Focal Intensity Distribution Research Articles

A protocol for registration and correction of multicolour STED superresolution images.

Multicolour fluorescence imaging by STimulated Emission Depletion (STED) superresolution microscopy with doughnut-shaped STED laser beams based on different wavelengths for each colour channel requires precise image registration. This is especially important when STED imaging is used for co-localisation studies of two or more native proteins in biological specimens to analyse nanometric subcellular spatial arrangements. We developed a robust postprocessing image registration protocol, with the aim to verify and ultimately optimise multicolour STED image quality. Importantly, this protocol will support any subsequent quantitative localisation analysis at nanometric scales. Henceforth, using an approach that registers each colour channel present during STED imaging individually, this protocol reliably corrects for optical aberrations and inadvertent sample drift. To achieve the latter goal, the protocol combines the experimental sample information, from corresponding STED and confocal images using the same optical beam path and setup, with that of an independent calibration sample. As a result, image registration is based on a strategy that maximises the cross-correlation between sequentially acquired images of the experimental sample, which are strategically combined by the protocol. We demonstrate the general applicability of the image registration protocol by co-staining of the ryanodine receptor calcium release channel in primary mouse cardiomyocytes. To validate this new approach, we identify user-friendly criteria, which - if fulfilled - support optimal image registration. In summary, we introduce a new method for image registration and rationally based postprocessing steps through a highly standardised protocol for multicolour STED imaging, which directly supports the reproducibility of protein co-localisation analyses. Although the reference protocol is discussed exemplarily for two-colour STED imaging, it can be readily expanded to three or more colours and STED channels.

Changes of intensity distribution of a tightly focused plane-wave pulse induced by lens dispersion

The tightly focusing properties of a linearly polarized plane-wave pulse through a high numerical aperture (NA) lens with dispersion are formulated. The effects of lens dispersion on the tightly focused intensity distribution in the focal region are studied in detail. It is found that, because of the lens dispersion, the intensity of the side lobe of the focused light spot strengthens in the transverse direction and the size of the main lobe of the focused light spot increases in the longitudinal direction as the pulse duration decreases. In addition, we compare the effects of dispersion of lens made by different types of glass on tightly focusing properties of a pulse beam. The results will be helpful to choose suitable high NA objective lens in experiment.

Focusing properties of Lorentz-Gaussian beam with trigonometric function modulation

Wavefront distribution of linearly polarized Lorentz-Gaussian beam was modulated with trigonometric functions, and focusing properties of the modulated beam were investigated by vector diffraction theory. The complex wavefront modulation includes sine function phase distribution and cosine amplitude distribution with one modulation parameter. Results show that the focal intensity distributions can be altered considerably by modulation parameter and the beam parameters. And the effect of numerical aperture on focal pattern evolution is weaker than that of modulation parameter and the beam parameters. Under condition of different beam parameters, the focal pattern evolves differently, and many novel focal patterns can appear, including two-peak focal pattern and shallow dark hollow focus, which may be employed to construct tunable optical traps.

Modeling keyhole oscillations during laser deep penetration welding at different spatial laser intensity distributions

Process dynamics have a significant effect on the formation of unwanted weld defects like pores in deep penetration laser beam welding. The dynamics of the keyhole, typically evolving in the process, are assumed to be one of the main influencing factors on the welding process. One of the factors influencing the keyhole dynamics is the laser intensity distribution. In order to get a better understanding of the formation of weld defects, the influence of the focal spatial laser intensity distribution on keyhole dynamics is investigated in this work. An analytical description is presented, that offers the possibility to quickly calculate the keyhole dynamics for different spatial laser intensity distributions. Frequency analysis of the calculated keyhole dynamics show that a top hat intensity distribution leads to higher maximum frequencies of the keyhole oscillations compared to a Gaussian beam profile. Experiments using process observation of acoustic emissions confirm the model´s results.

Experimental verification 3D subwavelength resolution beyond the diffraction limit with zone plate in millimeter wave

ABSTRACTThe results of experimental investigations of resolution power of millimeter‐wave phase reversal binary Fresnel zone plate with short focal distance are described. It has been experimentally shown that in the near‐field of single diffractive lens with subwavelength focal distance without the immersion medium a resolution of 0.3–0.4 were obtained. The “Abbe barrier” can be completely broken by such diffractive lenses with unique three‐dimensional super resolution. Also it was experimentally shown the focal spot in the high numerical aperture diffractive lenses is no longer an Airy pattern and focal intensity distribution is not circularly symmetric. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:2436–2439, 2014

Coupled electron-nuclear wavepacket dynamics in potassium dimers

Recently we have demonstrated control of valence-bond excitation of a molecule due to the interplay of the induced charge oscillation with the precisely tailored phase of the driving laser field (Bayer et al 2013 Phys. Rev. Lett. 110 123003). In this contribution we describe in more detail the two-colour experiment—a control pulse sequence followed by an ionizing probe pulse of a different wavelength. We provide details on the quantum dynamics simulations carried out to reproduce and to analyse the experimental results. The procedure for averaging over the focal intensity distribution in the interaction region and the method for orientation averaging, which are both crucial for the reproduction of our strong-field measurements, are also described in detail. The analysis of the temporal evolution of the expectation values of the wavepackets on the relevant potentials, the induced energetic shifts in the molecule and the modulation in the charge oscillation provides further insights into the interplay of the coupled nuclear-electron dynamics. Because the measured photoelectron spectra reveal the population of the target states we describe the quantum mechanical approach to calculate the photoelectron spectra and rationalize the results using Mulliken's difference potential method.

Efficient saturation of an ion in free space

We report on the demonstration of a light-matter interface coupling light to a single $^{174}\textrm{Yb}^+$ ion in free space. The interface is realized through a parabolic mirror partially surrounding the ion. It transforms a Laguerre-Gaussian beam into a linear dipole wave converging at the mirror's focus. By measuring the non-linear response of the atomic transition we deduce the power required for reaching an upper-level population of $1/4$ to be $692\pm20~\textrm{pW}$ at half linewidth detuning from the atomic resonance. Performing this measurement while scanning the ion through the focus provides a map of the focal intensity distribution. From the measured power we infer a coupling efficiency of $7.2\pm0.2~\%$ on the linear dipole transition when illuminating from half solid angle, being among the best coupling efficiencies reported for a single atom in free space.

Ground Testing Strategies for Verifying the Slew Rate Tolerance of Star Trackers

The performance of a star tracker is largely based on the availability of its attitude solution. Several methods exist to assess star tracker availability under both static and dynamic imaging conditions. However, these methods typically make various idealizations that can limit the accuracy of these results. This study aims to increase the fidelity of star tracker availability modeling by accounting for the effects of detection logic and pixel saturation on star detection. We achieve this by developing an analytical model for the focal plane intensity distribution of a star in the presence of sensor slew. Using the developed model, we examine the effects of slew rate on star detection using simulations and lab tests. The developed approach allows us to determine the maximum slew rate for which a star of a given stellar magnitude can still be detected. This information can then be used to describe the availability of a star tracker attitude solution as a function of slew rate, both spatially, across the entire celestial sphere, or locally, along a specified orientation track.

3D dif fractive lenses to overcome the 3D Abbe subwavelength dif fraction limit

The innovative radiating structures as a conical millimeter wave FZP lens are proposed for subwavelength focusing. The results of FDTD simulation and experimental verification are discussed. It has been shown that in contrast to the flat diffractive optics the curvilinear 3D diffractive conical optics is capable of overcoming 3D Abbe barrier with a focal distance F greater than 2λ. The focal intensity distribution for such type of lenses is not circularly symmetric and thus the focal spot in the high numerical aperture case is no longer an Airy pattern. These results may find useful applications in optical microscopes, including

The Beynon Gabor zone plate: a new tool for de Broglie matter waves and hard X-rays? An off axis and focus intensity investigation

Optical elements based on Fresnel zones are used in a range of applications, from X-ray telescopy to microscopy and recently also in the manipulation of de Broglie matter waves. In 1992 Beynon and co-workers presented a binary Gabor type zone plate (henceforth referred to as the Beynon Gabor zone plate). Because this zone plate has no higher order foci, it is in principle a very attractive candidate for focusing of de Broglie matter waves and in some cases X-rays. So far the Beynon Gabor zone plate investigations presented in the literature have concentrated on the intensity distribution along the optical axis and in the focal plane. Here we present a detailed numerical investigation of the Beynon Gabor zone plate, including an investigation of the off-optical axis, off focal plane intensity distribution for point source illumination. We show that at integer fractions of the focal length, the beam becomes nearly toroidal (doughnut-shaped). This offers potentially interesting new possibilities for de Broglie matter wave and X-ray optics, for example in STED-like applications. We further show that the increased intensity at the focal point predicted in the literature for a particular Beynon Gabor zone plate transmission function configuration is an artifact due to the lack of sampling nodes. We support our calculations with experimental measurements in the visible light range, using a Beynon Gabor zone plate fabricated with electron beam lithography.

A Monte Carlo study of the influence of focal spot size, intensity distribution, breast thickness and magnification on spatial resolution of an a-Se digital mammography system using the generalized MTF

In this study the generalized Modulation Transfer Function (GMTF) and the geometric sharpness (Sgeo) were used (i) to study the effects of various focal spot sizes (0.04 mm–0.3 mm), x-ray intensity distributions (Gaussian and double Gaussian), breast thicknesses (2–7 cm) and magnifications M (1.0–2.0) on the spatial resolution of an a-Se digital mammography system, (ii) to identify suitable focal spots for magnification mammography and (iii) derive optimum magnifications. For the calculation of GMTF the required components were: focal spot MTF, obtained from theory, detector MTF, scatter MTF and scatter fraction obtained from Monte Carlo simulations. The results showed that focal spots with sizes up to 0.18 mm are suitable for magnification mammography offering a GMTF which is >50% and >20% at the respective object frequencies of 6.5 mm−1 and 9 mm−1. Focal spots with sizes < 0.16 mm and Gaussian. intensity distribution, or sizes ≤ 0.1 mm and double Gaussian, offer a system resolution which improves or does not deteriorate with magnification for most object frequencies. For larger focal spots, i.e. 0.16–0.18 mm for a Gaussian and 0.12–0.18 mm for a double Gaussian. intensity distribution, optimum magnifications exist which depend on the object frequency and breast thickness. System resolution (in terms of Sgeo) is maximized at M = 1.8–2.0 (all breast thicknesses) for Gaussian intensity distribution, and at M = 1.4–1.6 (breast thicknesses ≤ 4 cm) and M = 1.6–1.8 (thicker breasts) for double Gaussian.

A Highly Efficient Superresolving Phase Filter for a Radially Polarized Beam

We simulate the focal intensity distribution of a radially polarized beam, in view of the vector diffraction theory. We summarize two important rules: (i) the marginal ray of the aperture determines the focal size on the focal plane; (ii) the ratio of the longitudinal component to the transversal component affects the shape of the focus. We design a continuous phase filter using these rules for a confocal system. We chose the tangent of the semi-aperture angle to build up the phase function, because it is sensitive to the marginal rays, which have large aperture angles. To achieve a flexible modulation, we use a quadratic function for unwrapping the phase. We optimize the parameters of the quadratic function and achieve a transverse superresolving focus. Aiming at different Strehl ratios, we obtain a series of superresolution phase filters. Compared with others, the filter proposed has the advantages of superior superresolution effect and higher energy utilization ratios. The phase-filter design is universal and proved to be valid. It can be employed in either high or low NA systems, superresolving or donut focus applications.

Increasing energy coupling into plasma waves by tailoring the laser radial focal spot distribution in a laser wakefield accelerator

By controlling the focal spot quality with a deformable mirror, we are able to show that increasing the fraction of pulse energy contained within the central part of the focal spot, while keeping the total energy and central spot size constant, significantly increases the amount of energy transferred to the wakefield: Our measurements show that the laser loses significantly more laser energy and undergoes greater redshifting and that more charge is produced in the accelerated beam. Three dimensional particle in cell simulations performed with accurate representations of the measured focal spot intensity distribution confirm that energy in the wings of the focal spot is effectively wasted. Even though self-focusing occurs, energy in the wings of the focal spot distribution is not coupled into the wakefield, emphasising the vital importance of high quality focal spot profiles in experiments.

On the use of an analytic source model for dose calculations in precision image-guided small animal radiotherapy

Precision image-guided small animal radiotherapy is rapidly advancing through the use of dedicated micro-irradiation devices. However, precise modeling of these devices in model-based dose-calculation algorithms such as Monte Carlo (MC) simulations continue to present challenges due to a combination of very small beams, low mechanical tolerances on beam collimation, positioning and long calculation times. The specific intent of this investigation is to introduce and demonstrate the viability of a fast analytical source model (AM) for use in either investigating improvements in collimator design or for use in faster dose calculations. MC models using BEAMnrc were developed for circular and square fields sizes from 1 to 25 mm in diameter (or side) that incorporated the intensity distribution of the focal spot modeled after an experimental pinhole image. These MC models were used to generate phase space files (PSFMC) at the exit of the collimators. An AM was developed that included the intensity distribution of the focal spot, a pre-calculated x-ray spectrum, and the collimator-specific entrance and exit apertures. The AM was used to generate photon fluence intensity distributions (ΦAM) and PSFAM containing photons radiating at angles according to the focal spot intensity distribution. MC dose calculations using DOSXYZnrc in a water and mouse phantom differing only by source used (PSFMC versus PSFAM) were found to agree within 7% and 4% for the smallest 1 and 2 mm collimator, respectively, and within 1% for all other field sizes based on depth dose profiles. PSF generation times were approximately 1200 times faster for the smallest beam and 19 times faster for the largest beam. The influence of the focal spot intensity distribution on output and on beam shape was quantified and found to play a significant role in calculated dose distributions. Beam profile differences due to collimator alignment were found in both small and large collimators sensitive to shifts of 1 mm with respect to the central axis.

Mapping 3D Focal Intensity Exposes the Stable Trapping Positions of Single Nanoparticles

The photonic interactions between a focused Gaussian laser beam and a nanoscopic particle are highly dependent on exact particle location and focal intensity distribution. So far, the 3D focal intensity distribution and the preferred position of a nanoparticle confined within the focal region were only theoretically predicted. Here, we directly map the three-dimensional focal intensity distribution, quantify stable trapping positions, and prove that certain sizes of nanoparticles stably trap in front of the focus.

Focussing over the edge: adaptive subsurface laser fabrication up to the sample face

Direct laser writing is widely used for fabrication of subsurface, three dimensional structures in transparent media. However, the accessible volume is limited by distortion of the focussed beam at the sample edge. We determine the aberrated focal intensity distribution for light focused close to the edge of the substrate. Aberrations are modelled by dividing the pupil into two regions, each corresponding to light passing through the top and side facets. Aberration correction is demonstrated experimentally using a liquid crystal spatial light modulator for femtosecond microfabrication in fused silica. This technique allows controlled subsurface fabrication right up to the edge of the substrate. This can benefit a wide range of applications using direct laser writing, including the manufacture of waveguides and photonic crystals.

Nanoplasma Dynamics of Single Large Xenon Clusters Irradiated with Superintense X-Ray Pulses from the Linac Coherent Light Source Free-Electron Laser

The plasma dynamics of single mesoscopic Xe particles irradiated with intense femtosecond x-ray pulses exceeding 10(16) W/cm2 from the Linac Coherent Light Source free-electron laser are investigated. Simultaneous recording of diffraction patterns and ion spectra allows eliminating the influence of the laser focal volume intensity and particle size distribution. The data show that for clusters illuminated with intense x-ray pulses, highly charged ionization fragments in a narrow distribution are created and that the nanoplasma recombination is efficiently suppressed.

Focusing properties of vector vortex-bearing beams

Focusing properties of the vector vortex-bearing beams are investigated theoretically by vector diffraction theory. Simulation results show that the intensity distribution in focal region can be altered considerably by adjusting topological charge m and the numerical aperture (NA) of the focusing optical system. Focal pattern evolves from one focal spot to two overlapped intensity peaks. The two overlapped intensity peaks separate with increasing topological charge m, which leads to the focal splitting. It was found that evolution principle of focal pattern differs very remarkably with different numerical aperture of the focusing optical system. And focal split appears in focal evolution with different topological charge m in different numerical aperture of the focusing optical system. Results show that the topological charge of the vector vortex-bearing beams influences the focal intensity distribution considerably, and some novel focal patterns appear.

Polarization Effect on Superfocusing of a Plasmonic Lens Structured with Radialized and Chirped Elliptical Nanopinholes

Tuning effect of different polarization states was presented in this paper. It can be realized by a plasmonic lens constructed with elliptical pinholes ranging from submicron to nanoscales distributed in variant period along radial direction. Propagation properties of the lens illuminated under four different polarization states: linear, elliptical, radial, and cylindrical vector beam, were calculated and analyzed combining with finite-difference time-domain algorithm. Different focusing performances of the lens were illustrated while the polarized light passes through the pinholes. Our calculation results demonstrate that polarization effect of the elliptical pinholes-based plasmonic lens can generate high transmission intensity and sharp focusing for our proposed specific structures. Beam focal region, position, and transmission intensity distribution can be tailored by the four polarization states.

Fractional vortex lens

The properties of a fractional vortex lens are discussed and its focal plane intensity distribution is investigated. The azimuthal phase pattern of a fractional topological charge vortex and the quadratic phase variation of the lens are displayed on a spatial light modulator (SLM) that is used in the phase mode. The intensity distribution possesses a low intensity radial opening in contrast to the doughnut pattern formed by a vortex beam with integer charge. The presence of multiple singularities in the radial opening of the doughnut structure is detected interferometrically.