How to calculate the impulse response from the transmission function of an optical device?
If the function $t(x,y)$ is an optical transfer function (OTF) then your goal is not to find a function $h(x,y)$ such that the convolution with your input $f(x,y)$ equals the multiplication with $t(x,y)$. Convolution with the impulse response (point spread function (PSD) in optics) happens in a different domain. The OTF is the Fourier transform of the PSD, and the equality

$$f'(x,y)=f(x,y)t(x,y)$$

corresponds to the equality

$$\mathcal{F}^{-1}\{f'(x,y)\}=\mathcal{F}^{-1}\{f(x,y)\}\star h(u,v)$$

where $h(u,v)$ is the impulse response (PSD) given by

$$h(u,v)=\mathcal{F}^{-1}\{t(x,y)\}$$