Focal length

If there is a space restriction, the maximum focal length is calculated from the sensor to object distance OO’ by

{!{!{f=\frac{OO'}{\beta+\frac{1}{\beta}+2}}!}!}
or for a magnification β < 0.1

{!{!{f\approx\frac{OO'}{\frac{1}{\beta}+2}}!}!}

Example

Magnification     β = 0.099

Sensor to object distance       OO’ = 605 mm

Focal length      f = 605 mm/ (10.1 + 2) = 50 mm

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)