How the optics plots work¶

valerian optics reads the stars of one image and shows what they say about the telescope: an aberration inspector, FWHM and eccentricity maps across the field, a tilt and backfocus hint, and the radial profile of the stars with a Moffat fit. These are the views of PixInsight's AberrationInspector and FWHMEccentricity scripts. The desktop app has them in the Optics tool of the Process step. For a worked example start with tutorial 13; this page says what each plot is, how it is made and what every option and control does.

Use a linear image (a single calibrated frame, or a stack), not a stretched one. Raw Bayer frames are demosaiced first. For judging the optics a stack is fine but its edges, where few dithered frames overlap, are noisier and registered less well; the sharpest single frame has the cleanest corners.

The stars¶

The stars are detected on the luminance (the mean of the colour planes) as valerian register does, at --threshold sigmas of the smoothed noise. A star is kept when it is not saturated, has a finite size and shape, and its peak is at least --min-snr times the noise (10 by default, so a faint star's noisy shape does not count). At least 30 must remain or the command stops and says how many it found. Each kept star has a position, a FWHM, an eccentricity (1 - b/a) and an orientation, from windowed second moments (see How subframe analysis works). field_stars.csv lists them.

The maps¶

A polynomial surface of total degree --order (3 by default; 1 is a tilted plane, 2 adds the bowl of field curvature, 3 and 4 asymmetric coma-like patterns) is fitted to the FWHM of the stars by least squares in coordinates scaled to -1..1 across the frame. Stars more than 3 robust sigmas (1.4826 MAD) from the surface are rejected and the fit is repeated, up to six times, so a double star or a galaxy does not pull it. The surface is drawn as an interpolated image on a 64-column grid, coloured over its 2nd to 98th percentile (viridis: dark is sharp, bright is soft), with seven contour lines by marching squares and the measured stars as small circles so you can see where there is data and where the surface is only extrapolated.

The eccentricity map is made the same way and adds whiskers: on a coarse grid of ten columns, the stars within a radius of 0.9 cells vote with the vector e (cos 2 theta, sin 2 theta); the mean vector gives the direction and size of the typical elongation, drawn as a line through the cell centre, longest at an eccentricity of 0.35 and over. Radial whiskers point to or from the middle of the picture; tangential ones go round it; parallel ones all along the same direction are tracking or wind.

fwhm_map.csv and eccentricity_map.csv hold the surface at the 16 by 12 cell centres.

The tilt and backfocus hint¶

The field is divided into a centre (within 17 per cent of the middle in each direction) and four corners (the outer quarter of the width and of the height). The median FWHM and eccentricity of each zone are taken when it holds at least 5 stars. From them:

Three of the four corners and the centre must have stars for a verdict. The hints are what the pattern is consistent with. One image cannot say which way to move a spacer, and a corrector with an off-centre sensor looks like a tilt, so each hint says to change one thing by a small step and measure again. tilt.png is a bar chart of the five zone FWHMs.

The aberration inspector¶

Nine crops of --crop pixels (128 by default, 32 to 512, even) are taken with their centres half a crop from each corner, at the middle of each edge and at the middle of the image, enlarged --zoom times (2; 1 to 6) by pixel replication so no pixel is invented, and stretched identically by one automatic stretch of the whole image (black point 2.8 robust sigmas below the sky, the midtone solved to put the sky at 25 per cent), so a soft corner is soft and not merely dimmer. Colour images show in colour. Each panel is labelled with its place and the median FWHM, the median eccentricity and the number of stars within one crop of its centre (three or more are needed for the numbers). aberration_inspector.png is the mosaic and optics.json has the numbers.

The star profile¶

Up to --psf-stars (50) of the brightest kept stars that have no neighbour within the window radius plus 4 pixels (unless the neighbour is fainter than 2 per cent of the star's peak) are stacked. The window radius is three times the median FWHM, between 6 and 20 pixels. For each star the sky is the median of an annulus just outside the window, every pixel within the window gets its distance from the star's sub-pixel centroid, and its value above the sky is divided by the star's peak above the sky. The pixels of all the stars are binned in 0.5 pixel rings (bins with fewer than 5 pixels are dropped) and the median of each ring is taken, which discards the pixels of neighbours and cosmic rays. Two functions are fitted to the rings by Levenberg-Marquardt least squares:

• the Moffat A (1 + (r/alpha)^2)^-beta, whose FWHM is 2 alpha sqrt(2^(1/beta) - 1). Beta describes the wings: 2.5 to 5 is typical of seeing-limited stars, a smaller beta means broader wings (scattered light, aberrations), and a beta that grows without limit (the fit then says "above 50") means the profile is Gaussian;
• the Gaussian A exp(-r^2 / 2 sigma^2), FWHM 2.3548 sigma, for comparison.

psf.png shows the pixels of every star, the median of each ring, and both curves, on a linear and on a logarithmic axis (the logarithmic one shows the wings, which is where a Moffat differs). psf.csv has the rings with both models, optics.json the fit parameters and the RMS residual of each. When the Moffat's residual is no better than the Gaussian's, the stars are Gaussian (as after a stack of resampled frames) and beta is unconstrained.

What is written¶

--report <DIR> (default optics-report) holds aberration_inspector.png, fwhm_map.png and fwhm_map.csv, eccentricity_map.png and eccentricity_map.csv, field_stars.csv, tilt.png, psf.png and psf.csv, optics.json (the summary, the zone table, the hints, the inspector panels and the fit) and report.html, the one-file page that gathers them (and any other section written into the same folder, such as the subframe analysis). valerian plot aberration|fwhm-map|eccentricity-map|tilt|psf IMAGE -o FILE.png draws one plot with its data beside it.

The Optics tool in the desktop app¶

Open an image, choose the Process step and the Optics chip. Measure the stars runs on a worker thread with progress and Cancel; the viewer then shows the plot chosen by the chips (Inspector, FWHM map, Eccentricity map, Corners, Star profile), and the panel gives the zone table, the Moffat and Gaussian FWHM and the hints in words.

Checked against astropy and numpy¶

scripts/compare_python_optics.py repeats the measurements with different code on two stacks: the 60-frame Seestar stack of IC 5070 (1080 by 1920, 329 stars kept) and the five-frame ASI1600MM H-alpha stack (587 stars). Astropy 8.0.2 fitted a two-dimensional Gaussian plus a constant to a 21 by 21 pixel cut-out of every star Valerian kept, and numpy fitted the same polynomial to Valerian's star table with the same clipping.

FWHM in pixels of the Seestar IC 5070 stack, Valerian against astropy fits, from the table above: the zones sit just above the dashed line of equality.

FWHM in pixels of the ASI1600MM H-alpha stack, Valerian against astropy fits, from the table above: Valerian reads 0.24 to 0.37 higher.

The zone FWHMs follow the Gaussian fits to 0.0 to 0.17 pixel on IC 5070 and 0.24 to 0.37 on the H-alpha stack (up to 6 per cent; Valerian reads higher as second moments weight the wings more than a fit does), and the difference between zones is the same in both, so what matters for a tilt, the comparison of one zone with another, agrees. The surface is the same polynomial to 0.0002 pixel. The Moffat of the stacked profile is 3 to 6 per cent wider than the median of per-star fits, because the stars of a field differ in width and the stack of their pixels is their blend; both say the profile is near Gaussian (beta from 7 upwards), which is what stacks of resampled frames give.

Limits of the method¶

• One image has one focus and one pointing: the hints cannot separate a tilted sensor from a decentred corrector, nor say which way to move a spacer. They say what to try.
• A stack, drizzle or mosaic has edges made of fewer frames; judge a corner on the sharpest single frame when it matters.
• The maps are smooth surfaces: they cannot show a feature smaller than the degree allows, and they extrapolate where there are no stars (the circles show where there are).
• Crowded or nebulous fields give fewer clean stars; lower --min-snr or --threshold to get more, at the cost of fainter, noisier ones.