The parity of self-images obtained at a half of Talbot distance is investigated. Conditions for i... more The parity of self-images obtained at a half of Talbot distance is investigated. Conditions for inversion are found. A subset of the functions fulfilling Montgomery's condition, namely those composed of sinusoids with frequencies in the ratio of the square root of odd numbers, replicate in inverted form. Some examples are commented, numerically simulated and verified by experiment.
erators, and a large number of optical systems associated with it are found. At the same time, th... more erators, and a large number of optical systems associated with it are found. At the same time, the output of ampies. Mathematical definitions for the P-order convolution and correlation are proposed as generalizations of the classical ones such that, when the P-order FRT is applied to them, theorems that generalize the classical convolution and correlation are verified.
Imaging of three-dimensional objects by lenses and mirrors is sometimes poorly indicated in textb... more Imaging of three-dimensional objects by lenses and mirrors is sometimes poorly indicated in textbooks and can be incorrectly drawn. We stress a need to clarify the concept of longitudinal magnification, with simulated images illustrating distortions introduced along the optical axis. We consider all possible positions of the object for both a convergent and a divergent lens, producing real and virtual images. We also discuss spherical mirrors, elementary telescopes and microscopes.
The recently developed concept of refracting profiles and that of refraction holodiagrams are com... more The recently developed concept of refracting profiles and that of refraction holodiagrams are combined so that the classical Abramson holodiagrams can be generalized taking into account a wider class of wave fronts and refraction at an interface, whenever regions of caustics are avoided. These holodiagrams are obtained as envelopes of specific families of Cartesian Ovals with an appropriate parametrization. Classical and reflecting holodiagrams are particular cases of this class. Several of the properties of the classical holodiagrams are shared by their richer generalized versions.
Speckle is being used as a characterization tool for the analysis of the dynamics of slow-varying... more Speckle is being used as a characterization tool for the analysis of the dynamics of slow-varying phenomena occurring in biological and industrial samples at the surface or near-surface regions. The retrieved data take the form of a sequence of speckle images. These images contain information about the inner dynamics of the biological or physical process taking place in the sample. Principal component analysis (PCA) is able to split the original data set into a collection of classes. These classes are related to processes showing different dynamics. In addition, statistical descriptors of speckle images are used to retrieve information on the characteristics of the sample. These statistical descriptors can be calculated in almost real time and provide a fast monitoring of the sample. On the other hand, PCA requires a longer computation time, but the results contain more information related to spatial-temporal patterns associated to the process under analysis. This contribution merges both descriptions and uses PCA as a preprocessing tool to obtain a collection of filtered images, where statistical descriptors are evaluated on each of them. The method applies to slow-varying biological and industrial processes.
The concept of spatial coherence is usually hard to comprehend the first time that it is studied.... more The concept of spatial coherence is usually hard to comprehend the first time that it is studied. We propose here a fully intuitive geometric description that does not contain mathematical difficulties, and permits one to understand how a Young's fringe stationary system is obtained with a source not spatially coherent. It is based in a very simple experiment that permits the detection of spatial coherence in a scene. Experimental results are shown. Using this approach, a Babinet-like principle for the visibility of the Young's fringes is proposed and experimentally demonstrated.
12th Education and Training in Optics and Photonics Conference, 2014
The concept of spatial coherence is usually hard to be understood the first time that it is studi... more The concept of spatial coherence is usually hard to be understood the first time that it is studied. We propose here a geometric description that does not contain mathematical difficulties and permits to understand how a Young´s Fringes system is obtained with a source not spatially coherent. It is based in a very simple experiment that permits the detection of spatial coherence in a scene. Experimental results are shown
This paper proposes the design of decision models based on Computational Intelligence techniques ... more This paper proposes the design of decision models based on Computational Intelligence techniques applied to image sequences of dynamic laser speckle. These models aim to identify image regions of biological specimens illuminated by a coherent beam coming from a laser. The field image is pseudo colored using a Self Organizing Map projection. This process is carried out using a set of descriptors applied to the intensity variations along time in every pixel of an image sequence. The models use descriptors selected to improve effectiveness, depending on the specific application. We present two examples of the application of the proposed techniques to assess biological tissues. The results obtained are encouraging and significantly improve those obtained using a single descriptor.
The concept of spatial coherence is usually hard to be understood the first time that it is studi... more The concept of spatial coherence is usually hard to be understood the first time that it is studied. We propose here a fully intuitive geometric description that does not contain mathematical difficulties and permits to understand how a Young Fringes system is obtained with a source not spatially coherent. It is based in a very simple experiment that permits the detection of spatial coherence in a scene. Experimental results are shown.
The diffraction phenomenon produced by a Fabry-Perot interference pattern record is analizcd. As ... more The diffraction phenomenon produced by a Fabry-Perot interference pattern record is analizcd. As a result of this analysis, a compact device for interferometric holography has been developed. It is presented as example an application of this device to the interferometric determination of deformations in a loaded metallic cantilever.
In recent years there has been renewed interest in the development of novel grain classification ... more In recent years there has been renewed interest in the development of novel grain classification methods that could complement traditional empirical tests. A speckle pattern occurs when a laser beam illuminates an optically rough surface that flickers when the object is active and is called biospeckle. In this work, we use laser biospeckle to classify maize (Zea mays L.) kernel hardness. A series of grains of three types of maize were cut and illuminated by a laser. A series of images were then registered, stored, and processed. These were compared with results obtained by floating test. The laser speckle technique was effective in discriminating the grains based on the presence of floury or vitreous endosperm and could be considered a feasible alternative to traditional floating methods. The results indicate that this methodology can distinguish floury and vitreous grains. Moreover, the assay showed higher discrimination capability than traditional tests. It could be potentially us...
A new method for vibrational analysis is proposed. It is based on the 48blurring of time-averaged... more A new method for vibrational analysis is proposed. It is based on the 48blurring of time-averaged Young's fringes inside speckle grains in the image of a vibrational object. A spatial filtered image of the recording of those speckles, modulated by Young's fringes, shows the loci of points of equal vibratory amplitude.
A ne11• method for subtracting images is proposed. It is based on assigning complementary Young's... more A ne11• method for subtracting images is proposed. It is based on assigning complementary Young's fringes to the speckles of the common parts of two images. In this way, carrier frequency is cancelled, and "a-posteriori" spatial filtering shows only noncommon parts. Suggestions on applications of the method are briefly commented.
A simple inethod of pseudocoloring gray levelimages is proposed. It is based on Young's fringes m... more A simple inethod of pseudocoloring gray levelimages is proposed. It is based on Young's fringes modulated speckle encoding of images. Reconstruction from a photographic register is obtained using two light beams with different wavelengths at the same time. Pseudocoloring is produced by the superposition of a (diffracted) direct image in one color and a (directly transmitted) contrast reversed image in another color.
A simple method for pseudocolor encoding of gray level information is proposed. It is based on th... more A simple method for pseudocolor encoding of gray level information is proposed. It is based on the real-time addition of the positive and negative images of an object transparency, each one obtained in a different color. Conventional white light lamps with adequate color filters are used. Some experimental results are shown.
In this work we propose some experiments with the use of optical computer mouse, associated to lo... more In this work we propose some experiments with the use of optical computer mouse, associated to low cost lasers that can be used to perform several measurements with applications in industry and in human health monitoring. The mouse was used to grab the movements produced by speckle pattern changes and to get information through the adaptation of its structure. We measured displacements in wood samples under strain, variations of the diameter of an artery due to heart beat and, through a hardware simulation, the movement of an eye, an experiment that could be of low cost help for communication to severely handicapped motor patients. Those measurements were done in spite of the fact that the CCD sensor of the mice is monolithically included into an integrated circuit so that the raw image cannot be accessed. If, as was the case with primitive optical mouse, that signal could be accessed, the quality and usefulness of the measurements could be significantly increased. As it was not possible, a webcam sensor was used for measuring the drying of paint, a standard phenomenon for testing biospeckle techniques, in order to prove the usefulness of the mouse design. The results showed that the use of the mouse associated to a laser pointer could be the way to get metrological information from many phenomena involving the whole field spatial displacement, as well as the use of the mouse as in its prime version allowed to get images of the speckle patterns and to analyze them.
We present a dynamic laser speckle method to easily discriminate filamentous fungi from motile ba... more We present a dynamic laser speckle method to easily discriminate filamentous fungi from motile bacteria in soft surfaces, such as agar plate. The method allows the detection and discrimination between fungi and bacteria faster than with conventional techniques. The new procedure could be straightforwardly extended to different microorganisms , as well as applied to biological and biomedical research, infected tissues analysis, and hospital water and wastewaters studies.
The parity of self-images obtained at a half of Talbot distance is investigated. Conditions for i... more The parity of self-images obtained at a half of Talbot distance is investigated. Conditions for inversion are found. A subset of the functions fulfilling Montgomery's condition, namely those composed of sinusoids with frequencies in the ratio of the square root of odd numbers, replicate in inverted form. Some examples are commented, numerically simulated and verified by experiment.
erators, and a large number of optical systems associated with it are found. At the same time, th... more erators, and a large number of optical systems associated with it are found. At the same time, the output of ampies. Mathematical definitions for the P-order convolution and correlation are proposed as generalizations of the classical ones such that, when the P-order FRT is applied to them, theorems that generalize the classical convolution and correlation are verified.
Imaging of three-dimensional objects by lenses and mirrors is sometimes poorly indicated in textb... more Imaging of three-dimensional objects by lenses and mirrors is sometimes poorly indicated in textbooks and can be incorrectly drawn. We stress a need to clarify the concept of longitudinal magnification, with simulated images illustrating distortions introduced along the optical axis. We consider all possible positions of the object for both a convergent and a divergent lens, producing real and virtual images. We also discuss spherical mirrors, elementary telescopes and microscopes.
The recently developed concept of refracting profiles and that of refraction holodiagrams are com... more The recently developed concept of refracting profiles and that of refraction holodiagrams are combined so that the classical Abramson holodiagrams can be generalized taking into account a wider class of wave fronts and refraction at an interface, whenever regions of caustics are avoided. These holodiagrams are obtained as envelopes of specific families of Cartesian Ovals with an appropriate parametrization. Classical and reflecting holodiagrams are particular cases of this class. Several of the properties of the classical holodiagrams are shared by their richer generalized versions.
Speckle is being used as a characterization tool for the analysis of the dynamics of slow-varying... more Speckle is being used as a characterization tool for the analysis of the dynamics of slow-varying phenomena occurring in biological and industrial samples at the surface or near-surface regions. The retrieved data take the form of a sequence of speckle images. These images contain information about the inner dynamics of the biological or physical process taking place in the sample. Principal component analysis (PCA) is able to split the original data set into a collection of classes. These classes are related to processes showing different dynamics. In addition, statistical descriptors of speckle images are used to retrieve information on the characteristics of the sample. These statistical descriptors can be calculated in almost real time and provide a fast monitoring of the sample. On the other hand, PCA requires a longer computation time, but the results contain more information related to spatial-temporal patterns associated to the process under analysis. This contribution merges both descriptions and uses PCA as a preprocessing tool to obtain a collection of filtered images, where statistical descriptors are evaluated on each of them. The method applies to slow-varying biological and industrial processes.
The concept of spatial coherence is usually hard to comprehend the first time that it is studied.... more The concept of spatial coherence is usually hard to comprehend the first time that it is studied. We propose here a fully intuitive geometric description that does not contain mathematical difficulties, and permits one to understand how a Young's fringe stationary system is obtained with a source not spatially coherent. It is based in a very simple experiment that permits the detection of spatial coherence in a scene. Experimental results are shown. Using this approach, a Babinet-like principle for the visibility of the Young's fringes is proposed and experimentally demonstrated.
12th Education and Training in Optics and Photonics Conference, 2014
The concept of spatial coherence is usually hard to be understood the first time that it is studi... more The concept of spatial coherence is usually hard to be understood the first time that it is studied. We propose here a geometric description that does not contain mathematical difficulties and permits to understand how a Young´s Fringes system is obtained with a source not spatially coherent. It is based in a very simple experiment that permits the detection of spatial coherence in a scene. Experimental results are shown
This paper proposes the design of decision models based on Computational Intelligence techniques ... more This paper proposes the design of decision models based on Computational Intelligence techniques applied to image sequences of dynamic laser speckle. These models aim to identify image regions of biological specimens illuminated by a coherent beam coming from a laser. The field image is pseudo colored using a Self Organizing Map projection. This process is carried out using a set of descriptors applied to the intensity variations along time in every pixel of an image sequence. The models use descriptors selected to improve effectiveness, depending on the specific application. We present two examples of the application of the proposed techniques to assess biological tissues. The results obtained are encouraging and significantly improve those obtained using a single descriptor.
The concept of spatial coherence is usually hard to be understood the first time that it is studi... more The concept of spatial coherence is usually hard to be understood the first time that it is studied. We propose here a fully intuitive geometric description that does not contain mathematical difficulties and permits to understand how a Young Fringes system is obtained with a source not spatially coherent. It is based in a very simple experiment that permits the detection of spatial coherence in a scene. Experimental results are shown.
The diffraction phenomenon produced by a Fabry-Perot interference pattern record is analizcd. As ... more The diffraction phenomenon produced by a Fabry-Perot interference pattern record is analizcd. As a result of this analysis, a compact device for interferometric holography has been developed. It is presented as example an application of this device to the interferometric determination of deformations in a loaded metallic cantilever.
In recent years there has been renewed interest in the development of novel grain classification ... more In recent years there has been renewed interest in the development of novel grain classification methods that could complement traditional empirical tests. A speckle pattern occurs when a laser beam illuminates an optically rough surface that flickers when the object is active and is called biospeckle. In this work, we use laser biospeckle to classify maize (Zea mays L.) kernel hardness. A series of grains of three types of maize were cut and illuminated by a laser. A series of images were then registered, stored, and processed. These were compared with results obtained by floating test. The laser speckle technique was effective in discriminating the grains based on the presence of floury or vitreous endosperm and could be considered a feasible alternative to traditional floating methods. The results indicate that this methodology can distinguish floury and vitreous grains. Moreover, the assay showed higher discrimination capability than traditional tests. It could be potentially us...
A new method for vibrational analysis is proposed. It is based on the 48blurring of time-averaged... more A new method for vibrational analysis is proposed. It is based on the 48blurring of time-averaged Young's fringes inside speckle grains in the image of a vibrational object. A spatial filtered image of the recording of those speckles, modulated by Young's fringes, shows the loci of points of equal vibratory amplitude.
A ne11• method for subtracting images is proposed. It is based on assigning complementary Young's... more A ne11• method for subtracting images is proposed. It is based on assigning complementary Young's fringes to the speckles of the common parts of two images. In this way, carrier frequency is cancelled, and "a-posteriori" spatial filtering shows only noncommon parts. Suggestions on applications of the method are briefly commented.
A simple inethod of pseudocoloring gray levelimages is proposed. It is based on Young's fringes m... more A simple inethod of pseudocoloring gray levelimages is proposed. It is based on Young's fringes modulated speckle encoding of images. Reconstruction from a photographic register is obtained using two light beams with different wavelengths at the same time. Pseudocoloring is produced by the superposition of a (diffracted) direct image in one color and a (directly transmitted) contrast reversed image in another color.
A simple method for pseudocolor encoding of gray level information is proposed. It is based on th... more A simple method for pseudocolor encoding of gray level information is proposed. It is based on the real-time addition of the positive and negative images of an object transparency, each one obtained in a different color. Conventional white light lamps with adequate color filters are used. Some experimental results are shown.
In this work we propose some experiments with the use of optical computer mouse, associated to lo... more In this work we propose some experiments with the use of optical computer mouse, associated to low cost lasers that can be used to perform several measurements with applications in industry and in human health monitoring. The mouse was used to grab the movements produced by speckle pattern changes and to get information through the adaptation of its structure. We measured displacements in wood samples under strain, variations of the diameter of an artery due to heart beat and, through a hardware simulation, the movement of an eye, an experiment that could be of low cost help for communication to severely handicapped motor patients. Those measurements were done in spite of the fact that the CCD sensor of the mice is monolithically included into an integrated circuit so that the raw image cannot be accessed. If, as was the case with primitive optical mouse, that signal could be accessed, the quality and usefulness of the measurements could be significantly increased. As it was not possible, a webcam sensor was used for measuring the drying of paint, a standard phenomenon for testing biospeckle techniques, in order to prove the usefulness of the mouse design. The results showed that the use of the mouse associated to a laser pointer could be the way to get metrological information from many phenomena involving the whole field spatial displacement, as well as the use of the mouse as in its prime version allowed to get images of the speckle patterns and to analyze them.
We present a dynamic laser speckle method to easily discriminate filamentous fungi from motile ba... more We present a dynamic laser speckle method to easily discriminate filamentous fungi from motile bacteria in soft surfaces, such as agar plate. The method allows the detection and discrimination between fungi and bacteria faster than with conventional techniques. The new procedure could be straightforwardly extended to different microorganisms , as well as applied to biological and biomedical research, infected tissues analysis, and hospital water and wastewaters studies.
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Papers by Héctor Rabal