Advanced Mueller Matrix Imaging Ellipsometry: Silicon Strain Imaging, Visualisation of Collagen Fibre 3-D Orientation & Development of a Mueller Matrix Imaging Microscope

A custom built near-infra-red (NIR) Mueller matrix imaging ellipsometer (MMI) based on ferroelectric liquid crystals (FLCs) and waveplates (WPs) is described in detail. The instrument is used to perform strain-induced birefringence imaging of crystalline silicon, and visualise the 3-D orientation of collagen fibres expressing linear retardance.The development of a spectroscopic Mueller matrix imaging microscope ellipsometer (µMMI) is presented. Preliminary verification indicate that the constructed µMMI works as expected.The theory behind Mueller matrix ellipsometry is outlined, including the description of polarised light, and its representation by the Mueller-Stokes formalism. Detailed analysis of the Mueller matrix, encompassing both the forward polar and the differential decomposition, is presented. These techniques are used in the study of both organic and in-organic samples. Photoelastic theory is briefly discussed in order to explain the phenomena of birefringence in strained silicon crystals, and a simple model was developed in order to estimate the maximum shear-stress. Vertical cross-sections of bi-crystal silicon separated by near-coincident site lattice grain boundaries $\Sigma9$ and $\Sigma27a$ ingots were studied using the custom built near infra-red MMI at 1300 nm. The obtained images were decomposed using the forward polar decomposition. The resulting optical properties were used to map the internal shear-stress of the samples. The shear-stress was found to be in the range of 2.5 MPa to 5 MPa. Further studies are proposed in order to verify this technique.Chicken tendon is imaged at 940 nm with different incidence angles (0 deg and +/-30 deg) using the custom built MMI. The differential decomposed Mueller matrix measurements were used to calculate the 3-D directional orientation of the collagen fibres. Validation of the obtained 3-D directional orientation was done by comparing the results with second-harmonic generation (SHG) images. The two methods were found to be in good agreement.Development of an optimal broadband spectroscopic Mueller matrix imaging system to work in the range 550nm to 1150 nm is described. A design similar to the earlier presented MMI based on FLCs and WPs was chosen. The concept of genetic algorithms is introduced and utilised in order to improve on the design. Realisation of the instrument is documented from the choice of components, characterisation, re-optimisation of the design, and lastly, building and verifying the instrument

Mueller matrix three-dimensional directional imaging of collagen fibers

A method for measuring three-dimensional (3-D) direction images of collagen fibers in biological tissue is presented. Images of the 3-D directions are derived from the measured transmission Mueller matrix images (MMIs), acquired at different incidence angles, by taking advantage of the form birefringence of the collagen fibers. The MMIs are decomposed using the recently developed differential decomposition, which is more suited to biological tissue samples than the common polar decomposition method. Validation of the 3-D direction images was performed by comparing them with images from second-harmonic generation microscopy. The comparison found a good agreement between the two methods. It is envisaged that 3-D directional imaging could become a useful tool for understanding the collagen framework for fibers smaller than the diffraction limit