  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 {\lambda}/4{\pi}{\nu_0} femto square-meters, where {\nu_0} is
the density of groves in the diffraction grating and {\lambda} 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.
