= Solution
The fundamental angular floor is the <diffraction limit of a telescope>, of order $\lambda/D$. The ideal <diffraction grating> has $R_g=mW/d$, whereas its slit-limited resolving power has $R\theta D=mW\lambda/d$. Requiring $R\le R_g$ gives
$$
\boxed{\theta D\gtrsim\lambda.}
$$
The coefficient depends on the adopted line-resolution and aperture conventions. Below this scale, a narrower <spaxel> oversamples the same spatial mode rather than creating a new independently resolved element. Equivalently a spatial optical mode occupies <etendue> of order $\lambda^2$.
There is also an engineering floor before arbitrary shrinkage: the <optical camera> <focal length>, <photodetector> size and support clearances do not shrink, while the number of <photodetectors> increases as $\theta^{-2}$. Thus the shrinking-beam model's constant combined <optical camera> volume is eventually overtaken by fixed per-camera overheads. For fixed brightness, smaller <spaxels> receive fewer <photons>, so <read noise> and <photon shot noise> can constrain useful sampling before the formal optical floor. \b[<Diffraction> limits independent spatial information; fixed <photodetector> and mechanical dimensions limit practical volume reduction.]
Back to article page
