Focal Spot Distribution Research Articles

Multifocal tornado beams carrying chirality

The significance of abruptly autofocusing vortex beams with a unique helical phase structure lies in particle trapping and optical spanner applications. This paper presents a novel modulation of a circular Pearcey beam utilizing a multicyclic helical phase and a chirp factor. Both theoretical analyses and experimental results demonstrate that we have successfully designed a beam with tornado properties and optically chiral structure. This beam has multidimensionally tunable parameters, allowing not only different focusing intensities, focal lengths and focal spot shape distributions, but also controllable rotational propagation directions. Furthermore, it has the ability to produce two dual focusing modes with dissimilar focal spot distributions. We believe that such a beam holds potential applications in the realisation of optical spanners, multi-region trapping of particles and the fabrication of chiral metamaterials.

Influence of Focal Spot Distribution on Characteristics of Continuous Phase Plates

Influence of Focal Spot Distribution on Characteristics of Continuous Phase Plates

Target Design in SEM-Based Nano-CT and Its Influence on X-ray Imaging.

Nano-computed tomography (nano-CT) based on scanning electron microscopy (SEM) is utilized for multimodal material characterization in one instrument. Since SEM-based CT uses geometrical magnification, X-ray targets can be adapted without any further changes to the system. This allows for designing targets with varying geometry and chemical composition to influence the X-ray focal spot, intensity and energy distribution with the aim to enhance the image quality. In this paper, three different target geometries with a varying volume are presented: bulk, foil and needle target. Based on the analyzed electron beam properties and X-ray beam path, the influence of the different target designs on X-ray imaging is investigated. With the obtained information, three targets for different applications are recommended. A platinum (Pt) bulk target tilted by 25° as an optimal combination of high photon flux and spatial resolution is used for fast CT scans and the investigation of high-absorbing or large sample volumes. To image low-absorbing materials, e.g., polymers or organic materials, a target material with a characteristic line energy right above the detector energy threshold is recommended. In the case of the observed system, we used a 30° tilted chromium (Cr) target, leading to a higher image contrast. To reach a maximum spatial resolution of about 100 nm, we recommend a tungsten (W) needle target with a tip diameter of about 100 nm.

Statistical Properties of Partially Coherent Higher-Order Laguerre-Gaussian Power-Exponent Phase Vortex Beams

In this paper, partially coherent radially polarized (RP) Laguerre-Gaussian (LG) rotationally symmetrical power-exponent phase vortex (RSPEPV) beams with the LG-correlated Schell-model (LGSM) were introduced. The statistical properties of the tightly focused beams, including intensity distribution, degrees of polarization and coherence, and Stokes vector, were studied based on vectorial Richards-Wolf diffraction integral theory. Moreover, when the distance between focal plane and the observation plane z = 0, the relationships between the tight-focusing properties of RP-LG-RSPEPV beams with LGSM and the order of LGSM p’, topological charges l, power exponent n, spatial correlation δ, and radial index p were investigated. The results show that by changing the order of LGSM, topological charge, power exponent, spatial correlation length, and radial index, the focal spot distribution of various shapes can be obtained. This work provides ideas for the application of partially coherent beams in particle capture and optical tweezers.

Single-shot measurement of the near-field and focal spot profiles of a 351 nm laser beam for SGII-upgraded facility with multiple-focal-plane constraint coherent modulation imaging.

Inertial confinement fusion (ICF) places an urgent demand for precise measurement of 351 nm (3ω) laser beam parameters when performing physical experiments on high-power laser facilities. The near-field and focal spot distributions are the utmost important parameters to characterize the quality of the laser beam. Coherent modulation imaging (CMI) is a promising technique for online laser beam measurement, however, it fails to reconstruct the near-field and focal spot profiles when it is used to measure the beam quality of a 351 nm laser beam for SGII-upgrade facility. To solve this problem, a novel CMI reconstruction algorithm is proposed in this work, and the performance of the algorithm in 3ω laser beam measurement can be obviously improved. By adopting multiple-virtual-focal-plane constraint in the proposed algorithm, the near-field and focal spot profiles of the 3ω laser beam can be successfully reconstructed. Experiments have been conducted on SGII-upgrade facility to verify the feasibility of the proposed method.

Three-focal-spot terahertz diffractive optical element-iterative design and neural network approach.

The redistribution of an incoming radiation into several beams is necessary in telecommunication to demultiplex data signals. In the terahertz spectral range, it can be realized by easy-to-manufacture diffractive optical elements (DOEs) allowing to focus the radiation into multiple focal spots in a single plane. In this article, we present diffractive optical elements focusing THz radiation into three focal spots. Different focal spot distributions (symmetric and asymmetric) are designed using an iterative algorithm. The phase distribution forming asymmetric focal spots can be realized by iterative design, which is a novel approach, to our knowledge. Then, the structures are manufactured using a sintering-based 3D-printing method from polyamide 12 (PA 12) and measured in an experimental setup for 150 GHz frequency. A novel approach based on neural networks (NNs) is proposed to optimize the phase delay maps of the structures to further improve their performance - the higher efficiency and the lower unwanted background noise.

Reconstruction of x-ray focal spot distribution using a rotating edge.

The size and shape of an x-ray source's focal spot is a critical factor in the imaging system's overall spatial resolution. The conventional approach to imaging the focal spot uses a pinhole camera, but this requires careful, manual measurements. Instead, we propose a novel alternative, simply using the collimator available on many x-ray systems. After placing the edge of a collimator blade in the center of the beam, we can obtain an image of its edge spread function (ESF). Each ESF provides information about the focal spot distribution - specifically, the parallel projection of the focal spot in the direction parallel to the edge. If the edge is then rotated about the beam axis, each image provides a different parallel projection of the focal spot until a complete Radon transform of the focal spot distribution is obtained. The focal spot can then be reconstructed by the inverse Radon transform, or parallel-beam filtered backprojection. We conducted a study on a clinical C-arm system with 3 focal spot sizes (0.3, 0.6, 1.0 mm nominal size), comparing the focal spot obtained using the rotating edge method against the conventional pinhole approach. Our results demonstrate accurate characterization of the size and shape of the focal spot.

Design and implementation of a 38 kW dish-Stirling concentrated solar power system

Dish-Stirling concentrated solar power system (DS-CSP) is an important pathway for converting solar energy into electricity at high efficiency. In this study, a rated power 38 kW DS-CSP system was developed (installed in Xiangtan Electric Manufacturing Group). The heat engine adopted the alpha-type four cylinders double-acting Stirling engine (Stirling Biopower Flexgen S260). The absorber flux distribution simulation was conducted using ray tracing method and then the 204 m2 parabolic dish concentrator system (diameter is 17.70 m and focal length is 9.49 m) with single concentrator plus single pillar supporting has been designed and built. A water-cooled disc target and an absorber imitation device were adopted to test the tracking performance of the dish concentrator system, homogeneity of the focal spot and flux distribution of the absorber. Finally, the S260 Stirling engine was installed on the focal position of the dish concentrator and then the net output power date of the 38 kW DS-CSP system was tested. The absorber overheating problem on the DS-CSP system performance was discussed when the DS-CSP system was installed in different locations. The testing result shows that this system achieved the net output power of 38 kW and solar-to-electricity efficiency (SEE) of 25.3% with the direct normal irradiation (DNI) at 750 W/m2. The net output power can further increase to 40.5 kW with the SEE of 26.6% when the DNI reaches up to the maximum of 761 W/m2. The net output power of the 38 kW DS-CSP system has a linear function relationship with the DNI. The fitting function is Net power output=0.1003×DNI－36.129, where DNI is at the range of 460∼761 W/m2. This function could be used to predict the amount of the 38 kW DS-CSP system annual generation power.

Studies on design of 351 nm focal plane diagnostic system prototype and focusing characteristic of SGII-upgraded facility at half achievable energy performance.

In order to obtain the intensity distribution of a 351 nm focal spot and smoothing by spectral dispersion (SSD) focal plane profile of a SGII-upgraded facility, a type of off-axis imaging system with three spherical mirrors, suitable for a finite distance source point to be imaged near the diffraction limit has been designed. The quality factor of the image system is 1.6 times of the diffraction limit tested by a 1053 nm point source. Because of the absence of a 351 nm point source, we can use a Collins diffraction imaging integral with respect to λ=351 nm, corresponding to a quality factor that is 3.8 times the diffraction limit at 351 nm. The calibration results show that at least the range of ±10 mrad of view field angle and ±50 mm along the axial direction around the optimum object distance can be satisfied with near diffraction limited image that is consistent with the design value. Using this image system, the No. 2 beam of the SGII-upgraded facility has been tested. The test result of the focal spot of final optics assembly (FOA) at 351 nm indicates that about 80% of energy is encompassed in 14.1 times the diffraction limit, while the output energy of the No. 2 beam is 908 J at 1053 nm. According to convolution theorem, the true value of a 351 nm focal spot of FOA is about 12 times the diffraction limit because of the influence of the quality factor. Further experimental studies indicate that the RMS value along the smoothing direction is less than 15.98% in the SSD spot test experiment. Computer simulations show that the quality factor of the image system used in the experiment has almost no effect on the SSD focal spot test. The image system can remarkably distort the SSD focal spot distribution under the circumstance of the quality factor 15 times worse than the diffraction limit. The distorted image shows a steep slope in the contour of the SSD focal spot along the smoothing direction that otherwise has a relatively flat top region around the focal spot center.

X-ray focal spot reconstruction by circular penumbra analysis-Application to digital radiography systems.

The quality of a radiography system is affected by several factors, a major one being the focal spot size of the x-ray tube. In fact, the measurement of such size is recognized to be of primary importance during acceptance tests and image quality evaluations of clinical radiography systems. The most common device providing an image of the focal spot emission distribution is a pin-hole camera, which requires a high tube loading in order to produce a measurable signal. This work introduces an alternative technique to obtain an image of the focal spot, through the processing of a single radiograph of a simple test object, acquired with a suitable magnification. The radiograph of a magnified sharp edge is a well-established method to evaluate the extension of the focal spot profile along the direction perpendicular to the edge. From a single radiograph of a circular x-ray absorber, it is possible to extract simultaneously the radial profiles of several sharp edges with different orientations. The authors propose a technique that allows to obtain an image of the focal spot through the processing of these radial profiles by means of a pseudo-CT reconstruction technique. In order to validate this technique, the reconstruction has been applied to the simulated radiographs of an ideal disk-shaped absorber, generated by various simulated focal spot distributions. Furthermore, the method has been applied to the focal spot of a commercially available mammography unit. In the case of simulated radiographs, the results of the reconstructions have been compared to the original distributions, showing an excellent agreement for what regards both the overall distribution and the full width at half maximum measurements. In the case of the experimental test, the method allowed to obtain images of the focal spot that have been compared with the results obtained through standard techniques, namely, pin-hole camera and slit camera. The method was proven to be effective for simulated images and the results of the experimental test suggest that it could be considered as an alternative technique for focal spot distribution evaluation. The method offers the possibility to measure the actual focal spot size and emission distribution at the same exposure conditions as clinical routine, avoiding high tube loading as in the case of the pin-hole imaging technique.

Capsule illumination uniformity illuminated by direct laser-driven irradiation from several tens of directions

Capsule illumination uniformity obtained by direct driving lasers from several tens of directions is studied systematically. The best polar angles of the three focal spot rings on the capsule are determined to be 22.4, 47.7, and 73.6by a spherical-harmonic mode analysis and a numerical simulation. Based on the configuration of indirect laser driven facility, we have optimized the beam re-directions and the focal spot distributions for polar direct drive, which smooth successfully the illumination distribution on the capsule.Laser driven inertial confinement fusion is an important way to achieve controllable nuclear fusion for human beings, which includes two laser-driven schemesdirectly driving and indirectly driving scheme. Since the indirect driving scheme considerably relaxes the strict requirements for laser performance and decreases the engineering difficulties, the main laser facilities around the world have adopted the indirect driving scheme, such as the National Ignition Facility in the U. S., the Laser Megajoule in France, and the SG series laser drivers in China.Meanwhile, scientists keep developing the key technologies for directly driving and have made great progress. For example, the fast ignition and shock ignition are two new methods to achieve fusion ignition in the direct driving scheme, which attracted lots of attention in the past few years. However, the main laser drivers for inertial confinement fusion research are configured as indirect drivers, which are not suitable for direct driving experiments. So a compromising suggestion was proposed that by redirecting the lasers, changing the laser energy distributions, designing new type of targets, and so on, a radiation field which is very close to a direct driving radiation field can be simulated in a laser facility that is configured as an indirect driver. This is the so called polar direct drive method that provides a feasible way for primary researches on direct driving technologies in an indirect laser driver. Such experiments have already been conducted in the National Ignition Facility.In China, the large indirect laser driver with an output capability in the level of hundreds kilojoule will finish its engineering construction and routinely operate for physical experiments soon. To achieve a good polar direct drive performance in this laser facility is much more difficult than in previous smaller laser drivers. In this paper, capsule illumination uniformity by directly driving laser from several tens of directions is studied systematically. The best polar angles of the three focal spot rings on the capsule are determined to be 22.4, 47.7, and 73.6 by a spherical-harmonic mode analysis and a numerical simulation. Based on the configuration of indirect driving laser facility, we have optimized the beam re-directions and the focal spot distributions for polar direct drive, which successfully smoothes the illumination distribution on the capsule.

Focusing properties of the vector beam with complicated polarization and helical phase

We report a vector beam with complicated polarization and helical phase and derive the corresponding focusing model of the aplanatic system, where the 10 variables optimized provide a more powerful and flexible tool to construct various interesting focal spots. By optimizing these 10 variables, we directly construct some specific focal spots, including the single focal spot with lateral resolution beyond the Abbe diffraction limit and without axial electric field component and the focal spots with unique structures in the intensity, such as the square and triangular bright spots, the various double lines, the cross lines, the ring-shaped square, the ring-shaped hexagon, and so on. Some of those focal spots with unique structures in the intensity have high resolution, even beyond the Abbe diffraction limit. We conclude the functions of some variables affecting the structures of the focal spots, draw some regulars constructing the focal spot with high quality, and indicate how to find the new values of various variables optimized in order to rotate the focal spot distribution. Although only the focal spot structures of the intensity distribution are discussed in this paper, the ideas and the developed focusing model can be used for the investigations of the various focal spot structures of polarizations, gradient forces, and spin and orbital angular momentums.

Rectangular Fixed-Gantry CT Prototype: Combining CNT X-Ray Sources and Accelerated Compressed Sensing-Based Reconstruction

Carbon nanotube (CNT)-based multibeam X-ray tubes provide an array of individually controllable X-ray focal spots. The CNT tube allows for flexible placement and distribution of X-ray focal spots in a system. Using a CNT tube, a computed tomography (CT) system with a noncircular geometry and a nonrotating gantry can be created. The noncircular CT geometry can be optimized around a specific imaging problem, utilizing the flexibility of CNT multibeam X-ray tubes to achieve the optimal focal spot distribution for the design constraints of the problem. Iterative reconstruction algorithms provide flexible CT reconstruction to accommodate the noncircular geometry. Compressed sensing-based iterative reconstruction algorithms apply a sparsity constraint to the reconstructed images that can partially account for missing angular coverage due to the noncircular geometry. In this paper, we present a laboratory prototype CT system that uses CNT multibeam X-ray tubes; a rectangular, nonrotating imaging geometry; and an accelerated compressed sensing-based iterative reconstruction algorithm. We apply a total variation minimization as our sparsity constraint. We present the advanced CNT multibeam tubes and show the stability and flexibility of these new tubes. We also present the unique imaging geometry and discuss the design constraints that influenced the specific system design. The reconstruction method is presented along with an overview of the acceleration of the algorithm to near real-time reconstruction. We demonstrate that the prototype reconstructed images have image quality comparable with a conventional CT system. The prototype is optimized for airport checkpoint baggage screening, but the concepts developed may apply to other application-specific CT imaging systems.

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.

Comparison of subwavelength focusing properties of diffraction and Fresnel zone plate plasmonic planar lenses

The subwavelength focusing properties of diffractive plasmonic planar lenses (DPLs) and Fresnel zone plate plasmonic planar lenses (FZPs) have been compared in this paper. To that end, we use the same lens material, incident wavelength, thickness and focal length for comparison. Both DPLs and FZPs consist of central circular slits surrounded by transparent and opaque zones and can get clear focusing performances. By using the rigorous electromagnetic numerical method, the fields in the focal region are analyzed in detail, and our results demonstrate that FZP can generate higher transmission efficiency, and higher peak field intensity at the focal plane. Focusing polarization properties of the lens illuminated by linearly polarized state, are calculated and analyzed also. The numerical results show that both the DPL and the FZP produce asymmetrical focal spot distributions with a low f-number. To the FZP, the full-width at half-maximum (FWHM) varies from 256nm (along y-axis) to 516nm(along x-axis) and to the DPL, the FWHM varies from 256nm(along y-axis) to 580nm(along x-axis), respectively. But for a high f-number, the asymmetrical performance of the focal spot will be reduced due to complicated electromagnetical field interferences and micro waveguide effect. Otherwise, the DPL can get a higher depolarization effect than the FZP does.

Evaluation of the microangiographic fluoroscope (MAF) using generalized system performance metrics

The performance of a newly developed, high resolution, microangiographic fluoroscope (MAF) (35 μm pixel pitch and 300 μm thick CsI phosphor) was evaluated using a generalized linear system analysis and compared with that of a standard amorphous Si thin film transistor flat panel detector (FPD) (194 μm pixel pitch and 600 μm thick CsI phosphor). The linear system metrics such as modulation transfer function (MTF), noise power spectrum, and detection quantum efficiency (DQE) are commonly used to gauge the intrinsic detector performance in the detector plane. However, these linear system metrics do not provide information about the image receptor performance in a real system since they do not include the effects of other parameters such as focal spot distribution, scatter radiation, and geometric unsharpness, which may compromise detector performance characteristics. Use of generalized linear system metrics [generalized modulation transfer function (GMTF), generalized normalized noise power spectrum (GNNPS), and generalized detection quantum efficiency (GDQE)] that include these effects gives a more meaningful, complete, and appropriate evaluation of detector performance as part of the imaging system. A uniform head equivalent phantom was used to simulate realistic clinical parameters and x-ray spectra. The detector MTFs were measured using the slanted edge method and the focal spot MTFs were measured using a pinhole assembly. The scatter MTF was simulated and the scatter fraction was measured for a head-equivalent phantom. The generalized system metrics were calculated for different combinations of three choices of focal spots and three different magnifications with two different air-gaps. The performance of the MAF was also illustrated using stent images obtained with different focal spots under similar conditions. Results for the generalized metrics provide a quantitative description of the performance of the imaging system for both detectors. This generalized analysis demonstrated that both detectors have similar imaging capabilities at lower spatial frequencies, but that the MAF has superior performance over the FPD at higher frequencies even when considering focal spot blurring and scatter. This generalized performance analysis demonstrates the significance of focal spot size, magnification, and scatter on the system performance metrics (GMTF, GNNPS, and GDQE). Although the ideal detector performance characteristics of the MAF are not fully realized due to these other system factors, it still retains an advantage in DQE at high spatial frequencies over the FPD. Similar studies based on the generalized linear system metrics can serve as an efficient tool to evaluate total system capabilities under different realistic conditions to enable optimal design for specific imaging tasks.

Relationship between x‐ray illumination field size and flat field intensity and its impacts on x‐ray imaging

X-ray cone-beam CT (CBCT) is being increasingly used for various clinical applications, while its performance is still hindered by image artifacts. This work investigates a new source of reconstruction error, which is often overlooked in the current CBCT imaging. The authors find that the x-ray flat field intensity (I(0)) varies significantly as the illumination volume size changes at different collimator settings. A wrong I(0) value leads to inaccurate CT numbers of reconstructed images as well as wrong scatter measurements in the CBCT research. The authors argue that the finite size of x-ray focal spot together with the detector glare effect cause the I(0) variation at different illumination sizes. Although the focal spot of commercial x-ray tubes typically has a nominal size of less than 1 mm, the off-focal-spot radiation covers an area of several millimeters on the tungsten target. Due to the large magnification factor from the field collimator to the detector, the penumbra effects of the collimator blades result in different I(0) values for different illumination field sizes. Detector glare further increases the variation, since one pencil beam of incident x-ray is scattered into an area of several centimeters on the detector. In this paper, the authors study these two effects by measuring the focal spot distribution with a pinhole assembly and the detector point spread function (PSF) with an edge-spread function method. The authors then derive a formula to estimate the I(0) value for different illumination field sizes, using the measured focal spot distribution and the detector PSF. Phantom studies are carried out to investigate the accuracy of scatter measurements and CT images with and without considering the I(0) variation effects. On our tabletop system with a Varian Paxscan 4030CB flat-panel detector and a Varian RAD-94 x-ray tube as used on a clinical CBCT system, the focal spot distribution has a measured full-width-at-half-maximum (FWHM) of around 0.4 mm, while non-negligible off-focal-spot radiation is observed at a distance of over 2 mm from the center. The measured detector PSF has an FWHM of 0.510 mm, with a shape close to Gaussian. From these two distributions, the author calculate the estimated I(0) values at different collimator settings. The I(0) variation mainly comes from the focal spot effect. The estimation matches well with the measurements at different collimator widths in both horizontal and vertical directions, with an average error of less than 3%. Our method improves the accuracy of conventional scatter measurements, where the scatter is measured as the difference between fan-beam and cone-beam projections. On a uniform water cylinder phantom, more accurate I(0) suppresses the unfaithful high-frequency signals at the object boundaries of the measured scatter, and the SPR estimation error is reduced from 0.158 to 0.014. The proposed I(0) estimation also reduces the reconstruction error from about 20 HU on the Catphan©600 phantom in the selected regions of interest to less than 4 HU. The I(0) variation is identified as one additional error source in x-ray imaging. By measuring the focal-spot distribution and detector PSF, the authors propose an accurate method of estimating the I(0) value for different illumination field sizes. The method obtains more accurate scatter measurements and therefore facilitates scatter correction algorithm designs. As correction methods for other CBCT artifacts become more successful, our research is significant in further improving the CBCT imaging accuracy.

TH-E-110-04: Relationship Between X-Ray Illumination Volume Size and Flat Field Intensity and Its Impacts on X-Ray Imaging

Purpose: This work investigates the variation of x-ray flat field intensity (I_0) as the illumination volume size changes with different collimator settings, an important phenomenon that is commonly ignored in the current implementations of x-ray volumetric imaging and results in significant reconstruction errors. Methods: A relationship between I_0 and the collimator width is first derived. We propose to calculate the focal spot distribution from flat field projections acquired with different collimator widths. I_0 variation effects on reconstruction and scatter measurement accuracy are evaluated using phantom studies. We compare CT images of an evaluation phantom reconstructed from fan-beam projections using I_0 acquired in fan-beam and cone-beam geometries. Conventional methods measure scatter as the difference between cone-beam and fan-beam projections, which results in measurement errors due to the I_0 variation. We improve the scatter measurement method by considering the I_0 difference in the two projections. Results are compared in projection domain and reconstruction domain. Results: The full width of the measured focal spot distribution is 0.68mm at half maximum, and increases to 2.76mm at 5% maximum. This results in an I_0 value difference up to 17% as the geometry varies from cone-beam to fan-beam, and a reconstruction error of ∼ 20 HU if the I_0 is assumed to be unchanged. The improved scatter measurement method achieves more accurate scatter signals and reduces the reconstruction error from ∼20 HU to less than 6 HU. The method also eliminates the skin-line artifacts with a magnitude of ∼50 HU. Conclusions: The I_0 variation due to large focal spot sizes at low intensities causes CT number inaccuracy and image artifacts, which are often misinterpreted in the current research. Our finding of the I_0 effect identifies one potential error source in the reconstruction, and may facilitate scatter correction algorithm designs which require accurate characterization of scatter signals.

Determination of the focusing power of flat lenses using the radiovisor

Focusing of electromagnetic radiation of a point source with a wavelength of 3 cm by flat negative-refraction lenses formed by a hexagonal structure of metal cylindrical rods was studied. The spatial distribution of microwave field of H polarization in the lens focal plane was recorded by a radiovisor screen which converts it into a visible image. The full width at half maximum of the focal spot distribution at optimum focusing did not exceed half the emission wavelength.

Spring constant modulation in a zone plate tweezer using linear polarization

At large NAs a micro-Fresnel zone plate produces a focal spot that is more elliptical than that produced by an objective lens with the same NA. Using this anisotropy we demonstrate a method for modulating the spring constant of an optical trap by rotating the linear input polarization. The focal spot ellipticity is enhanced by the apodization factor of the zone plate and its extremely high NA. By measuring the positions of trapped particles we obtain two-dimensional histograms of particle position. These indicate that the trap spring constant is 2.75 times larger perpendicular to the incident polarization than along it. The elliptical focal spot distribution can be rotated by rotating the incident polarization, allowing the spring constant along a given direction to be modulated.