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# Lens calculator - Calculating the imaging scale ß (magnification)

Usually no focal length is indicated for telecentric measuring lenses or macro-lenses, which would serve to calculate and select the optics. These lens types are characterised by the imaging scale β (beta). It can easily be calculated.

using sensor size
& object size
using focal length
and working distance

## Calculating the imaging scale ß using sensor size and object size

ß= y´ / y

Note: Even when using the drop-down lists own values can be entered. Please use the first entry "user def."!

 Sensor size : User def. (mm) 1/4" 3.2 mm 1/3" 4.8 mm 1/2.5" 5.7 mm 1/2" 6.4 mm 1/1.8" 7.2 mm 2/3" 8.8mm 10.5 mm 1" 12.8 mm 1.2" 14.2 mm 15.3 mm 4/3 17.9 mm APS/C 23.7 mm KB 36.0 mm line .5K 14µm line 1K 10µm line 1K 14µm line 2K 10µm line 2K 14µm line 4K 7µm line 4K 10µm line 6K 7µm line 8K 7µm line 12K 5µm Object size/ field of view in mm: Calculated reproduction scale ß:

Attention: Calculated imaging scales beyond 100 are declared unrealistic (an object field which is 100x smaller than the sensor surface is rather unlikely in industrial machine vision). Extreme values are nevertheless displayed.

## Calculating the imaging scale ß using focal length and object size

Also for entocentric lenses it is possible to calculate the magnification or imaging scale. this value changes for any working distance, which leads to problems in measurement applications.

(The estimation of this measurement error can be calculated here: "Calculating measurement errors caused by height variations".)

ß = f´ / ( a - f´)

Note: Even with drop-down lists own values ​​can be entered. Please select the list entry "User def."!

 Focal length: Userdef. (mm) 2.8 3.2 4.8 6 8 9 12 16 17 23 25 35 50 60 75 85 100 125 150 Working distance in mm: Calculated reproduction scale ß:

Attention: Calculated imaging scales beyond 1 are declared unrealistic. Working distance must be greater 2* focal length.

Further details on optical calculations can be found in chapter Optical basics.