# Sensor to object distance

## 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 ### 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)