Sensor to object distance

With magnification β and focal length f the sensor to object distance is

{!{!{OO'=(\beta+\frac{1}{\beta}+2)\cdot f+HH'}!}!}

For magnifications β ≤ 1/10 this can be approximated to

{!{!{OO'\approx(\frac{1}{\beta}+2)\cdot f+HH'}!}!}

The value OO’ provides an indication of the required space (the length of camera housing attached to the sensor, without taking into account the space required for connectors and cables).

Example 1

Video lens B1614A

Focal length f = 16 mm

Principal point distance HH’ = 3.85 mm

Length of ROI L = 290 mm

Sensor length S = 13.3 mm:

Sensor to object distance OO’ = (L/S + 2)f + HH’= (290/13.3 + 2)16 mm + 3.85 mm= 384.7 mm (as an approximation)

Example 2

Rodagon 4.0/80

Focal length f = 81 mm

Principal point distance HH’ = -2.5 mm

Magnification β = 1/6:

Sensor to object distance OO’ = (1/β+β+2)f + HH’= (1/6+6+2)81mm - 2.5 mm= 658.7 mm

Lens parameters scheme

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)