1 

Coherent transient phenomena in quantum systems by spatially shaping femtosecond optical pulses
Providing a femtosecond optical pulse with a proper transverse spatial profile represents a fast and relatively simple method to force a quantum system to follow a prescribed temporal evolution. In the present work, we show that the quantum system presents a surprisingly high sensitivity with respect to the spatial shape of the pulse. We discuss an explicit example where differences on the order of a few nanometers in the initial pulse’s spot size induce completely different responses in the system under study.

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2 

A bound for the range of a narrow light beam in the near field
We investigate the possibility of light beams that are both narrow and long range with respect to the wavelength. On the basis of spectral electromagnetic field representations, we have studied the decay of the evanescent waves, and we have obtained some bounds for the width and range of a light beam in the nearfield region. The range determines the spatial bound of the near field in the direction of propagation. For a number of representative examples we found that narrow beams have a short range. Our analysis is based on the uncertainty relations between spatial position and spatial frequency.

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3 

Photon budget analysis for fluorescence lifetime imaging microscopy
We have constructed a mathematical model to analyze the photon efficiency of frequencydomain fluorescence lifetime imaging microscopy (FLIM). The power of the light source needed for illumination in a FLIM system and the signaltonoise ratio of the detector have led us to a photon “budget.” These measures are relevant to many fluorescence microscope users and the results are not restricted to FLIM but applicable to widefield fluorescence microscopy in general. Limitations in photon numbers, however, are more of an issue with FLIM compared to other less quantitative types of imaging. By modeling a typical experimental configuration, examples are given for fluorophores whose absorption peaks span the visible spectrum from Fura2 to Cy5. We have performed experiments to validate the assumptions and parameters used in our mathematical model. The influence of fluorophore concentration on the intensity of the fluorescence emission light and the Poisson distribution assumption of the detected fluorescence emission light have been validated. The experimental results agree well with the mathematical model. This photon budget is important in order to characterize the constraints involved in current fluorescent microscope systems that are used for lifetime as well as intensity measurements and to design and fabricate new systems.

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4 

Angular Dependence of the IonInduced Secondary Electron Emission for He+ and Ga+ Beams
In recent years, novel ion sources have been designed and developed that have enabled focused ion beam machines to go beyond their use as nanofabrication tools. Secondary electrons are usually taken to form images, for their yield is high and strongly dependent on the surface characteristics, in terms of chemical composition and topography. In particular, the secondary electron yield varies characteristically with the angle formed by the beam and the direction normal to the sample surface in the point of impact. Knowledge of this dependence, for different ion/atom pairs, is thus the first step toward a complete understanding of the contrast mechanism in scanning ion microscopy. In this article, experimentally obtained ioninduced secondary electron yields as a function of the incidence angle of the beam on flat surfaces of Al and Cr are reported, for usual conditions in Ga+ and He+ microscopes. The curves have been compared with models and simulations, showing a good agreement for most of the angle range; deviations from the expected behavior are addressed and explanations are suggested. It appears that the maximum value of the ioninduced secondary electron yield is very similar in all the studied cases; the yield range, however, is consistently larger for helium than for gallium, which partially explains the enhanced topographical contrast of helium microscopes over the gallium focused ion beams.

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5 

On focused fields with maximum electric field components and images of electric dipoles
We study focused fields which, for a given total power and a given numerical aperture, have maximum electric field amplitude in some direction in the focal point and are linearly polarized along this direction. It is shown that the optimum field is identical to the image of an electric dipole with unit magnification. In particular, the field which is the image of an electric dipole whose dipole vector is parallel to the optical axis, is identical to the field whose longitudinal component is maximum at the image point.

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6 

Percolationenhanced generation of terahertz pulses by optical rectification on ultrathin gold films
Emission of pulses of electromagnetic radiation in the terahertz range is observed when ultrathin gold films on glass are illuminated with femtosecond nearIR laser pulses. A distinct maximum is observed in the emitted terahertz amplitude from films of average thickness just above the percolation threshold. Our measurements suggest that the emission is through a secondorder nonlinear optical rectification process, enhanced by the excitation of localized surface plasmon hot spots on the percolated metal film.

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7 

A fast algorithm for computing and correcting the CTF for tilted, thick specimens in TEM
Today, the resolution in phasecontrast cryoelectron tomography is for a significant part limited by the contrast transfer function (CTF) of the microscope. The CTF is a function of defocus and thus varies spatially as a result of the tilting of the specimen and the finite specimen thickness. Models that include spatial dependencies have not been adopted in daily practice because of their high computational complexity. Here we present an algorithm which reduces the processing time for computing the ‘tilted’ CTF by more than a factor 100. Our implementation of the full 3D CTF has a processing time on the order of a Radon transform of a full tiltseries. We derive and validate an expression for the damping envelope function describing the loss of resolution due to specimen thickness. Using simulations we quantify the effects of specimen thickness on the accuracy of various forward models. We study the influence of spatially varying CTF correction and subsequent tomographic reconstruction by simulation and present a new approach for spacevariant phaseflipping. We show that our CTF correction strategies are successful in increasing the resolution after tomographic reconstruction.

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8 

A contrast source method for nonlinear acoustic wave fields in media with spatially inhomogeneous attenuation
Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented fullwave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, threedimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.

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9 

Timefrequency distribution of interferograms from a frequency comb in dispersive media
We investigate general properties of the interferograms from a frequency comb laser in a nonlinear dispersive medium. The focus is on interferograms at large delay distances and in particular on their broadening, the fringe formation and shape. It is observed that at large delay distances the interferograms spread linearly and that its shape is determined by the source spectral profile. It is also shown that each intensity point of the interferogram is formed by the contribution of one dominant stationary frequency. This stationary frequency is seen to vary as a function of the path length difference even within the interferogram. We also show that the contributing stationary frequency remains constant if the evolution of a particular fringe is followed in the successive interferograms found periodically at different path length differences. This can be used to measure very large distances in dispersive media.

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10 

High Resolution Scanning Ion Microscopy
The structure of the thesis is the following. The first chapter is an introduction to scanning microscopy, where the path that led to the Focused Ion Beam (FIB) is described and the main differences between electrons and ion beams are highlighted. Chapter 2 is what is normally referred to (which I do not really like) as ‘the theory chapter’. The theory of ion/matter interaction is presented in the first part of the chapter. The treatment is the standard one that can be found in the literature, but of course mine is the choice of the topics and the way in which they are presented. The second part of the chapter is a short introduction toMonte Carlo codes, and in particular to the two pieces of software that I have used for my basic simulations, SRIM/TRIM from J. Ziegler, and IONiSE from D. Joy. The third chapter is almost entirely made up of an article published in Microscopy & Microanalysis in 2011, on the subject of ioninduced Secondary Electron Emission; the paper is introduced by two small sections, the first being an introduction to ion beam imaging, the second presenting a standard theory of noise in scanning microscopy. Chapter 4 introduces the main topic of this thesis work, the one that is more dear to me: resolution in scanning ion microscopy. The chapter is a hybrid, for the theory of resolution that is presented is quite standard, but interlaced with a lot of rethinking and personal points of view, and finally adapted to the specific field of scanning ion microscopy. Chapters 5 and 6 are the first two articles published during my PhD, in Journal of Vacuum Science & Technology B. They both tackle the problem of resolution evaluation in scanning ion microscopy, the first for the GaFIB, the second for the HeFIB. The two papers have been published in 2008 and 2009, respectively, a time when the uniformity of the formalism was not yet mature, reason for which symbolic inconsistencies can be found in relation to the rest of the thesis, and to the list of symbols in appendix B. Choice was made to leave the papers in their published version, but this should not represent a problem, because each quantity is clearly defined. The last journal paper published within my project makes chapter 7. The scope of the paper is broad, for it proposes a method to simulate ion imaging that does not employ any Monte Carlo calculation. It can be regarded as a kind of summary of all the studies performed in the course of the project, and is followed by an appendix that explains the details of the noise analysis whose results are presented in the article. Conclusions and recommendations find their place in chapter 8. With referiment to the original main motivation, i.e. exploring the possibility of achieving atomic resolution with a Scanning IonMicroscope, it is shown that this is not possible, at least in the general case, because the sputtering of the sample limits the ultimate obtainable resolution to the nanometer range, even using very light ions. Also, it is pointed out that, in imaging systems causing strong sample modification, the concept of resolution itself can not be thought of as static; it must be regarded as dynamic instead. On the subject of IonInduced Secondary Electron Emission, a procedure to obtain curves of Secondary Electron yield versus incident angle of the beam is presented; the behaviour of those curves contributes to explain the much sharper contrast achievable with a HeFIB, as opposite to the more traditional GaFIB. Finally, it is shown that simulation of ion imaging based on the ‘yield vs. incidence angle’ curves is feasible, overcoming the computational problems that affect any Monte Carlo based approach.

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11 

Surface plasmonenhanced terahertz emission from a hemicyanine selfassembled monolayer
Emission of terahertz radiation is observed when surface plasmons are excited on a thin film of gold, in the Kretschmann geometry. When a hemicyanineterminated alkanethiol selfassembled monolayer of thickness 1.2 nm is deposited on the gold film, stronger terahertz emission is observed. Our experimental results confirm that enhanced terahertz emission is possible from planar gold surfaces when surface plasmons are excited.

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12 

Intravascular ultrasound chirp imaging
We demonstrate the feasibility of intravascular ultrasound (IVUS) chirp imaging as well as chirp reversal ultrasound contrast imaging at intravascular ultrasound frequency. Chirp excitations were emitted with a 34 MHz single crystal intravascular transducer and compared to conventional Gaussianshaped pulses of equal acoustic pressure. The signal to noise ratio of the chirp images was increased by up to 9 dB relative to the conventional images. Imaging of contrast microbubbles was implemented by chirp reversal, achieving a contrast to tissue ratio of 12 dB. The method shows potential for intravascular imaging of structures in and beyond coronary atherosclerotic plaques including vasa vasorum

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13 

Modeling nonlinear acoustic waves in media with inhomogeneities in the coefficient of nonlinearity
The refraction and scattering of nonlinear acoustic waves play an important role in the realistic application of medical ultrasound. One cause of these effects is the tissue dependence of the nonlinear medium behavior. A method that is able to model those effects is essential for the design of transducers for novel ultrasound modalities. Starting from the Westervelt equation, nonlinear pressure wave fields can be modeled via a contrast source formulation, as has been done with the INCS method. An extension of this method will be presented that can handle inhomogeneities in the coefficient of nonlinearity. The contrast source formulation results in an integral equation, which is solved iteratively using a Neumann scheme. The convergence of this scheme has been investigatedfor relevant media (e.g., blood, brain, and liver). Further, as an example, the method has been applied to compute the 1D nonlinear acoustic wave field in an inhomogeneous medium insonified by a 1 MHz Gaussian pulse propagatingup to 100 mm. The results show that the method is able to predict the propagation and the scattering effects of nonlinear acoustic waves in media with inhomogeneities in the coefficient of nonlinearity. This motivates a similar extension ofthe 3D INCS method.

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14 

Feasibility study of superharmonic imaging using chirps
Superharmonic imaging (SHI) targets a combination of the 3rd to 5th harmonics. It was proven to have certain advantages in comparison with the established imaging standards in medical utrasound. SHI enhances the spatial resolution and improves the quality of echographic images, mainly by eliminating reverberation artifacts at the chest wall. However, SHI suffers from ripple artifacts, originating from the spectral gaps in between harmonics, and degrading the temporal resolution. To solve this a chirpbased SHI protocol was employed and its characteristics investigated, i.e. point spread function (PSF). The protocol was implemented for an interleaved phased array probe (44+44 elements tuned at 1.0+3.7MHz), connected to a fully programmable ultrasound system. A linear chirp (center frequency 1MHz; bandwidth 40%) was used for excitation. To obtain the PSF, the RF traces were recorded at focus along the lateral axis and convolved with the decoding signal. This was computed using KZK simulations. A PSF comparison between a superharmonic chirp and the 3rdharmonic of a 2.5cycle Gaussian apodized sinus burst at 1MHz showed a decrease in axial pulse length of 46% at 6dB and 32% at the 20dB level in favor of SHI. Chirp based SHI is virtually free of ripple artifacts and therefore feasible.

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15 

Application of the finitedifference contrastsource inversion algorithm to seismic fullwaveform data
We have applied the finitedifference contrastsource inversion (FDCSI) method to seismic fullwaveform inversion problems. The FDCSI method is an iterative nonlinear inversion algorithm. However, unlike the nonlinear conjugate gradient method and the GaussNewton method, FDCSI does not solve any full forward problem explicitly in each iterative step of the inversion process. This feature makes the method very efficient in solving largescale computational problems. It is shown that FDCSI, with a significant lower computation cost, can produce inversion results comparable in quality to those produced by the GaussNewton method and better than those produced by the nonlinear conjugate gradient method. Another attractive feature of the FDCSI method is that it is capable of employing an inhomogeneous background medium without any extra or special effort. This feature is useful when dealing with timelapse inversion problems where the objective is to reconstruct changes between the baseline and the monitor model. By using the baseline model as the background medium in crosswell seismic monitoring problems, high quality timelapse inversion results are obtained.

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16 

Nearfield selfinduced hollow spot through localized heating of polycarbonate/ZnS stack layer
We have found an alternative way of achieving a doughnutlike focused spot by simply melting a subwavelength scatterer in a polycarbonate/ZnS sample. The nearfield microscopy technique is used to directly measure the induced doughnut spot in the nearfield regime. A numerical model based on rigorous solution of the Maxwell’s equations is proposed to study the phenomena. The simulations help to understand the optical mechanism behind the spot formation.

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17 

Terahertz emission from surfaceimmobilized gold nanospheres
Electromagnetic wave emission based on optical rectification at terahertz (THz) wavelengths was observed from surfaceimmobilized gold nanospheres (SIGNs) above a gold surface. Although the excitation wavelength is offresonant with the localized surface plasmons, the THz emission field was observed to be approximately 4.8 times greater than that from a percolated gold thin film of 10 nm thickness. A theoretical calculation predicts that the light electric field is enhanced in the SIGN system, even at offresonance wavelengths. The observed THz field amplitude was quadratic with the illumination light field, suggesting that the THz generation is due to a secondorder nonlinear optical process.

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18 

Phase anomalies in BesselGauss beams
BesselGauss beams are known as nondiffracting beams. They can be obtained by focusing an annularly shaped collimated laser beam. Here, we report for the first time on the direct measurement of the phase evolution of such beams by relying on longitudinaldifferential interferometry. We found that the characteristics of BesselGauss beams cause a continuously increasing phase anomaly in the spatial domain where such beams do not diverge, i.e. there is a larger phase advance of the beam when compared to a referential plane wave. Simulations are in excellent agreement with measurements. We also provide an analytical treatment of the problem that matches both experimental and numerical results and provides an intuitive explanation.

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19 

An innovative and efficient method to control the shape of pushpull membrane deformable mirror
We carry out performance characterisation of a commercial push and pull deformable mirror with 48 actuators (Adaptica Srl). We present a detailed description of the system as well as a statistical approach on the identification of the mirror influence function. A new efficient control algorithm to induce the desired wavefront shape is also developed and comparison with other control algorithms present in literature has been made to prove the efficiency of the new approach.

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20 

Superresolution imaging visualizes the eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution
One of the most complex molecular machines of cells is the nuclear pore complex (NPC), which controls all trafficking of molecules in and out of the nucleus. Because of their importance for cellular processes such as gene expression and cytoskeleton organization, the structure of NPCs has been studied extensively during the last few decades, mainly by electron microscopy. We have used superresolution imaging by direct stochastic optical reconstruction microscopy (dSTORM) to investigate the structure of NPCs in isolated Xenopus laevis oocyte nuclear envelopes, with a lateral resolution of ~15 nm. By generating accumulated superresolved images of hundreds of NPCs we determined the diameter of the central NPC channel to be 41±7 nm and demonstrate that the integral membrane protein gp210 is distributed in an eightfold radial symmetry. Twocolor dSTORM experiments emphasize the highly symmetric NPCs as ideal model structures to control the quality of corrections to chromatic aberration and to test the capability and reliability of superresolution imaging methods.

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