ABCD Matrix Calculator

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1. Purpose:

   2. 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.
   3. Note: if you want to learn more about how ABCD matrices work please visit the ABCD Matrix Tutorial page or click here

2. Instructions:

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

3. References for ABCD Matrices for Simple Optical Components

   2. 
   3. If you'd like to see an example system using these elements go to the ABCD Matrix Tutorial Page

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Transverse Offset ( r ): mm

Offset Angle ( θ ): °

Element Type	Distance	Initial 'N'	Final 'N'	Radius	Focal length	Resulting ABCD Matrix
Element 1: N/A Free Space or medium of constant 'N' Refraction at a flat Interace Refraction at a curved interface Reflection from a flat mirror Reflectin from a curved mirror Thin Lens	mm			mm	mm
Element 2: N/A Free Space or medium of constant 'N' Refraction at a flat Interace Refraction at a curved interface Reflection from a flat mirror Reflectin from a curved mirror Thin Lens	mm			mm	mm
Element 3: N/A Free Space or medium of constant 'N' Refraction at a flat Interace Refraction at a curved interface Reflection from a flat mirror Reflectin from a curved mirror Thin Lens	mm			mm	mm
Element 4: N/A Free Space or medium of constant 'N' Refraction at a flat Interace Refraction at a curved interface Reflection from a flat mirror Reflectin from a curved mirror Thin Lens	mm			mm	mm
Element 5: N/A Free Space or medium of constant 'N' Refraction at a flat Interace Refraction at a curved interface Reflection from a flat mirror Reflectin from a curved mirror Thin Lens	mm			mm	mm
Element 6: N/A Free Space or medium of constant 'N' Refraction at a flat Interace Refraction at a curved interface Reflection from a flat mirror Reflectin from a curved mirror Thin Lens	mm			mm	mm
Element 7: N/A Free Space or medium of constant 'N' Refraction at a flat Interace Refraction at a curved interface Reflection from a flat mirror Reflectin from a curved mirror Thin Lens	mm			mm	mm

Output ( r' ): mm

output angle ( θ' ): °