The granulation and seeing report

A stack of the Sun's surface is only as good as the detail it holds. For white-light and sodium D captures (the photospheric filters, the ones that show granulation) Helia turns the finished stack into a short report you can compare between runs, settings, nights and equipment (#56). It is printed by helia stack after the stack, written into the FITS header, returned by the API as summary.granulation, shown as one line in the Stack step of the app, and available for any finished image with helia measure.

Hydrogen-alpha, calcium and the other chromospheric filters have no granulation to measure, so they get no report.

What it measures

The report is made on the central 240 x 240 pixel square of the disc, which keeps it away from the limb in most captures. Before anything is measured the square is flattened: it is divided by a copy of itself blurred by an eighth of its side, which removes limb darkening, vignetting and any slow gradient but not granules. Everything below is therefore independent of how bright the capture was.

• RMS contrast. The standard deviation of the flattened square. This is the number that matters scientifically: it falls with seeing and defocus and rises with sharpening, so report it on the unsharpened stack (the FITS file is that). It depends on bit depth and noise, so quote the conditions.
• Power spectrum. The azimuthally averaged power of the square, with its noise floor taken from the highest frequencies. Two landmarks are read from it: the roll-off, the frequency where the power above the noise has fallen to 10% of its peak (seeing and defocus move it down), and the resolved frequency, the highest one still above 1% of the peak (noise limits it). They are given in cycles per pixel, as a period in pixels, and in arcseconds when the image scale is known (the fitted limb gives it).
• Diffraction cut-off. With the aperture (--aperture-mm, API aperture_mm) Helia also gives D / lambda in cycles per pixel, taking 550 nm for white light and 589.3 nm for sodium, and how much of it the data reaches. No stack resolves all of it: the optics' transfer function falls to zero there.
• Cell size. The square is band-passed at the scale where the contrast peaks, the bright cells are labelled and counted, and the report gives the mean spacing of granules (the square root of the area per cell) and the mean diameter of those that lie wholly inside. It is only meaningful when a granule covers at least three pixels; the report says when it does not.

$ helia stack Sun_Test.ser -o sun.fits --preset na --aperture-mm 80
...
granulation: region:         240 x 240 at (708, 416)
granulation: RMS contrast:   3.756%
granulation: cell size:      pitch 13.65 px (29.45 arcsec), diameter 7.69 px (16.59 arcsec) (309 cells)
granulation: power spectrum: roll-off 0.146 cycles/px (period 6.86 px, 14.79 arcsec), resolved to 0.292 (period 3.43 px, 7.39 arcsec)
granulation: telescope:      diffraction cut-off 1.419 cycles/px lies above the sampling limit (0.5): the pixel scale, not the telescope, limits the detail; resolved 58% of the sampling limit
granulation: noise floor:    3.091e-5
granulation: note:           a granule (1.5 arcsec) spans 0.7 px at this scale; below 3 px the cell size measures larger structure and noise, not granules. The contrast and the spectrum still compare runs of the same capture.

The Stack step of the app shows the RMS contrast in one line once a white-light or sodium stack has finished, with the whole report in the tooltip.

(The picture is the app's synthetic demo capture with fixed example figures in the report lines, not measurements of it; the seeing line is the one of Seeing estimation.)

The FITS header gets GRANRMS, GRANPITC, GRANDIAM, GRANPARC, GRANGPIX, GRANROLL, GRANRESO and, with the aperture, GRANCUT.

On any image: helia measure

helia measure sun.fits --scale 2.16 --aperture 150 --wavelength 589.3

prints the three band-pass contrasts of helia measure and the report above. --scale is arcseconds per pixel; --aperture needs --wavelength and --scale.

How well it tells good from poor

Known-answer tests (cargo test -p helia-core granulation) on synthetic Voronoi mosaics with a known cell size and contrast, blurred by known Gaussians and with added noise:

On the project's four sodium captures (ASI482MC; Na D preset, GPU; FITS output, so unsharpened). Each is stacked three ways: the preset's best 12% of frames with alignment points; all frames (--keep 100%); the best 12% with global alignment only (--no-multipoint). The eye ranks the first above the others, and the report agrees:

• The contrast ranks all four captures as expected: alignment points above global alignment, and a selected 12% above all the frames. The roll-off period agrees or ties on every pair (it cannot tell points from global alignment on the first two captures, whose seeing is good).
• 14_42_57.avi is the blocky capture with no visible granulation: its contrast is mostly compression blocks and its resolved frequency flips between stacks, so read nothing into it beyond "much worse".
• The cell size is not in the table because it is not granulation on these captures. At 2.16 arcsec per pixel (Sun_Test.ser, 15_20_57.ser), 4.31 (15_32_09.avi) and 1.44 (14_42_57.avi) a 1.5 arcsec granule is 0.3 to 1 pixel, so the cells found are 9 to 14 pixels across (20 to 30 arcsec): larger structure and noise texture. The report prints a note saying so. The cell size becomes meaningful at about 0.5 arcsec per pixel or finer.
• The report is repeatable: it uses no random numbers.

Limits

• The region is the disc centre. A spot, a facula or a filament there raises the contrast; check the crop, and use helia measure --crop or crop the image first.
• A sharpened image reads higher. Compare sharpened with sharpened, or use the FITS stack.
• Hydrogen-alpha has no granulation: no report is made for it.