  The development of metasurfaces has enabled unprecedented portability and
functionality in flat optical devices. Spaceplates have recently been
introduced as a complementary element to reduce the space between individual
metalenses. This will further miniaturize entire imaging devices. However, a
spaceplate necessitates a non-local optical response -- one which depends on
the transverse spatial frequency component of a light field -- therefore making
it challenging both to design them and to assess their ultimate performance and
potential. Here, we employ inverse-design techniques to explore the behaviour
of general thin-film-based spaceplates. We observe a tradeoff between the
compression factor R and the numerical aperture NA of such devices; we obtained
a compression factor of R = 5.5 for devices with an NA = 0.42 up to a record R
= 340 with NA of 0.017. Our work illustrates that even simple designs
consisting of realistic materials (i.e., silicon and glass) permit capable
spaceplates for monochromatic applications.
