We believe we have two important new insights. Brief summaries are posted below, pending detailed reports.
Summary As light from a point source passes through an aperture, the light begins to distort and spread out beyond the geometrical optics boundaries defined by the aperture (i.e., "diffract"). It is widely believed this distortion is irreversible. However, we show (1) the distortion is easily reversed, and (2) the light can be recorded in an (essentially) distortion-free state, including even in an imaging system. The well-known rotational-shear interferometer (RSI), when appropriately configured, is such a system.
Summary Our results from "New Insight #1" (and possibly those of Tamari - more analysis needed) indicate significant problems with the current conceptual understanding of what limits the lateral spatial resolution of a general single-aperture system that uses linear media to image a scene of point source emitters that are many wavelengths away from the aperture and spatially incoherent from each other. We investigate further, and find some surprising results related to resolution. (1) We discover a specific way in which Fermat's principle blocks certain attempts to image with resolution sharper than the Rayleigh limit. This significantly demystifies some of the physical mechanisms behind the Rayleigh limit. (2) We show that a metric Feynman used for resolution, when extended to handle multi-beam systems, can be used to showcase a remarkable low-level advantage certain systems have over conventional systems for achieving sharp resolution. There are at least three such systems in existence, one of which is the rotational-shear interferometer. It is known that the RSI has up to a factor of two advantage over a conventional imaging system for achieving sharp resolution, as measured by area under the Modulation Transfer Function. But it has not been appreciated how fundamental this advantage is.