P OLARIZATION MICROSCOPY : BIOMEDICAL IMAGING AND DIAGNOSTICS Yuriy - PowerPoint PPT Presentation

Winter College on Optics: Advanced Optical Techniques for Bio-imaging P OLARIZATION MICROSCOPY : BIOMEDICAL IMAGING AND DIAGNOSTICS Yuriy A. Ushenko Chernivtsi National University Ukraine 1 Date & time: (Lecture) February 17, 2017 (Friday), 15.30 (Experiment) February 23 , 2017 ( Thursday), 14.00 Room: Leonardo Building - Budinich Lecture Hall

L IST OF L ECTURES � Introduction. � Lecture 1. Basic concepts. Polarization. Stokes vector. Mueller matrix. Basics of laser polarimetry. � Lecture 2. Basics of model description of structure and optical anisotropy of biological tissues. � Lecture 3. Methods and resources of analysis and processing of biological tissues polarization- inhomogeneous images. � Lecture 4. Principles and methods of polarization and Mueller-matrix mapping. 2

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I NTRODUCTION � Optical methods of diagnostics of biological objects and visualization of their structures occupy a leading position thanks to their high information content, multi-functional capabilities (photometric, spectral, and polarization correlation). � It should be stated that new scientific direction - optics of biological tissues and fluids was finally formed and rapidly developing. The main areas of basic research are the results of theoretical and experimental studies of photon transport in biological tissues and fluids. � A separate direction in optics of biological tissues formed polarimetric investigations. Analysis of polarization characteristics of the scattered radiation allows to obtain qualitatively new results on morphological and physiological state of biological tissues. � A new step in the development of methods of optical diagnostics of biological tissues was successful unification of polarimetric and fluorescent techniques. 7

L ECTURE 1. B ASIC CONCEPTS . P OLARIZATION . S TOKES VECTOR . M UELLER MATRIX . B ASICS OF LASER POLARIMETRY . Light as transverse electromagnetic wave The electric and magnetic fields of an electromagnetic wave are perpendicular to each other and transverse to the direction of propagation. An electromagnetic wave is propagating along z-axis. Its electric field is aligned to the x-axis and magnetic field along the y-axis. � � � � E ( z, t ) E cos( kz - t) x x 0x � � � � � � E ( z, t ) E cos( kz - t ) y Parameters: y 0y 1. Amplitude ω = 2πν – angular frequency 2. Frequency 8 3. Phase k = 2π/λ – wave number 4. Polarization � – phase (initial)

L ECTURE 1. B ASIC CONCEPTS . P OLARIZATION . S TOKES VECTOR . M UELLER MATRIX . B ASICS OF LASER POLARIMETRY . Polarization of electromagnetic wave Polarization is a important property of electromagnetic waves. In communications, completely polarized waves are used. In radio astronomy un- polarized components exist. The techniques to analyze polarization known as polarimetry. The complete polarization types of electromagnetic waves are: ( i) Linear Polarization. ( ii) Circular Polarization. ( iii) Elliptical Polarization. Electromagnetic waves from of radio astronomical sources may posses: ( i) Random polarization (also known as un-polarized waves). ( ii) Partial polarization (completely polarized + un-polarized) 9

L ECTURE 1. B ASIC CONCEPTS . P OLARIZATION . S TOKES VECTOR . M UELLER MATRIX . B ASICS OF LASER POLARIMETRY . Polarization of electromagnetic wave. Graphical representation. Polarization ellipse � � Some algebra 2 2 � � � � � � E E E ( z, t ) E cos( kz - t) x E E � � x 0x � � � y � y � � � � � 2 x 2 x cos sin � � � � � � � � � � E E E E E ( z, t ) E cos( kz - t ) y � � � � y 0y 0x 0y 0x 0y equation of an ellipse An ellipse can be characterized by : 1. size of minor axis 2. size of major axis 3. orientation (tilt angle, azimuth) 4. Axial ratio (ellipticity) 5. sense (CW, CCW) Axial ratio - is a ratio of length of minor to the length of major axis. 10 OB � � � arctan( OA ) - ellipticity (angle)

L ECTURE 1. B ASIC CONCEPTS . P OLARIZATION . S TOKES VECTOR . M UELLER MATRIX . B ASICS OF LASER POLARIMETRY . Polarization of electromagnetic wave. Types of polarization. Linear polarization Any form of complete polarization resulting from a coherent source can be analyzed using polarization ellipse !!! � � � � E ( z, t ) E cos( kz - t) x x 0x � � 0 0 � � � � � � E ( z, t ) E cos( kz - t ) y y 0y If there is no amplitude in y (E 0y = 0), there is only one component, in x (vertical). If there is no amplitude in x (E 0x = 0), there is � � 0 90 only one component, in y (horizontal). � � � 0 ; Phase difference ( )) and E 0x = E 0y , � � � 0 45 then E x = E y 11

L ECTURE 1. B ASIC CONCEPTS . P OLARIZATION . S TOKES VECTOR . M UELLER MATRIX . B ASICS OF LASER POLARIMETRY . Polarization of electromagnetic wave. Types of polarization. Circular polarization � � � � � 0 If the phase difference is and E 0x = E 0y 90 � � E ( z, t ) E cos( kz - t) x x 0x then: E x / E 0x = cos � , E y / E 0y = sin � and we get the � � � � � � E ( z, t ) E cos( kz - t ) y equation of a circle with CW or CCW rotation and y 0y wave is said to be circularly polarized : 2 2 � � � � E E � � � � � y � � � � � 2 2 x cos sin 1 � � � � E E � � � � 0x 0y 12

L ECTURE 1. B ASIC CONCEPTS . P OLARIZATION . S TOKES VECTOR . M UELLER MATRIX . B ASICS OF LASER POLARIMETRY . Polarization of electromagnetic wave. Types of polarization. Elliptical polarization. If the magnitudes of E x and E y are not equal, and there exists a phase difference between the two, the tip of the electric field vector describes an ellipse and wave is said to be elliptically polarized. Linear + circular polarization = elliptical polarization Any wave may be written as a superposition of the two polarizations 13 ANIMATIONS

L ECTURE 1. B ASIC CONCEPTS . P OLARIZATION . S TOKES VECTOR . M UELLER MATRIX . B ASICS OF LASER POLARIMETRY . Stokes parameters 1852 : Sir George Gabriel Stokes took a very different approach and discovered that polarization can be described in terms of observables using an experimental definition. The polarization ellipse is only valid at a given instant of time (function of time)!!! 2 2 � � � � E E E E � � � � � y � y � � � � � 2 x 2 x cos sin � � � � E E E E � � � � 0x 0y 0x 0y To get the Stokes parameters, do a time average (integral over time) and a little bit of algebra... � � � � � � � � 2 2 2 2 � � � � � � � 2 2 2 2 E E E E 2 E E cos 2 E E sin 0x 0y 0x 0y 0x 0y 0x 0y � � � 2 2 I E E S 0 0x 0y � � � 2 2 Q E E S The 4 Stokes parameters 1 0x 0y are: � � � U 2 E E cos S 14 2 0x 0y � � � V 2 E E sin S 3 0x 0y

L ECTURE 1. B ASIC CONCEPTS . P OLARIZATION . S TOKES VECTOR . M UELLER MATRIX . B ASICS OF LASER POLARIMETRY . Stokes parameters described in geometrical terms. Stokes vector � � � � I 1 � � � � � � Q cos 2 cos 2 � � � � � � � � � � � U cos 2 sin 2 � � � � � � � � � V sin 2 � � � � The Stokes parameters can be arranged in a Stokes vector: � � � � � 2 2 � � I E E intensity � � � � 0x 0y � � � � � � � � 2 2 � � � � Q E E I 0 I 90 � � � � � 0x 0y � � � � � � � � � � � � � � � U 2 E E cos I 45 I 135 � � � � � � 0x 0y � � � � � � � � � � � � V 2 E E sin I RCP I LCP � � � � � � 0x 0y � � � Q 0, U 0, V 0 • Linear polarization 15 � � � Q 0, U 0, V 0 • Circular polarization • Fully polarized light 2 � 2 � 2 � 2 I Q U V

L ECTURE 1. B ASIC CONCEPTS . P OLARIZATION . S TOKES VECTOR . M UELLER MATRIX . B ASICS OF LASER POLARIMETRY . Mueller matrices If light is represented by Stokes vectors, optical components are then described with Mueller matrices: [output light] = [Muller matrix] [input light] � � � � � � I' I m m m m � � � 11 12 13 14 � � � Q' Q � � � � � � m m m m � 21 22 23 24 � � � � � � U' U m m m m � � � � � � 31 32 33 34 � � � � � � V' V � � m m m m � � � � 41 42 43 44 Element 1 Element 2 Element 3 M M M 1 2 3 16 S’ = M 3 M 2 M 1 S