Fourier optics analysis of grating sensors with tilt errors

Dynamic diffraction gratings can be microfabricated with precision and offer extremely sensitive displacement measurements and light intensity modulation. The effect of pure translation of the moving part of the grating on diffracted order intensities is well known. This study focuses on the parameters that limit the intensity and the contrast of the interference. The effects of grating duty cycle, mirror reflectivities, sensor tilt and detector size are investigated using Fourier optics theory and Gaussian beam optics. Analytical findings reveal that fringe visibility becomes

Phase Retrieval and Gaussian Beam Mode Decomposition of Gyrotron Beams

In this dissertation, we have developed the necessary basis for the characterization of the RF output of a gyrotron. The characterization includes the phase reconstruction and Gaussian beam mode decomposition. In order to analyze the phase reconstruction in detail, we have developed an accurate field propagation method using the complete Rayleigh-Sommerfeld scalar diffraction integral (RSDI) and the Huygens-Fresnel diffraction integral (HFDI), using a fast Fourier Transform (FFT) based approach. The discretization of the two diffraction integrals is analyzed analytically and numerically. In the case of the HFDI, a condition on the distance of propagation, where aliasing and replication are completely removed, is found. It relates the distance of propagation Δz, the number of sampling points M, the grid cell size Δx and the wavelength λ as: Δz = M(Δx)2 · 1/λ. The two formalisms are also studied using a zero-padding technique, which can be used to propagate the field to any arbitrary distance. These propagation methods are then used in the Iterative Phase Retrieval Algorithm (IPRA) for phase reconstruction. The effects of several parameters on the IPRA (the number of planes, the measurement plane size, the distance of propagation, the number of sampling points and the grid cell size, the misalignment along the optical axis, etc.) are then analyzed. For the theoretical field profiles used in this dissertation, the misalignment along the optical axis in the form of a transverse shift affects the IPRA most severely. The experimental procedure to measure the beam intensity patterns using infrared (IR) thermography is explored extensively. Out of the many target materials used, Robax is the most appropriate in terms of dynamic range, temperature linearity and for the possibility to perform measurements from the front side and the back side. Further, infrared image data processing is investigated for intensity pattern enhancement. This includes various steps: Fixed Pattern Noise (FPN) correction by subtracting the background image of the target taken before the microwave irradiation, defective pixels correction, perspective correction, image pattern enhancement by filtering and denoising. Further, the intermodal decomposition of the reconstructed phase and amplitude is analyzed in detail using two methods, in order to extract the Gaussian content: Finding a set of Gaussian beam parameters and a mode content matrix which maximizes the power in the fundamental mode |C00|2. This method is commonly used by the gyrotron tube developers. Finding a set of Gaussian beam parameters and a mode content matrix which minimizes the error between the corresponding reconstructed field and the input (theoretical and/or experimental) field. It is found that, the two methods may give significantly different results. As a general rule, the second method gives more precise and more reliable results, but the solution is unfortunately not unique and depends both on the measured profile and the measurement parameters. Therefore, the concept of Gaussian content adopted by the community seems to be incomplete, and the corresponding optimized parameters should be associated to it. The definition of Gaussian content should then be reexamined, and completed by an analysis of the power coupling coefficient of the microwave beam to the transmission line (corrugated waveguide or a quasi-optical line).

EPFL2010

Single molecule detection and fluorescence correlation spectroscopy on surfaces

Kai Hassler

In this thesis a new approach for single molecule detection and analysis is explored. This approach is based on the combination of two well established methods, fluorescence correlation spectroscopy (FCS) and total internal reflection fluorescence microscopy (TIRFM). In contrast to most existing fluorescence spectroscopy techniques, the subject of primary interest in FCS is not the fluorescence intensity itself but the random intensity fluctuation around the mean value. Intensity fluctuations are induced by thermal noise in a minute observation volume, which is in classical FCS the confocal volume of a confocal microscope. E.g. FCS is commonly utilized to investigate diffusion. In this case, diffusing fluorescent molecules entering or leaving the observation volume cause intensity fluctuations, which are analyzed by calculating the temporal autocorrelation of the observed signal. The autocorrelation is a measure for the self-similarity of a signal and contains information about the average fluctuation strength and duration. The confocal observation volume, i.e. the measurement volume that is actually seen by the detector is approximately given by the product of the optical transfer function with the fluorescence exciting intensity distribution of a focused laser beam. To achieve a high signal-to-background ratio a small observation volume is absolutely essential, first of all because the background from e.g. scattered light increases with the size of the observation volume. Second, a small volume assures for a small average number of fluorophores inside the observation volume and therefore for a high fluctuation amplitude i.e. FCS signal. This thesis proposes and discusses an alternative to confocal FCS specially conceived for measurements on surface-bound molecular systems, such as biological receptors or immobilized enzymes. In contrast to confocal FCS, fluorescence is excited within an evanescent field generated by total internal reflection (TIR) of a laser beam at the interface between a microscope coverslip and the sample. This is achieved by focusing the laser beam off-axis at the back focal plane of a high NA oil-immersion objective. The collimated beam that emerges from the objective is incident at an oblique angle at the coverslip-sample interface and totally internal reflected. In contrast to confocal FCS, the generated observation volume is completely confined to the surface and background fluorescence as well as scattered light from the bulk is efficiently suppressed. Our method, called objective-type TIR-FCS in the following, features an increased collection efficiency compared to existing techniques that combine evanescent wave excitation and FCS. Existing techniques use total internal reflection on the surface of a prism to generate an evanescent field. This leads to a configuration where the choice of objectives is limited to air or water-immersion objectives. In our system we use a high NA oil-immersion objective, specially conceived for TIR applications, which collects light efficiently. The collection efficiency is further enhanced by a naturally occurring change of the emission properties of fluorophores close to interfaces between dielectric media. The presence of the interface favors emission into the optically denser medium so that about 60% of the emitted light can be collected. These factors, together with a reduced observation volume lead to a very sensitive method with a high potential for applications in single molecule detection and analysis. The performance of the proposed method was experimentally shown for measurements on molecules subject to Brownian motion and binding to modified coverslips. In particular, it was experimentally shown that objective-type TIR-FCS features high signal-to-background ratio on a single molecule level. In this thesis, concise derivations of analytical expressions for autocorrelation functions for diffusion and most important, the case of ligands reversibly binding to a single and localized binding site are presented. The derived model allows for the quantitative determination of binding rates for a single receptor. We strongly believe that the application of these results in the context of investigations of receptor-ligand binding kinetics will allow for deeper understanding of cellular signaling. Moreover, this thesis discusses the applicability of the proposed method in enzymology. Enzymes, as most proteins are subject to continuous changes of their structure or conformation. These conformational changes are correlated with the function of the enzyme. In the discussed example the enzyme catalyzes an oxidation where the product is fluorescent but the substrate is not. The function of the enzyme i.e. the recurring product formation leads to observable intensity fluctuations. Since function and conformational states are correlated, conformational fluctuations can be investigated by means of FCS as was already shown for confocal FCS. A technique closely related to FCS is fluorescence lifetime spectroscopy (where lifetime refers to the mean lifetime of the electronic excited state). Whereas in FCS the relaxation after random deviations from thermal equilibrium is investigated, relaxation of excited fluorophores towards their electronic ground-state is investigated in lifetime spectroscopy. The technique is used for e.g. discrimination between fluorophores with different lifetimes. Lifetime spectroscopy combined with imaging is used in many domains of life-science, including microarray reading and medical diagnostics. In preliminary work we developed a novel approach to perform lifetime imaging that is based on a multiplexing technique. The proposed method requires no mechanical scanning stage and only a single-point detector. Furthermore, noise is reduced under certain circumstances if the signal is low. Characteristics of this technique as well as advantages and disadvantages are shortly discussed.

EPFL2006

Mid-infrared surface plasmon resonance sensing applied to refractive index measurements of liquids

Sylvain Herminjard

There has been a very strong development of the sensors based on surface plasmon resonance during the last thirty years, mostly for biological and biomedical applications. If the first experiments in this field were carried out at the beginning of the 20t century, it would have been necessary to wait for the end of the sixties to see the first devices performing accurate measurements of the refractive indices of gas and liquid samples. Indeed, the surface plasmon resonance phenomenon allows to measure refractive index variations with a high sensitivity that is hardly obtained with other optical measurement techniques. The basic principle consists of exciting the free electrons of a metallic layer with light, which induces the formation of a surface wave called surface plasmon. This resonant phenomenon depends on the wavelength of the excitation light and the refractive indices of the metallic layer and the material located close to the metallic layer. A variation of the refractive index of the latter induces a variation of the resonance condition, which allows to realize optical sensors designed to measure determined samples. An appropriate calibration allows to set a relationship between the variation of the concentration of the sample and the measured refractive index value. Among the various parameters that describe the performances of the sensor, one of the most important is the sensitivity. It is possible to demonstrate that the excitation wavelength has an impact on the sensitivity of the system : the latter increases if the measured sample has an absorption peak at a wavelength close to the excitation wavelength. The main goal of this thesis is to explore this sensitivity enhancement technique based on the absorption properties of the probed medium. A proof-of-principle is experimentally demonstrated with an optical setup constituted of laser sources working in the visible range of the electromagnetic spectrum. However, many materials have absorption peaks located in the mid-infrared range due to their fundamental molecular vibrations. Therefore, the realization of a plasmonic sensor working in the mid-infrared could allow to measure these materials with an increased sensitivity. To the best of our knowledge, surface plasmon resonance based sensors have never been developed above the near-infrared. This thesis presents for the first time the design and realization of a plasmonic sensor working in the mid-infrared range able to measure refractive index variations of gas and liquids samples. Even if the optical sources, components and detectors designed for the mid-infrared are clearly different from the ones designed for the visible range, it has been possible to successfully realize two systems working in the mid-infrared range during this project. The first is able to perform gas measurements. As the excitation wavelength depends on the measured sample, it was necessary to select a laser source that had a wavelength located close to the absorption peak of the gas under measurement. For this purpose, we designed a plasmonic sensor working at a 4.4 µm wavelength able to measure carbon dioxide (CO2) absorbing at 4.3 µm. It has been demonstrated that the experimental sensitivity of this system is five times higher than the theoretical sensitivity obtained with a system working in the visible range at a 633 nm wavelength. The second has been conceived to measure liquid samples in order to measure variations of concentration of CO2 dissolved in water. If measurements of refractive index variations (without using the sensitivity enhancement technique) could be performed successfully with variations of concentration of alcohol in water, further work is necessary to get decisive results for CO2 dissolved in water. This project was carried out in collaboration with an industrial partner in order to take into account some industrial constraints during the development of the sensor. Therefore, particular care has been taken in order to design a system that is compact, mechanically robust, without any mechanical moving parts, cheap and easily reproducible. The technological development presented in this thesis finds many applications mainly in the chemical, biological and biomedical fields. Indeed, many proteins show absorption peaks in the mid-infrared. It could be possible to measure their concentration or the modification of their properties – like their composition or structure – with an increased sensitivity. The interest of surface plasmons is that the measurement is not a transmission-based technique, but rather a "reflection-based technique", as the light does not go through the gas or liquid sample. This measurement technique is also adapted for high volume samples that are present in industrial production processes like water or soft drink quality control.

EPFL2010

Mid-infrared surface plasmon resonance sensing applied to refractive index measurements of liquids

Sylvain Herminjard

EPFL2010

Phase Retrieval and Gaussian Beam Mode Decomposition of Gyrotron Beams

EPFL2010

Single molecule detection and fluorescence correlation spectroscopy on surfaces

Kai Hassler

EPFL2006