We have applied a tomographic imaging method to recreate the full three-dimensional distribution of photoelectrons produced in a strong-field photodetachment process. The method is general and can be applied to any laser polarization. This stands in contrast to traditional imaging inversion methods, such as Abel inversion, which require prior knowledge of the symmetries of the electron distribution and are therefore limited to experiments using linear or circular polarization. Our method is also useful in a situation where linear polarization is used, since it compensates for detector inhomogeneities by spreading the information on a larger detector surface. In addition, it facilitates a method to detect polarization defects. Measurements were made for photodetachment of ${\mathrm{Ag}}^{\ensuremath{-}}$ at laser wavelengths of 1310 and 2055 nm, and were found to agree well with simulations in the strong field approximation. The data in the 1310 nm case revealed an unexpected asymmetry in the plane in which the laser polarization axis is rotated. Using a quasistationary quasienergy state model, a residual elliptical polarization of $\ensuremath{\varepsilon}=0.21\ifmmode\pm\else\textpm\fi{}0.01$ consistently explains the observed asymmetry. We conclude that the method described in this paper has the potential to be applied in experiments where a more complete characterization of electron emission distributions is required.