Spectral Information Content of Diffraction-Limited Images
Abstract
High-resolution optical imaging is fundamentally limited by diffraction, which imprints wavelength-dependent structure onto the point spread function (PSF) of the optical system. This intrinsic chromaticity implies that in addition to spatial structure, images encode spectral information. We develop the theory of this spectral information content and provide strategies for its optimal extraction with calculations of Fisher information. We show that polychromatic PSF formation can be expressed as a convolution in logarithmic coordinates and define the corresponding spectral transfer function. We derive this function for the Airy disk and find algebraic decay in spectral log-frequency, implying the existence of arbitrarily fine spectral structure in the ideal, noiseless PSF. We use a differentiable forward model to numerically construct the spectral information eigenbasis and quantify the spectroscopic capability of diffraction-limited imaging across a range of noise and detector systematics. We demonstrate injection and recovery of the constrained spectral modes in a realistic simulated example and compare these results with previously reported methods. Our information-theoretic framework provides a generalisable method for spectral characterisation of PSFs spanning a variety of imaging contexts.
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BibTeX
@misc{langker2026spectral,
title = {{Spectral Information Content of Diffraction-Limited Images}},
author = {Milo Langker and Hayden Greer and Benjamin Pope and Peter Tuthill},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41092},
eprint = {2610.41092},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41092},
}
RIS
TY - UNPB
TI - Spectral Information Content of Diffraction-Limited Images
AU - Milo Langker
AU - Hayden Greer
AU - Benjamin Pope
AU - Peter Tuthill
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41092
UR - https://arxiv.org/abs/2610.41092
AB - High-resolution optical imaging is fundamentally limited by diffraction, which imprints wavelength-dependent structure onto the point spread function (PSF) of the optical system. This intrinsic chromaticity implies that in addition to spatial structure, images encode spectral information. We develop the theory of this spectral information content and provide strategies for its optimal extraction with calculations of Fisher information. We show that polychromatic PSF formation can be expressed as a convolution in logarithmic coordinates and define the corresponding spectral transfer function. We derive this function for the Airy disk and find algebraic decay in spectral log-frequency, implying the existence of arbitrarily fine spectral structure in the ideal, noiseless PSF. We use a differentiable forward model to numerically construct the spectral information eigenbasis and quantify the spectroscopic capability of diffraction-limited imaging across a range of noise and detector systematics. We demonstrate injection and recovery of the constrained spectral modes in a realistic simulated example and compare these results with previously reported methods. Our information-theoretic framework provides a generalisable method for spectral characterisation of PSFs spanning a variety of imaging contexts.
ER -