Muellerkalkyl

Muellerkalkyl, often referred to in English as Mueller calculus, is a mathematical framework used in polarization optics to describe how optical elements and systems transform the polarization state of light. The central object of the formalism is the Mueller matrix, a real 4x4 matrix that operates on the Stokes vector of light.

A light beam is described by a Stokes vector S = [I, Q, U, V]^T, where I is the total intensity, Q and U describe linear polarization, and V describes circular polarization. The effect of an optical element or system with Mueller matrix M is given by S' = M S.

Mueller matrices can encode diattenuation, retardance, and depolarization. Diattenuation refers to differential attenuation of orthogonal polarization states; retardance to phase shifts; depolarization to loss of polarization purity. Typical elements like ideal polarizers, waveplates, and rotators have characteristic simple Mueller matrices. Real components may depolarize light, giving non-ideal M.

Mueller calculus extends Jones calculus to partially polarized light. When the light is fully polarized, the Jones vector formalism and Mueller calculus are related; the 4x4 Mueller matrix reduces to a corresponding Jones matrix for certain ideal cases.

Applications include ellipsometry, optical metrology, biomedical optics, remote sensing, and photography/color science. It is widely used to model and analyze polarization-dependent measurements and to calibrate instruments.

Determining M experimentally involves illuminating with known input polarization states and measuring outputs; the matrix is then reconstructed by solving a system of linear equations.

Assumptions include linear, stationary, spatially uniform media; nonlinearity or time variation requires extended formalisms.

Muellerkalkyl is a standard tool in optics and instrumentation; its Swedish usage is common in physics and engineering literature.