I am trying to understand the image created when a coherent light source is incident on a diffraction grating as it is swept through the focal point of a lens. The situation is illustrated in the figure below,
where $P_1$ is the object (diffraction grating) plane, located at the lens focal point. $P_2$ is the image plane. $s$ and $s'$ are the distances between $P_1$ and the (convex) lens, and $P_2$ and the lens, respectively. $F$ is the back focal plane of the lens at distance $f$ from the lens. $\theta$ is the angle of diffraction due to the grating. $D$ is the distance between diffraction orders, which have been focused to form bright spots in the back focal plane $F$.
In the case where $P_1$ is located at the focal point of the lens, and the lens' numerical aperture is large enough to capture sufficient diffraction orders, the image at $P_2$ will be a real, magnified, inverted copy of the grating. This is explained nicely at the following link: https://users.physics.ox.ac.uk/~lvovsky/471/labs/abbe.pdf
My question is, assuming that everything else remains the constant, how will the image change as $s$ is increased or decreased such that $P_1$ no longer lays at the focal point?
I understand that as $s$ is increased, higher diffraction orders that lay outside of the lens' numerical aperture will be filtered out, resulting in interference fringes appearing in the grating image. I also believe that there is the effect of point-spread function (PSF) blur to consider? Although I am slightly confused as to how this differs from the aforementioned filtering. Finally, what about the case where $s$ is decreased?
Ultimately I am trying to understand whether or not the image at $P_2$ can be used to determine how far $P_1$ is from the lens focal point.