Imaging Equation

Object range and image range are related by the imaging focal length.The formulae on lens extension, tube length, sensor to object distance OO’ and focal length are derived from the imaging equation:

{!{!{\frac{1}{a}+\frac{1}{a'}=\frac{1}{f}}!}!}

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)