Diffraction Limit

Diffraction Limit

The resolution of a lens is limited by diffraction and calculated using the effective F-number K’. The best possible resolution is achieved by closing the lens aperture by 1 to 2 steps, so that the lens resolution approaches the diffraction limit. Adjacent image elements become distinguishable when their distance is:

{!{!{∆y'≥2.4\cdot λ\cdot K'}!}!}

With a optical wavelength λ for visible radiation of 550 nm this leads to e.g.:

Effective F-number K’Diffraction limit Resolution* ∆y’min [μm]
22.6
2.83.7
45.3
5.67.4
810.8
1114.5
1621.1
2229
  
*at wavelength λ= 550 nm  

Example

Effective F-number   K’ = 8
Wavelength    λ = 550 nm
Diffraction Limit   ∆y’min = 10.6 μm

Imaging Parameters

Schematic depiction of the imaging system and definition of variables used.

f = Lens focal length (mm)
S = Sensor length (mm)
L = Length of Region of Interest (ROI) of object (mm)
a = Object range (mm)
a’ = Image distance: Distance from sensor to HH’ (mm)
β Magnification
w = Field angle
OO’ = Distance from sensor to measured zone (mm)
s’A = Flange focal length (mm)
∆s’  = Lens extension (mm)
LT = Tube length 
A = Working distance (mm)
HH’ = Principal point distance (mm) (can lengthen or shorten OO’)
s’K = Camera flange length consisting of focus adapter series FA22 and extension rings series ZR (mm)
LO = Lens length (mm)