How to calculate the impulse response from the transmission function of an optical device? Let $f(x,y)$ be the electric field in complex representation processed by an optical device described by a transmission function $t(x,y)$ such as:
$$
f'(x,y)=f(x,y)t(x,y)
$$

Where $f'$ is the output electric field.

How can I calculate the impulse response of the device? I don't understand how to determine a function $h(x,y)$ such as:
$$
f'(x,y) = f(x,y)*h(x,y)
$$

More specifically I'm working with a lens transmission function in the paraxial approximation:
$$
t(x,y)= P(x,y)\exp\left[-\frac{jk}{2f}(x^2+y^2)\right]
$$
where $P(x,y)$ is the pupil function of the lens (usually a $circ(x,y)$ function).

P.S.
I wonder if there is a general solution to the mathematical problem of finding a function $h$ for a given $t$ which satisfy $ft=f*h$ for a generic function $f$.

I've posted the same question here: https://physics.stackexchange.com/questions/304444/ but I haven't received any answer.
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

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