Indexing the archive…
Your Universe of Digital Possibilities
In 1990 the Hubble Space Telescope opened its eye and every star was a smear: the primary mirror had been polished to the wrong shape, too flat at the edge by about 2.2 µm. A veiled sky is imaged here through that kind of flaw. The rebuild knows only the counts and the blur, and deconvolution recovers the detail the blur merely weakened— and nothing of what the aperture never passed. You may turn around when it stops.
The image is the sky convolved with the point-spread function — the squared Fourier transform of the pupil P, with the wavefront error W as its phase — plus photon noise. For Hubble in 1990, W was a spherical aberration from a mirror ground to the wrong shape.
The transfer function is the pupil’s autocorrelation, and a pupil of diameter D has none beyond D/λ: finer detail reaches the detector multiplied by exactly zero. Deconvolution can divide by a small number; it cannot divide by zero.
Divide by the blur where the signal is stronger than the noise and give up where it is not; the signal-to-noise per frequency is the prior, here estimated from the data’s own spectrum. Beyond the cutoff H = 0 and the filter returns exactly nothing.
The maximum-likelihood iteration for photon counts: multiplicative, so it stays positive. Its misfit falls without end — past the noise, into fitting it — so it is stopped where χ²/N first reaches 1 (Morozov’s discrepancy principle). Positivity can extrapolate a little past the cutoff for point stars: that is the prior, not the sky.
The Orfeo Edition’s fifth shadow is the one with a known blur. The forward model is exact — the PSF of this very pupil — and still the inversion is two different problems: inside the cutoff a division by a small number (noise amplification, tamed by stopping where the misfit reaches the noise), beyond it a division by zero (the null space — no prior is evidence). That is why the remedy in 1993 was a pair of mirrors, not a program. The Lens bends light by gravity; The Scan shares the projection-slice picture of what a measurement can and cannot sample; The Noise is the other side of the photon count.