Alumni



Guillaume Allain, MSc
Yasmine Alikacem, MSc
Aymen Arfaoui, PhD
Alexandre Baril, MSc
Caleb Bayard, MSc
Simon-Gabriel Beauvais, MSc
Gabriel Boivin
Sébastien Bouchard, PhD
Jeck Borne, MSc
Alexandre Cléroux Cuillerier, MSc
Olivier Côté, MSc
Xavier Dallaire, PhD
William Deschênes, MSc
Mathieu Gagnon, MSc
Rafael Guillermo González-Acuña, PhD
Jason Guénette, MSc
Erik Kretschmer, PhD
Jonathan Laberge, MSc
Gabriel Lachance, MSc
Jean-Philippe Langelier, MSc
Martin Larivière-Bastien, PhD
Raphaël Larouche, MSc
Jean-Philippe Leclerc, MSc
Hugo Lemieux, MSc
Renaud Lussier, MSc
Julie Mandar, MSc
Stephane Melanson, MSc
Simon Munger
Mireille Ouellet, MSc
Denis Panneton, PhD
Deven Patel, MSc
Jocelyn Parent, PhD
Charles Pichette, MSc
Anne-Sophie Poulin-Girard, PhD
Mireille Quémener, MSc
Madison Rilling, PhD
Frédéric Roy, MSc
Cédric Vallée
Maxime Vernier, MSc



Guillaume Allain, MSc

Université Laval

Master's Project: Spatially modulated low-order wavefront sensor (2019)
Direct imaging aimed at the detection of exoplanets raises new challenges in astronomical instrumentation. The use of high-contrast coronographs to do such tasks requires that the optical system as well as all atmospheric turbulance are corrected near the limit of diffraction in order to remove the light from the adjacent star and detect faint objects that could be near that star. These tight requirements on stability require the use of wavefront sensor specialised in the fast and accurate detection of low-order aberrations (typically pointing and focus errors) to achieve the contrast of 10-7 to 10-9 between the star and the planet.

In missions using small telescope where the light collection is limited, pyramidal wavefront sensing become more interesting because of the more efficient use of light. When these types of wavefront sensor need to detect aberrations of larger amplitudes, they usually use temporal modulation of the beam py the use of high frequency piezo-electric mirror. These kind of modulation add new risks that cannot be waived for spatial missions or stratospheric balloon-borne missions. The solution presented in this thesis makes use of an optical element (axicon) in order to emulate instantly the behavior of these modulating wavefront sensor and still maintains enough performances to be used as a low-order wavefront sensor. The integration of this spatially modulated wavefront sensor in two astronomical systems shows the viability of this solution to detect and correct in closed loop the aberrations from a star.




Yasmine Alikacem, MSc

Doric Lenses

Master's Project: Design, construction, calibration and experimental validation of a miniature detector to measure in-ice nutrients concentrations (2021)
Blooms of microalgae in the ocean require abundance of both light and nutrients. After the polar night, ice algae start growing as soon as enough light reaches the bottom of sea ice. Because of climate change, the Arctic icescape is getting thinner and dominated by first year ice, which results in earlier ice algal blooms. An early bloom, however, does not necessarily imply an increase in annual ice algae net primary production in the Arctic. The intricate balance between nutrients, specifically nitrate in the Arctic ocean, and light availability have been shown to control annual primary production. The amount of available nutrients for ice algae depends on the flux nutrients from the upper ocean to sea ice, and transport within sea ice. Both processes are difficult to quantify because they take place at small space and time scales. Traditional sea-ice sampling methods hardly allow capturing such variations. To better understand how the flux of nutrients from the upper ocean to sea ice and their transport within sea ice are controlled by the physical properties of the two media is especially important in a context where the Arctic icescape is profoundly changing together with sea-ice biology. This research project aims at developing an optical sensor to measure in situ sea-ice nitrate concentration at small scale. This sensor will be integrated onto a Sea Ice Endoscopic (SIE) platform, a non-destructive multimodal probe which will be used to characterize sea ice radiative transfer and brine biophysical systems.




Aymen Arfaoui, PhD

Revenu Québec

PhD Project: Calibration and modelling of a hybrid panoramic stereoscopic vision system (2015)
This thesis aims to present our contributions to the resolution of two problems encountered in the field of computer vision and photogrammetry, which are camera calibration and stereovision. These two problems have been extensively studied in the last years. Different camera calibration techniques have been developed in the literature depending on the type of camera (classical or panoramic, with zoom lens or fixed lens..). Our first contribution is a compact and accurate calibration setup, based on diffractive optical elements, which is suitable for different kind of cameras. The technique is very robust and optimal results were achieved for different types of cameras. With the multiplication of camera types and the diversity of the projection models, a generic model has become very interesting. Our second contribution is a generic model, which is suitable for conventional and panoramic cameras. In this model, composed cubic splines functions provide more realistic model of both radial and tangential distortions. Such an approach allows to model either hybrid or panoramic stereovision system and to convert panoramic image to classical image. Consequently, the processing challenges of a hybrid stereovision system or a panoramic stereovision system are turned into simple classical stereovision problems. Keywords: Calibration, panoramic vision, distortions, fisheye, zoom, panomorph, epipolar geometry, three-dimensional reconstruction, hybrid stereovision, panoramic stereovision.




Alexandre Baril, MSc

Ver-Mac

Master's Project: LED smart lighting prototype using light modulator (2017)
Since the massive invasion of LED lighting over the illumination market, a clear trend of need appeared for a more efficient and targeted lighting. The project leads this trend by developing an evaluation board to test smart lighting applications with a new liquid crystal light modulator recently developed for broadening LED light beams. These modulator are controlled by electricals signals and they are characterised by a very linear working zone. This feature allows the implementation of a closed loop control with a sensor feedback. We show that the use of computer vision is a promising opportunity for closed loop control. The developed evaluation board integrates the liquid crystal modulator, a camera, a LED light source and all the required electronics to implement a closed loop control with a computer vision algorithm.




Caleb Bayard, MSc

MDA

Master's Project: Characterization of a freeform image slicer for the GIRMOS instrument (2021)
GIRMOS (Gemini Infrared Multi-Object Spectrograph) is an infrared multi-object spectrograph intended for the twin 8.1-meter diameter optical/infrared telescopes of Gemini Observatory. The spectrograph optical design is based on the image slicer concept. Image slicer systems are usually composed of three distinct subsets: mirror-slicer, pupil-mirrors (or lenses) and slit-mirrors (or lenses). Their function is to cut the image from the telescope focal plane into slices, then to align each of these slices end to end; while keeping the image of the telescope pupil.

Image slicer system is central to the proper functioning of the GIRMOS spectrograph module, it is essential that it meets the established criteria and requirements. So, this research project consists to characterize a freeform image slicer system by performing a test series. The project is divided in three parts. The first part is to define the elements to characterize and the methodology to use. The second part is the implementation of tests through the design and development of test bench. The final step is to evaluate the performance and impact of image slicer systems on the GIRMOS spectrograph module.




Simon-Gabriel Beauvais, MSc

Immervision

Project: Artificial intelligence and predictive adaptive optics
Adaptive optics allows for the correction of atmospheric aberrations on images taken from ground based telescopes. Following the development of this technique, great advancements in the field of astronomy were made possible, from exoplanet discoveries to the study of atmospheric pattern within our solar system. The problem with the real time correction of images is the considerable investment in materials and the computational time required. With the recent advances in artificial intelligence and machine learning, the application of neural networks to adaptive optics would allow for the reduction of the computation load required while also improving the quality of the images post correction. This would render this technique more accessible and portable, allowing for it’s installation in more observatories and telescopes.

This project consists in the development of a neural network capable of operating a deformable mirror and work out the correction required to remove the aberration from the images while also allowing for the prediction of the next corrections to apply. The training of this network will be accomplished with a observation simulator, an optical bench capable of reproducing atmospheric aberrations, and observations from the telescope HiCIBaS, allowing us to also resolve application problems with the neural networks in realistic context.




Gabriel Boivin

Master's Project: Characterization of a blazed diffraction grating used for infrared spectroscopy
Diffraction gratings are optical device that make an angular differentiation of a light beam as a function of the wavelength. Wavelength separation is essential for spectroscopy, especially in astronomy. With the grating being a key element in the optical design of a spectrometer, making sure that the chosen grating will meet the requirements is essential. Unfortunately, the characterization and performance evaluation of diffraction grating is a challenging task. Currently, no standardized method is recognized in the community; every manufactured has its own way to do it. Therefore, the main objective of my master's project is to design and implement an experimental setup and procedure to measure the performance and characterize diffraction gratings. It will enable the comparison of various gratings from different manufacturers to select the most appropriate component for an astronomical instrument.




Sébastien Bouchard, PhD

Creaform

PhD Project: Design and implementation of a novel solar concentrator reducing the need for solar tracking (2016)
Since a long time, the Sun is seen as an interesting source of renewable energy. However, the prohibitive cost of solar energy has made it mostly unused. To increase it acceptance, it is necessary to bring the cost down and make it competitive with fossil fuels. To achieve that, many possibilities exist. One method is the use of an optical system to concentrate sunlight. This thesis presents a solution based on the design of a new type of solar concentrator of low-medium concentration level made of polymer to be able to achieve low-cost fabrication. The performances of this condensed optical system which uses microlenses were then improved by the introduction of a refractive index gradient in the polymer matrix. A short analysis of the cost of the energy produced by such solar concentrators permitted to conclude that they are of commercial interest for the solar community. For this reason, the most promising design based on the use of a graded-index to increase the efficiency has been protected by a patent.

Master's Project: Study of the effet of current and temperature on high-intensity white LED degradation (2011)
Light-emitting diodes have the potential to significantly reduce electrical consumption needed for lighting. Their long life gives hope for light sources that do not need frequent replacement. However, many problems still need to be solved if lightemitting diodes want to attain the promises of energy saving and long lifetime of the manufacturers. So, there is a need for independent testing of the diodes to confirm claims written on the datasheet.

So, three different accelerated life tests were carried on two different types of lightemitting diodes. The results were compared to a reference sample used under the guidance of the manufacturers. The objective of these tests is to verify the effect on the diodes of high temperature storage and high current injection with or without heat control. This allows extraction of the influence of each specific parameter on the diode's degradation and, at the same time, to determine if the accelerated degradation is proportional to the increase in the operating conditions. It seems that the degradation pattern is different for each light-emitting diode model, which will cause problems for the development of a global degradation model.




Jeck Borne, MSc

Université Laval

Master's Project: Toward the validation and generalization of the extended Richards-Wolf formalism (2019)
This project is part of the modeling effort around extreme focusing phenomenon taking place in the research groups of professor Thibault and Piché. At first, this thesis shows the comparison between the modeling by the extended RichardsWolf formalism (ERWT) and by FDTD simulations of the field propagation. Both methods used for computing the electromagnetic distribution resulting from the reflection on a mirror in a non paraxial setup show satisfactory agreement. In fact, the extended formalism is suited to accurately model a large spectrum of reflecting surfaces such as elliptic mirrors, for which the description is not possible with the classical formalism of Richards-Wolf. Some intrinsic limitations of the used FDTD algorithm and the divergence of the illumination could explained the observed variations. Then, looking to solve the illumination problem, the inversion formalism has been developed. The integral of the Richards-Wolf formalism (RWT) of an axisymetric optical system can be inverted to define the radially polarized illumination pattern as a function of the electromagnetic distribution at the focus over a given axis (radial or the optical axis). Using only one axis at the focus, the field distribution is not overdefined and a criterion is given to check the physical validity of the obtained illumination pattern. The method gives numerical or, in some cases, analytic solutions that can be used to obtain the optimized focal pattern for a given application. The analytical solutions are relevant as they can intuitively show the differences between the paraxial and non paraxial regimes. An article has been submitted on this particular subject. Finally, this thesis describes the generalization of the extended formalism to cover aspheric surfaces with aberrations. The procedure gives the possibility to accurately model complex reflecting surfaces that would otherwise be out of reach of the formalism. However, the complexity of the formalism increases compared to the initial diffraction integral. The proposed technique is demonstrated with a slightly tilted parabolic mirror.




Alexandre Cléroux Cuillerier, MSc

Université Laval

Master's Project: Integration of metasurfaces in optical design (2022)
An intuitive understanding of the intrinsic properties of traditional materials has enabled the development of a multitude of optical instruments limited by the classical laws of optics. The arrival at the beginning of the millennium of metamaterials and their two-dimensional counterparts, metasurfaces, proposes an innovative approach to the manipulation of electromagnetic waves using exotic properties not found in ordinary materials. Although this technology promises to overcome the limitations of conventional optics, the integration of metasurfaces into existing optical systems poorly investigated avenue. My project aims to explore, through an experimental approach, the design of optimized metasurfaces in a context of integration with complex optical systems. Effective integration of metasurfaces into existing optical systems offers a wide range of technological, scientific, and medical applications. For example, this integration would, among other things, enable superior imaging performance using metalenses that greatly limit aberration. Besides, the reduction of complex systems to a few meta surface-based components has enormous potential in the industry.




Olivier Côté, MSc

Exfo

Master's Project: HiCIBaS: Design of a pointing and guiding system for a stratospheric balloon borne telescope (2019)
This project is part of the High Contrast Imaging Balloon System (HiCIBaS) project. The aim of the HiCIBaS project is to launch at an altitude of 40km a telescope equipped with an adaptive optics system to perform high contrast imaging of stars. My responsibility in this project is to design the system that orients the telescope to a target star. Also, the system must be able to stabilize the telescope to a precision of less than an arc second. There are three main parts to this project. First, the system must be able to find the orientation of the telescope by analyzing only an image of the sky. Second, the system must be able to detect the nacelle’s movement in roll, pitch, and yaw. Finally, the system must communicate direction commands to the telescope’s motors.




Xavier Dallaire, PhD

Leddartech

PhD Project: Wide-angle lenses miniaturisation (2018)
The miniaturization of optical systems, particularly wide-angle systems, is a subject of great importance. The reduction in size of optical components allows the integration of cameras in a wider range of applications. Even though continuous improvements in production techniques have led to great advances in the field of miniaturization, new techniques have to be developed in order to further miniaturize. The aim of this PhD project is to adapt and develop miniaturization techniques applicable to wide-angle optical systems. Through the study of various miniaturization techniques, the folded lens joined to foveated imaging and the correction of aberration via plenoptic imaging were retained as candidates allowing the miniaturization of wide-angle camera. Chapitre 3 gives an overall picture of the various avenues used in the literature for the miniaturization of optical systems. A short description of the techniques is presented as well as the reasons why some were discarded. An original miniature wide-angle endoscope design is presented in Chapitre 4, as well as the entire design and tolerancing process. The use of a fold in the system reduces the effective size of the system. Foveated imaging is used to control magnification in areas of interest. Two versions of the endoscope with different variations of their lfl are analyzed. It is shown that active control of distortion at during design can maintain the performance of an optical system in certain key regions of the field of view while reducing the number of elements that compose it. A reprojection algorithm for reconstructing an aberrated plenoptic image is presented in Chapitre 5. It is shown, through simulations, that it is possible to correct aberrations present in an optical system. Monochromatic, polychromatic and wide angle cases were successfully addressed and corrected. It was also demonstrated that the correction algorithm do not amplify the noise present in the original image. Finally, a simple prototype of a plenoptic camera was designed and tested in the laboratory.

Master's Project: Analysis and tolerancing of systems using a freeform frontal lens (2013)
In light of the new development of the production methods, free-form lens are used more frequently in optical design. However, their mathematical definitions as well as their specific shapes tend to make their tolerancing and reactions to perturbations hardly predictable. In consequence, the tools used by optical designers, like optical design programs, are not always able to help as they should. First, this document presents the recent developments and the theoretical concepts concerning these subjects. Thereafter, the analysis of a panomorph lens which has a free-form lens as a first surface reveals numbers of particular behavior showing relations between the field curvature and the footprint. Finally, a new tolerancing technique is presented. Using a perturbative analysis requiring a minimum of computing power, it is possible to reduce the allowed margins of error of certain variables while maximising the gain in image quality. This technique was particularly efficient in cases where the adjustment of the focus was spatially limited.




William Deschênes, MSc

Fiso

Master's Project: Adaptive optics testing focal plane box for the Observatoire du Mont-Mégantic (2016)
New technologies for large scale telescope projects need to reach a high level of technological maturity before they can be integrated. The project involves the creation of an adaptive optics test bench for evaluating the onsky performance of adaptive optics related devices. The test bed was successfully installed on the Mont Mégantic observatory, and was used to evaluate the performance of a pyramid wavefront sensor. The system effectively halved point-spread function size. Several improvements to the system are possible to improve performance.




Mathieu Gagnon, MSc

Teraxion

Master's Project: Wide-angle 3D vision system based on Kinect V2 for outdoor navigation (2019)
In collaboration with the Innovative Vehicule Institute (IVI), we are developing off-road autonomous vehicle for application in agriculture. More precisely, our project is to conceive and build a 3D captor for navigation. Features include resistance to dust, vibrations and lighting conditions for outdoor application. Our approach consists in using low-cost system like Kinect V2 from Microsoft and increasing its angle of view up to 180 degrees using panomorphic lenses, while keeping enough resolution for good environment perception.

The first step is to analyse the Kinect V2 on its technical features and its operation. Also, identifying and quantifying the Kinect V2 limitations on lighting and 3D measurement will be necessary. The second step is to conceive an optical attachment increasing the Kinect angle of view. The third step is to implement this attachment with a module directly fixed on the hardware. The final step is to test in real condition our system to obtain a working product for autonomous off-road vehicle.




Rafael Guillermo González-Acuña, PhD

Huawei Finland Camera Lab

Postdoctoral fellowship (2021-2022)
Rafael G. González-Acuña holds a bachelor degree in physics, a bachelor degree in mathematics, and a master’s degree in Opto-mechatronics. He obtained his PhD at the Tecnológico de Monterrey (Mexico). During his PhD thesis, he worked on the general equation of stigmatic lenses and he studied its properties. He currently has authored a total of 19 journal papers as the first and corresponding author, receiving two Editor’s pick distinctions. He has obtained 17 awards and scholarships including the 2019 Optical Design and Engineering Scholarship (SPIE), the Romulo Garza science award 2019 for the best postgraduate research at Tecnológico de Monterrey and an invitation to 70th Lindau Nobel Laureate Meeting. He is the co-author of the book Analytical lens design and Stigmatic optics (Institute of Physics Publishing Ltd). He has also joined several institutions for research internships, including the Institut für Technische Optik (Germany), Yachaytech (Ecuador) and Auckland University of Technology (New Zeland).




Jason Guénette, MSc

Université Laval

Master's Project: Design and test of a index gradient axicon (2019)
Axicons are mostly known for their capacity to produce Bessel beam. However, some axicon has the propriety to produce annular focusing whether directly or by adding a lens. In this text we have study the possibility to produce an axicon with gradient index of refraction that produce an annular focusing. More precisely we study the possibility to produce a component which incorporates the linear function of a conical lens and the parabolic function of a lens. The study refraction index profile has a radial variation and allow to a periodic annular focalisation. A similar refractive index profile has already been study by E. Marchand then by Rosa M. However, the solutions proposed by them are approximate solutions and their studies are limited. Some optical fiber already has index profile like the one we are interest so this axicon have the potential to be use for optical fiber application. We have demonstrated theoretically the exact refractive index profile that produce annular focusing and we have demonstrated theoretically that the ring produce is of good quality. We have also studied the possibility to produce a Bessel beam with this device that we name GLA (Grin Lens Axicon) and the simulation show that the beam could be of excellent quality. Some experimental tests have been done to show that it is possible to produce a Bessel beam with a GLA.




Erik Kretschmer, PhD

Karlsruher Institut für Technologie

PhD Project: Modelling of the instrument spectral response of conventionnal and imaging fourier transform spectrometers (2014)

Spectroscopy and the measurement of light spectrum have become essential tools in a large number of fields, from analytic laboratories to remote sensing field measurements. In these applications, the use of Fourier transform spectrometers (FTS) is widespread and, more recently, imaging Fourier transform spectrometers (iFTS) are becoming ever more popular. The iFTS instruments enable spatially resolved highresolution spectral analysis within a single measurement, thus allowing the study of fine spectral variations in observed scenes. Such measurements inherently include systematic errors which can be in large part described by the instrument spectral response function, often referred to as SRF. In the case of iFTS, each pixel of the instrument will sport a different spectral response, which opens a whole new dimension not only in the measurement itself, but also for error analysis and instrument design. Because of their unique imaging capacity, iFTS instruments are a prime choice for remote sensing applications from airborne or spaceborne platforms for the measurement of the Earth atmosphere, as well as the atmosphere of other celestial bodies. The requirements on the spectral accuracy demanded by such missions are very high. To achieve these requirements, an excellent knowledge of the instrument spectral response is essential. Modelling of the spectral response of iFTS instruments is a possible approach to achieve the desired knowledge of instrument performances. This thesis offers a review of the factors affecting the spectral performances of FTS instruments from which a numerical model of the spectral response specifically designed with imaging instrument in mind is proposed. This model integrates optical effects which were up to now only studied separately – if at all – and not integrated in a global performance model of the instrument. The necessity to consider these effects, such as those caused by the optical transfer function of the detector imaging optic or the architecture of the imaging focal plane array (FPA), is demonstrated. Using dedicated measurement of the airborne iFTS GLORIA (Gimballed Limb Observer for Radiance of the Atmosphere), the application of the model for performance analysis and review is demonstrated.




Jonathan Laberge, MSc

Cégep de Rimouski

Master's Project: Analysis of the telescope's optical aberrations at the Observatoire du Mont-Mégantic (2012)
The telescope at the Observatoire du Mont-Mégantic is in operation since late 70's. The wide range of instruments available makes it one of the most versatile telescopes in the world. However, very few data exist with respect to its optical aberrations. It is important to know these aberrations if we want to improve the optical performance ofthe telescope.

In order to evaluate thess aberrations, two methods of wavefront reconstruction were used: the Shack-Hartmann wavefront sensor and the wavefront curvature sensor. Analysis of the reconsctructed wavefronts identifies the dominant aberrations as well as several parameters influencing these aberrations. Furthermore, the methods are compared in order to know if they can be used to align the primary and secondary mirrors.




Gabriel Lachance, MSc

Université Laval

Master's Project: Design and test of underwater fibre-optic irradiance measurement and logging system (2020)
The research project consists of creating and installing an underwater light sensor system that will be used in the fresh water lakes of the Canadian arctic using resources from the COPL, the CEN and Sentinel North. We now know that a system using fiber optic sensors would be ideal for this purpose as it is autonomous. This method of using a fiber optic sensor is able to detect light at different depth in water simultaneously. By using a passive fiber optic sensor system, it is possible to create tools that are able to be deployed in the field for long periods of time and be able to take measurements without the need for a technician. To be able to do that, the instrument is required to not have any moving parts and needs to be tested rigorously to assure the well-being of the instrument for long periods of measurement in the extreme conditions of the Canadian’s arctic. Experiments in laboratory are going to be required to test the different parts of the project and to assemble the system. Then, the detectors coupled to the fibers must be tested to increase their efficiency. It will be required to make and use an optomechanics and electronic assembly to be able to obtain a first prototype that can be submitted to conditions like those that will be experienced on the field. Finally, the assembly and the deployment of the instrument will be done as a way to test how it works on the field and to gather data concerning the quantity of light present underwater in arctic lakes. By deploying the instrument, it will be possible to gather some preliminary data which will be used by the biology research team involved to this project to draw conclusion concerning the amount of light available underwater and the changes that it can cause to the microbiome of the lakes.




Jean-Philippe Langelier, MSc

Master's Project: Measuring polarimetric properties of snow (2022)

The study and measurement of the properties of snow has occupied scientists for almost a century for many reasons. Few of them are to learn more about the process of avalanches, to understand the hydrology of certain regions, to study climate change or to study lemming populations. Wind and temperature gradients in the snowpack influence the structure and macroscopic physical properties of snow throughout the winter. Currently, no device is able to monitor all of these changes. However, few optical devices have been designed to characterize certain parameters influencing radiative transfer: the specific surface area SSA, the absorption enhencement parameter B and the asymmetry parameter g. These are limited to making intensity measurements that can retrieve a single parameter per geometry. The other parameters are estimated, which may induce errors from 10% to 15% on the retrieved parameters. Making these devices sensitive to polarization would allow them to make measurements in intensity and polarization, resulting in retrieving two parameters per geometry and avoiding to make estimates. For this, the polarization must vary differently from the intensity to the snow properties and can’t depend on unknown properties other than ρ, SSA, B and g. Many research has attempted to find a link between polarization and snow properties, but none has succeeded in determining an analytical equation. This research goal was to investigate whether the introduction of polarization in an optical device would allow a new type of measurement, thus helping to characterize the four target parameters. For this, the effect of each of the parameters SSA, ρ, g and B on the polarization is studied. First, the effect of the snow crystal shape via parameters B and g is studied by ray tracing for a single particle. It is found that these parameters vary greatly with polarization and that the radiative transfer depends on the polarized form of B and g. Thus, in a porous medium, the radiative transfer for a polarized beam would depend on the polarized forms of B and g. Therefore, polarization cannot be used when the shape of the snow crystal could vary, unless a link between the non-polarized forms and the polarized forms of B and g is found. Then, the effect of ρ and SSA are studied in a porous medium by designing a Monte-Carlo raytracing and a raytracing in a two-phase medium. It is shown, that the two types of raytracing converge very well when the size parameter x inferior to 5000 and the porosity φ inferior to 0.5. The intensity (I) and the degree of polarization (DOP) are studied under several geometries in transmission and in reflection. For a weakly absorbent medium (µₐ ≪ µʹₛ), it is seen that the DOP varies according to SSA and ρ in the asymptotic diffusion domain as DOP(z) proportional to e[exp SSA*ρ*z], where z is the distance between the source and the detector. This relation seems to be independent of the geometries tested. The effect of absorption is also studied. No equation has been found to characterize his effect. However, it has been shown that, for a weakly absorbing medium (µₐ ≪ µʹₛ), the DOP is independent of µa and, therefore, of the variation of B to the polarization. Laboratory tests on glass beads medium are made to confirm the relation DOP(z) proportional to e[exp SSA*ρ*z]. It is shown that, for the three smallest beads, the effect of absorption is negligible on the DOP (µₐ ≪ µʹₛ). Using the laboratory measurements for the DOP and the intensity, ρ and SSA are retrieved. This method is only valid for the geometric optics approximation (x much smaller than 100), for a weakly absorbing medium and for a known crystal shape.


Martin Larivière-Bastien, PhD

Telops

PhD Project: Performance improvement for panoramic and Panomorph imaging systems (2014)

Because of their large field of view, panoramic and Panomorph imagers are modules of interest in optical design. An important field of view introduces many aberrations in a system. To obtain the desired image quality, aberrations are generally minimized by the optimization of certain optical components, but this practice has its limits. The goal of this project is hence to investigate other techniques that would allow breaking these limits. Three types of techniques are investigated: hardware, software and hybrid. In the hardware section, the curved sensor and the freeform field lens are analyzed. It is shown that they allow for a best focus effect on the whole image. The curved sensor can also be used to create a monocentric system which simplifies the optical design and gives increased performances compared to the traditional system. In the software section, the gains obtainable by image processing are highlighted. It is shown that even with the important variation of the PSF across the field of view, deconvolution still increases image quality as a whole. Lateral color correction gives additional improvement of the image. Both methods are sufficiently fast to consider a video application. The last section addresses wavefront coding. Two methods of optimization are presented: optimization by the MTF and optimization by the variance between object and image. The optimization by the variance requires more computation time but gives better results because it considers the effect of image reconstruction and noise. In this section, simulations are also used to compare the performances and the applicability of two phase mask types. It is shown that the cubic phase mask is more useful to correct defocus and astigmatism while the quartic phase mask is better for coma and Gaussian white noise. Using the information obtained with the simulations, a prototype based on the IMV1 ImmerVision lens was built. Unfortunately the cubic phase mask manufactured had a surface roughness that was too high and the resulting images are noisy.




Raphaël Larouche, MSc

Immervision

Master's Project: Design, construction, calibration and experimental validation of a miniature detector to measure in-ice radiance distribution (2021)

This research project consists in designing and building a miniature instrument to measure angular radiance distributions within sea ice. In Northern Hemisphere, sea ice is thinning and decreasing in extent, which has impacts on climate and biology. Radiance is a fundamental radiometric quantity related to medium's inherent optical properties by the radiative transfer equation. Inherent optical properties depend solely on physical properties. Improving structural-optical links would allow better understanding of radiative transfers in sea ice which influence energy/mass budgets and primary production. Previous studies sampled in-ice radiance angular distributions, but those measurements were constrained by bulky radiometer destroying the medium, provided limited vertical and angular resolution or inducing shadowing.

Therefore, we aim at integrating miniature fish-eyes to the probe. This type of lens permits collection of radiance from all directions simultaneously. To account for sea ice structural components spectral signatures, an optic filtration system will be included. The first step of the project consists at defining requirements and choosing a design. The second part is to build a prototype, characterize it and calibrate it for angles and absolute radiance. Finally, field deployment will allow sampling of preliminary measurements to confirm the performances of the probe.




Jean-Philippe Leclerc, MSc

Nutriart

Master's Project: Real-time characterization of sugar particles in a chocolate flow (2020)

The chocolate industry is increasingly competitive. Industrial players in this field must manufacture a product of very high quality at the lowest possible cost. Consumers expect a product of great finesse and smoothness comparable to chocolate considered very high-end only a few years ago. To do so, manufacturers must have the tools to measure and control their process with great precision. One of the main characteristics of chocolate is the size of the sugar particles: the smaller the sugar particles, the thinner and smoother the chocolat. On the other hand, the production of fine chocolate is costly in terms of time and raw material. The goal of this project is to develop a measurement method to characterize the size of sugar particles during production in order to be able to correct it in real time. The concept developed is faster, more reliable and easier to set up than the devices currently available on the market and does not require complex calibration. Once integrated into a 5-roller refiner, it allows the size of the sugar particles to be controlled to within 3 microns. The use of this method allows to reduce machine and human time, limit the use of expensive ingredients and ensure high quality chocolate day after day.




Hugo Lemieux, MSc

Eddyfi

Master's Project: Study and comparison of LED lamp power supply strategies (2011)

As energy efficiency is becoming a priority, light-emitting diodes (LEDs) luminaires are a first choice light source. Although more expansive than other sources, they offer, in addition to a great efficiency, a long useful lifetime, which makes them a very interesting option in the long run. As all other light sources, they suffer from luminosity degradation, which reduces their luminous flux as well as their efficiency. In order to better control this luminosity degradation, power strategies can be used. Two of these strategies are current control and chain control, the first varying the current and the second the number of open LEDs. To study and compare those two strategies, a mathematical model has been developed and a simulation program has been designed. Results showed that in addition to keep a more constant luminous flux, power strategies can enhance energy efficiency and lifetime of a LEDs luminaire or reduce the required number of LEDs, reducing the initial cost.




Renaud Lussier, MSc

PhD Project: Polymer/magnetic nanoparticle nanocomposite based new deformable mirrors

Deformable mirrors are the master piece of an adaptive optics system. Their size, the materials they are made of, their actuation system and their deformability are driven by the desired application. There is no mirror that is appropriate to every application. Low cost and versatile deformable mirrors could help democratize adaptive optics technologies. Research for new types of deformables mirror is thus relevant. The doctoral project pursue the motivation of developping new deformable mirrors for adaptive optics. The technology of interest is based on polymer/magnetic nanoparticle composites. Polymer, more precisely elastomers, have a high deformability, are generally easy to process and have diverse mechanical properties. Magnetic nanoparticles can be incorporated into elastomers to produce deformations using localized magnetic fields.

The proposed technology stands out from the current deformable mirrors by the low cost of the materials used and by the relative ease of assembly. Also, the deformable surface is totally independent of the actuating system since there is no physical contact between them and the material is uniform. This type of deformable mirroir will thus be very versatile. During the project, the assembly process is developped and the properties/performances of the device are optimized in order to produce operational magnetically deformable mirrors.




Julie Mandar, MSc

ABB

Master's Project: Development of SITELLE's performance model (2012)

SITELLE is a new imaging Fourier transform spectrometer to be installed at the Canada-France- Hawaii Telescope. The development of its dedicated performance model drives the design of the instrument and the flow down of the science cases requirements into system requirements. First, the selected configuration with off-axis flat mirrors makes the achievement of a high efficiency in the near ultra violet easier. Secondly, servomechanism’s desirable performances were defined in order to design a photon noise limited instrument, based on a relevant scene. These performances should be maintained during a 4 hours data-cube acquisition, under operational vibrations and external effects such as wind gust hitting the telescope. Ultimately, this instrument performance model is the core of the signal to noise ratio simulator that will help observers to evaluate the potential benefits of SITELLE for their target.




Stephane Melanson, MSc

D-Pace

Master's Project: Colour control of quadrichromatic LEDs using a color detector (2014)

Light emitting diodes (LEDs) are good candidates to become the main light sources of the future given their good efficiency and long life. However, a problem associated to the use of LEDs is the color shift observed at different temperatures, currents and lifetime. The purpose of this work was to implement a control algorithm that uses a color sensor as feedback. Two algorithms were developed to calibrate the detectors. The algorithms were implemented to control RGBA and RGBW LEDs. The first algorithm provides a good calibration for a restricted range of color near the calibration. The second algorithm gives good performances for the entire range of color available to the lamp, but it is less precise than the first algorithm.




Simon Munger

Teraxion

Master's Project: Sub-cellular nanoscopy achievable by focused coherent attosecond X-ray absorption

My project involves the development of a laser beam focusing system in the X-ray and ultraviolet range. These wavelengths were chosen because they are not absorbed by water, but mainly by the atoms composing the organic molecules such as carbon, nitrogen and oxygen. The system is designed with the help of the Zemax optical design software to best simulate the configurations envisaged for the microscope. Implantation in the vacuum chamber is an important step in the project, as space is limited and the ability to move and adjust mirrors is difficult. If the project proceeds as expected, it would theoretically be possible to see biological and organic processes at attosecond scales and resolutions better than conventional optical microscopy.




Mireille Ouellet, MSc

Leiden Observatory

Master's Project: High-contrast optical imaging system on-board of a stratospheric balloon (2019)

Several space telescope projects aim to study exoplanets using high-contrast direct imaging techniques. In order to achieve the required difference in contrast between the light from the star and that reflected by the exoplanet, those systems must use a coronagraph to mask the light of the star and correct in real time wavefront errors with adaptive optics techniques.The aberrations are detected by a wavefront sensor, then a control loop sends a command that modifies the surface of a deformable mirror to compensate for the wavefront errors. However, the performance of adaptive optics systems is often limited by the present quasi-static errors that are caused by the optical path difference between the science camera and the wavefront sensor. A high contrast imaging system has been developed to demonstrate the potential of a control technique which enables the reduction of this kind of error. This control loop has the particularity of using a coronagraph which allows the analyze of the wavefront errors directly from the science camera’s image. The optical system developed within the frameworkof this master’s project has been tested in a laboratory and was also optimized to perform afunctional demonstration in space-like conditions during a balloon flight in the stratosphere.The flight results validated the readiness level of some components that could potentially beused for the next generation of space telescopes.




Denis Panneton, PhD

INO

PhD Project: Extreme focalisation using non-paraxial optical elements

This project is part of a global effort toward modelization and development of mathematical tools describing non-paraxial focusing of electromagnetic fields. Vectorial solutions are proposed, according to a generalization of the Richards-Wolf formalism. The objective of this thesis is two-fold. The first part covers the Richards-Wolf formalism with a modern mathematical formulation, which permits the formal description of focused vectorial electromagnetic fields. An in-depth exploration of the theory is exposed and multiple analytical solutions of the integrals are given. The second part covers the generalization of the Richards-Wolf formalism to systems without a single-point focus, by combining geometrical optics and diffraction principles. The vectorial analysis agrees with the assumption of non-paraxial focusing while the development is free of constraints upon the existence of an optical focus. Finally, the analytical treatment helps forge a physical intuition of the electromagnetic solutions and the development of inverse methods, which would help find the necessary illumination upon a system to produce a given electromagnetic pattern near the focus. The mathematical tools presented in this thesis may lead to advances in high-resolution microscopy, data encryption, optical tweezers and particle.




Deven Patel, MSc

Actalent

Master's Project: Mechanical structures and thermal management scheme for HiCIBaS's stratospheric balloon mission (2019)

The HiCIBaS (High-Contrast Imaging Balloon System) project is a balloon-borne telescope mission with the big-picture goal of exoplanet-imaging using high-contrast techniques. For the scope of the pilot mission in 2018, the main goals were to develop the necessary systems and validate their performance, acquire flight data, and prove the survivability of all systems and major components in near-space conditions. This Master’s project deals with two aspects of the overall payload: the design of the dynamic alt-az telescope mount for the pointing system and the development of the custom thermal straps for the optics system. The telescope mount is the structure that supports the telescope and allows the pointing system’s motors to direct it to the desired position. The custom thermal straps are a solution that was developed to dissipate the heat generated by the optics system’s main components (cameras, controllers, etc.). Both solutions were tested during an overnight flight in August of 2018 under the Canadian Space Agency’s STRATOS campaign in Timmins, Ontario. This mémoire will define the requirements for both systems, present the development of the designs, detail the analyses and tests performed, demonstrate conformance to the requirements, comment on mission performances, and provide insight on ways to improve both designs for future iterations.




Jocelyn Parent, PhD

Immervision

PhD Project: Locally-variable magnification imaging system for active distortion control (2012)

This thesis presents a novel type of optical system, a locally magnifying imager. The idea behind it is to modify in real-time the distortion by using an active component placed far from pupils, allowing to modify each field individually. With the correct shape on the active surface, it is thus possible to create zones of increased magnification. Also, if the total field of view has to remain constant, it is possible to do so by combining theses zone of interest to zones of settling back where the magnification is decreased. To fully understand how systems with controlled distortion work, an analysis of surface errors is presented. After, from theses results of image plane displacement from a given error, the concept of the locally magnifying imager is developed. ZEMAX simulations are done, confirming the mathematically obtained parameters. The simulations finally lead to an experimental prototype using a ferrofluidic déformable mirror as the active surface. Experimental results with a system that can produce ratios of magnification larger than 3 in a zone of interest are presented and analysed. In short, if the fundamental limits are countered, this locally magnifying imager has the potential of changing some imaging domains thank to their novel capabilities in optical design.




Charles Pichette, MSc

Université Laval

Master's Project: Design and optimisation of detection channels using single-photon avalanche diodes (SPADs) for photon counting in optical diffuse tomography (2017)

This dissertation showcases the improvements suggested for the diffuse optical tomography scanner of the TomOptUS group at Université de Sherbrooke. Diffuse optical tomography is an imaging modality that uses near infrared light (650 - 950 nm) to image small animals such as mice in depth (> 1 cm). This technique is very interesting for pharmacology or oncology where it can be used to track medicine or the progress of pathology. It also decreases the number of necessary sacrifices since it is a non-invasive technique. The temporal progress of the object under consideration can, in that case, be acquired with ease. This technique can also be used with fluorescent agents to track different objects of interest in the animal. This scanner works in time domain where the time of flight of individual photons that propagated through the subject is registered to reconstruct the laser pulse via time-correlated single photon counting with an ultra-fast laser source. The current scanner uses 7 no-contact detection channels positioned in a ring around the subject. This number of channels is too low to obtain a satisfying acquisition time. It was determined that the limiting factor is the need to mechanically rotate the channels around the subject to obtain the necessary angular coverage. To reduce the acquisition time, it was suggested to increase the number of detection channels to 32 or even 64. However, the current channels use photomultiplier tubes which are too bulky to be used with such a high density of detectors. Single photon avalanche diodes have been considered to replace them because of their relative small size, excellent temporal resolution, and better quantum efficiency. These characteristics make them especially efficient for photon counting. These photodiodes, however, have a photosensitive surface with a very small diameter compared to the photomultiplier tubes (25 - 100 μm compared to ≈ 1 cm for photomultiplier tubes). This reduces the photon count rate, lowers the signal to noise ratio, and makes the alignment difficult. The goal of this project is to optimize the design of new detection channels that use these single photon avalanche diodes. A primary analysis of the parameters and constraints on the system was first conducted to pinpoint the optimal parameters. Several optical designs are then presented and analyzed. These channels can achieved a maximum photon count rate with the use of immersion lenses. These immersion lenses act as optical concentrators and achieve a concentration ratio of ≈ n² which is ≈ 4 in our case. This translates to an increase in the photon count rate and signal to noise ratio of the same ratio. The affixing of the immersion lens on a custom photodiode module was then performed and the experimental confirmation of the increase in photon count was obtained with intrinsic and fluorescence measurements. This experimental increase is supported with Zemax simulations which are in good agreement with the experiments. Finally, it was experimentally confirmed that those immersion lenses do not affect the excellent temporal resolution of the single photon avalanche diodes.




Anne-Sophie Poulin-Girard, PhD

Université Laval

PhD Project: Stereoscopic Panomorph pair for 3D reconstruction of objects of interest in a scene (2016)

A wide variety of panoramic lenses are available on the market. Exhibiting interesting characteristics, the Panomorph lens is a panoramic anamorphic optical system. Its highly non-uniform distortion profile creates areas of enhanced magnification across the field of view. For mobile robotic applications, a stereoscopic system for 3D reconstruction of objects of interest could greatly benefit from the unique features of these special lenses. Such a stereoscopic system would provide general information describing the environment surrounding its navigation. Moreover, the areas of enhanced magnification give access to smaller details. However, the downfall is that Panomorph lenses are difficult to calibrate, and this is the main reason why no research has been carried out on this topic. The main goal of this thesis is the design and development of Panomorph stereoscopic systems as well as the evaluation of their performance. The calibration of the lenses was performed using plane targets and a well-established calibration toolbox. In addition, new mathematical techniques aiming to restore the symmetry of revolution in the image and to make the focal length uniform over the field of view were developed to simplify the calibration process. First, the field of view was divided into zones exhibiting a small variation of the focal length and the calibration was performed for each zone. Then, the general calibration was performed for the entire field of view. The results showed that the calibration of each zone does not lead to a better 3D reconstruction than the general calibration method. However, this new approach allowed a study of the quality of the reconstruction over the entire field of view. Indeed, it showed that is it possible to achieve good reconstruction for all the zones of the field of view. In addition, the results for the mathematical techniques used to restore the symmetry of revolution were similar to the results obtained with the original data. These techniques could therefore be used to calibrate Panomorph lenses with calibration toolboxes that do not have two degrees of freedom relating to the focal length. The study of the performance of stereoscopic Panomorph systems also highlighted important factors that could influence the choice of lenses and configuration for similar systems. The challenge met during the calibration of Panomorph lenses led to the development of a virtual calibration technique that used an optical design software and a calibration toolbox. With this technique, simulations reproducing the operating conditions were made to evaluate their impact on the calibration parameters. The quality of 3D reconstruction of a volume was also evaluated for various calibration conditions. Similar experiments would be extremely tedious to perform in the laboratory but the results are quite meaningful for the user. The virtual calibration of a traditional lens also showed that the mean reprojection error, often used to judge the quality of the calibration process, does not represent the quality of the 3D reconstruction. It is then essential to have access to more information in order to asses the quality of a lens calibration.

Master's Project: Optical testing setup for panoramic lenses (2011)

Panoramic lenses' characteristics are unique and their characterization can be a challenge. For vision applications like security or inspection, a precise knowledge of the distortion introduced by panoramic lenses is essential to produce natural unwrapped views. Also, the image quality must be uniformed over the field of view because all directions are important. For these reasons, we have developed a dedicated testing setup for panoramic lenses and a quick and easy measuring process. Using referenced equally-spaced targets, we obtained the radial image mapping curves for various azimuthal angles, allowing us to calculate the instant full-field resolution map. Also, transition targets were used to find field-dependent spatial frequency where the MTF is 50%. We tested two panomorph lenses and two fisheyes with two different cameras. For each lens, we discussed the experimental resolution and MTF curves and compared some of those results to theoretical design data.




Mireille Quémener, MSc

CERVO Brain research centre

Master's Project: Design, fabrication and characterization of a GRIN-Axicon for a multi-photon microscopy application (2021)

Technological advances in microscopy have enabled the creation of a wide variety of optical systems dedicated to the investigation of the dynamic behavior of cells in vivo. The challenge in neuroscience is to observe interactions between neurons labeled with a fluorophore that are located at different depths in the tissue. In order to achieve this, it is necessary to scan the sample on several transverse planes to fully cover its volume. Since this procedure decreases the temporal resolution, it has been proposed to use an axicon to increase the depth of field of the microscope and minimize the number of scans to be performed. However, the axicon is difficult to manufacture and generally has defects on the tip of the cone, thus degrading the beam quality.

In order to replace the axicon with another optical component of which the manufacture does not cause defects, it was envisaged to use a gradient-index lens (GRIN-Axicon). Simulations have shown that the GRIN-Axicon coupled to a lens has the potential to produce a good quality beam. However, the experimental tests have been very brief and there is a need to further investigate the behavior of this component in the lab. The objective of the master's project is therefore to design, manufacture and characterize a GRIN-Axicon for an application in multi-photon microscopy.




Madison Rilling, PhD

Optonique

PhD Project: Design and optimisation of detection channels using single-photon avalanche diodes (SPADs) for photon counting in optical diffuse tomography (2020)

Modern external beam radiotherapy treatments mostly take advantage of dynamic modalities to deliver optimal dose distributions to patients. To minimize the risk of possible treatment errors, radiation detectors which can measure 3D dose distributions are ideal quality-assurance candidates to assure the precise and safe delivery of the planned treatment. However, available dosimetry tools are limited to 2D measurements, or are inadequate for measuring doses that rapidly vary spatially or temporally. In this context, my research project aims to develop a clinical tool capable of real-time, high-precision and high-resolution measurements of 3D dose distributions delivered in external beam radiotherapy. My doctoral project builds on the proof of concept of a 3D scintillation dosimetry system that has previously been established. As a target, the system uses a plastic scintillator volume which, when irradiated, emits a fluorescent light proportional to the locally absorbed dose. While the volume is irradiated, a plenoptic camera captures images of the scintillating light field, which records both spatial and directional information of the incident light. We then attempt to reconstruct the measured 3D dose distribution by applying tomographic algorithms to the acquired images, in order to compare the measured dose to the planned dose prior to treatment delivery. To achieve this goal, my research involves designing and optimizing the optics of a system which exploits the joint principles of scintillation dosimetry and plenoptic technology, all the while taking into account the clinical constraints of external beam radiotherapy treatments.




Frédéric Roy, MSc

Béton Provincial

Master's Project: Design of a measurement tools for discomfort glare from a LED luminary for night conditions for a pedestrian (2020)

The discomfort glare produced by the LED luminary becomes a more important issue with the explosion of their use in urban lighting. The project focus is the discomfort glare fell by pedestrian in an urban night condition against the majority of precedents study who focus on motorists at night or indoor office lighting. First, an angular luminance profile limiting discomfort glare would be found using mathematical models of eye respond. The discomfort glare fell by pedestrians can’t be faithfully described by one measurement at one angle, because the perception of the luminance changes to the position inside the field of view, so we need the luminance for any position inside the field of view. The angular profile should consider the entire discomfort glare feel by the pedestrian all along his walk under the luminary. Second, a new scale for discomfort using the divergence of this “perfect” profile would be postulated. Using this new scale in combination with an image processing algorithm should describe accurately the discomfort glare generated by LED luminaries for pedestrians. This algorithm would use a video and source angle to calculating the discomfort glare. This algorithm would be compatible with a cellphone resource for a possible mobile application version.




Cédric Vallée

Nuvu Caméras

Master's Project: Measure and analysis of the residual atmosphérical turbulences in high altitude with the data of a low order wavefront sensor

Within the project HiCIBaS (High-Contrast Imaging Balloon System), a 14 inch telescope equipped with a wavefront sensor and a deformable mirror is lifted up to 35Km to test the usage of a MEMS (Microelectromechanical systems) deformable mirror, EMCCD Nüvü cameras and other instruments in space-like conditions. Apart from this, the project has the scientific goal to use the data from the embarked LOWFS (Low Order Wavefront Sensor) and extract a measurement of the atmospheric turbulences in high altitude. The work packages of this master are to design and develop the software that will ensure communication with ground and control the subsystems, define the performance requirements and design a on-board computer and develop the data reduction and data analysis softwares. The communication interface will use the network provided by the canadian space agency to communicate with the ground. The control software will be autonomous and will use a database management software to ensure the data produced will have the chronological coherence needed to detect any bugs or glitches in data that would come from the system itself. The turbulences measure will be obtained by decomposing the wavefront aberrations with Kolmogorov phenomenological statistics.




Maxime Vernier, MSc

Febus Optics

Master's Project: Simulation of orbital debris detection on Matlab (2021)

The research project consists of a study of the detection of space debris. This project is a collaboration between Université Laval and ABB. The first step is to code a Matlab simulation of the situation. The objective is to determine if it is possible to detect small space debris (<10 cm) using an onboard camera on a satellite. We choose the sphere model for the debris, the specular and the diffuse reflection are considered in the calculation of magnitude. The phase angle between the sun, the debris and the satellite is an important parameter in the apparent magnitude of the debris, as well as the size of the debris or their distance from the satellite. Satellite and debris velocities are also considered in order to determine the length of the streak that the debris creates on the camera's sensor. Different backgrounds and other noises are also simulated. Then, we can obtain the photo of the debris taken by the camera on the satellite. A study of the distribution of debris in orbit should be considered. Also, a study of the re-detection would be an interesting point and would allow a more complete answer to the problem.