Cristina M. Gómez-Sarabia

Conjugate phase plate use in analysis of the frequency response of imaging systems designed for extended depth of field

We unveil a relationship between generating a point spread function with a pair of conjugate phase elements and visualizing the modulation transfer function (MTF) of a single phase element for a variable focus error, at a tunable spatial frequency. We show that the defocused MTF of a pair of conjugate phase elements can be expressed as the modulus of the second order ambiguity function of a single phase element. Finally, we propose a tunable wavefront coding technique with a pair of quartic (4th power) conjugate phase elements.

Tuning field depth at high resolution by pupil engineering

We present a simple comprehensive treatment on the use of free-form optical elements, and of nonuniform optical windows, either for increasing focal depth [by regulating the width of the axial point spread function (PSF)] or for tuning the depth of field [by controlling the influence of focus error on the modulation transfer function (MTF)]. We employ the rising notation of pupil engineering, which incorporates techniques for controlling the spread of the axial PSF, as well as methods for governing the impact of focus errors on the MTF. Our discussion also includes the use of vortex lenses for designing nonconventional optical systems.

Tunable apodizers and tunable focalizers using helical pairs

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

Multiple-frame photography for extended depth of field

For extending the depth of field, we analyze the result of superimposing several snapshots, which are taken while changing the amount of focus error, at full pupil aperture. We unveil the use of a varifocal lens for controlling the amount of focus error, without modifying either the lateral magnification or light throughput. After recording a set of snapshots, we use suitable acquisition factors for shaping an optical transfer function, which has reduced sensitivity to focus errors.

Optical processor arrays for controlling focal length or for tuning the depth of field

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

Adaptive photodetector for assisted Talbot effect

We use an adaptive photodetector for measuring the visibility of the Fresnel diffraction patterns generated by a grating. Visibility is measured in real time, with high spatial resolution, and without any signal processing. This method is well suited for analyzing the Talbot effect and its many applications.

Tunable focalizers: axicons, lenses, and axilenses

We propose the use of a pair of phase masks, which have both radial and angular variations, for implementing several varifocal devices. One mask of the proposed pair has a complex amplitude transmittance that is the complex conjugate of the other member of the pair. We show that the overall complex amplitude transmittance has only a radial variation after introducing an in-plane rotation, say by an angle β, between the members of the pair. However, we note that the optical power is proportional to the rotation angle β. As examples of the proposed method, we show that the refractive pair is useful for implementing varifocal lenses, tunable axicons, controllable axilenses, as well as annularly distributed focalizers.

Hyper Gaussian windows with fractional wavefronts

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

Ambiguity function analysis of pulse train propagation: applications to temporal Lau filtering

We use the periodic-signal ambiguity function for visualizing the intensity-spectrum evolution through propagation in a first-order dispersive medium. We show that the degree of temporal coherence of the optical source plays the role of a low-pass filter on the signals ambiguity function. Based on this, we present a condition on the temporal Lau effect for filtering harmonics at fractions of the Talbot length. This result allows one to increase the repetition rate of a pulse train obtained from a sinusoidally phase-modulated CW signal.

Focal depth: optimum annular apodizer.

We discuss an annular apodizer that minimizes the second moment of the Strehl ratio vs defocus for a prespecified light gathering power.