Edge intensity

The edge intensity [in %] of a line scan signal is determined by the illumination and the field angle w. Even for homogeneous illumination, the signal amplitude decreases towards the ends of the line

{!{!{{\rm Intensity}_{edge}=100\cdot \cos^4w}!}!}

Rule of thumb: The focal length should be equal to or greater than the sensor length. 

Edge intensity

In these examples, the edge intensities are 90% and 73% of the center intensity, respectively.

Example

Edge intensities calculated for two different fieldangles using the same sensor length S = 28.7 and magnification β = 0.25:
a) Focal length      f = 50 mm 
Field angle    w = 13°
Edge intensity = 90%
b) Focal length      f = 28 mm 
Field angle    w = 22.3° 
Edge intensity = 73%

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)