Department of Physics and Mathematics

Based upon the prophylactic strategy for optical design developed in Department of Applied Optics & Photonics, University of Calcutta, this paper reports an overview of the design of multi-component zoom lens. This strategy includes the effective use of the thin lens aberration theory and paraxial ray optics in reducing a formidable design problem with large degrees of freedom into a set of sub-problems with considerably lower degrees of freedom. Some of the design steps involve global or quasiglobal optimization of design variables, and others are facilitated by computer implementation of analytical methods. The total primary aberrations of the whole system in selected zoom positions are kept within a given targeted value. Illustrative numerical results of the design procedure are presented.

Point spread function (PSF) Engineering using Pupil plane phase filters is currently an active area of research and provides a convenient energy-efficient technique for tailoring of three dimensional point spread function near the focal plane of a rotationally symmetric imaging system. Azimuthal Walsh filters, derived from Azimuthal Walsh functions, which can take the values either +1 or -1 over a specified phase domain, form a set of orthogonal binary phase filters which can be reliably realized in practice, and used for the purpose. This paper reports our recent exploration on the far-field diffraction characteristics of Azimuthal Walsh filters, and the corresponding axial as well as off-axial intensity distributions.

Pupil plane phase filtering provides a convenient energy-efficient technique for tailoring of three dimensional point spread function in imaging systems. Walsh filters, derived from orthogonal Walsh functions which can take the values either +1 or -1 over a specified domain, are a set of binary phase filters which can be reliably realized in practice, and used for the purpose. This paper reports our recent exploration on self-similarity in the set of polar Walsh filters in two dimensions, and the self-similarity in three dimensional point spread function obtained by use of corresponding polar Walsh filters.

Azimuthal Walsh filters derived from azimuthal Walsh
functions can provide a viable and interesting tool for the
analysis and synthesis of microwave antenna and optical imaging systems. They can provide a convenient energy-efficient technique for tailoring of three dimensional point spread function near the focal plane of a rotationally symmetric imaging system. Starting with a brief description of the basic properties of azimuthal Walsh functions, this paper reports the generation of azimuthal Walsh filters along with their far-field diffraction characteristics for tailoring three dimensional point spread function near the focal plane of a rotationally symmetric imaging system.

Azimuthal Walsh Functions can be utilized to obtain an orthogonal set of Azimuthal Walsh Filters where the transmission values of +1 and-1 are achieved by using 0 and pi phase respectively. The inherent asymmetry in the azimuthal Walsh filters leads to asymmetrical Point Spread Function (PSF) in the far field diffraction pattern. This report presents results of our preliminary investigation on the effects of phase asymmetry in the filters on the PSF in the Far-field patterns.

Azimuthal Walsh filters derived from azimuthal Walsh functions can be used for tailoring the axial as well as transverse intensity distribution in and around the focal plane of a rotationally symmetric imaging system. As a special application, it can be used for trapping contact-free handling of particles of the size of micro-and nano-scale where light and matter can possibly interact. This paper reports brief description of generation of lower and higher orders of azimuthal Walsh filters, examines their phase asymmetries on far-field diffraction pattern. The possibility of using them as basis functions for 3d optical micro-trapping in optical micro-and macro-manipulations required for biomedical research, Cell Biology, Statistical thermodynamics and colloid science has also discussed. .

Binary Polar Walsh filters derived from one and two dimensional radial and azimuthal Walsh functions can be used as effective and interesting tool for manipulating the far-field diffraction characteristics of three dimensional point spread function (PSF) near the focal plane of a rotationally symmetric imaging system. They can provide a convenient energy-efficient technique for improving the imaging characteristics of a diffraction limited system when used as pupil functions. Starting with definition and brief description of the basic properties of binary polar Walsh functions, this paper reports the generation of one and two dimensional Walsh filters of different orders along with their far-field diffraction characteristics simulated. The results have been compared and further scopes of research for analysis and synthesis of more complex pupil functions have been predicted. Utilization of depth of focus to improve the figure of merit of PSF for both cases may also be considered as further scope of study. The scope of practical implementation of these filters in the field of micromanipulation has also been discussed in the concluding section.

Binary polar Walsh filters derived from two dimensional polar Walsh functions provides an effective tool for tailoring the three dimensional intensity distributions of a point spread function (PSF) in the pupil plane in a diffraction limited imaging system. This paper reports the study of radial as well as azimuthally variant polar Walsh filters and observation on their imaging characteristics near the focal plane of a rotationally symmetric imaging system.

The Proceedings of 2nd International Conference on Opto-Electronics and Applied Optics 2015, IEM OPTRONIX 2015 in technical collaboration with IEEE Photonics Society supported by IEEE Vancouver Section is an effort to present the research contributions presented in the conference by the researchers from India and abroad. The book has been organized to enable easy access on various topics. The first part includes the Keynote addresses by Brian Culshaw, University of Strathclyde, UK, followed by Graham Reed, University of Southampton, Guildford, UK and Jϋrgen Jahns of Fern Universität, Hagen, Germany. The second part focuses on the Plenary Talks given by eminent scientists of International repute namely, Azizur Rahman, City University, London, Bahram Jalali, University of California, Los Angeles, USA, James B Cole, University of Tsukuba, Japan, Raman Kashyap, Polytechnique Montreal, Canada,
Tigran Galstian, University of Laval, Canada, Motoharu Fujigaki, University of Fukui, Japan, Navin Kumar Nishchal, Indian Institute of Technology, Patna, India, Takeo Sasaki, Tokyo University of Science, Japan. The subsequent parts focuses on contributory papers sub-divided into four different tracks namely :
Track 1 : Silicon Photonics, Image Processing, Bio-Medical Optics
Track 2 : Fibre Optics, Photonics, Interferometry, Nano-Photonics
Track 3 : Holography, Solar Cells, Opto-electronic Materials
Track 4 : Optical Communications, Photonic Crystal Fibers

The possibility of using azimuthal Walsh filters, derived from the orthogonal set of azimuthal Walsh functions, as base functions have been proposed, to manipulate the far-field diffraction pattern at and along the region of the transverse far-field plane, of a rotationally symmetric imaging system has been proposed in this investigation. The existence of self-similarity observed in the 2D intensity distributions exhibited by members of self-similar Groups and Sub-Groups of azimuthal Walsh filters has also been reported. The rotational self-similarity portrayed in the 2D intensity distributions by corresponding adjacent as well as distant orders of self-similar azimuthal Walsh filters rotated by specific angles has been demonstrated and this provides a unique property exhibited by azimuthal Walsh filters compared to radial and annular categories. We have used MATLAB 2017a platform for the advance level computation and generate high quality graphics for the study of the far-field diffraction pattern for different orders of azimuthal Walsh filters.

Practical implementation of these filters can be achievable by the availability of high-speed Spatial Light modulators where the in-situ generation of different orders of azimuthal Walsh filters are possible and combinations of lower orders filters to achieve higher orders may be explored.  The lossless azimuthal Walsh filters are energy efficient and can be used to solve the problem of direct implementation of a finite number of constant as well as varying phase levels.   
Further scope of research includes the use of azimuthal Walsh filters as phase-shifted zone plates to generate complex 3D beam structures like petal shaped and optical ring lattice beams.  Azimuthal Walsh filters can be used very efficiently near the focus of an imaging system to cater the needs of 3D imaging, lithography, optical superresolution, optical tomography and so on. Optical micro- and macro-manipulations using azimuthal variant Walsh filters or combinations with radial variety can be used to form gradient force trap for optical tweezers for manipulating objects of size comparable to a single atom to 100µm without mechanical contact.
The two unique characteristics, namely, the orthogonality of azimuthal and radial Walsh filters and the self-similarity in different orders may be used to facilitate tackling of the inverse problem where a phase filter needs to be synthesized in accordance with pre-specified diffraction characteristics which may provide as an energy efficient solution to circumvent different problems related to Biology, Physics and Environmental issues.

We demonstrate by a simple calculation that tight focusing of a Gaus-sian beam in optical tweezers leads to spin-momentum locking, where the spin momentum density is rendered independent of helicity while the Poynting vector becomes helicity dependent. We hypothesize that the presence of a stratified medium in the path of the trapping beam would enhance the transverse spin momentum leading to exotic controlled rotation of optically trapped single mesoscopic particles for input circularly polarized light. Keywords Spin Momentum Locking · Optical Tweezers · Gaussian Beam · Optical Manipulation · Light Matter Interaction Introduction: Light carries both orbital and spin angular momentum, and the Poynting vector-which is considered to be the vector representative of the flow of energy-has contribution from both the orbital and spin part of the momentum. The spin contribution in Poynting vector, introduced by Belinfante through the equation p = p o + p s [1], where p s represents the contribution of spin in poynting vector, is rather enigmatic. This is because the term p s , though being responsible for spin angular momentum, does not contribute to the energy flow, so that it may be considered to be a virtual quantity. On the other hand, p o represents canonical momentum that is responsible for generating orbital angular momentum (OAM) (l = r × p o). It has recently been discovered that a phase shifted longitudinal component of field plays a major role in the appearance of spin (polarization) dependent transverse momentum and spin (polarization) independent transverse spin angular momentum (SAM) (p s)[1–4]. This particular feature is well known as spin momentum locking in condensed matter physics in the context of topological insu-lators [5, 6]. On the surface of a topological insulator, special states exist which fall

Azimuthal Walsh filters derived from radially invariant polar Walsh functions can be used as an effective tool for producing 2D and 3D light structures near the focal plane of a rotationally symmetric imaging system by manipulating far-field diffraction characteristics when used as pupil filters. Starting with the definition of azimuthal Walsh filters, this research work reports the possibility of modifying the beam structure around far-field plane by the diffraction characteristics of azimuthal Walsh filters placed at exit pupil plane when computed analytically. The asymmetrical beam produced due to the phase asymmetries introduced by azimuthal Walsh filters can be used to form gradient force trap for optical tweezers for manipulating objects of size comparable to a single atom to 100µm without mechanical contact, is also proposed in this paper.

Azimuthal Walsh filters derived from radially invariant azimuthal Walsh functions can be used as an effective tool for producing 2D and 3D light structures near the focal plane of a rotationally symmetric imaging system by manipulating the far-field diffraction characteristics when used as pupil filters. Starting with the definition of azimuthal Walsh functions and using the scalar diffrac-tion theory, this research work reports the possibility of modifying the beam structure around the far-field plane by diffraction characteristics of azimuthal Walsh filters placed on the exit pupil plane when computed analytically. The asymmetrical beam produced due to the inherent phase asymmetries introduced by azimuthal Walsh filters may find many important applications in micro-and nano-photonics.

Azimuthal Walsh filters derived from radially invariant azimuthal Walsh functions can be used as an effective tool for producing 2D and 3D light structures near the focal plane of a rotationally symmetric imaging system by manipulating the far-field diffraction characteristics when used as pupil filters. Starting with the definition of azimuthal Walsh functions and using the scalar diffrac-tion theory, this research work reports the possibility of modifying the beam structure around the far-field plane by diffraction characteristics of azimuthal Walsh filters placed on the exit pupil plane when computed analytically. The asymmetrical beam produced due to the inherent phase asymmetries introduced by azimuthal Walsh filters may find many important applications in micro-and nano-photonics.

Azimuthal Walsh filters are placed on the exit pupil plane of a rotationally symmetric imaging system and the intensity distributions on the axially shifted image planes are studied by taking into consideration of the defocus aberration term.

This book explores the possibility of using azimuthal Walsh filters derived from azimuthal Walsh functions as an effective tool for generation of 2D and 3D light structures by manipulating far-field diffraction characteristics near the focal plane of a rotationally symmetric imaging system when used as pupil filters. Starting with the definition of Walsh functions, this book reports the generation and synthesis of azimuthal Walsh filters. The inherent self-similarity present in the various orders of the azimuthal Walsh filters have been explored and the filters are classified into self-similar groups and sub-groups. Azimuthal Walsh filters are observed to possess a unique rotational self-similarity exhibited among adjacent orders is also presented in this book.

Artikkelit Luonnontieteiden ja metsätieteiden tiedekunta 2020 Self-similarity in azimuthal Walsh filters and corresponding far-field diffraction characteristics : a unique study to control tightly focused fields and coupling of light into metamaterials, plasmonic structure and waveguides Bhattacharya, Indrani SPIE Artikkelit ja abstraktit tieteellisissä konferenssijulkaisuissa © Society of Photo-Optical Instrumentation Engineers (SPIE). One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this publication for a fee or for commercial purposes, and modification of the contents of the publication are prohibited.

In the presence of astigmatism, the three-dimensional distribution of rays in the image region passes through two orthogonal lines, the vertical sagittal foci and the horizontal tangential foci. With increasing astigmatic behaviour of the imaging system, the sagittal and tangential foci will be farther removed from each other and the separation between these two planes serves as the measure of astigmatism. Midway between these planes, i.e., corresponding to the defocus term, 𝑊20 = −𝑊22⁄2 , where 𝑊22 is the co-efficient of astigmatism, the intensity spread is found to be minimum and the transverse plane passing through this point is referred to as the plane of minimum aberration variance. For a diffraction limited
imaging system, the IPSF on this plane is the Airy pattern. In our study, each sector of the azimuthal Walsh aperture is masked by suitably oriented linear polarizers. The polarization phase introduced is a function of the state of polarization (SOP) of the input beam, the transmission axis of orientation of the masking polarizer and the orientation of the analyzer.
A feasible method to assess the degree of astigmatic compensation is to compute the IPSF at the plane of minimum astigmatic variance and compare the intensity distribution with that of airy pattern. IPSFs for different values of 𝑊22 are computed with the presence of compensating polarization masked azimuthal Walsh filters at 0° and 90° with input beam
parameters a=b=1 , 𝛿 = 90° and analyser kept at a particular angle. The results are compared with IPSFs computed for an unmasked lens and airy pattern.

"Effects of exercise on different body systems, especially cardiovascular and musculoskeletal systems have been proven. In the haemostatic system the influence of training has been extensively studied but there are a few investigations that analyze the effects of training programs on coagulation factors. In this study we have surveyed the effect of physical fitness on coagulation factors in healthy young men. Subjects were 26 young men without any history of cardiac, coagulation or respiratory problems in themselves or their immediate family, a cardiologist confirmed their cardiovascular health. These men were divided in two groups; the physically active group (Ac) and the sedentary group (Se). The groups were similar in life style except their activity. The physically active men (Ac; n=10) were involved in regular exercise at least three times a week during the last six months. The sedentary men (Se; n = 16) did not participated in any sport activity. According to preliminary clinical examinations, Anthropometric variables had no significant differences in either group, but the Bruce test and a standardized ergometery test proved that functional capacity of cardiovascular system in the Ac group is significantly higher than the Se group. Blood data analysis showed that the basal levels of FVIII:c and FIX:c were significantly higher in the Ac group. FVIII:c, FIX:c, fibrinogen and vWF:ac increased in response to exercise while vWF:ag, FVII:c and aPTT decreased significantly. All of these parameters, except fibrinogen, FVIII:c and vWF:ag, returned to resting values during passive recovery. In the Se group elevation in vWF:ag during active recovery, reduction of aPTT and elevation of FVIII:c and FIX:c during passive recovery was statistically significant. Active and sedentary young men are different in resting values of some coagulation factors and their coagulation markers also vary in response to a submaximal exercise program on cycle ergometer. This is due to the difference between physical fitness levels of these two groups. Considering the unfavorable effects of imbalance between coagulation and fibrinolysis, it seems in any type of physical activity especially sport activities the haemostatic balance should be evaluated. Controlling the markers of these systems will help us improve safety of patients in whom exercise is a part of their rehabilitation program, this way it will be possible to enhance positive effects and reduce the possible risks of professional sports for healthy individuals."