Telescope Optics and Resolution

Point your best refractor at Vega on a still night, crank the magnification, and stare. The star is not a point. It is a tiny bright disk surrounded by a faint ring, and outside that, a fainter ring, and another. This is the Airy pattern, named for George Airy, Astronomer Royal who worked out its shape in 1835.

The pattern exists because light is a wave. When it squeezes through a circular aperture, the edges of the aperture act like the rim of a drum — the wave diffracts, and the far-field intensity rearranges itself into a central blob with concentric rings. You cannot avoid it. A lens fabricated atom-by-atom at zero cost, cooled to match the air, and pointed at a single photon source would still show an Airy disk. The only way to shrink it is to make the aperture bigger.

The angular radius of the central disk — from the peak to the first dark ring — is:

θ = 1.22 · λ / D

where λ is the wavelength of light and D is the aperture. Plug in green light (λ ≈ 550 nm) and convert to arcseconds:

The first ring carries 1.7% of the peak intensity, the second 0.4%. On a bright star in perfect seeing, you can count the first ring or two; everything beyond vanishes into the background. On a faint star, even the first ring is invisible and you see only the central disk. Either way, what reaches your retina is an Airy pattern — and the size of that pattern, not the actual angular size of the star, is what your telescope can tell you about the star.

Point a telescope at a close double star. As you separate two Airy patterns, at some point they stop overlapping enough to look single and start being recognizable as two. Where exactly is that point? Two answers, both useful.

The Rayleigh criterion says the stars are "resolved" when the peak of one sits exactly on the first dark ring of the other. That's the angular radius of the Airy disk: θ = 1.22 λ/D. It's the theoretically clean cutoff — above it, the contrast dip between the two stars disappears.

The Dawes limit is sneakier. In the 1860s, English clergyman and amateur observer William Rutter Dawes tested himself on hundreds of equally bright double stars and found he could reliably elongate pairs much closer than Rayleigh predicted — down to

θ_Dawes ≈ 116 / D arcseconds, with D in millimetres

This is about 20% tighter than Rayleigh. Not because Dawes was magical — but because the human eye-brain pipeline is a remarkably good pattern matcher, and "I see an elongated blob" is a lower bar than "I see two fully-separated disks."

Neither limit is a hard wall. Both fail when the pair is unequal in brightness — the fainter star drowns in the glare of the primary long before its Airy disk would overlap the primary's first null. Splitting Sirius A from its white-dwarf companion Sirius B (mag 8.5, inside Sirius A's glare) needs much more than Dawes — it needs a steady night, a masked aperture, and a lot of patience.

Imagine a perfectly spherical mirror. A sphere is easy to grind — you can make one by grinding any two random glass blanks against each other with abrasive between them; given enough time, both converge to spheres. But the sphere does not bring parallel light to a single focus. Light striking near the rim focuses shorter than light striking near the center. The image of a point is not a point — it's a bright core surrounded by a halo. This is spherical aberration.

The cure, discovered and implemented by Newton and refined over centuries, is to grind a paraboloid instead of a sphere. Every Newtonian reflector — the whole family — uses a parabolic primary specifically to eliminate spherical aberration on-axis.

But paraboloids are expensive to grind. In the 1930s, the Estonian optician Bernhard Schmidt had a different idea: leave the mirror spherical and undo the aberration with a thin, oddly shaped glass plate at the front of the tube. This plate — the Schmidt corrector — has a complex polynomial profile, thicker at the center and the rim than halfway out. Each ray gets exactly the phase kick needed to make a sphere behave like a parabola.

This is why every Schmidt-Cassegrain (SCT) — the C6, C8, C11, C14 family, and their Meade cousins — has that distinctive glass lens at the front. It is not a window to keep dust out (though it does that too). It is the corrector plate, and without it the telescope would barely work. The Maksutov-Cassegrain (MCT) uses the same trick with a deeply curved meniscus lens instead of an aspheric plate.

A parabolic mirror is perfect on-axis — but only on-axis. Light that enters at even a small angle from the optical axis focuses into a comet-shaped smear with the tail pointing away from the field center. This is coma, and it is the single biggest reason fast Newtonian reflectors frustrate astrophotographers.

Coma grows linearly with field angle and inversely with the cube of the focal ratio. An f/4 Newtonian has roughly eight times the coma of an f/8 Newtonian at the same field angle. For a 150 mm f/5 Newtonian, stars start looking visibly seagull-shaped about 6 mm off-axis — well inside the field of a typical 25 mm eyepiece.

The cure is a coma corrector — a small multi-element lens assembly that screws into the focuser. The two popular ones for amateur use are the Televue Paracorr (visual and photographic) and the Baader MPCC (photographic). They add a tiny amount of aberration of their own but cancel the dominant coma, flattening stars across the whole field.

Refractors, Schmidt-Cassegrains, and Maksutov-Cassegrains have their own optical designs that reduce coma substantially — it's a parabolic-mirror problem first and foremost. A well-designed SCT or apo refractor shows coma only at the very edge of a wide-field eyepiece, if at all.

If coma is the Newtonian's signature flaw, field curvature is the refractor's. A refractor focuses its field not onto a flat plane but onto a curved surface — a shallow bowl, concave toward the objective. Your eyepiece focal plane is flat; your camera sensor is flat; the bowl won't fit either. You can focus the center sharply, or focus the edge sharply, but not both.

At the eyepiece, field curvature is forgiving: your eye accommodates a little, and you can refocus subtly as you pan. At the camera sensor, it is merciless — edge stars are round but soft, and no amount of focusing saves them.

The fix is a field flattener: a small negative lens group placed just ahead of the focal plane. It bends the outer parts of the light cone inward, effectively stretching the curved focal surface into a flat one. Every modern astrophotography refractor either includes a built-in flattener or has a dedicated matched flattener sold alongside — different for every scope, because the correction depends on the objective's specific curvature.

A catalog lens or mirror is often advertised with λ/4, λ/8, or "diffraction-limited". These numbers refer to how smoothly the surface matches its intended shape — peak-to-valley wavefront error, measured in wavelengths of visible light. But PV errors are a coarse metric: one tiny dimple can make a surface look terrible on PV and excellent in practice.

The Strehl ratio is a better summary number. It's defined as the ratio of the actual peak intensity in the star image to the theoretical peak of a perfect optic of the same aperture. A perfect mirror has Strehl = 1.00. An optic with small random errors spreads light out of the central Airy disk into the rings, dropping the peak.

The convention is:

The 0.80 threshold comes from Karl Strehl himself (1895) and corresponds roughly to an RMS wavefront error of λ/14. Below that, the aberrations are large enough to notice on high-contrast targets — planetary detail looks soft, double stars are harder to split.

In practice, any reasonably priced modern optic — a decent SCT, a Chinese ED refractor, a good Newtonian primary — ships at Strehl ≈ 0.90 or better when new. The bottleneck for almost every amateur, almost every night, is the atmosphere, not the glass. A 0.95 mirror in mediocre seeing performs identically to a 0.82 mirror in mediocre seeing: both limited by the same wobbling air. Strehl matters most when the seeing is genuinely excellent — and when it is, it matters a lot.

Glass bends different colors by different amounts — blue light bends more than red. A single lens therefore focuses blue light closer than red light, and the image of a star is surrounded by a purple halo. This is chromatic aberration, and it's the reason Galileo's first refractors showed everything smeared in false color, and the reason Newton abandoned refractors in favor of mirrors.

The fix, developed in the 18th century, is the achromatic doublet: two lenses of different glass types, one positive (crown), one negative (flint), whose dispersions partially cancel. An achromat brings two wavelengths — typically red and blue — to the same focus, leaving green slightly off. The residual color is small but visible on bright stars and planets, especially at fast focal ratios.

An apochromat (apo) goes further, using three or more lens elements or a specialty glass (ED, fluorite) to bring three wavelengths to the same focus. The residual color is essentially invisible. Modern triplet apos — with FPL-53, FPL-55, or fluorite elements — are what allow a 100 mm refractor to deliver planetary views that rival a good 150 mm reflector.

Mirrors, reflectively, don't bend light by wavelength, so all reflectors (Newtonian, SCT, MCT, Cassegrain) are completely free of chromatic aberration. This is the single biggest reason reflectors dominate the aperture-per-euro ranking: you pay for glass or for silvering, and silvering is a lot cheaper than an ED triplet.

All of the above assumes the optics are aligned. They almost never are.

A Newtonian has two mirrors (primary and secondary) and a focuser, and each has three degrees of freedom. Knock the scope in transit, let it cool unevenly, or simply look at it wrong, and the mirrors drift out of alignment. A misaligned Newtonian still forms an image — but that image sits off-axis relative to the center of the field, and coma that should only appear at the edge now contaminates the middle.

A collimated C8 is a 200 mm telescope. A decollimated C8 is an expensive 80 mm. The optics don't get worse — they get displaced.

Collimation tools, in increasing order of fussiness:

• Cheshire eyepiece — a simple sighting tube with a crosshair and an illuminated 45° surface. Perfectly adequate for most Newtonians.
• Laser collimator — fast and satisfying; works well for primary/secondary alignment but must itself be collimated (a laser with a miscentered beam introduces its own error).
• Star test — defocus a star slightly and center the resulting "donut." If the central obstruction is off-center, tweak the primary. Doesn't get easier than a real star.

The full procedure for each telescope type is too long to cover here; Nightbase has a dedicated collimation guide with step-by-step photos and an interactive simulator.

Every sharp view is the product of the same short list:

1. Enough aperture for the Airy disk to be small enough to show the detail you want.
2. Enough optical quality (Strehl ≥ 0.80) that the aperture is the bottleneck, not the glass.
3. The right aberration corrections for the design — corrector plate for an SCT, parabolic primary for a Newtonian, apo or flattener for a refractor.
4. Collimation that's current with tonight's temperature and handling.
5. Seeing — atmospheric steadiness — good enough to let the optic show what it can. Typical nights cap resolution at 2–3″ regardless of aperture; excellent nights (a few per year) let a 200 mm scope hit its 0.55″ Airy limit.

You can't do anything about seeing. But the first four are yours to manage, and understanding them is the difference between "my scope is fine, the sky was bad" and "my scope is decollimated and I've been blaming the sky for three months."