An ExB probe is a pass-band velocity filter for an ion beam. The ExB probe measurement is related to the ion velocity distribution function (IVDF); however, the finite pass-band filter window size leads to differences in the true IVDF and measured ExB probe spectrum. We derive for the first time an analytical ExB probe transmittancy matrix and use it to examine differences in the IVDF and the probe spectrum. The probe spectra are compared to a synthetically defined test IVDF to study how probe geometry and ion species affect the differences. It is found that the difference in the probe spectrum and the true IVDF is dependent on the ion species, and the deviation is larger for heavier ions. The peak velocity of the spectrum was shifted by up to 13%, and the velocity spread was broadened by up to 276%. The relative ion species fraction is calculated from the probe spectra by two different methods and compared to the true fraction. Using the approach of this work, direct integration of the spectrum resulted in a 2% difference, while a more common approach from literature overestimated one ion species by 184%.
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