Our approach uses an analytical description of the time dependent heating and sample deformation based on Green's functions. This model is a better match to real-world problems encountered in the life and material sciences than previously described analytical models, such as lumped linear proportional models. It provides exact mathematical expressions for the variables of interest, yielding clear insights into their relationships in an easily interpretable form. While models based on finite element modeling (FEM) are able to incorporate more details, here, our approach excels in computational efficiency. This Green's function approach, whereby the response of a system to an excitation is determined by convolving the distribution of the absorbers and the time domain shape of the pump laser pulse with a system response function has some interesting parallels to signal processing and optical microscopy: along the temporal axis, the sample can be understood to act as a low pass filter upon the excitation pulse shape and in the spatial dimension, our model exhibits similarities to a point spread function (PSF) that is typically used to understand and characterize spatial resolution in optical imaging. Thus, this "PSF model of AFM-IR" enables us to directly compare the spatial resolution in optical imaging techniques and with those achieved in AFM-IR.