Stacked, Sharpened — and Beside the Point

Three pages of the Unknown Luminaries chapter, at pp. 155–157, are given to how planetary photographs are made: lucky imaging, ten thousand frames, stacking software, wavelet deconvolution. The heading is “Image stacking + Deconvolution = Reality?” and the caption is “How to manipulate a photo to achieve the desired planet 101.” It is a short section and it does a lot of work, because the two arguments that follow it both rest on photographs, and one of them is captioned “(image stacked and edited)” in his own hand.

We think a good deal of this is right, and we say so below at some length. We also think it is aimed at the wrong target, and that granting every word of it costs the argument nothing at all.

What the claim is

p. 156 quotes a working tutorial from the astrophysicist whose flat-Earth challenge video the chapter uses throughout: capture around ten thousand frames with FireCapture, stack them in AstroSurface, assemble the result. The book’s reply is “Is he implying that Photoshop is the best method to prove to myself that the Earth is not flat?” p. 157 sets a raw frame beside a processed one — “Real Jupiter” against “Jupiter 4.0?” — over a quotation about applying a wavelet setting that “brings out a lot of the detail.”

The charge is that the detail is put in rather than drawn out, and by p. 161 it has become “Do these deconvoluted and sharpened images even resemble an 88,800-mile-wide ball of gas?”

The concession, and it is not a small one

Sharpening can invent. This is not a debating point, it is what the mathematics says. Deconvolution is an inverse problem, and inverse problems amplify noise into structure unless they are held back deliberately; push a wavelet slider far enough and you get ringing at the limb, haloes around moons, and belt edges crisper than anything the atmosphere delivered. Over-processed amateur planetary images are full of exactly this, and two people working the same raw capture routinely produce visibly different planets.

The pipeline also has genuinely subjective steps. How many frames to keep, how hard to sharpen, what to do about colour — none of these has a right answer written down anywhere, and the operator's taste is in the result. And the broader instinct is sound: manipulated images are a real problem in real science, and “it came out of image-processing software” is a fair thing to want explained rather than waved through.

So we are not going to argue that the pictures are unimpeachable. We are going to argue something else.

The detail was never the evidence

Here is the thing the chapter does not seem to have weighed. Essentially nothing in the case for a heliocentric, moving Earth rests on what a planet looks like through a telescope. It rests on where planets are, and when — and a position needs only a dot.

Every one of these predates photography, let alone stacking software. They are the load-bearing results, and they were obtained by writing down where a point of light was on a given night.

Neptune is the case that settles it

Neptune was not found by looking. It was calculated — from nothing but the accumulated discrepancy between where Uranus was predicted to be and where it was measured to be. Le Verrier published a position; Galle pointed a telescope at it on the evening of 23 September 1846 and found the planet about one degree away.

And nobody could see anything on it. Neptune’s surface features are not visible from the ground at all; it took the Hubble Space Telescope and adaptive optics before any detail was observed. An entire planet — its existence, its mass, its orbit — was derived, confirmed and used, from position measurements alone, by people who had never seen and could never have seen a single feature on its disc.

How small these things actually are

Computed for the evening of Dury’s photograph, 22 February 2025:

Ordinary atmospheric seeing blurs a point to between one and four arcseconds. Uranus and Neptune are therefore at or below the resolution the sky itself allows — they are barely more than points from the ground on any night, through any telescope, however processed.

And they are not only visible. They are pulling on us.

Everything above concerns light — what reaches a sensor and what a pipeline does to it. There is a second channel entirely, and the book’s objection cannot touch it, because it does not run through a camera at all. These bodies exert forces we can measure, and some of the measurements are not made by looking at the sky.

Mercury’s orbit turns, and mostly the other planets turn it

Mercury’s perihelion advances by about 575″ per century against a fixed frame. This is usually told as the Einstein story, and the famous residual is real — but the residual is 43″. The other 532″, some 92 per cent of the whole effect, is simply the other planets pulling on Mercury, computed from their masses and positions and agreeing with what is observed. Venus and Jupiter do most of it. Long before relativity was needed to close the gap, the bulk of that turning had been accounted for by treating the planets as masses at known places doing known work.

A planet found entirely by its pull

Neptune, as above: located from discrepancies in Uranus’s measured positions and found within a degree of the calculated place. Nobody could see a feature on it then and effectively still cannot from the ground. It was detected by gravity and confirmed by pointing.

Venus and Jupiter are written into rock

This is the one that ends the argument. The largest-amplitude term in the variation of Earth’s orbital eccentricity is the g₂ − g₅ term — the difference between the rate at which Venus’s orbit precesses and the rate at which Jupiter’s does. It has a period of about 405,000 years, it drives Earth’s climate through insolation, and it is recorded in sediment.

It is read in the lake beds of the Newark and Hartford basins, in the Chinle Formation at Petrified Forest, in Japanese pelagic ribbon cherts and in the Early Jurassic marine sequences of the Bristol Channel. It has been shown stable across the Late Triassic and Early Jurassic, roughly 223 to 199 million years ago, and it is now used as a calibration clock for geological time — a “geological orrery” that constrains the planets’ past motions from strata rather than predicting strata from the planets.

Jupiter weighed with a neutron star

Millisecond pulsars are clocks. To time one, you must convert arrival times at the telescope to arrival times at the solar system’s centre of mass — and if a planet’s assumed mass is wrong, that error appears as a periodic wobble in the residuals with the planet’s own orbital period. So the mass can be fitted for. From four millisecond pulsars, the Jovian system mass comes out at 9.547921(2)×10⁻⁴ solar masses — about four times better than the Pioneer and Voyager flyby values, and within a factor of twenty of what Galileo achieved in orbit.

Jupiter, weighed using radio pulses from a dead star thousands of light years away, in agreement with what a spacecraft got by falling around it.

Where this does and does not reach

• This is not astrology, and the distinction is quantitative. Planetary tides on Earth are utterly negligible — the Moon and the Sun do essentially all of it. The effects above are secular and orbital, accumulating over centuries and hundreds of millennia. Nothing here says Jupiter influences a Tuesday.
• These are inferences inside a gravitational model, not proofs of it. What they add is channels with unrelated failure modes: celestial mechanics, sedimentology and radio pulsar timing do not share an instrument, a pipeline or a community of practice.
• The sedimentary link runs through climate. Orbit to insolation to lake level to lithology is a chain, and each link has its own literature and its own uncertainty. The 405,000-year signal is unusually robust, which is why it is the one used as a metronome, but it is not a direct measurement of Jupiter.

The compact form of all of it: a photograph of Jupiter could be a forgery from end to end and the case would be untouched, because Jupiter’s mass is in the rock under Petrified Forest, in the turning of Mercury’s orbit, and in the arrival times of pulses from a neutron star.

The ladder does not stop at the amateur

The two sections above step around the objection rather than answering it: they say the pictures were never carrying the weight. But the objection deserves answering on its own ground too, because it contains an assumption that is simply false. The argument at pp. 155–157 treats the processed amateur image as though it were the thing our knowledge of these planets rests on. It never was — and there are instruments further up the ladder that produce comparable or better pictures without needing the disputed step at all.

Read the fourth column before the third. The disputed technique runs continuously from a garden telescope to a professional observatory. The 1.05 m telescope at the Pic du Midi is a research instrument that images planets by capturing thousands of frames, keeping the sharpest and stacking them — the same pipeline the book calls “how to manipulate a photo,” operated at an altitude observatory under formal professional–amateur collaboration, with the results feeding planetary science. There is no line on this ladder where dubious amateur practice stops and respectable astronomy begins. There is one method, scaling with aperture, and then two rungs that do not need it at all.

There is a prediction buried in that column, and it is not the obvious one. Above roughly 100 mm every single frame is seeing-limited rather than aperture-limited — the atmosphere blurs to one or a few arcseconds whatever the mirror is doing. So a raw frame from a 356 mm telescope and a raw frame from the Pic du Midi metre should look much the same, and only the stacked versions should separate by aperture. That is what the simulation below produces, and it is checkable against real frames by anyone who has both.

Hubble is the one that matters most here, because the problem lucky imaging exists to solve does not exist for it. There is no seeing above the atmosphere, so a single exposure is already at the diffraction limit — no frame selection, no stacking to beat turbulence, none of the machinery the book objects to. It resolves about seven times finer than a good fourteen-inch stack, and about twice as fine as the Pic du Midi metre. And a large ground-based telescope with adaptive optics corrects the wavefront in hardware, which is a completely different mechanism with completely different failure modes from choosing sharp frames in software.

The right way to put it is that stacking is a booster, not a source. It moves a small aperture toward the resolution it already has and which the atmosphere was hiding — and the result can be checked against instruments that started higher up and needed no boosting.

Nobody’s image is raw, and that is not the point

Worth conceding before it is offered as a rebuttal: the professional images are processed too. Hubble frames are calibrated, dark-subtracted, flat-fielded, drizzled from multiple exposures, composited across filters and stretched for display; spacecraft images are mosaicked and colour-mapped. The same principle applies to them as to the amateur, from a higher starting point. So the honest contrast is not processed against unprocessed — there is no unprocessed.

It is independent pipelines with unrelated failure modes converging on the same structure. Frame selection, adaptive optics and flying past are three ways of being wrong that have nothing in common. Agreement between them is not something a shared artefact can produce, because there is no shared step to produce it.

How the booster works, and where it stops

An aperture has a hard resolution limit, θ = 1.22λ/D, and no amount of processing passes it. That turns the book’s suspicion into something testable rather than something to argue about: if sharpening manufactured detail, the detail would not care how big the telescope was.

Ordinary seeing is 1–4″, so above about 100 mm every single frame is seeing-limited and extra aperture buys nothing on its own. That is what the technique is for. Lucky imaging and stacking are not cosmetics; they are the route to the resolution the instrument already has.

We ran it

A simulation, and labelled as one. The target is a synthetic phantom rather than a photograph — a banded field beside a ladder of line pairs at 1.6, 0.8, 0.4 and 0.2 arcseconds — so nothing real can leak in through the back door. Each frame is that phantom seen through the aperture’s diffraction, through a randomly drawn moment of seeing around a 2.5″ median, shifted by tip-tilt and given photon noise. Four hundred frames per aperture; the sharpest five per cent registered, averaged, then deconvolved.

The code is in the repository at scripts/stacking_demo.py and scripts/stacking_figure.py, seeded, and runs in about twenty seconds. Change the aperture list and re-run it.

Then we ran it on somebody’s real data

A simulation shows what the mechanism can do. It cannot show what a working astrophotographer’s actual capture does, so we asked one. Christopher Go — who images Jupiter from Cebu with a 356 mm Celestron C14, and whose work appears in the professional literature — sent us a complete raw capture and permission to use it.

His covering note contained a correction worth more than the file:

“I really don’t have a single capture because we actually capture videos of planets that we process.”

Which reframes the demand. There is no unprocessed photograph to produce, in the way there is no unprocessed frame of a long exposure. The unit of planetary imaging is a video, and the picture is what you compute from it. Asking to see the raw photograph is asking for a thing that was never made.

What arrived, and what we did with it

3,215 frames at 107 per second — thirty seconds of Jupiter on 22 July 2022 at 20:41 UT, 720×620, eight-bit, raw RGGB sensor data straight off the camera. We wrote the pipeline ourselves: demosaic, register every frame by phase correlation against a fixed reference, average. No commercial software, no hand-tuning, no wavelet sliders.

First, a check that the file is what it claims to be. The planet measures 501 pixels across, and the ephemeris gives Jupiter an apparent diameter of 43.82″ that night — so the image scale is 0.085″ per pixel, and the capture is of the object, date and instrument stated.

The measurement

Eyes are poor judges of this, so we measured the power at each spatial scale on an identical patch of the disc, in a single frame and in the stack.

That is the answer to “Image stacking + Deconvolution = Reality?”, measured rather than argued, on a working amateur’s own data. The capture is his; the processing and the code are ours; anyone with the file can check both.

Honest notes on this run. The seeing was unusually steady — sharpest and worst frames differed by only 7% on our metric — so frame selection contributed almost nothing and the averaging did the work. On a poor night the balance would shift the other way. We applied no deconvolution at all to this data, so the panels above are what registration and averaging alone produce.

And down the ladder, on the same night

One capture at one aperture cannot show the ladder. But it can be walked downwards: take Go’s frames and impose on each the diffraction limit and the reduced light grasp of a smaller mirror, then stack as before. Everything below is his real Jupiter, his real seeing, his real sensor noise — only the telescope is hypothetical, and only in the first three columns.

That is the shape of the whole argument in one picture. Stacking climbs to the ceiling the aperture sets. It does not climb past it, and no telescope's stack ever reaches the next telescope's.

Why a position is a much weaker thing to ask for

Resolving a feature means separating two points that are close together, which is hard and is what seeing destroys. Locating an object means finding the centre of its light, which is easy and which averaging actively helps — a blurred blob has a well-defined centroid, and the blur is symmetric. You can measure a position far finer than you can resolve a detail, and routinely do.

There is a second difference that matters more. An astrometric frame carries its own calibration. The same exposure that contains the planet contains field stars whose catalogue positions are known, and those stars fix the plate scale, the orientation and the distortion of that particular image. The measurement is checkable inside the frame that produced it. Nothing of the sort is available for a wavelet-sharpened planetary disc, which is precisely why the objection at pp. 155–157 has force there and none here.

The book’s own two tests run on positions, not pictures

Worth noticing rather than scoring a point off. The eight-planet challenge at pp. 162–163 asks whether a simulation reproduces the placement of the planets — a positional question. The Jupiter argument at pp. 158–161 turns on where a shadow sits relative to a moon and when it moves — a positional and timing question, and the test we have published for it needs a telescope and a wristwatch and nothing else.

Both of the chapter’s own chosen tests are astrometry. The imaging critique and the tests it is meant to support are not measuring the same thing.

Even so: is the stacking legitimate?

The above would hold even if the answer were no, but the answer is mostly yes, and the reasons are checkable rather than authoritative.

• Stacking is averaging, and averaging cannot add information. Signal repeats from frame to frame; noise does not. Signal-to-noise therefore improves as the square root of the frame count — ten thousand frames buys a factor of a hundred. Everything that emerges was present in every frame; what goes away is what was never correlated. Stack pure noise and no planet appears. That is a demonstration, not an argument, and it takes an evening.
• Lucky imaging is selection, not synthesis. Seeing varies frame to frame; you keep the sharpest few per cent and discard what the atmosphere ruined. The retained frames agree with one another before anything is combined, which is the part an onlooker can audit.
• Deconvolution can be honest or not, and the difference is visible in the workflow. The telescope’s point-spread function is measurable — photograph a star, that is the blur. Deconvolving with the measured PSF undoes a known distortion. Dragging a wavelet slider until the picture looks pleasing does not, and the book is right to be suspicious of the second. The distinction is auditable and rarely audited, which is a fair criticism of the hobby.
• Invention cannot hit a target set in advance. The Great Red Spot appears at a longitude computable years ahead; moon shadows arrive at a computed minute; the Cassini division falls where it must. A pipeline that manufactures detail has no way of manufacturing it in the right place at the right time.
• Independent operators converge. Different observers, telescopes, software and countries on the same night produce the same features in the same places. Artefacts of a process are specific to that process; they do not agree across processes.

We had to do this to ourselves

The Mirrored Reflections measurement rests on a nature photograph, and that photograph turned out to carry aesthetic stretching applied in post-production. We did not trust the pixels. We recovered the frame’s true scale from the surveyed bearings of the mountains in it, corrected for the stretch, and stated the correction and its uncertainty on the page.

That is what taking this objection seriously looks like, and we agree with the book that it should be taken seriously. It is also why we do not think a processed image is worthless — it is why we think a processed image needs its processing accounted for, which is a different and much more workable claim.

Where detail does matter, honestly

• Historically it mattered enormously once. The phases of Venus are a shape observation, they are crude, and they killed the Ptolemaic system. Detail can be decisive; the claim here is only that the dynamical results do not depend on it.
• Some of our own arguments use resolved measurement. The Jupiter page measures shadow sizes on the disc, and Is the Moon a Ball? is an appearance argument throughout. Those inherit this objection and have to answer it on their own terms.
• “Does it look like a ball of gas?” is not answerable by astrometry. That question at p. 161 is about appearance, and this page does not address it. It is a separate argument and deserves one.

What would change our mind

• A stack of noise that produces a planet. If frames containing no correlated signal can be made to yield structure by any standard pipeline, the averaging argument fails and we would want to know immediately.
• A known-target stack that disagrees with the target. Photograph a resolution chart at distance through the same pipeline. If the stack shows detail the chart does not have, that is a real result.
• Raw frames that separate by aperture. If unprocessed single frames from a 356 mm and from a metre-class telescope differ in resolved detail the way their apertures would suggest, then seeing is not the limiting term we say it is, and the account of why stacking exists at all is wrong.
• An amateur stack showing a feature the orbital image does not. Same target, same rotation phase, a good ground-based stack against a Hubble frame that resolves seven times finer. Anything present in the first and absent from the second is either an artefact of the pipeline or a real transient, and either answer is worth having. This is the cheapest decisive test on the page.
• Astrometric positions that fail the field-star check. If planetary positions measured against catalogue stars in the same frame do not reproduce, the whole of this page’s reframing goes with them.
• To do: complete this list.

Where this page could be wrong

• It is a shell, and the demonstrations are unrun. The noise stack and the known-target stack are proposed here, not reported. They are cheap and we should do them.
• The historical table is a summary and deserves proper citation. Each row is standard history of astronomy, but the page should lean on sources rather than on our recollection of them.
• “Averaging cannot add information” is true of averaging and not of every step. Deconvolution genuinely does add assumptions, and a badly chosen PSF genuinely does create features. The argument here is that the astrometry does not route through that step, not that the step is harmless.
• One capture, one night, one instrument. The Go data is a single thirty-second run in good seeing. It shows what stacking did on that occasion; it is not a survey.
• The convergence claim is asserted, not shown. We argue that amateur stacks agree with orbital and spacecraft imagery; we have not yet put a matched set side by side on this page. Until we do, that section is reasoning about what the comparison would show.
• To do: name the specific video and tutorial at pp. 155–157 with a stable reference.

Sources & further reading

• Levi Miller, Globe Deconstruction? (prerelease) — pp. 155–157 (the imaging-process argument), p. 161 (“deconvoluted and sharpened images”), and pp. 158–163 for the two arguments that depend on it.
• Neptune’s discovery within about one degree of Le Verrier’s predicted position, 23 September 1846, and the unavailability of its surface detail to ground-based telescopes. Neptune, Wikipedia.
• The 1.05 m telescope at the Pic du Midi and its planetary programme, including the professional–amateur observing collaboration: t1m.omp.eu.
• Raw capture 2022-07-22-2041_2-CG-L-18.avi — 3,215 frames, Celestron C14, courtesy of Christopher Go, used with his permission. Our processing code accompanies this page in the repository.
• Diffraction limits computed as 1.22λ/D at 550 nm. ESA/Hubble imagery is released under CC BY 4.0 with visible credit, and NASA imagery is public domain, so a published comparison is possible without a licensing problem.
• Mercury’s perihelion advance, planetary versus relativistic contributions: Fitzpatrick, Celestial Mechanics.
• The 405,000-year Jupiter–Venus eccentricity cycle, its g₂ − g₅ origin, the Newark, Hartford, Chinle, Japanese chert and Bristol Channel records, and the geological-orrery programme: Olsen et al., Mapping Solar System chaos with the Geological Orrery, PNAS; and Kent et al., Empirical evidence for stability of the 405-kiloyear Jupiter–Venus eccentricity cycle, PNAS 2018.
• Planetary masses from pulsar timing: Champion et al., Measuring the Mass of Solar System Planets Using Pulsar Timing, ApJL 720 L201 (2010).
• Apparent disc diameters computed from JPL DE440 via Skyfield for 2025-02-22, using IAU equatorial radii.
• Cross-references on this site: Jupiter’s Shadows and The Eight-Planet Photograph (the two arguments this one sits underneath), Mirrored Reflections (where we had to account for processing in our own source image).