Nuclear imaging modalities are commonly used tools in today's diagnostics and therapy planning. However for interventional use they suffer from drawbacks which limit their application. Freehand SPECT was developed to provide 3D functional imaging during interventions. It combines a nuclear detector with an optical tracking system to obtain its position and orientation in space and synchronizes this with the detector readings. This information can be used to compute a 3D tomographic reconstruction of an activity distribution of a nuclear tracer. As there is no fixed geometry, the system matrix has to be computed on the fly. This is done with models of the detection process for completely arbitrary freehand acquisitions. The accuracy of the reconstructions is highly dependent on the used models of the detection process. Different models of the detection process were developed and evaluated in this work, in particular two analytical models as well as lookup tables generated from either real measurements or Monte Carlo simulations. We showed that it is possible to perform acceptable reconstructions with a simple but efficient analytical model. The use of lookup tables to generate the system matrix in Freehand SPECT is a fast solution with good accuracy.