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High Quality Content by WIKIPEDIA articles! Ray transfer matrix analysis (also known as ABCD matrix analysis) is a type of ray tracing technique used in the design of some optical systems, particularly lasers. It involves the construction of a ray transfer matrix which describes the optical system; tracing of a light path through the system can then be performed by multiplying this matrix with a vector representing the light ray. The technique uses the paraxial approximation of ray optics, i.e., all rays are assumed to be at a small angle ( ) and a small distance (x) relative to the optical axis of the system. The approximation is valid as long as sin( ) (where is measured in radians).