A layer of biological tissue is illuminated at 800 nm (a wavelength commonly used for…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Polarisation and anisotropic media · Polarisation and anisotropic media

What an Instrument Can See, Ch Polarisation as a statistical object: coherency and Mueller matrices

Problem

A layer of biological tissue is illuminated at 800 nm (a wavelength commonly used for near-infrared tissue imaging) and its polarimetric response is measured to be diagonal: MM=diag⁡(1, 0.85, 0.55, 0.55).\mathbf{M}_{\mathrm{M}} = \operatorname{diag}(1,\,0.85,\,0.55,\,0.55). ((a)) State the relation between the coherency matrix Jcoh\mathbf{J}_{\mathrm{coh}} before and after a single optical element with Jones matrix J\mathbf{J}, and show how its determinant transforms. Combine this with the fact that det⁡Jcoh=0\det\mathbf{J}_{\mathrm{coh}}=0 exactly for a fully polarised beam (P=1P=1) to state a necessary condition that every Mueller matrix built from a single Jones matrix must satisfy when fed a fully polarised input. ((b)) Test MM\mathbf{M}_{\mathrm{M}} above against this condition, using horizontal linear light, Stokes vector (S0,S1,S2,S3)=(1,1,0,0)(S_0,S_1,S_2,S_3)=(1,1,0,0), as the input, and state whether MM\mathbf{M}_{\mathrm{M}} can be the Mueller matrix of any single deterministic optical element.

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