Depth of focus

The depth of focus 2z is calculated from
{!{!{2z=2\cdot ∆y'\cdot K\cdot \frac{1}{\beta}(1+\frac{1}{\beta})}!}!}

using the F-number K, the pixel pitch (mm) ∆y’, and the magnification β.

Depth of focus 2z

Line scan sensor with pixel pitch ∆y’ focal length f and 
F-number K.
The depth of focus is defined as 2z.

Example

Pixel pitch  ∆y’ = 0.014 mm

1/magnification 1/β = 10 

 F-number     K = 4 

Depth of focus   2z = 2·0.014mm·4·10·(1+10) = 12.3mm

F-number KDepth of Focus 2z (mm)*Relative signal amplitude
26.216
2.88.68
412.34
5.617.22
824.61
1133.91/2
2267.81/4
3298.6 1/8
* for ∆y' = 0.014 mm and β = 1/10    

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)