A measure of the spatial resolution of a system is the modulation transfer function (MTF), which is simply the modulus of the Fourier transform of the system's point spread function (PSF). The system MTF is the product of the MTF of the components. However, the discretized CCD is anisoplanatic, i.e. the PSF is not invariant under spatial translation (a different distribution is found for a point light source focused on the intersection of four pixels compared with the same source centered on a single pixel). This adds a degree of complication in the analysis of small data sets.

The back-illuminated CCD's MTF is simply a sinc function, the Fourier transform of the square pulse. Thus

where W is the pixel pitch (mm), and k is the spatial frequency (lp/mm).

The EBCCD MTF is comprised of four terms. The first term is for charge spread in the vacuum diode, the second is due to charge spread in the CCD and depends only on the thickness of the field-free region as described above. Due to the field in a proximity focused vacuum diode, backscattered secondaries create a 'halo' around the incident primary spot, accounted for by the third term. Finally a CCD MTF term is needed.

where, Vim is the maximum radial emission energy of photoelectrons from the cathode (eV), Vs is the cathode to anode voltage (V), k is the spatial frequency (2p lp/mm), L is the cathode to anode spacing of the proximity focused diode (mm), d is the field-free region thickness(mm), h is the backscattering coefficient, (G/G₀.) is the ratio of the average EBS gain of the secondary electrons to the primary gain, and W is the CCD pixel pitch (mm).

MTF alone is not sufficient to determine spatial performance of a system because the presence of noise tends to 'wash out' higher frequency signals. The signal to noise ratio (SNR) vs frequency curve is a better barometer of low light level performance. The signal (in electrons) in the bright area of a target at spatial frequency k and wavelength(l) can be written as:

where f(l) is the incident optical flux (photons/s/mm²), QE_PC(l) is the photon to electron conversion quantum efficiency, G is the system gain, p/(kW) is the number of pixels in the bright area, MTF(k,l) is the system MTF at incident wavelength l and spatial frequency k, t   is the integration time(s), and A is the area of the faceplate that is mapped onto a single CCD pixel (mm²).

The variance (in e²) over both the bright and dark areas can be given by:

where f is the gain noise factor (the Fano factor for EBCCD's), I_dk-PC is photocathode dark current density (e/s/mm²), I_dk-CCD is CCD dark current density (e/s/mm²), A_CCD is the area of a CCD pixel (mm²) and N_read is the read noise per pixel (e).

For both the ICCD and the EBCCD the shot noise term dominates, however the noise factor of the MCP (~2.0) compared to the nearly noiseless Fano factor makes the ICCD variance much higher. In addition, the poorer MTF of the ICCD contributes to the fact that the EBCCD dramatically outperforms the ICCD at all signal levels and spatial frequencies.

In 1991 Blouke, et al presented a simple model of the back illuminated CCD which included the effects of surface recombination, the surface field, and the length of the field-free diffusion region. An analytic solution for optical quantum efficiency was found which produced excellent agreement with experimental data taken on anti-reflective coated, backside-enhanced CCDs. This model was extended to the general case by finding the probability of collection of an electron generated at any given depth. The general solution was applied to the special cases of optical generation and keV electron generation and using the same values of surface recombination, electric field strength and field-free region thickness, was used to generate curves which were in agreement with experiment.