Signal-to-noise ratio determines how clean an image is.
Sampling determines how that signal is distributed across pixels.
You cannot understand one without the other.
Pixel scale is the angular size of sky covered by a single pixel.
It is usually expressed in arcseconds per pixel (″/pix).
Pixel Scale (arcsec/pixel) = 206.265 × Pixel Size (µm) / Focal Length (mm)
Pixel scale defines how finely the image is sampled.
Seeing describes atmospheric blurring caused by turbulence in the air column above the telescope.
It sets a hard resolution limit, regardless of optics or sensor.
Typical seeing values:
Excellent site: ~1.5″
Good site: ~2″
Average UK conditions: ~2.5–3.5″
Poor nights: 4″+
Seeing is usually quoted as FWHM (Full Width at Half Maximum) of star images.
Sampling describes how many pixels are used to represent a seeing-blurred star.
Under-sampling: too few pixels
Critical sampling: optimal
Oversampling: too many pixels
Sampling is the relationship between:
Pixel scale (″/pix)
Seeing (″)
The Nyquist criterion states that to preserve information:
Pixel Scale ≤ Seeing / 2
(2″ seeing → 1″/pix)
This is the theoretical maximum needed to preserve spatial information.
In real astrophotography, this is rarely optimal.
In long-exposure deep-sky imaging:
Seeing varies during the exposure
Guiding error adds blur
Optical aberrations contribute
Noise dominates faint detail
As a result, slight under-sampling is usually optimal.
Seeing defines the atmospheric PSF.
To fully sample this PSF, Nyquist theory requires a pixel scale of seeing / 2.
In deep-sky imaging, however, signal-to-noise limits which parts of the PSF are measurable.
While finer sampling preserves all information in principle, coarser sampling can improve
per-pixel SNR and increase the detectability of faint extended structures.
Oversampling spreads the same photons across more pixels.
Each pixel carries:
Less signal
The same read noise
The same sky noise
If signal is split across 4 pixels:
Signal per pixel ÷ 4
Noise per pixel does not ÷ 4
This directly reduces per-pixel SNR.
For extended objects (nebulae, galaxies):
Signal per pixel scales with pixel area
Noise per pixel scales with √(signal + background)
Halving pixel scale (oversampling by 2×):
Pixel area ÷ 4
Signal per pixel ÷ 4
Noise ÷ √4 = 2
SNR per pixel ÷ 2
This is why oversampled systems look noisy even with long integration.
Moderate under-sampling:
Improves per-pixel SNR
Reduces read-noise impact
Is often invisible for faint structures
Under-sampling becomes problematic when:
Stars become blocky
Star shapes distort
Astrometry suffers
For wide-field and deep imaging, under-sampling is often a feature, not a bug.
Focal length does not determine resolution on its own.
Resolution is limited by:
Seeing
Sampling
SNR
A long focal length system that is oversampled:
Does not always resolve more detail
Has worse SNR
Requires longer exposures
Demands more integration time
Shorter focal lengths often go deeper.
UK seeing is typically 2-4". So, one would think 1" is appropriate! No! 1" per pixel is actually oversampled most of the time... The average is 3", so we would want 1.5"/pix.
1 Squared / 1.5 Squared = 2.25! We'd need two and a quarter times more integration at 1"/pix compared to 1.5"/pix for the same SNR!
And, on average, we would not expect and detail loss because of =>3" seeing!
This is a drop from a 600mm focal length scope to a 400mm one using the ZWO 533 or 585!
Now, even 1.5"/pix is somewhat oversampled for 4" seeing, which we may have say 25% of the time, so if we use a 300mm FL telescope/lens, we trade some detail for 2-3" seeing, but not 4" seeing, and gain a huge advantage again in integration time reduction. Compared to 1"/pix, we gain 400% more SNR for the same time. So an image of a target that may take some 12 hours of integration at 600mm FL would take 3 hours at 300mm, and we will not lose much detail at all if the seeing is actually ~4" most of the time!
Astrophotography is about signal to noise and concessions. In the UK we have limited clear nights.
A slightly under-sampled pixel scale (our 2"/pix in 3" seeing vs 1"/pix) will be both much easier to image, with regards to:
tracking accuracy,
weight of kit and mount lugging required,
take hugely less time to produce (4 times less for the same SNR),
be easier to process
and cost far less in kit investment.
Astrophotography in the UK is about friction and practicality. Oversampling by 0.5"-1"/pix doesn't sound like much, but it could make the difference between a fantastic looking image form 1-2 nights work, to having a noisy mess after sacrificing much needed sleep, lugging heavy gear outside over many nights, spending hours setting up and sitting there in denial using curves to try and stretch somthing out from the noise. I've been there!
This is why we have a quiet return in populatiry of smart star trackers, and smaller petzval telescopes like the FRA and Redcat, they make sense, and produce amazing images.