Consider a prism with a krypton white-light laser being shone through it. Imagine that different colors in the white light source represent different signal carriers, like communications, guidance, and other signals. On the prism's other side is an array of photodetectors spaced precisely so that each one will detect a separate color in the ROYGBIV spectrum.
This is what the Bragg cell does. The difference being that piezo-transduced microwaves actively alter the acousto-optic crystal's refractive index and steer the light beam towards one or another photoreceptor in the array. Some of the earliest applications for Bragg cells were in laser printers. The problem with them is that relative large amounts of change in driving energy don't produce much angular deflection. It was only with the advent of truly compact high efficiency photosensors that these analysers didn't require relative long "throw" lengths between the Bragg cell and the detector array. Long throw lengths required large bulky assemblies that were more sensitive to vibration and G-force related structural deflection (dimensional stress).
Major advances in crystal growth have allowed for other even more exotic crystals such as tellurium oxide, as shown in the following figure. It illustrates how an acousto-optic spectral filter works:
At the very bottom, please note the radio frequency input. This drives a piezoelectric transducer that introduces mechanical stress into the crystal thereby altering its refractive index. This, in turn, alters the path of light travelling through the crystal according to the wavelength of that illumination. In effect, giving you a tunable optical filter. These are used in making ultra-compact spectrophotometers the size of a matchbox that used to take up an entire bench top with their mirrors, gratings and prisms.
If the RF input corresponds to your external microwave environment, then the scattering of the transverse light source will be proportionally directed towards various locations on the crystal's other side. By calibrating the crystal with known RF frequency sources, the detectors can be positioned in correspondence with where expected in-flight RF frequencies need to be detected.