Analytic inversion of the Mueller-Jones polarization matrices for homogeneous media

Abstract

In this Letter we present the equations to calculate the six independent polarization effects of an arbitrary normalized Mueller-Jones matrix corresponding to homogenous media. A comparison between this method and other inversion procedures is discussed, and the application of the analytic inversion to experimental Mueller matrices is illustrated.

Mueller matrix microscope with a dual continuous rotating compensator setup and digital demodulation

“…This is most likely due to the presence of some oriented dye molecule in the scales. Figure 7 shows the linear dichroism in radians as calculated from the MM following the method indicated in [7]. The scales in the wing margin are highly contrasted due to their high linear dichroism and some slight linear dichroism is also appreciable in the wing veins.…”

“…Approaches based on the comparison of the interference polarization colors with the Michel-Levy interference color chart, or on getting the maximum darkness when using a Berek compensator, are only semi-quantitative since, in most configurations, they ultimately rely on the visual and technical skills of the microscope user. Mueller matrix (MM) microscopy is the natural generalization of polarized light microscopy because it brings quantitative results and allows the simultaneous determination of linear birefringence, linear dichroism, circular birefringence, circular dichroism, and depolarization [6][7][8][9][10][11].…”

Conversion of a polarization microscope into a Mueller matrix microscope. Application to the measurement of textile fibers

“…The images are continuously captured by a CMOS camera while two rotating compensators modulate the polarization of light [9,10]. The images are frequency analyzed at the pixel level by digital demodulation as the intensity is detected [3].…”

“…As the Mueller matrix provides a complete quantitative characterization of the sample, linear birefringence and linear dichroism effects can be well distinguished from the usually much weaker circular birefringence and circular dichroism effects. The algorithm that we use to recover all these optical effects from the Mueller matrix is based on an analytic inversion [9].…”

“…A map of the linear birefringence in this polyamide fiber is provided in Fig. 3, which is calculated from the Mueller Matrix [9]. However, for these types of fibers the linear birefringence tends to be quite large, sometimes crossing various orders of birefringence.…”