Calculate telescope Rayleigh resolution or microscope diffraction limits, reverse-solve aperture, NA, or wavelength, and convert practical units.
Diffraction Limit Formula
The formula for a diffraction limit is as follows:
- Where DL is the diffraction limit (radians)
- w is the wavelength of the light (cm)
- d is the diameter of the telescope (cm)
For a clear circular aperture in the small-angle regime, Rayleigh angular separation ≈ 1.22 × wavelength/diameter, using matching length units. This calculator limits the approximation to θ ≤ 0.1 rad. The inverse modes solve the same threshold equation. Optional target separation ≈ distance × θ.
Diffraction Limit Definition
A diffraction limit describes an ideal resolution criterion. Telescope mode reports angular Rayleigh separation; microscope mode reports an object-space lateral Abbe limit d = λ/(2NA), with 0.61λ/NA as a Rayleigh comparison. The model requires NA ≤ immersion refractive index n and appropriate illumination. Aberrations, seeing, contrast and alignment can make actual resolution poorer. For periodic Abbe detail with period d, spatial cutoff is 1/d; this is not a camera sampling recommendation.
Why is diffraction limit important?
A diffraction limit is important because it defines the limit of the strength of a telescope. Decreasing the diffraction limit allows a telescope to distinguish between objects that are very far away, but relatively close together.
What is a diffraction-limited aperture?
A diffraction-limited aperture is an aperture whose performance is capped by the size of the aperture. That is, it has reached its maximum resolution for the size that it currently is.
How to calculate diffraction limit?
To calculate the diffraction limit, first, determine the wavelength of the light entering the telescope. Next, determine the diameter of the lens. Finally, calculate the diffraction limit using the formula DL = 1.22 * w / d.
