  In active imaging protocols, information about a landscape is encoded into
the spatial mode of a scattered photon. A common assumption is that the
landscape is rigid; however, in principle it can be altered by radiation
pressure, a concept that has found fruitful application in the field of quantum
optomechanics. Here we explore active imaging of a mechanical resonator with an
eye to generalizing the concept of radiation pressure backaction to spatially
multimode light. As a thought experiment, we consider imaging the flexural
modes of a membrane by sorting the spatial modes of a laser reflected from its
surface. We show that backaction in this setting arises from spatial photon
shot noise, an effect that cannot be observed in single-mode optomechanics. We
also derive the imprecision-backaction product for coherent illumination in the
limit of purely spatial backaction, revealing it to be equivalent to the
standard quantum limit for purely dispersive, single-mode optomechanical
coupling. Finally, we show that optomechanical correlations due to spatial
backaction can give rise to two-mode entangled light. In conjunction with
high-$Q$ nanomechanics, our findings point to new opportunities at the
interface of quantum imaging and optomechanics, including sensors and networks
enhanced by spatial mode entanglement.
