System Matrix, Hecht FormFor systems of multiple thick lenses, it is sometimes useful to represent the system by a system matrix. The matrix is built up by multiplying the refraction matrices and translation matrices. This is the form of the system matrix used by Hecht. An alternate form is used by MeyerArendt.

Index Lens concepts Thick lens concepts References MeyerArendt Hecht  

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Refraction and Translation MatricesHecht form

Index Lens concepts Reference MeyerArendt  

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Refraction MatrixThe use of vergence to describe the refraction at an interface can be used as a starting point for developing a matrix to perform the refraction. The vergence relationship is and for small angles (paraxial approximation): Arbitrarily treating the numerator and denominator of the vergence fraction as the elements of a column vector, we can construct the matrix relationship for refraction. 
Index Lens concepts Reference MeyerArendt  

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Translation MatrixThe geometry of translation across the thickness of a lens can be put in matrix form for rays satisfying the paraxial approximation. 
Index Lens concepts Reference MeyerArendt  

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