Angle-resolved photoelectron spectroscopy (ARPES) is commonly applied to ma
p the shape of Fermi surfaces. Here we quantify the errors of simple criter
ia for extracting Fermi vectors by ARPES that are induced by strongly varyi
ng matrix elements. Sophisticated methods for determining the three-dimensi
onal Fermi victor based on temperature and photon energy dependent photoemi
ssion are discussed with reference to data of the quasi-two-dimensional sys
tem 1 T-TiTe2.