Piotr L. Makowski

Generalized total variation iterative constraint strategy in limited angle optical diffraction tomography

Due to incompleteness of input data inherent to Limited Angle Tomography (LAT), specific additional constraints are usually employed to suppress image artifacts. In this work we demonstrate a new two-stage regularization strategy, named Generalized Total Variation Iterative Constraint (GTVIC), dedicated to semi-piecewise-constant objects. It has been successfully applied as a supplementary module for two different reconstruction algorithms: an X-ray type solver and a diffraction-wise solver. Numerical tests performed on a detailed phantom of a biological cell under conical illumination pattern show significant reduction of axial blurring in the reconstructed refractive index distribution after GTVIC is added. Analogous results were obtained with experimental data.

Synthetic aperture Fourier holography for wide-angle holographic display of real scenes

A novel approach for wide-angle registration and display of digital holograms of static 3D scenes is presented. The registration setup design combines Fourier holography with the synthetic aperture technique, which results in recording performance of a wide spherically curved detector. The coherent object wavefield extracted from the synthetic exposition has a simple Wigner distribution function (WDF) representation and can serve as input for a variety of processing tools necessary to adopt the captured data for display in a chosen configuration. Here we use WDF diagrams for optimization of the 3D imaging space and as a basis for development of an aliasing-free numerical algorithm for adjustment of the magnification and axial position of the reconstructed image. The influence of the pixel size and wavelength mismatch between the registration and reconstruction systems is also discussed within the paraxial regime. For experimental tests we take a 60 megapixel synthetic aperture hologram of a bulk object recorded by use of a single spherical reference wave with divergence angle reaching 16°. The display system consists of six reflective liquid crystal on silicon spatial light modulators working in pure phase mode and illuminated by a single collimated beam.

Lyot depolarizer in terms of the theory of coherence--description for light of any spectrum.

A coherence-based description of the Lyot depolarizer illuminated by polychromatic light of any spectral density distribution is proposed as a generalization of the formulas provided for symmetrical spectra by Burns [J. Lightwave Technol. 1, 475 (1983)] and Mochizuki [Appl. Opt. 23, 3284 (1984)]. The structure of the derived expressions is explained in physical terms, and a numerical comparison with the previous solutions is performed. The results of the numerical analysis show that the proposed description, when applied to any configuration of a two-segment anisotropic depolarizer, is fully equivalent with the Mueller-Stokes calculus for broadband light. Following this consistency, the range of accuracy of the formula by Mochizuki has been verified.

Problem of degree of polarization for photons

In this paper a quantum description of degree of polarization (DOP) is presented. The analysis includes differences between quantum and quasi-classic description of photons and what they are in comparison with coherent states of electric field. In the end a possible interpretation for single-photon experiments is given to allow DOP calculation for photons.

Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise-constant structures

Standard tomographic algorithms applied to optical limited-angle tomography result in the reconstructions that have highly anisotropic resolution and thus special algorithms are developed. State of the art approaches utilize the Total Variation (TV) minimization technique. These methods give very good results but are applicable to piecewise constant structures only. In this paper, we propose a novel algorithm for 3D limited-angle tomography – Total Variation Iterative Constraint method (TVIC) which enhances the applicability of the TV regularization to non-piecewise constant samples, like biological cells. This approach consists of two parts. First, the TV minimization is used as a strong regularizer to create a sharp-edged image converted to a 3D binary mask which is then iteratively applied in the tomographic reconstruction as a constraint in the object domain. In the present work we test the method on a synthetic object designed to mimic basic structures of a living cell. For simplicity, the test reconstructions were performed within the straight-line propagation model (SIRT3D solver from the ASTRA Tomography Toolbox), but the strategy is general enough to supplement any algorithm for tomographic reconstruction that supports arbitrary geometries of plane-wave projection acquisition. This includes optical diffraction tomography solvers. The obtained reconstructions present resolution uniformity and general shape accuracy expected from the TV regularization based solvers, but keeping the smooth internal structures of the object at the same time. Comparison between three different patterns of object illumination arrangement show very small impact of the projection acquisition geometry on the image quality.

Approach for modeling influence of birefringence dispersion on polarization properties of multi-section systems

We present a method for including an arbitrary birefringence dispersion curve in some known models describing polarization state of a collimated uniform beam after passing a birefringent non-image-forming system. By the use of a modified definition of the complex degree of coherence it is shown that the presence of birefringence dispersion is analytically equivalent to a transformation of the spectrum profile of the beam passing through a non-dispersive system. This remark is then utilized for error reduction in numerical calculations of depolarization in a system with a frequency dependent differential group delay when the power spectrum density is given in discretized form. The same numerical technique applies both for implementations of coherence-based solutions and for the Mueller-Stokes formalism with polychromatic illumination, without imposing any restrictions on the power spectrum shape or width.

Degree of polarization fading of light passing through birefringent medium with optical axis variation

Numerical implementation of Mueller-Stokes matrix calculus for polychromatic light is used to analyze and plainly illustrate polarization properties of multi-section linearly birefringent systems illuminated by the light of any spectrum profile. Numerical investigations are preceded by a detailed review of known concepts for modeling the depolarization phenomenon in anisotropic media. The numerical study examines efficiency of the Lyot depolarizer system undergoing variations from the optimal configuration. In addition, the power spectrum density profile and intrinsic polarization state of light passing through the system are considered as interesting degrees of freedom. The comparative analysis makes use of the degree of polarization and the depolarization index diagrams.

Optical properties of polymer microtips investigated with workshop tomographic system

We present a novel methodology for optical fiber polymer microtip manufacturing ant testing, which supports the structure optimization process through utilization of an optical diffraction tomography system based on the lateral shear digital holographic microscope. The most important functional parameter of an optical fiber microtip is the output beam distribution in the far-field region, which depends on geometrical properties and refractive index distribution within the microtip. These factors, in turn, are determined by the optical power distribution of the actinic light and the exposition time during the photopolymerization process. In order to obtain a desired light field distribution we propose to govern the manufacturing process by a hybrid opto-numerical methodology, which constitutes a convenient feedback loop for modification of the fabrication parameters. A single cycle of the proposed scheme includes numerical modeling, tomographic measurements and modifications of fabrication process. We introduced the real values of three-dimensional refractive index distribution of microtips into the finite-difference time-domain (FDTD) simulations, which leaded to controlled modification of technology parameters and finally to improvement of a functional parameter of microtips.

An optical fiber loop sensor for vibration monitoring

The paper presents the way that colour can serve solving the problem of calibration points indexing in a camera geometrical calibration process. We propose a technique in which indexes of calibration points in a black-and-white chessboard are represented as sets of colour regions in the neighbourhood of calibration points. We provide some general rules for designing a colour calibration chessboard and provide a method of calibration image analysis. We show that this approach leads to obtaining better results than in the case of widely used methods employing information about already indexed points to compute indexes. We also report constraints concerning the technique. Nowadays we are witnessing an increasing need for camera geometrical calibration systems. They are vital for such applications as 3D modelling, 3D reconstruction, assembly control systems, etc. Wherever possible, calibration objects placed in the scene are used in a camera geometrical calibration process. This approach significantly increases accuracy of calibration results and makes the calibration data extraction process easier and universal. There are many geometrical camera calibration techniques for a known calibration scene [1]. A great number of them use as an input calibration points which are localised and indexed in the scene. In this paper we propose the technique of calibration points indexing which uses a colour chessboard. The presented technique was developed by solving problems we encountered during experiments with our earlier methods of camera calibration scene analysis [2]-[3]. In particular, the proposed technique increases the number of indexed points points in case of local lack of calibration points detection. At the beginning of the paper we present a way of designing a chessboard pattern. Then we describe a calibration point indexing method, and finally we show experimental results. A black-and-white chessboard is widely used in order to obtain sub-pixel accuracy of calibration points localisation [1]. Calibration points are defined as corners of chessboard squares. Assuming the availability of rough localisation of these points, the points can be indexed. Noting that differences in distances between neighbouring points in calibration scene images differ slightly, one of the local searching methods can be employed (e.g. [2]). Methods of this type search for a calibration point to be indexed, using a window of a certain size. The position of the window is determined by a vector representing the distance between two previously indexed points in the same row or column. However, experiments show that this approach has its disadvantages, as described below. * E-mail: A.Nowakowski@ire.pw.edu.pl Firstly, there is a danger of omitting some points during indexing in case of local lack of calibration points detection in a neighbourhood (e.g. caused by the presence of non-homogeneous light in the calibration scene). A particularly unfavourable situation is when the local lack of detection effects in the appearance of separated regions of detected calibration points. It is worth saying that such situations are likely to happen for calibration points situated near image borders. Such points are very important for the analysis of optical nonlinearities, and a lack of them can significantly influence the accuracy of distortion modelling. Secondly, such methods may give wrong results in the case of optical distortion with strong nonlinearities when getting information about the neighbouring index is not an easy task. Beside this, the methods are very sensitive to a single false localisation of a calibration point. Such a single false localisation can even result in false indexing of a big set of calibration points. To avoid the above-mentioned problems, we propose using a black-and-white chessboard which contains the coded index of a calibration point in the form of colour squares situated in the nearest neighbourhood of each point. The index of a certain calibration point is determined by colours of four nearest neighbouring squares (Fig.1). An order of squares in such foursome is important. Because the size of a colour square is determined only by the possibility of correct colour detection, the size of a colour square can be smaller than the size of a black or white square. The larger size of a black or white square is determined by the requirements of the exact localisation step which follows the indexing of calibration points [3]. In this step, edge information is extracted from a blackand-white chessboard. This edge information needs larger Artur Nowakowski, Wladyslaw Skarbek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, A.Nowakowski@ire.pw.edu.pl Received February 10, 2009; accepted March 27, 2009; published March 31, 2009 http://www.photonics.pl/PLP

Depolarization of elliptically polarized light in birefringent crystal

The paper presents the way that colour can serve solving the problem of calibration points indexing in a camera geometrical calibration process. We propose a technique in which indexes of calibration points in a black-and-white chessboard are represented as sets of colour regions in the neighbourhood of calibration points. We provide some general rules for designing a colour calibration chessboard and provide a method of calibration image analysis. We show that this approach leads to obtaining better results than in the case of widely used methods employing information about already indexed points to compute indexes. We also report constraints concerning the technique. Nowadays we are witnessing an increasing need for camera geometrical calibration systems. They are vital for such applications as 3D modelling, 3D reconstruction, assembly control systems, etc. Wherever possible, calibration objects placed in the scene are used in a camera geometrical calibration process. This approach significantly increases accuracy of calibration results and makes the calibration data extraction process easier and universal. There are many geometrical camera calibration techniques for a known calibration scene [1]. A great number of them use as an input calibration points which are localised and indexed in the scene. In this paper we propose the technique of calibration points indexing which uses a colour chessboard. The presented technique was developed by solving problems we encountered during experiments with our earlier methods of camera calibration scene analysis [2]-[3]. In particular, the proposed technique increases the number of indexed points points in case of local lack of calibration points detection. At the beginning of the paper we present a way of designing a chessboard pattern. Then we describe a calibration point indexing method, and finally we show experimental results. A black-and-white chessboard is widely used in order to obtain sub-pixel accuracy of calibration points localisation [1]. Calibration points are defined as corners of chessboard squares. Assuming the availability of rough localisation of these points, the points can be indexed. Noting that differences in distances between neighbouring points in calibration scene images differ slightly, one of the local searching methods can be employed (e.g. [2]). Methods of this type search for a calibration point to be indexed, using a window of a certain size. The position of the window is determined by a vector representing the distance between two previously indexed points in the same row or column. However, experiments show that this approach has its disadvantages, as described below. * E-mail: A.Nowakowski@ire.pw.edu.pl Firstly, there is a danger of omitting some points during indexing in case of local lack of calibration points detection in a neighbourhood (e.g. caused by the presence of non-homogeneous light in the calibration scene). A particularly unfavourable situation is when the local lack of detection effects in the appearance of separated regions of detected calibration points. It is worth saying that such situations are likely to happen for calibration points situated near image borders. Such points are very important for the analysis of optical nonlinearities, and a lack of them can significantly influence the accuracy of distortion modelling. Secondly, such methods may give wrong results in the case of optical distortion with strong nonlinearities when getting information about the neighbouring index is not an easy task. Beside this, the methods are very sensitive to a single false localisation of a calibration point. Such a single false localisation can even result in false indexing of a big set of calibration points. To avoid the above-mentioned problems, we propose using a black-and-white chessboard which contains the coded index of a calibration point in the form of colour squares situated in the nearest neighbourhood of each point. The index of a certain calibration point is determined by colours of four nearest neighbouring squares (Fig.1). An order of squares in such foursome is important. Because the size of a colour square is determined only by the possibility of correct colour detection, the size of a colour square can be smaller than the size of a black or white square. The larger size of a black or white square is determined by the requirements of the exact localisation step which follows the indexing of calibration points [3]. In this step, edge information is extracted from a blackand-white chessboard. This edge information needs larger Artur Nowakowski, Wladyslaw Skarbek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, A.Nowakowski@ire.pw.edu.pl Received February 10, 2009; accepted March 27, 2009; published March 31, 2009 http://www.photonics.pl/PLP