  As a label-free imaging technique, quantitative phase imaging (QPI) provides
optical path length information of transparent specimens for various
applications in biology, materials science, and engineering. Multispectral QPI
measures quantitative phase information across multiple spectral bands,
permitting the examination of wavelength-specific phase and dispersion
characteristics of samples. Here, we present the design of a diffractive
processor that can all-optically perform multispectral quantitative phase
imaging of transparent phase-only objects in a snapshot. Our design utilizes
spatially engineered diffractive layers, optimized through deep learning, to
encode the phase profile of the input object at a predetermined set of
wavelengths into spatial intensity variations at the output plane, allowing
multispectral QPI using a monochrome focal plane array. Through numerical
simulations, we demonstrate diffractive multispectral processors to
simultaneously perform quantitative phase imaging at 9 and 16 target spectral
bands in the visible spectrum. These diffractive multispectral processors
maintain uniform performance across all the wavelength channels, revealing a
decent QPI performance at each target wavelength. The generalization of these
diffractive processor designs is validated through numerical tests on unseen
objects, including thin Pap smear images. Due to its all-optical processing
capability using passive dielectric diffractive materials, this diffractive
multispectral QPI processor offers a compact and power-efficient solution for
high-throughput quantitative phase microscopy and spectroscopy. This framework
can operate at different parts of the electromagnetic spectrum and be used for
a wide range of phase imaging and sensing applications.
