# Diffraction Limit

This is Section 3.1 of the Imaging Resource Guide

Every lens has an absolute upper performance limit dictated by the laws of physics. This limitation is controlled by the working f/# of the lens and the wavelength(s) of light that pass through the lens. Known as the Diffraction Limit, this limitation is given in line pairs/mm and determines the theoretical maximum resolving power of the lens. Even a perfect lens that is not limited by design will be diffraction limited. This limit is the point where two Airy patterns (Limitations on Resolution and Contrast: The Airy Disk) are no longer distinguishable from each other. To calculate the diffraction limit, a simple formula that relates it to the f/# of the lens and the wavelength of light can be used. Learn more about f/# in f/# (Lens Iris/Aperture Setting).

(1)$$\text{Diffraction Limit} \left[ \tfrac{\text{lp}}{\text{mm}} \right] = \frac{1000 \tfrac{ \large{\unicode[arial]{x03BC}} \text{m}}{\text{mm}}}{\left( f/ \# \right) \times \text{Wavelength} \left[ \large{\unicode[arial]{x03BC}} \text{m} \right]}$$

After the diffraction limit is reached, the lens becomes incapable of resolving greater frequencies. The diffraction limit detailed in Table 1 shows contrast at 0% for given frequencies. These numbers may appear rather high, but are strictly theoretical – a number of other practical factors must also be considered. First, as a general rule, imaging sensors cannot reproduce information at or near 0% contrast. Due to inherent noise, contrast generally needs to be above 10% to be reliably detected on standard imaging sensors. To avoid imaging complications, it is recommended to target 20% contrast or higher at the application’s critical lp/mm resolution. Additionally, lens aberrations and variations associated with manufacturing tolerances also reduce performance. Modulation Transfer Function (MTF) curves are used to determine whether a lens will effectively utilize a sensor's capabilities and fulfill the desired application’s requirements.

f/#0% Contrast Limit (lp/mm) @0.520μm
1.4 1374
2 962
2.8 687
4 481
5.6 343
8 240
11 175
16 120

Table 1: The diffraction limit calculated at different f/#s for 0.520μm light (green light).

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