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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.

ß= B / G

calculation of reproduction scale for telecentric lens / macro optics

Calculating the imaging scale ß using sensor size and object size

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


Sensor size :
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´ / ( g - f´)

Abbildungsmaßstab beta

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


Focal length:
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.

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