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Broadband performance limits of ultra-thin lenses using time-domain analysis.

Thin lenses of sufficient diameter and focusing power cannot fully compensate for variation in free-space time of flight to maintain and focus an intact wavefront and instead combine successive wavefronts. The limited temporal coherence of broadband light reduces the effectiveness of such interference. Using effective medium theory and scalar diffraction we exploit time-domain analysis to show that the temporal coherence of illumination imposes hard limits on the performance of thin lenses as measured by the Strehl ratio. These limits apply equally to diffractive optical elements and metalenses.