 180 deg), so the intensity of these rays diminishes along the face. Therefore the intensity of the left hand beam is greater than that of the right hand beam. The tilt in this example corresponds to a peak of the S-curve. Rotating the wavefront about point b by 2 in a clockwise direction would produce the other peak of the S-curve.