Resolution Limits Visualizer

Compare the achievable angular resolution of several imaging setups. The total resolution is the root-sum-square (RSS) of four blurring contributions — seeing, guiding, diffraction, and the sensor (pixel sampling) — combined in quadrature. Smaller is sharper. The equations are at the bottom of the page.

Pixel Scale Visual Guide

Over-sampledAcceptableOptimal (1.0–1.5″)Under-sampledYour setups

	80D ETX90	R6 ETX90	80D 400mm	R6 400mm
Seeing (″)	3.0	3.0	3.0	3.0
Guiding (″)	1.5	1.5	1.5	1.5
Diffraction (″)	1.7	1.7	2.1	2.1
RSS on sensor (″)	3.7	3.7	4.0	4.0
Image scale (″/px)	0.6	1.1	1.9	3.4
Sampling (px/FWHM)	6.1	3.5	2.1	1.2
k(s) (sensor coeff.)	0.7	0.7	2.8	3.0
Sensor (″)	0.4	0.7	5.5	10.1
Total RSS (″)	3.8	3.8	6.7	10.9

All values in arcseconds (") except image scale ("/px), sampling (px per FWHM), and k(s) (dimensionless).

Equations

Inputs: D = aperture (mm), f = focal length (mm), p = pixel size (µm); seeing & guiding in arcsec. All θ are in arcsec; image scale θ_px in ″/px; sampling N in px per FWHM.

Image scale (″/px)

θ_{px} = \frac{206.265 \cdot p}{f}

Diffraction limit

θ_{diff} = \frac{149}{D}

Optics blur (RSS)

θ_{optics} = \sqrt{θ_{see}^{2} + θ_{guide}^{2} + θ_{diff}^{2}}

Sampling (px/FWHM)

N = \frac{θ_{optics}}{θ_{px}}

Sensor coefficient (logistic blend)

k (N) = k_{o} + \frac{k_{u} - k_{o}}{1 + e^{α (N - N_{0})}}

k_u = 3.0, k_o = 0.68, α = 6, N₀ = 2.5 k_o is the pixel-integration FWHM (2.355/√12 ≈ 0.68, derived below); k_u, α and N₀ are chosen values that penalise sampling below ~2.5 px per FWHM (a well-sampled target).

Sensor blur

θ_{sensor} = k (N) \cdot θ_{px}

Total resolution

θ_{total} = \sqrt{θ_{optics}^{2} + θ_{sensor}^{2}}

Bar segment (variance share)

h_{i} = \frac{θ_{i}^{2}}{\sum_{j} θ_{j}^{2}} \cdot θ_{total}

Derivation — pixel-integration blur (k_o)

The oversampled coefficient k_o is the FWHM that one square pixel contributes purely by integrating light across its own width p, expressed in pixels.

Model the pixel as a top-hat (uniform) aperture of width p, with normalised profile $u (x) = 1 / p$ for $| x | \leq p / 2$ (and 0 outside).
Its RMS width is the standard deviation of that uniform distribution:
$σ^{2} = \int_{- p / 2}^{p / 2} x^{2} \frac{1}{p} d x = \frac{p^{2}}{12} ⟹ σ = \frac{p}{\sqrt{12}}$
Convert that RMS width to the FWHM of an equivalent Gaussian $g (x) = e^{- x^{2} / 2 σ^{2}}$ , which falls to half its peak at $x = σ \sqrt{2 \ln 2}$ , so the full width at half maximum is
$FWHM = 2 σ \sqrt{2 \ln 2} = 2 \sqrt{2 \ln 2} σ \approx 2.3548 σ$
Substitute $σ = p / \sqrt{12}$ and divide by p to get the coefficient (FWHM per pixel):
$k_{o} = \frac{FWHM}{p} = \frac{2 \sqrt{2 \ln 2}}{\sqrt{12}} = \frac{2.3548}{3.4641} \approx 0.68$

Resolution Limits Visualizer v20260612