Interpretation of convolution of impulse response of a lens

Question

Following "Introduction to Fourier Optics" by Goodman, in section 5.3 it is explained how to derive the impulse response of a lens.

Where $(u,v)$ are the coordinates of the output plane while $(xi, eta)$ are the coordinates of the input plane.

I don't understand how to apply convolution to this impulse response function as it depends also on the input coordinates.
I would have expected a function like  $h(u,v)$ in order to obtain the final image like:
$$
U_f(u,v)=h(u,v)*U_i(u,v) = int h(u-u',v-v')U_i(u',v') du'dv'
$$

How should I interpret the convolution operator?

Andrea Maiani · Answer

In the book this function is maybe improperly called "impulse response" because as I said it depends on the coordinates of the input image. The real impulse response of the lens, also called Point Spread Function, is derived in subsequently and is:
$$
h(x,y) = iint_{-infty}^{+infty} P(lambda z_2  x', lambda z_2 y')exp[-j2pi (x x'+yy')]dx'dy'
$$

Interpretation of convolution of impulse response of a lens

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