Divergent Wavefront Research Articles

Large angle and high uniform diffractive laser beam splitter with divergent spherical wave illumination

Splitting angle, generally limited by the feature size of diffractive optical element (DOE), is one of the significant metrics of the diffractive laser beam splitter. In this study, we realize large angle and high uniform split beams by using a divergent spherical wave front incidence. For designing this diffractive beam splitter, the Gerchberg-Saxton (GS) optimization algorithm which is known as a widely used method in DOE design is modified. Meanwhile, a negative feedback method is proposed to further improve the uniformity in experiment to compensate the incident wavefront distortion. Finally, a phase-only spatial light modulator (SLM) was used to test the feasibility and adaptiveness of our design strategy. In the experiment, we achieved several kinds of beam splitters and the uniformities are all better than 3.0% which the uniformity is measured by the peak-to-valley (PV) ratio.

Reconstructing highly divergent wavefronts from sparse measurements

The paper presents a concept for the sparse measurement and reconstruction of highly divergent wavefronts enabling measurements at high throughputs and beyond the dynamic range of the wavefront sensor. In the proposed concept, a direct measurement of the wavefront is carried out, where a few segments of the wavefront are measured with Shack–Hartmann sensors (SHSs). In total about 1% of the wavefront is measured and used for the reconstruction of the entire wavefront, which makes the concept suitable for applications where low measurement times are needed. A simulation analysis and an experimental validation of the concept are carried out, and results show that a wavefront with a divergence of 62° can be reconstructed with a root-mean-square error of about 200 nm.

Improving the precision of parallel registration by incorporating a priori information.

This paper presents an algorithm for the precise registration of optical wavefronts. A wavefront exceeding the spatial or dynamic measurement range of a wavefront sensor, e.g. a Shack-Hartmann sensor, can be measured in multiple sub-measurements, each providing a segment of the wavefront. Sensor misalignment during the measurements results in the demand for registration algorithms to precisely reconstruct the entire wavefront from the segments. The proposed algorithm registers the segments in parallel and incorporates a priori information about the uncertainty of the sensor misalignment obtaining high-quality registration. A simulative analysis of the algorithm with respect to sensor misalignment and measurement errors is presented together with an application of the algorithm to a measured divergent wavefront. In the scope of the analysis, the algorithm is compared to state-of-the-art registration algorithms, such as the iterative closest point (ICP) algorithm, where an improvement of the registration performance by a factor of 3 is obtained. Results show that the algorithm is able to reconstruct a divergent and a freeform wavefront with an RMS registration error of a few tens of nanometers with a standard deviation of 80 µm and 2.4 mrad.

Iterative parallel registration of strongly misaligned wavefront segments.

The paper presents an algorithm for the precise registration of multiple wavefront segments containing large misalignment and phase differences. The measurement of a wavefront with huge dynamics or a large aperture size can be carried out in multiple Shack-Hartmann sensor measurements of segments of the wavefront. The registration algorithm is flexible with respect to the shape of the wavefront and can reconstruct a plane as well as divergent wavefronts, making it suitable for freeform wavefronts. The algorithm enables parallel registration of the wavefront segments which is carried out in an iterative manner to compensate for large misalignment errors. A simulative analysis of the proposed algorithm compares its performance to a fast parallel registration (FPR) algorithm and the established iterative closest point (ICP) algorithm. For a sensor misalignment of up to 100 μm and 3 mrad the algorithm registers a plane and a divergent wavefront with a precision that is a factor 4 and 12 better than the registration precision of the FPR and ICP algorithm.

Fast, precise, and shape-flexible registration of wavefronts

A fast and precise algorithm for wavefront reconstruction by the registration of wavefront segments is presented. If the wavefront exceeds the sensor aperture or the dynamic range of the sensor, a Shack-Hartmann sensor can measure only segments of an optical wavefront. The algorithm registers the wavefront segments in parallel, where they are simultaneously transformed to minimize their overlap mismatch for precise reconstruction of the entire wavefront. The original nonlinear optimization problem is approximated by a convex optimization problem that can be solved more efficiently. A simulation-based analysis of the algorithm and a comparison to a previously proposed parallel registration (PR) algorithm as well as to the iterative closest point (ICP) algorithm are presented. It is shown that despite measurement noise, the algorithm can precisely register plane as well as divergent wavefronts with root mean square registration errors smaller than 10 nm. Particularly for the divergent wavefront, this enables a reduction of the registration error by a factor of up to 750 as compared to the established algorithms. Analysis and comparison to the ICP and PR algorithm also show that the computation time of the proposed algorithm can be from one to three orders of magnitude smaller.

Postfilament supercontinuum on 100 m path in air.

Pulses at 744 nm with 90 fs duration, 6 mJ energy, and a weakly divergent wavefront propagate for more than 100 m and generate a filament followed by an unprecedently long high intensity (≥1TW/cm2) light channel. Over a 20 m long sub-section of this channel, the pulse energy is transferred continuously to the infrared wing, forming spectral humps that extend up to 850 nm. From 3D+time carrier-resolved simulations of 100 m pulse propagation, we show that spectral humps indicate the formation of a train of femtosecond pulses appearing at a predictable position in the propagation path.

Rigorous multi-slice wave optical simulation of x-ray propagation in inhomogeneous space.

The simulation of the propagation of divergent beams using Fourier-based angular spectrum techniques can pose challenges for ensuring correct sampling in the spatial and reciprocal domains. This challenge can be compounded by the presence of diffracting objects, as is often the case. Here, I give details of a method for robustly simulating the propagation of beams with divergent wavefronts in a coordinate system where the wavefronts become planar. I also show how diffracting objects can be simulated, while guaranteeing that correct sampling is maintained. These two advances allow for numerically efficient and accurate simulations of divergent beams propagating through diffracting structures using the multi-slice approximation. The sampling requirements and numerical implementation are discussed in detail, and I have made the computer code freely available.

Scanning Wavefront Sensor for Measurement of Highly Divergent Wavefronts

This paper deals with the characterization of freeform optics by means of a wavefront sensor. Freeform optics show an increasing demand since they have the potential to improve optical system performance while reducing size, weight and complexity. To directly measure the performance of a freeform optical part, a novel scanning wavefront sensor approach is proposed which is faster than a coordinate measuring machine and more flexible than an interferometer. The challenges lie in the limited dynamic range of a Shack-Hartmann sensor concerning wavefront slope and curvature. Both limits can be overcome by repositioning the sensor and orienting it tangentially to the wavefront. An automatic setup is developed and first measurements are demonstrated on a highly divergent wavefront. It is shown that the dynamic range of the sensor is increased by scanning the sensor along the wavefront and orienting the sensor tangential to the wavefront in each position. Measurements are taken over a range of ±15°, which is an improvement by a factor 5 compared to the typical dynamic range of ±3° for a static Shack-Hartmann sensor.

Convergent and divergent beam electron holography and reconstruction of adsorbates on free-standing two-dimensional crystals

Van der Waals heterostructures have been lately intensively studied because they offer a large variety of properties that can be controlled by selecting 2D materials and their sequence in the stack. The exact arrangement of the layers as well as the exact arrangement of the atoms within the layers, both are important for the properties of the resulting device. Recently it has been demonstrated that convergent beam electron diffraction (CBED) allows quantitative three-dimensional mapping of atomic positions in three-dimensional materials from a single CBED pattern. In this study we investigate CBED in more detail by simulating and performing various CBED regimes, with convergent and divergent wavefronts, on a somewhat simplified system: a 2D monolayer crystal. In CBED, each CBED spot is in fact an in-line hologram of the sample, where in-line holography is known to exhibit high intensity contrast in detection of weak phase objects that are not detectable in conventional in-focus imaging mode. Adsorbates exhibit strong intensity contrast in zero and higher order CBED spots, whereas lattice deformation such as strain or rippling cause noticeable intensity contrast only in the first and higher order CBED spots. The individual CBED spots can be reconstructed as typical in-line holograms, and the resolution of 2.13 A can be in principle achieved in the reconstructions. We provide simulated and experimental examples of CBED of a 2D monolayer crystal. The simulations show that individual CBED spots can be treated as in-line holograms and sample distributions such as adsorbates, can be reconstructed. Individual atoms can be reconstructed from a single CBED pattern provided the later exhibits high-order CBED spots. Examples of reconstructions obtained from experimental CBED patterns, at a resolution of 2.7 A, are shown.

Inscription and analysis of non-uniform diffraction gratings in azobenzene molecular glass thin films.

Non-uniform surface relief diffraction gratings were laser-inscribed on azobenzene molecular glass thin films using a modified Lloyd's mirror interferometer. The azobenzene films were exposed to an adjustable interference pattern produced by the recombination of collimated and spherically divergent laser wave fronts. The localized pitch, grating vector orientation and depth of the resulting non-uniform gratings were measured using an atomic force microscope and a theoretical model was analytically developed to explain the experimental results. The fabricated gratings exhibited a chirping or pitch variation along the imposed X-axis as well as an angular change in the grating vector orientation along the imposed Y-axis. Studies were conducted on various non-uniform grating configurations having central pitches of 500 nm, 1000 nm, 1500 nm and 2000 nm.

Probe reconstruction for holographic X-ray imaging.

In X-ray holographic near-field imaging the resolution and image quality depend sensitively on the beam. Artifacts are often encountered due to the strong focusing required to reach high resolution. Here, two schemes for reconstructing the complex-valued and extended wavefront of X-ray nano-probes, primarily in the planes relevant for imaging (i.e. focus, sample and detection plane), are presented and compared. Firstly, near-field ptychography is used, based on scanning a test pattern laterally as well as longitudinally along the optical axis. Secondly, any test pattern is dispensed of and the wavefront reconstructed only from data recorded for different longitudinal translations of the detector. For this purpose, an optimized multi-plane projection algorithm is presented, which can cope with the numerically very challenging setting of a divergent wavefront emanating from a hard X-ray nanoprobe. The results of both schemes are in very good agreement. The probe retrieval can be used as a tool for optics alignment, in particular at X-ray nanoprobe beamlines. Combining probe retrieval and object reconstruction is also shown to improve the image quality of holographic near-field imaging.

Investigation of shock detonation of TATB using proton radiography

The initiation of detonation of plasticized TATB by shock loading using an initiator pressure charge of an HMX based explosive was studied by radiography. In the experiments, the size of the initiator and the initial density of the TATB charge were varied. During initiation of TATB detonation, part of the material did not react, forming so-called dark zones. As the process goes on, the detonation wave bends around the dark zones, without initiating the material within them. The evolution of the area of dark zones was compared for samples of different initial density and initiators of different sizes. The characteristic boundaries and X−t diagrams of detonation front propagation under different loading conditions were constructed from images of the explosive process. Density distributions behind a divergent detonation wave front at different times were obtained and analyzed.

Generation of Optical Vortex Arrays Using Single-Element Reversed-Wavefront Folding Interferometer

Optical vortex arrays have been generated using simple, novel, and stable reversed-wavefront folding interferometer. Two new interferometric configurations were used for generating a variety of optical vortex lattices. In the first interferometric configuration one cube beam splitter (CBS) was used in one arm of Mach-Zehnder interferometer for splitting and combining the collimated beam, and one mirror of another arm is replaced by second CBS. At the output of interferometer, three-beam interference gives rise to optical vortex arrays. In second interferometric configuration, a divergent wavefront was made incident on a single CBS which splits and combines wavefronts leading to the generation of vortex arrays due to four-beam interference. It was found that the orientation and structure of the optical vortices can be stably controlled by means of changing the rotation angle of CBS.

Soft X-ray holographic microscopy of chromosomes with high aspect ratio pinholes

We used digital in-line soft X-ray holography (DIXH) in the Gabor geometry to image human chromosomes. The divergent wave front was generated by diffraction of synchrotron radiation from a high aspect ratio pinhole. As under our experimental conditions the achievable resolution depends on the pinhole radius, high aspect ratio holes with diameters in the 100 nm range were prepared by focused ion beam (FIB) milling. The central maximum of the obtained Airy pattern was used to image chromosomes prepared from metaphase HeLa cells at experimental resolutions of 370 ± 40 nm with soft X-rays at 260 eV photon energy provided by the BESSY II synchrotron radiation facility.

Use of Convergent and Divergent Illumination with Plane Gratings*

The properties of a plane grating when it is illuminated by a convergent or divergent wave front are investigated. The investigation shows that the image principally suffers an unsymmetric aberration of coma type in the direction of dispersion. Remedies have been indicated to correct this aberration.