On Space-spectrum Uncertainty Analysis for Coded Aperture Systems
This work addresses a critical limitation in spectral imaging systems for applications like remote sensing or medical diagnostics, though it is incremental as it formalizes an existing trade-off rather than proposing a new solution.
The paper tackles the fundamental trade-off between spatial and spectral resolution in spectrally programmable cameras, showing that high-resolution spatial images cannot be simultaneously captured with high-resolution spectral programming due to a Fourier relationship, with a lower bound of λ/4πν₀ femto square-meters for the product of their standard deviations.
We introduce and analyze the concept of space-spectrum uncertainty for certain commonly-used designs for spectrally programmable cameras. Our key finding states that, it is impossible to simultaneously capture high-resolution spatial images while programming the spectrum at high resolution. This phenomenon arises due to a Fourier relationship between the aperture used for obtaining spectrum and its corresponding diffraction blur in the (spatial) image. We show that the product of spatial and spectral standard deviations is lower bounded by λ/4π{ν_0} femto square-meters, where {ν_0} is the density of groves in the diffraction grating and λ is the wavelength of light. Experiments with a lab prototype for simultaneously measuring spectrum and image validate our findings and its implication for spectral filtering.