Calculator
Example data
| Telescope aperture | Rayleigh resolution | Dawes limit | Notes |
|---|---|---|---|
| 70 mm | 1.98 arcsec | 1.66 arcsec | Good for Moon and bright doubles. |
| 130 mm | 1.07 arcsec | 0.89 arcsec | Typical mid-size reflector performance. |
| 200 mm | 0.69 arcsec | 0.58 arcsec | Often seeing-limited under average skies. |
Formula used
- Rayleigh criterion (diffraction limit): θ = 1.22 · λ / D (radians), where λ is wavelength and D is aperture diameter.
- Arcseconds conversion: arcsec = radians × 206264.806.
- Dawes limit (empirical, visual): θ ≈ 116 / D(mm) (arcseconds).
- Seeing combination (optional): θ_total = √(θ_base² + seeing²) (arcseconds), useful for estimating real-world blur.
- Pixel scale (optional): scale = 206.265 · pixel(µm) / focal(mm) (arcsec/pixel).
- Linear separation (optional): s = θ_total(radians) · distance (meters).
How to use this calculator
- Enter your telescope aperture and select mm or inches.
- Pick a wavelength preset, or choose Custom for a specific band.
- Select Rayleigh or Dawes as your primary reported criterion.
- Add seeing (arcseconds) to estimate realistic sky-limited results.
- Optional: enter focal length and pixel size for sampling guidance.
- Press Calculate to view results above this form.
- Use Download CSV or Download PDF for saved outputs.
1) What angular resolution means
Angular resolution is the smallest separation your telescope can distinguish on the sky. It is usually reported in arcseconds, where 60 arcseconds make one arcminute. Smaller numbers mean finer detail, but real images also depend on optics, tracking, focus, and atmospheric blur.
2) Rayleigh criterion data
The Rayleigh limit estimates diffraction performance with θ = 1.22·λ/D. For light near 550 nm, a 70 mm aperture gives about 1.98 arcsec, 130 mm gives about 1.07 arcsec, and 200 mm gives about 0.69 arcsec. Doubling aperture roughly halves this diffraction angle.
3) Dawes limit comparison
Dawes is an empirical double‑star rule: θ ≈ 116/D(mm). Using the same apertures, 70 mm is about 1.66 arcsec, 130 mm is about 0.89 arcsec, and 200 mm is about 0.58 arcsec. It often looks slightly “better” than Rayleigh because it reflects visual detection.
4) Seeing dominates most nights
Typical seeing at many sites ranges from 1 to 3 arcsec, and it can be worse in cities. This calculator combines diffraction and seeing by quadrature, so a 200 mm telescope with a 0.69 arcsec Rayleigh limit under 2.0 arcsec seeing becomes √(0.69²+2.0²) ≈ 2.12 arcsec total blur.
5) Wavelength changes the limit
Shorter wavelengths improve diffraction. If you move from 850 nm near‑IR to 450 nm blue, the Rayleigh limit scales by 450/850 ≈ 0.53, meaning about 47% tighter diffraction angles at the same aperture. Filters and sensor sensitivity decide what wavelength is realistic for your setup.
6) Central obstruction effects
Reflectors often have a secondary mirror. A 0.33 obstruction ratio reduces clear collecting area by 1 − 0.33² ≈ 0.89, or about 11% less light. Resolution formulas still use the full aperture diameter, but contrast on fine planetary detail can drop, so good collimation matters.
7) Imaging sampling numbers
For cameras, pixel scale is 206.265·pixel(µm)/focal(mm). With 3.76 µm pixels at 1000 mm, scale is about 0.78 arcsec/pixel. Nyquist sampling targets about half the total blur per pixel, so if your total blur is 2.0 arcsec, a scale near 1.0 arcsec/pixel or smaller is reasonable.
1) What aperture should I enter for a reflector?
Use the primary mirror diameter, not the tube size. If a mask or corrector reduces clear aperture, enter the effective clear opening because diffraction depends on the light‑collecting diameter.
2) Which is better, Rayleigh or Dawes?
Rayleigh is a physics‑based diffraction guideline and is widely used for imaging. Dawes is a visual, empirical rule for double stars. Compare both, then apply seeing to estimate real performance.
3) Why does my result get worse when I add seeing?
Atmospheric turbulence blurs the star image. The calculator combines diffraction and seeing in quadrature, so even a large aperture becomes seeing‑limited when the seeing value is larger than the diffraction limit.
4) How do I interpret pixel scale?
Pixel scale tells you arcseconds covered by one camera pixel. Smaller values mean finer sampling. A common target is about half your total blur per pixel (Nyquist), but oversampling can increase noise and file sizes.
5) Does central obstruction change the diffraction limit?
The diameter still sets the basic angular scale, but a larger obstruction redistributes light into diffraction rings and can reduce contrast. Use the obstruction ratio to estimate area throughput and keep collimation precise.
6) Can I use this for planets and lunar details?
Yes, but remember most locations are seeing‑limited. Use realistic seeing (often 1–3 arcsec) and compare it to your diffraction limit. Good focus, steady air, and thermal control usually matter more than tiny formula gains.