Diffraction-Limited Spot
Smallest resolvable spot size set by diffraction at aperture N.
Formula
Variables
Example
λ=0.55 µm, N=16: d ≈ 21.5 µm
How it works
This formula gives the diameter of the central bright spot formed by a circular aperture when light is limited by diffraction rather than by lens quality or sensor resolution. The factor 2.44 comes from the first dark ring of the Airy pattern: it is 2 × 1.22, where 1.22 is the angular position of the first minimum for a circular opening. Since the f-number N equals focal length divided by aperture diameter, the spot size grows linearly with both wavelength and f-number, so longer wavelengths and smaller apertures produce larger blur discs.
When to use it
Use this when estimating the diffraction floor of an optical system, such as a camera lens, microscope objective, telescope, or any imaging setup where stopping down may begin to soften fine detail. It is especially useful for comparing diffraction blur to pixel size, sampling, or desired resolution.
Worked example, step by step
Given: λ = 0.48 µm, N = 11 Step 1: Write the formula d = 2.44 λ N Step 2: Substitute the values d = 2.44 × 0.48 × 11 Step 3: Multiply d = 2.44 × 5.28 d = 12.8832 µm Step 4: Round appropriately d ≈ 12.9 µm Final answer: the diffraction-limited Airy disk diameter is about 12.9 µm.
Common mistakes to avoid
- Using the sensor pixel pitch instead of the wavelength in the formula
- Forgetting that N is the f-number, not the numerical aperture
- Mixing up radius and diameter of the Airy disk, which changes the result by a factor of 2
Did You Know?
Stopping down too far (f/22+) actually softens photos because diffraction blurs fine detail.
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