There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Vorlesungen uber theoretische Physik Von Prof. Arnold Sommerfeld. Band 1: Mechanik. Vierte, neubearbeitete Auflage. Pp. xii + 276. 18 D. marks. Band 2: Mechanik der deformierbaren Medien. Pp. xv + 376 + 4 plates. 18 D. marks. Band 3: Elektrodynamik. Pp. xvi + 368. 18 D. marks. Band 6: Partielle Differentialgleichungen der Physik. Pp. xiii + 332. 18 D. marks. (Wiesbaden: Dieterich'sche Verlagsbuchhandlung, 1947–1949.)

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Lectures on Theoretical Physics

We present a polarization-sensitive optical coherence-domain reflectometer capable of characterizing the phase retardation between orthogonal linear polarization modes at each reflection point in a birefringent sample. The device is insensitive to the rotation of the sample in the plane perpendicular to ranging. Phase measurement accuracy is ±0.86°, but the reflectometer can distinguish local variations in birefringence as small as 0.05° with a distance resolution of 10.8 μm and a dynamic range of 90 dB. Birefringence-sensitive ranging in a wave plate, an electro-optic modulator, and a calf coronary artery is demonstrated.

Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging

This tutorial-review introduces the fundamentals of polarized light interaction with biological tissues and presents some of the recent key polarization optical methods that have made possible the quantitative studies essential for biomedical diagnostics. Tissue structures and the corresponding models showing linear and circular birefringence, dichroism, and chirality are analyzed. As the basis for a quantitative description of the interaction of polarized light with tissues, the theory of polarization transfer in a random medium is used. This theory employs the modified transfer equation for Stokes parameters to predict the polarization properties of single- and multiple-scattered optical fields. The near-order of scatterers in tissues is accounted for to provide an adequate description of tissue polarization properties. Biomedical diagnostic techniques based on polarized light detection, including polarization imaging and spectroscopy, amplitude and intensity light scattering matrix measurements, and polarization-sensitive optical coherence tomography are described. Examples of biomedical applications of these techniques for early diagnostics of cataracts, detection of precancer, and prediction of skin disease are presented. The substantial reduction of light scattering multiplicity at tissue optical clearing that leads to a lesser influence of scattering on the measured intrinsic polarization properties of the tissue and allows for more precise quantification of these properties is demonstrated.

https://www.spiedigitallibrary.org/journals/journal-of-biomedical-optics/volume-21/issue-7/071114/Polarized-light-interaction-with-tissues/10.1117/1.JBO.21.7.071114.pdf

Polarized light interaction with tissues

An eye tracker having a waveguide for propagating illumination light towards an eye and propagating image light reflected from at least one surface of an eye, a light source optically coupled to the waveguide, and a detector optically coupled to the waveguide. Disposed in the waveguide is at least one grating lamina for deflecting the illumination light towards the eye along a first waveguide path and deflecting the image light towards the detector along a second waveguide path.

Apparatus for eye tracking

The correlation structure of 2-D Stokes vector parameters of physiologically normal and pathologicaly changed biotissues is investigated. The totality of diagnostically urgent interconnections between biotissue physiological state and statistical moments of 2-D Stokes vector parameters is found.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

2-D tomography of biotissue images in pre-clinic diagnostics of their pre-cancer states

We analyze and experimentally test the concept of laser polarization biotissue probing. The methods of increasing the SNR in coherent images of the optically anisotropic architectonics of the morphological biotissue structure are considered. The possibilities of polarization selection and contrasting of such images screened by other biotissues are examined. The influence of the depolarization degree of the scattered background on the SNR is investigated. The possibilities of polarization correction of the probing beam for contrasting biotissue images are analyzed.

https://www.spiedigitallibrary.org/journals/Journal-of-Biomedical-Optics/volume-10/issue-01/014010/Polarization-visualization-and-selection-of-biotissue-image-two-layer-scattering/10.1117/1.1854674.pdf

Polarization visualization and selection of biotissue image two-layer scattering medium

A method for polarization filtering, correlation processing, and wavelet analysis of coherent images of physiologically normal and necrotically changed (myocardium infarct) muscle tissue is presented. A technique for early optical diagnosis of the appearance of these biological tissues and the course of their degenerative-dystrophic changes is proposed.

Wavelet analysis of two-dimensional birefringence images of architectonics in biotissues for diagnosing pathological changes.

The dynamics of the changes in the statistical polarization structure of coherent images of biological tissues are studied for the visualization process of their optically anisotropic (collagen) structure.

Polarization-based visualization of multifractal structures for the diagnostics of pathological changes in biological tissues

The transformation of the polarization and correlation structure of low-intensity laser radiation by skin is considered. The method of matrix modeling of optical properties of skin epidermis and derma is proposed. This approach is employed to analyze the mechanisms behind the transformation of the polarization state of scattered laser radiation field and the formation of an ensemble of coherent biospeckles. The technique for the polarization diagnostics of the structure of the collagen network in skin derma is proposed.

Alexander G. Ushenko

Papers

2-D tomography of biotissue images in pre-clinic diagnostics of their pre-cancer states

Polarization visualization and selection of biotissue image two-layer scattering medium

Wavelet analysis of two-dimensional birefringence images of architectonics in biotissues for diagnosing pathological changes.

Polarization-based visualization of multifractal structures for the diagnostics of pathological changes in biological tissues

The vector structure of laser biospeckle fields and polarization diagnostics of collagen skin structures