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ABCD Matrix Calculator



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  1. Purpose:

    1. ABCD Matrix: To calculate the ABCD matrix that is used in describing an element's or a series of elements' effect on a light ray.
    2. Note: if you want to learn more about how ABCD matrices work please visit the ABCD Matrix Tutorial page or click here
  2. Instructions:

    1. 1. Enter the transverse offset and the angle.
    2. 2. Add however many elements you need for your system, this calculator provides seven elements max that you can use in your system.
    3. 3. Enter the appropriate input depending on your element type.
    4. 4. Press the calculate button and your output will be displayed.
  3. References for ABCD Matrices for Simple Optical Components

    1. If you'd like to see an example system using these elements go to the ABCD Matrix Tutorial Page





Transverse Offset ( r ): mm

Offset Angle ( θ ):


Element Type Distance Initial 'N' Final 'N' Radius Focal length Resulting ABCD Matrix
Element 1: mm mm mm





Output ( r' ): mm

output angle ( θ' ):


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