The Aperture Radius Report

What this report does

Every aperture photometry measurement requires you to choose a measuring aperture radius. Choose it too small and you throw away starlight, so the star's brightness becomes poorly determined and very sensitive to small changes in seeing and centring. Choose it too large and you include a great deal of empty sky, whose own noise then swamps the star you are trying to measure. Somewhere between those two extremes lies a radius that gives the lowest scatter — the best photometry your data can produce.

The Aperture Radius report finds that radius for you, empirically, from your own images.

Rather than relying on a theoretical formula, Phoranso measures every star in your sequence at a whole range of aperture radii, works out how much scatter each radius produces in practice, and reports the radius where the scatter is lowest. Because it uses your actual data, the answer automatically accounts for your telescope, your camera, your sky conditions and the seeing on the night in question.

The report also tells you how much to trust its own answer, which matters just as much as the number itself.

The Aperture radius report is automatically generated when the follwoing conditions are met in the Photometry settings window:

• Multiple ringsets are selected.
• The From/to range contains a minimum of 5 aperture values. 

For instance, if you configure the range from 2.0 to 5.0 pixels with a step size of 0.5 pixels, Phoranso will generate reports for aperture values 2.0, 2.5, 3.0, 3.5, 4.0, 4.5 and 5.0 pixels. Since the total exceeds the 5-value minimum, the Aperture radius report will be generated.

Before you start

To ensure sufficient stars are present for robust calculations, you must select multiple Reference stars and multiple Comparison stars before running this report.

The report is produced from a Multiple Ringsets photometry run. Under the relevant settings you specify:

• From (pixels) — the smallest aperture radius to test
• To (pixels) — the largest aperture radius to test
• Step size (pixels) — the spacing between tested radii

A range of 2.0 to 6.5 pixels in steps of 0.5 is a sensible starting point for most setups. Two guidelines when choosing the range:

Make sure the range brackets the answer. If the best radius turns out to be the smallest or the largest one you tested, you have not found a genuine minimum — you have simply found the edge of your search. The report will warn you when this happens, and the remedy is to widen the range and run again.

Aim for a range centred near your typical star size. The optimum usually falls somewhere around one to one and a half times the FWHM of your stars. If your images typically show a FWHM of 3.5 pixels, a range of roughly 2 to 7 pixels will comfortably contain the answer.

The gap and background annulus scale automatically with the aperture, so you do not need to adjust them separately.

How the method works

Differential magnitudes

Phoranso does not examine the brightness of any single star on its own. The brightness of a lone star varies from image to image for reasons that have nothing to do with your aperture choice: thin cloud, changing transparency, rising or falling altitude. Those variations would completely mask the much smaller effect you are trying to measure.

Instead, the report works with magnitude differences between pairs of stars. Because both stars in a pair are photographed through the same air at the same moment, atmospheric effects largely cancel out in the subtraction. What remains is measurement noise — and measurement noise is precisely what depends on the aperture radius.

The star pairs

Depending on whether you are using a single reference star or an ensemble, Phoranso forms these pairs:

Having several independent pairs matters. If one star in your field has a problem — and this is more common than most observers expect — the other pairs will disagree with it, and that disagreement is visible in the report.

Note that when you use exactly two reference stars, the two Reference − Ensemble curves are mathematically guaranteed to be identical. Phoranso is aware of this and counts them only once, so that a single piece of information is not given double weight.

Measuring the scatter

For every star pair and every aperture radius, Phoranso computes the scatter of the magnitude differences across all your images.

The scatter is measured using a robust technique based on the median absolute deviation rather than an ordinary standard deviation. The reason is practical: a single bad frame — a cosmic ray strike, a satellite trail, a moment of poor guiding — can inflate an ordinary standard deviation dramatically, and small apertures are more vulnerable to this than large ones. That single frame could easily push the reported optimum to a completely wrong radius. The robust method is largely immune to a handful of bad frames, so the result reflects the typical quality of your data rather than its worst moment.

Combining the curves

Each star produces its own scatter-versus-radius curve, but the curves sit at very different levels: a bright, well-exposed star simply has lower scatter than a faint one at every radius. Comparing them directly would let the brightest star dominate the outcome.

Phoranso therefore rescales each curve relative to its own best point before combining them. This preserves the shape of each curve — how much its scatter actually varies with radius — while removing the overall brightness difference. A star whose scatter barely changes with aperture contributes little, as it should, because it carries little information about which radius is best. A star showing a pronounced minimum contributes strongly.

The rescaled curves are then combined and the lowest point of the combined curve is located. A small parabola is fitted through that point and its two immediate neighbours, which allows the reported optimum to fall between the radii you actually tested — so a scan in steps of 0.5 pixels can still return an answer such as 3.4. 

Extinction and transformation corrections

The report works with uncorrected magnitudes, and this is deliberate rather than a shortcoming.

Extinction correction compensates for starlight being dimmed by the atmosphere, which depends on how high the star sits above the horizon. Transformation correction compensates for your filters and camera responding to colour slightly differently from the standard photometric system, which depends on the colour of the star. Both are essential when you want to publish magnitudes on a standard scale.

Neither, however, depends in any way on your aperture radius. A star's colour is the same whether you measure it with a 3-pixel or a 6-pixel aperture, and so is its altitude at the moment of exposure. Applying these corrections would therefore add the same amount to every point on a curve, shifting the whole curve up or down without changing its shape. Since this report is concerned only with *scatter* — how much the measurements vary — and shifting a set of numbers by a constant leaves their scatter untouched, the recommended radius would come out exactly the same either way.

Extinction does change over the course of a night as the target rises or sets. That variation, though, affects both stars in a pair almost equally and largely disappears in the subtraction, which is one of the main reasons the report works with magnitude differences. Whatever small residual remains appears as a slow drift across the sequence, and Phoranso removes any such drift before measuring the scatter. Applying a formal extinction correction would be removing something that has already been dealt with.

One consequence is worth knowing. When the two stars in a pair differ considerably in colour, the cancellation is not quite perfect, and that pair will show somewhat more scatter than it otherwise would — more so at low altitude. This raises the whole curve for that pair rather than tilting it, so it costs a little sensitivity but does not move the minimum. Choosing comparison stars of similar colour to the star they are paired with keeps this to a minimum, and is good practice for photometry generally.

Reading the report

The report is laid out top to bottom in five parts.

1. Header

Observer details, site coordinates, the aperture range and step size you used, the solver, and whether extinction or transformation corrections were applied. The blue banner states how many observations the analysis is based on.

2. Individual star pairs

One block per star pair, each showing the two stars involved, the tested radii, and the measured scatter at each radius.

This is where you can see what each star is doing individually. A healthy curve is smooth, dips gently to a minimum, and rises gradually afterwards. It does not have to be dramatic — shallow curves are entirely normal for bright stars and do not indicate a problem.

Entries reading N.A. mean no valid measurement could be obtained for that star at that radius, usually because the star was not measured in enough images.

3. Phoranso Combined stddev

The combined curve, in the same units as the individual curves so you can compare them directly. This is the curve from which the optimum is determined.

4. Optimal Radius

The recommended aperture radius, highlighted in green.

5. Overall Assessment

Four independent checks on the trustworthiness of the result, each marked OK, CAUTION or FAIL, followed by an overall verdict reflecting the worst of the four.

• Observation count. How much data underlies the result. Scatter measured from few images is itself uncertain: with around 20 images the uncertainty in each point approaches 25%, which is often larger than the real variation across the whole aperture range. Below 50 observations the reported optimum is effectively meaningless; above 100 it becomes dependable.
• Boundary minimum. Whether the minimum lies safely inside the range you tested. A minimum at the very edge means the true optimum probably lies beyond it, and the range should be widened.
• Curve smoothness. How much any individual curve jumps between neighbouring radii. Adjacent radii share nearly all the same light, so a genuine curve must change smoothly. A large jump means something is entering and leaving the aperture as conditions vary — almost always a close neighbouring star blended with the one being measured.
• Star agreement. Whether the recommended radius suits all the stars, not just some of them. For each star, Phoranso works out how much worse its scatter would be at the recommended radius than at that star's own best radius. If every star loses only a few percent, the stars are in agreement. If one star would be substantially worse off, the recommendation is a compromise rather than a consensus.

The chart

All individual curves are plotted together with the combined curve as a heavy green line and the recommended radius as a vertical green line. The chart is often the fastest way to spot a problem star: a curve that is much higher than the others, or that zigzags while the rest are smooth, stands out immediately.

Interpreting the result

A good result

The observation count is comfortable, all curves are smooth, they agree on roughly the same region, and the minimum sits well inside the tested range. Where the curves are flat near their minimum, the precise value matters little in practice — if the scatter varies by only a few percent between 3.0 and 4.5 pixels, any radius in that region will serve you about equally well.

It is also reassuring when the optimum comes out similar on different nights with the same equipment. Large night-to-night swings suggest that something other than your optics is driving the result.

When one star misbehaves

The most common problem by far is a blended star — a faint companion close enough that it falls inside the larger apertures but not the smaller ones. As the seeing varies from image to image, the amount of contaminating light varies too, injecting scatter that has nothing to do with your aperture choice.

The signature is distinctive. Every pair involving the affected star shows much higher scatter than pairs that do not, and those curves jump erratically rather than varying smoothly. Because the check star appears in several pairs, a blended check star can distort a large part of the report at once.

If the reliability gate flags a specific star, examine that star in one of your images with the largest aperture displayed. If a companion is visible inside the aperture, choose a different star and run the report again. The improvement is usually dramatic.

When the minimum sits at the edge

Widen the tested range in the direction of the minimum and run again. Until the curve turns upward on both sides of the minimum, you have not established that there is a minimum there at all.

When there are too few observations

There is no analysis that can rescue this — the information simply is not present in the data. Use a value obtained from a longer sequence with the same equipment, which will generally be a far better estimate than anything a short run can provide.

Practical advice

• Select multiple Reference and Comparison stars. As noted before you start, ensure you have multiple reference and comparison stars selected to provide a sufficient and robust pool of stars for calculations.

• Gather enough images. A hundred or more gives a dependable result. This is the single most effective thing you can do to improve the report.
• Choose your check star with care. It should be reasonably close in brightness to your target and, above all, isolated. Since it takes part in several pairs, a poor check star affects much of the report.
• Prefer isolated comparison stars. The same reasoning applies, though a single problem comparison star does less damage than a problem check star.
• Widen the range once if in doubt. If the minimum lands near an edge, one extra run with a wider range settles the question.
• Do not chase the last tenth of a pixel. Near the minimum the curve is usually very flat. The difference between 3.4 and 3.6 pixels is rarely detectable in your final light curve; the difference between 3.5 and 6.0 very much is.
• Repeat occasionally. Seeing and focus change with the season. Re-running the report from time to time confirms that your standard aperture is still appropriate.

Summary

The Aperture Radius report determines the aperture radius that produces the lowest photometric scatter in your own data, by measuring differential magnitudes across a range of radii and combining the evidence from several independent star pairs. It reports both a recommended radius and an honest assessment of how much confidence that recommendation deserves.

Where the Overall assessment raises a concern, the concern is usually about the data rather than the analysis — too few images, or a star in the field that is not as clean as it appears. Addressing that, rather than adjusting the settings, is nearly always the route to a better answer.