In this work, we describe the use of a virtual learning environment that we have developed. The software is programmed in LabView code and it is devised to teach polarization concepts to students in Optics courses at the university, either at the degree or master levels. In order to consolidate the knowledge previously explained in theoretical and experimental courses, the applet tries to foster the interaction of students with different virtual environments, each one training one particular polarization feature or method. In particular, the following concepts are included in the applet: ellipse of polarization, Poincaré sphere, Stokes vectors, Mueller matrix transformations, and polarization dependence with light wavelength after material interaction. What is more, we perform a set of targeted questions to students, into a problem-solving approach. It consists of a series of brief questions that students must solve and answer, helped by the visual information they can found into the applet. In this way, some theoretical concepts related to polarization are thought and reviewed by students from a different perspective from that given in the theoretical classes at the classroom.
Recently, a set of polarimetric indicators, the Indices of Polarimetric Purity (IPPs), were described in the literature. These indicators allow synthesize depolarization content of samples, and provide further analysis of depolarizers than other existing polarimetric indicators. We demonstrate the potential of the IPPs as a criterion to characterize and classify depolarizing samples. In particular, the method is firstly analyzed through a series of basic polarization experiments, and we prove how differences in the depolarizing capability of samples, concealed from the commonly used depolarization index PΔ, are identified with the IPPs.
In the second part of this work, the method is experimentally highlighted by studying a rabbit leg ex-vivo sample. The obtained images of the ex-vivo sample illustrate how IPPs provide a significant enhancement in the image contrast of some biological tissues and, in some cases, present new information hidden in the usual polarimetric channels. Moreover, new physical interpretation of the sample can be derived from the IPPs which allow us to synthesize the depolarization behavior.
Finally, we also propose a pseudo-colored encoding of the IPPs information that provides an improved visualization of the samples. This last technique opens the possibility to highlight a specific tissue structure by properly adjusting the pseudo-colored formula.
We highlight the interest of using the Indices of Polarimetric Purity (IPPs) for the biological tissue inspection. These are three polarimetric metrics focused on the study of the depolarizing behaviour of the sample. The IPPs have been recently proposed in the literature and provide different and synthetized information than the commonly used depolarizing indices, as depolarization index (PΔ) or depolarization power (Δ). Compared with the standard polarimetric images of biological samples, IPPs enhance the contrast between different tissues of the sample and show differences between similar tissues which are not observed using the other standard techniques. Moreover, they present further physical information related to the depolarization mechanisms inherent to different tissues. In addition, the algorithm does not require advanced calculations (as in the case of polar decompositions), being the indices of polarimetric purity fast and easy to implement. We also propose a pseudo-coloured image method which encodes the sample information as a function of the different indices weights. These images allow us to customize the visualization of samples and to highlight certain of their constitutive structures. The interest and potential of the IPP approach are experimentally illustrated throughout the manuscript by comparing polarimetric images of different ex-vivo samples obtained with standard polarimetric methods with those obtained from the IPPs analysis. Enhanced contrast and retrieval of new information are experimentally obtained from the different IPP based images.
We present mathematical formulas generalizing polarization gating (PG) techniques. PG refers to a collection of imaging methods based on the combination of different controlled polarization channels. In particular, we show how using the measured Mueller matrix (MM) of a sample, a widespread number of PG configurations can be evaluated just from analytical expressions based on the MM coefficients. We also show the interest of controlling the helicity of the states of polarization used for PG-based metrology, as this parameter has an impact in the image contrast of samples. In addition, we highlight the interest of combining PG techniques with tools of data analysis related to the MM formalism, such as the well-known MM decompositions. The method discussed in this work is illustrated with the results of polarimetric measurements done on artificial phantoms and real ex-vivo tissues.
Diffraction is an important phenomenon introduced to Physics university students in a subject of Fundamentals of
Optics. In addition, in the Physics Degree syllabus of the Universitat Autònoma de Barcelona, there is an elective subject
in Applied Optics. In this subject, diverse diffraction concepts are discussed in-depth from different points of view:
theory, experiments in the laboratory and computing exercises. In this work, we have focused on the process of teaching
Fraunhofer diffraction through laboratory training. Our approach involves students working in small groups. They visualize and acquire some important diffraction patterns with a CCD camera, such as those produced by a slit, a circular aperture or a grating. First, each group calibrates the CCD camera, that is to say, they obtain the relation between the distances in the diffraction plane in millimeters and in the computer screen in pixels. Afterwards, they measure the significant distances in the diffraction patterns and using the appropriate diffraction formalism, they calculate the size of the analyzed apertures. Concomitantly, students grasp the convolution theorem in the Fourier domain by analyzing the diffraction of 2-D gratings of elemental apertures. Finally, the learners use a specific software to simulate diffraction patterns of different apertures. They can control several parameters: shape, size and number of apertures, 1-D or 2-D gratings, wavelength, focal lens or pixel size.Therefore, the program allows them to reproduce the images obtained experimentally, and generate others by changingcertain parameters. This software has been created in our research group, and it is freely distributed to the students in order to help their learning of diffraction. We have observed that these hands on experiments help students to consolidate their theoretical knowledge of diffraction in a pedagogical and stimulating learning process.
There are few Optics contents along the primary and secondary studies in Spain. So, the relation between Optics and Technology is usually poorly known by the students. As a consequence, the number of students in Physics in general, and Optics in particular is low. In this paper we explain a project to show some topics in Optics Technology in a primary-secondary school. This project involves some Optics teachers in the Autonomous University of Barcelona (UAB) and a group of teachers and students of a primary-secondary school also in Barcelona (I.E.S. Costa i Llobera). Several Optics posters (made by the SPIE) were shown during one week. More than 200 students from 8 to 17 years old visited the Optics exhibition during this week. A group of 4 students (17 years old) were trained to show the posters to younger students. For this study we chose three age levels. For each level, a 50% of the students attended the exhibition and the rest didn’t attend the poster session. So, it was possible to realize a survey to check whether some knowledge differences appeared between the two groups. A questionnaire was fulfilled by these groups. The results of this survey show that a significant new knowledge in Optics was learned by the students.
The radial and axial point spread function (PSF) and the 3D modulation transfer function (MTF) were calculated to
demonstrate the influence of phase only filters in classical optical imaging systems. The 3D line spread function (LSF)
makes it possible to discuss the influence of the degree of coherence in the optical imaging system with the phase only
filter as well. First, the phase only filter under discussion was divided in five equally area annuli. The phase variations are either
linearly increasing or decreasing with the annulus number or alternating between 0 and π. Second we have used a filter
that consists on one phase annulus with a phase shift of π in different positions over the pupil. Numerical and experimental results are shown in this paper. A spatial light modulator (SLM) was used to obtain experimentally the influence of the different phase only filters on the image of a sector star. The merit functions for filters with a phase shift of π in one annulus are also studied. These filters produce a wide variety of responses in dependence of the position of the phase shifting annulus. By studying the merit functions, a clear prediction of the imaging behaviour of an optical system is possible as well. The conclusion of our work has been that it is necessary to study the influence of the filter on the different merit functions in order to design an optimum filter for a given application.
Spatial light modulators (SLM) have found a wide range of applications in many fields of optical imaging and
measurement systems. We implement different phase only filters in the pupil plane of an imaging system. The phase
only filter is divided in five equally spaced annuli. Each annulus has a different phase transmission and inside each
annulus the phase is constant. We analyse first the influence of linear decreasing or increasing phase, second we use one
phase annulus with a phase shift of π in different positions over the pupil and finally an alternating phase between 0 and
π over the pupil.
Merit functions of the different filters are calculated. The radial and axial point spread function (PSF) or the 3D line
spread function show that in some cases these phase only filters will shift the best image plane. The experimental results
show the close correlation to the calculated shift of the best image plane.
The strong side lobes that appear in the merit functions lead to the conclusion that the image quality will be influenced
as well. This can be confirmed by the calculation and the measurement of the image intensity. So in order to get more
information about the expected image it is necessary to study the 3D modulation transfer function (MTF). With the MTF
one can see that the contrast decreases for the image obtained with each filter in comparison with the image obtained
with the clear pupil.
The conclusion of our work is, that it is necessary to study the influence of all merit functions in order to design an
optimum filter for a given application.
In the Physics degree in Spain the students have a mandatory course in Fundamentals of Optics as well as an Optics Laboratory course. With these two courses the students receive a general background of optics. There are also some optional courses on Optics in the last years of the degree. One of them is a course on Optical Image Processing and Holography. This course has 60 hours (equivalent to 6 credits of a total number of 300 credits in the Physics degree). Fifteen hours of the course correspond to the laboratory experiments. In this contribution we will describe the contents of this laboratory experiments and we will also discuss the influence of this laboratory in the background of a physicist. The laboratory works consist of three lab experiments about the following topics: Diffraction, Coherent Spatial Frequency Optical Filtering and Holography. Optical Image Processing and Holography course survey of students’ opinion is presented to analyze different pedagogical aspects.
In this work we propose different types of combination of several diffractive lenses written onto a single programmable
liquid crystal display (LCD) in order to increase the depth of focus (DOF) of the imaging system. Each lens is designed
in such a way that lenses with consecutive focal lengths provide amplitude distributions along the axis that overlap. The
lenses are spatially multiplexed onto the LCD following different schemes: by sectors, by rings and randomly. We
compare experimentally the Point Spread Function (PSF) in transversal planes along the optical axis with a single lens
and with the designed multiplexed lenses. The intensity profiles are also compared. The random multiplexing is the
combination technique that brings the best results in terms of DOF.
The amplitude and phase modulations provided by a liquid-crystal spatial light modulator (LCSLM) depend strongly on
the wavelength used for illumination. This is the main reason why usually LCSLMs are only applied with
monochromatic illumination. However, there are a number of potential applications where it would be very interesting
to combine the programmability provided by LCSLMs and the use of non- monochromatic illumination. In this work we
focus on two such applications. On one hand, we use an axial apodizing filter to compensate the longitudinal secondary
axial color (LSAC) effects of a commercial refractive optical system on the polychromatic point-spread function (PSF).
The configuration of the LCSLM has been optimized to obtain the amplitude-mostly regime in polychromatic light. On
the other hand, we show a programmable diffractive lens which is able to provide equal focal length for several
wavelengths simultaneously. To achieve this achromatization it is necessary that the LCD operates in the phase-only
regime simultaneously for the different wavelengths. Both experimental and numerical results will be provided in this
work showing the feasibility of the two applications, and thus the use of LCSLMs under non-monochromatic
In this paper we will revise the application of twisted nematic liquid crystal displays (TN-LCD) as spatial light modulators (SLM) for image processing and diffractive optics. In general two kind of responses are desired for the mentioned applications: amplitude-only and phase-only modulation. In general the users of commercially available LCDs do not know the optical properties of the used material. Thus, a reverse-engineering approach is needed to optimize the LCD response. First, we show a simplified model, that we recently proposed, for the orientation of the LC molecules. The model allows the determination of the physical parameters of the LCD by means of simple intensity measurements. Second, we demonstrate the capability of the model to provide very accurate predictions of the optical transmission. Therefore, we can perform computer searches for the optimum orientation of the added polarizing elements to obtain the required optical transmission. We demonstrate the need to insert wave plates in front and behind the LCD to obtain either amplitude-only or phase-only regimes with the LCD. Finally, we show the application of the optimized LCD to display images and filters in optical image processing, as well as we show the design of diffractive optical elements and apodizers.
We show the feasibility of two new programmable diffractive optical elements (DOE). On one hand, we demonstrate the realization of programmable apodizers. With the term apodizer we refer to non-uniform amplitude filters used to modify the point-spread function (PSF) of an optical system. On the other hand, we show the simultaneous realization of a Fresnel lens and an amplitude filter in a single DOE: the programmable amplitude apodized Fresnel lens (PAAFL). Two different modulation regimes are required to generate these DOEs: amplitude-only regime for the programmable apodizer and phase-only regime for the PAAFL. We show that a twisted-nematic liquid crystal spatial light modulator (TN-LCSLM) inserted between two wave plates and two polarizers is able to provide both modulation regimes. Different types of amplitude filters, such as axial hyperresolving, transverse apodizing and transverse hyperresolving have been implemented both as programmable apodizers and as PAAFLs. We provide experimental results for the performance of the two new DOEs. The agreement with the numerical results is excellent, thus demonstrating the feasibility of our proposal.
In this paper we show a technique to simultaneously encode a Fresnel lens and an amplitude filter in a single diffractive optical element (DOE) displayed on a spatial light modulator (SLM). IN particular we have displayed this new DOE, which we call amplitude apodized Fresnel lens (AAFL), on a twisted nematic liquid-crystal working in the phase-only regime. The programmability of the AAFL permits to change dynamically its focal length and its action on the point-spread function of an optical system. We provide a method to encode the complex amplitude information of the AAFL on a phase-only function. We also demonstrate how to compensate for the inherent equivalent apodizing effect due to the pixelated structure of SLMs. Different types of AAFLs, such as transverse apodizing AAFL and transverse hyper resolving AAFL are implemented. The excellent quantitative agreement between experimental and numerical results shows the feasibility of AAFLs on a phase-only SLM.
Here we study the focusing properties produced by apertures having supergaussian ring profiles, which contain the narrow ring as a limiting case. The supergaussian rings are compared with equivalent ring pupils for different amplitude transmission widths. Numerical results show that both types of pupils produce superresolution with great depth of focus (DOF). Though the annular pupil produces in general higher values of the superresolution and DOF for a given amplitude transmission width, the supergaussian ring concentrates better the energy into the focus.
We have studied nonuniform transmission filters to improve resolution and/or Depth of Focus in lithography. To understand the transmission behavior of these filters for periodic structures we discuss the Apparent Transfer Function in dependence on the defocus. We use the Apparent Transfer Function that is defined by the contrast of the corresponding spatial frequencies, and we analyze the behavior of the system for coherent, incoherent and partially coherent illumination.
Non-uniform transmission filters are used to modify the response of an optical system. We have applied different types of annular colour filters to systems with residual chromatic aberration and an achromatic correction. These filters can shift the chromaticity at the maximum (that is out of the white zone due to the residual chromatic aberration) to the white zone. They can also modify the illuminance distributions in different ways, producing effects like hyperresolution, apodization and variation of the depth of focus.