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Limitations on Resolution and Contrast: The Airy Disk

This is Section 2.5 of the Imaging Resource Guide

When light passes through any size aperture (every lens has a finite aperture), diffraction occurs. The resulting diffraction pattern, a bright region in the center together with a series of concentric rings of decreasing intensity around it, is called the Airy Disk (see Figure 1).

The diameter of this pattern is related to the wavelength (λ) of the illuminating light and the size of the circular aperture, which is important since the Airy Disk is the smallest point to which a beam of light can be focused. As focused Airy patterns from different details on the object come close together, they begin to overlap (refer to our application note Contrast for more information). When the overlapping patterns create enough constructive interference to reduce contrast, they eventually become indistinguishable from each other. Figure 1 shows the difference in spot sizes between a lens set at f/2.8 and a lens set at f/8.

As pixels continue to reduce in size, this effect becomes more of an issue and eventually is very difficult to overcome. The Airy Disk, or minimum spot size can be calculated using the f/# and wavelength in μm:

(1)$$\text{Minimum Spot Size (Airy Disk Diameter) [μm]} = 2.44 \cdot \lambda \left[ \text{μm} \right] \cdot f/ \#$$
Figure 1: Diffraction Increases as the Imaging Lens Iris is Closed (f/# Increases)

Table 1 shows the calculated Airy Disk diameter for different f/#s using green light (520nm or 0.520μm). The smallest achievable spot size can quickly exceed the size of small pixels. This leads to difficulties when trying to yield the full resolution capacities of a sensor with any usable level of contrast. Additionally, this does not take into account any lens design limitations and manufacturing errors associated with the fabrication of lens elements and optical assemblies, which can lead to reductions in the ability to produce the smallest physically achievable spot and thus reduced levels of resolution and contrast.

f/#Airy Disk Diameter (μm) at a Wavelength of 520nm
1.4 1.78
2 2.54
2.8 3.55
4 5.08
5.6 7.11
8 10.15
11 13.96
16 20.30

Table 1: The minimum spot size, or Airy Disk, increases with f/# and can quickly surpass pixel size.

Note: This is all theoretical and is the starting point for limitations in an optical system.

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