The whole disc,edge to edge, prominences and all.

Three problems, none of them deep sky problems

A solar frame is not a small faint thing on a dark sky, and almost nothing written for deep sky work applies to it. There is no gradient to model, because there is no sky in the frame. There are no stars to register on. There is no faint signal to integrate for hours - the exposure is a fraction of a millisecond and the subject is the brightest object anybody photographs.

What there is instead is a disc that is markedly brighter in the middle than at the edge, material off the limb that is thousands of times fainter than the surface beside it, and a single recorded channel that has to be turned into a picture. Those three things are what the solar path in Akastroid exists to solve, and it solves them in that order because each one depends on the last.

Limb darkening, measured from your own frame

The Sun is a ball of gas, so a sightline near the edge passes obliquely through the photosphere and reaches a cooler, dimmer layer. The disc is therefore brighter in the middle, typically by a factor of two or more, and any stretch that makes the centre look right leaves the edge crushed and featureless.

Akastroid measures the disc's brightness as a function of distance from its centre and divides that profile out. Measured rather than modelled: the analytic forms describe the Sun through a perfect telescope, and what reaches your sensor also carries the instrument's vignetting and whatever the seeing did to the edge. Your frame's own radial profile contains all of it.

Two details keep it honest. The correction stops short of complete, because a perfectly flat disc reads as a printed circle rather than as a sphere. And the profile is not smoothed across the disc's own edge - a smoothing filter run over a steeply falling curve reads low, the correction then divides by a number smaller than the data, and the result is the blown white ring that gives away an over-flattened solar image.

Prominences, on their own curve

Material arcing off the limb is orders of magnitude fainter than the surface. One stretch cannot serve both: expose for the disc and the prominences are black, expose for the prominences and the disc is a white hole.

So the region beyond the limb gets its own treatment - a power curve rather than a multiplier, so the faint material moves a long way and the bright material barely at all, with a noise floor underneath so an empty sky stays black instead of becoming a field of lifted grain. The reference it is scaled against is the brightest thing actually present off-limb in your capture, measured from an annulus just outside the disc, so the same curve suits a session with a huge hedgerow prominence and one with almost nothing.

The join with the disc is a soft annulus at the limb. A hard edge there is the giveaway of a composite, and it is exactly where the eye looks.

Colour, for a camera that recorded one channel

Both white light and hydrogen alpha record a single channel. The familiar gold or orange Sun is a choice about presentation, not a measurement, so Akastroid applies it as a stated palette rather than smuggling it in as though the camera had seen it. You get three:

• White light - a warm near-white, as the eye sees it through a safe filter. The photosphere is not orange, and this palette does not pretend otherwise.
• Hydrogen alpha - the deep orange-gold the wavelength is usually shown in, with the tint easing off in the highlights so a plage or a flare kernel goes pale rather than staying flatly tinted.
• As recorded - one channel in, one channel out, for anyone who would rather colour it themselves.

Switching palettes re-finishes the image rather than re-stacking it, so the change is immediate. The stack itself is untouched.

A session of stills, not just a video

Capture programs write video; smart telescopes and save-frames buttons write folders of FITS. Both work, and the folder path needed its own registration to work at all.

Deep sky stacking aligns frames by matching star patterns. A solar frame has no stars in it, so that approach does not merely do badly - it reports "too few stars to register" on every frame and throws the session away. Akastroid registers a solar session on the centre of the disc, which is measurable to a fraction of a pixel and drifts by translation as the mount tracks at the wrong rate. The frame grader is told the same thing, so a starless frame is no longer marked as a ruined one.

Sharpening, in the right place in the order

A video capture takes the lucky imaging path: every frame graded for the structure a solar surface actually holds divided by that frame's own noise, the sharpest kept, the disc tracked in pieces so the atmosphere's local warping comes out, and the survivors averaged.

Then the sharpening, and where it sits matters. It runs after the disc has been flattened and placed - so it lifts fibrils rather than fighting the limb darkening - and before the disc's contrast is opened, so the expansion is measured on the sharpened image instead of multiplying what the sharpener already did. The region outside the limb is kept as it was before the sharpener ran, because a wavelet threshold set by a frame full of disc deletes a prominence outright.

What you end up with

A disc placed high on the display scale with headroom left above it, its fibrils, filaments and plage opened to a contrast the eye reads immediately, its limb even rather than crushed, the prominences visible against a black sky, and a palette that says what it is. Export at 16 bits and take it further if you want to.

If you would rather read about the photography than the software, the guide on photographing the Sun covers filters, exposure and what to expect from white light against hydrogen alpha.

The same application does the rest of the sky

Planets and the Moon take the lucky imaging path, and nebulae and galaxies the deep sky path. One application, one licence.