An IFTS is an electronically programmable filter which obtains spectra for every pixel in the field of view. The free spectral range of an IFTS is theoretically infinite and in practice is limited only by the working wavelength range of the beam splitter and detector. The SNR performance of a camera equipped with filters and an IFTS are equivalent when they have perfect detectors. For example, the Hubble Deep Field was observed with four filters. A camera equipped with a set of narrow band filters will become readnoise and dark current limited.
Every photon is directed towards either one of two focal plane detector arrays.
The switching probability is a function of the optical path difference and the wavelength of the light. Of course, this only applies when the same image cube is acquired with each instrument. To build up the data cube the camera must cycle a set of filters and the dispesive spectrometer must scan a slit across the field. The exact number depends on the blaze angle, the order of interference, and the opening angle between the incident and diffracted beams. Real grating spectrographs also have slit losses, light scattered by irregularities in the ruling, absorption in the grating coatings, and limited free spectral range.