Calculator Inputs
Example Data Table
| Wavelength | Aperture | Distance | Angular Resolution | Minimum Linear Separation |
|---|---|---|---|---|
| 550 nm | 50 mm | 1000 m | 2.768074 arcsec | 13.420000 mm |
| 550 nm | 100 mm | 1000 m | 1.384037 arcsec | 6.710000 mm |
| 632.8 nm | 25 mm | 100 m | 6.369589 arcsec | 3.088064 mm |
| 450 nm | 5 mm | 2 m | 22.647876 arcsec | 219.600000 µm |
Formula Used
Rayleigh angular resolution:
θ = k × λ / D
Linear separation at distance L:
s = θ × L
Airy disk radius at focal plane:
r = k × λ × f / D
Effective wavelength in a medium:
λeffective = λ / n
θ is the minimum angular separation in radians.
k is the criterion factor. For circular apertures, it is usually 1.22.
λ is the wavelength of light.
D is the aperture diameter.
L is the observation distance.
f is the focal length when image-plane blur is needed.
n is the refractive index of the surrounding medium.
How to Use This Calculator
- Enter the wavelength and choose its unit.
- Enter the aperture diameter for the optical system.
- Provide the observation distance to convert angular resolution into linear separation.
- Keep the criterion factor at 1.22 for a standard circular aperture, or change it for a custom model.
- Add refractive index if the system is operating in water, glass, or another medium.
- Optionally enter focal length to estimate Airy disk radius and diameter at the image plane.
- Optionally enter object separation to test whether two details are resolvable.
- Press the calculate button to view the result table, trend graph, and export options.
FAQs
1) What does the Rayleigh criterion measure?
It estimates the smallest angular separation at which two point sources can still be distinguished by a diffraction-limited circular aperture. Smaller values mean better resolving power.
2) Why does a larger aperture improve resolution?
The equation places aperture diameter in the denominator. Increasing aperture size reduces diffraction spread, lowers the minimum resolvable angle, and improves the ability to separate close details.
3) Why does wavelength matter?
Longer wavelengths diffract more strongly, so the minimum angular separation increases. Shorter wavelengths usually provide better theoretical resolution when the aperture stays the same.
4) What is the default factor 1.22?
It comes from the first minimum of the Airy diffraction pattern for a circular aperture. That factor defines the classic Rayleigh limit used in optics and astronomy.
5) What does the linear separation result mean?
It converts angular resolution into a real spacing at the chosen distance. That tells you how far apart two points must be to appear just resolved.
6) Why is refractive index included?
Light travels with a shorter effective wavelength inside a medium. Dividing by refractive index adjusts the wavelength and changes the predicted diffraction-limited resolution.
7) What is the Airy disk output used for?
It estimates the diffraction blur size at the focal plane. That helps when comparing optical resolution with detector pixel size, sensor sampling, or image spot diameter.
8) Does this calculator include aberrations or turbulence?
No. It models ideal diffraction-limited behavior. Real systems may perform worse because of lens aberrations, alignment errors, atmospheric turbulence, sensor noise, or motion blur.