In Fourier optics, a 4$f$ setup is an arrangement of 4 lenses like so:
The idea is that the beam waist $\omega_f$ at the last position (at $x = 2f_1 + 2f_2$) is equal to the waist $\omega_i$ at x = 0 (times the magnification, given by the ratio of the two focal lengths).
Does this only happen when the lenses are separated by $f_1 + f_2$ ?
Ideally the distance between the lenses can be infinite, since the beam is collimated. Obviously the beam is Gaussian so one cannot do that, but still.
Is the image at $x = 2f_1 + 2f_2$ only focussed (at a waist) if the inter-lens distance is $f_1 + f_2$?