Scanning Locus Research Articles

A Single-Fiber Endoscope Scanner Probe Utilizing Two-Degrees-of-Freedom (2DOF) High-Order Resonance to Realize Larger Scanning Angle

An electromagnetically driven single-fiber scanner that utilizes a two-degrees-of-freedom (DOF) second-order resonance to realize a larger field scanning scale has been proposed and verified by experimental measurement. A 2DOF system structure, including fiber, magnet, and weight, has been designed, which can execute high-order resonance modal to extend the scanning angle in the limited dimensional tube of the endoscope with 2-mm outer diameter. A low-cost, flexible microcoil embedded in polyimide film is also fabricated to drive the fiber-magnet-weight 2DOF system to vibrate. The magnetic field distributions of the microcoil with different structural parameters are simulated. The experimental measurement verifies that the scanner utilizing the second-order resonance mode has successfully realized a 9.47° scanning scale, which is much larger than the 2.98° obtained at the traditional first-order resonance mode. The scanning locus of fiber tip in the fabricated scanner probe has been obtained in the xy plane by standard position sensitive detector (PSD). The developed fiber scanner probe is promising to the ultrathin endoscope used in the narrow space of the human body.

A comparative study on interpolation methods for controlled cardiac CT

AbstractBai et al. recently proposed to acquire random fan‐beam/cone‐beam projections with a linear/planar detector from a circular scanning locus for controlled cardiac computed tomography (CT). After specifying a uniform acquisition geometry required by FBP (filtration‐backprojection), we rebin the random fan‐beam/cone‐beam data via nearest‐neighbor, quadrilateral and triangle‐based linear interpolation methods. The fan‐beam and parallel‐beam FBP algorithms are employed for rebinned fan‐beam projections. The FDK (Feldkamp–Davis–Kress) and t‐FDK (tent‐FDK) methods are employed for rebinned cone‐beam data. Also, nonuniform weighting fan‐beam/FDK methods are used to reconstruct without rebinning. As a benchmark, the images are reconstructed using uniform weighting fan‐beam/FDK method from data collected at the specified uniform grid. To evaluate the different methods, effects of increasing the number of projections and adding Poisson noise are studied. The root mean square error (RMSE) is used to quantify the image quality by numerical tests with the cardiac phantom. Our results show that it is helpful to perform data interpolation for improvements of the image quality in controlled cardiac CT from random projections. Our simulations indicate that triangular interpolation gives the most satisfactory result for improved image quality whereas quadrilateral interpolationgives the best noise performance. © 2007 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 17, 91–98, 2007

A general exact reconstruction for cone-beam CT via backprojection-filtration

In this paper, we prove a generalized backprojection-filtration formula for exact cone-beam image reconstruction with an arbitrary scanning locus. Our proof is independent of the shape of the scanning locus, as long as the object is contained in a region where there is a chord through any interior point. As special cases, this generalized formula can be applied with cone-beam scanning along nonstandard spiral and saddle curves, as well as in an n-PI window setting. The algorithmic implementation and numerical results are described to support the correctness of our general claim.

A backprojection-filtration algorithm for nonstandard spiral cone-beam CT with an n-PI-window

For applications in bolus-chasing computed tomography (CT) angiography and electron-beam micro-CT, the backprojection-filtration (BPF) formula developed by Zou and Pan was recently generalized by Ye et al to reconstruct images from cone-beam data collected along a rather flexible scanning locus, including a nonstandard spiral. A major implication of the generalized BPF formula is that it can be applied for n-PI-window-based reconstruction in the nonstandard spiral scanning case. In this paper, we design an n-PI-window-based BPF algorithm, and report the numerical simulation results with the 3D Shepp–Logan phantom and Defrise disk phantom. The proposed BPF algorithm consists of three steps: cone-beam data differentiation, weighted backprojection and inverse Hilbert filtration. Our simulated results demonstrate the feasibility and merits of the proposed algorithm.

Filtered backprojection formula for exact image reconstruction from cone‐beam data along a general scanning curve

Recently, Katsevich proved a filtered backprojection formula for exact image reconstruction from cone-beam data along a helical scanning locus, which is an important breakthrough since 1991 when the spiral cone-beam scanning mode was proposed. In this paper, we prove a generalized Katsevich's formula for exact image reconstruction from cone-beam data collected along a rather flexible curve. We will also give a general condition on filtering directions. Based on this condition, we suggest a natural choice of filtering directions, which is more convenient than Katsevich's choice and can be applied to general scanning curves. In the derivation, we use analytical techniques instead of geometric arguments. As a result, we do not need the uniqueness of the PI lines. In fact, our formula can be used to reconstruct images on any chord as long as a scanning curve runs from one endpoint of the chord to the other endpoint. This can be considered as a generalization of Orlov's classical theorem. Specifically, our formula can be applied to (i) nonstandard spirals of variable radii and pitches (with PI- or n-PI-windows), and (ii) saddlelike curves.

Feldkamp-type VOI reconstruction from super-short-scan cone-beam data.

Based on the fan-beam reconstruction formula recently developed by Noo et al. [Phys. Med. Biol. 47, 2525-2546 (2002)] we develop a Feldkamp-type algorithm for the reconstruction of a volume of interest (VOI) from super-short-scan data. With either a circular or spiral scanning locus in our VOI reconstruction scheme, we first estimate fan-beam data from cone-beam data using the popular "cosine correction" scheme, and perform reconstruction based on Noo's FBP-type fan-beam reconstruction. Our proposed algorithm is tested using the three-dimensional (3-D) Shepp-Logan phantom. The experimental results show that the new algorithm can be applied to multi-source 4-D CT with significantly superior temporal resolution and temporal consistency relative to the Katsevich algorithm, which is the state of the art for exact helical cone-beam reconstruction.

Artifacts associated with implementation of the Grangeat formula.

To compensate for image artifacts introduced in approximate cone-beam reconstruction, exact cone-beam reconstruction algorithms are being developed for medical x-ray CT. Although the exact cone-beam approach is theoretically error-free, it is subject to image artifacts due to the discrete nature of numerical implementation. We report a study on image artifacts associated with the Grangeat algorithm as applied to a circular scanning locus. Three types of artifacts are found, which are thorn, wrinkle, and V-shaped artifacts. The thorn pattern is created by inappropriate extrapolation into the shadow zone in the radon domain. If the shadow zone is filled in with continuous data, the thorn artifacts along the boundary of the shadow zone can be removed. The wrinkle appearance arises if interpolated first derivatives of the radon data are not smooth between adjacent detector planes. In particular, the nearest-neighbor interpolation method should not be used. If the number of projections is not small, the bilinear interpolation method is effective to suppress the wrinkle artifacts. The V-shaped artifacts on the meridian plane come from the line integrations through the transition zones where derivative data change abruptly. Two remedies are to increase the sampling rate and suppress data noise.

427 極座標型ロボットによる非球面研磨の基礎検討(OS12 研削・砥粒加工)

The polishing operation of a large aspheric optics surface with a small polishing tool takes a very long time. Then, a polishing head with a number of small polishing tools has been manufactured in order to shorten the processing time. The polishing head scanned on the work surface by a r-θ coordinates robot. A basic research of a plane polishing surface has been carried out using a brass workpiece of 80mm diameter. Simulation has been carried out to search the scanning locus of polishing head, which agrees with the experimental result.

Equiangular fan-beam computerized tomography reconstruction for a noncircular scanning locus

A derivative-free, two-dimensional equiangular fan-beam reconstruction formula for a noncircular scanning locus is derived under three practical conditions. The formula contains the same terms as the traditional formula, except that the constant source-to-origin distance is replaced by the source-to-origin distance as a function of the rotation angle. The correctness of this formula is tested in numerical simulation. The potential applications of the formula include fourth-generation CT, electron-beam Ct, SPECT, and x-ray microtomography.

Study on New Arrangement Technique of Fine Particles by Laser Beam. 1st Report, Arrangement and Motion Control of Fine Particles in the Water.

The fine particle manipulation using optical radiation force has already been investigated in former research. Based upon that, the manufacturing method of the micro parts made up of some fine particles has been developed. However, when the micro parts consist of a lot of fine particles, the manipulation and assembly procedures become time consuming with low work efficiency because of the one by one operation. To solve this problem, a new arrangement method with a single laser beam was realized and proposed in the study, which is able to conduct the assembly procedures efficiently and practically. In detail, the method is to arrange particles by stopping the scanning of a YAG laser beam for a short interval at some appointed positions along the scanning locus to give out a larger amount of input laser energy so that fine particles can be trapped in priority at those stop positions. Therefore it becomes realizable to trap several fine particles at the appointed locations. Furthermore, if the stop positions of the laser scanning are arranged at the same time, the plural trapped fine particles can be manipulated simultaneously. This idea has also been experimentally realized.

Error analysis on a generalized Feldkamp's cone‐beam computed tomography algorithm

AbstractTo overcome the limitations of Feldkamp's cone‐beam reconstruction algorithm, we generalized it in the case of noncircular and nonplanar scanning. In this paper, an error analysis is performed on this generalized approximate algorithm. The study is based on a reconstruction error formula. Roughly speaking, the error is proportional to the distance from a voxel to the mid‐plane in the planar scanning mode, to the pitch of a scanning locus in the helix‐like scanning mode, and inversely proportional to the horizontal size of the scanning locus. The error also depends on longitudinal variation of a specimen function. Longitudinal partial derivative distributions of specimen transverse sections are modeled as stochastic fields. Practical factors are simulated as noise terms in the reconstruction error formula. The simulation results show that the generalized Feldkamp's algorithm is not sensitive to noise and allows more accurate reconstruction in the helix‐like scanning mode.

Half-scan cone-beam x-ray microtomography formula.

An x-ray shadow projection microtomographic system using a scannable point source is under development at AMIL-ARTS, SUNY at Buffalo. To overcome the limitations of the commonly used Feldkamp's cone-beam reconstruction formula, we have developed a generalized Feldkamp-type cone-beam reconstruction formula. In the generalized Feldkamp-type cone-beam reconstruction, a scanning locus can be either planar or helix-like, and a transaxial slice is reconstructed using projection data collected from a 360 degrees angular range (full scan). In this paper, the full-scan cone-beam formula is modified to require only projection data of approximate 180 degrees plus two fan-angles (half scan). First, a half-scan derivative-free noncircular fan-beam reconstruction formula is formulated. Then, a half-scan cone-beam reconstruction formula is derived as an extension of the half-scan fan-beam reconstruction formula using Feldkamp's procedure. Typical numerical simulation results are given for both half-scan formulae. Compared with the full-scan cone-beam formula, the half-scan cone-beam formula reduces the involved angular range of projection data and allows better longitudinal/temporal resolution.

Cone-beam 3D image reconstruction in x-ray microtomography

An X-ray shadow projection microscope system using a scannable point source of X-rays is under development at AMIL-ARTS, SUNY at Buffalo, USA. The point source is generated by a focussed electron beam, which can be steered electromagnetically in a plane perpendicular to the optical axis of the microscope. A specimen is mounted on a rotatable mechanical stage for microtomography. Considering the hardware characteristics of this system and the limitations of current cone-beam reconstruction algorithms, a generalized Feldkamp’s cone-beam image reconstruction algorithm has been developed at our laboratories. In our cone-beam reconstruction, there are mainly two kinds of scanning scanning modes: planar and helix-like. A planar scanning locus is used to handle spherical or plate-like specimens. A typical case of planar scanning loci is a circle, which is used in Feldkamp’s cone-beam reconstruction. A helix-like scanning locus is used to deal with rod-shaped specimens. Without loss of generality, a locus turn of the X-ray source can be defined in cylindrical coordinates by the following equation:

Comments on "A cone-beam filtered backprojection reconstruction algorithm for cardiac single photon emission computed tomography" by G. T. Gullberg and G. L. Zeng

In the above-titled work by G. T. Gullberg and G. L. Zeng (ibid., vol.11, no.1, p.91-101, 1992), a fan-beam reconstruction formula of a noncircular scanning locus was derived and extended for half-scan cone-beam reconstruction. However, the reconstruction formula is not exact mathematically unless a necessary condition is satisfied. In this correspondence, the commenters derive this necessary condition and provide a geometrical explanation of the condition.

A general cone-beam reconstruction algorithm

Considering the characteristics of the X-ray microscope system being developed at SUNY at Buffalo and the limitations of available cone-beam reconstruction algorithms, a general cone-beam reconstruction algorithm and several special versions of it are proposed and validated by simulation. The cone-beam algorithm allows various scanning loci, handles reconstruction of rod-shaped specimens which are common in practice, and facilitates near real-time reconstruction by providing the same computational efficiency and parallelism as L.A. Feldkamp et al.'s (1984) algorithm. Although the present cone-beam algorithm is not exact, it consistently gives satisfactory reconstructed images. Furthermore, it has several nice properties if the scanning locus meets some conditions. First, reconstruction within a midplane is exact using a planar scanning locus. Second, the vertical integral of a reconstructed image is equal to that of the actual image. Third, reconstruction is exact if an actual image is independent of rotation axis coordinate z. Also, the general algorithm can uniformize and reduce z-axis artifacts, if a helix-like scanning locus is used.

A derivative-free noncircular fan-beam reconstruction formula

In order to perform fan-beam reconstruction using projection data collected from a noncircular scanning locus, existing noncircular fan-beam formulas require a derivative of the scanning locus with respect to the rotation angle. A derivative-free noncircular fan-beam reconstruction formula that is based on a geometrical explanation of the circular equispatial fan-beam reconstruction formula is obtained here. A mathematical proof is then provided under the conditions that the source-to-origin distance is symmetric with respect to the origin of the reconstruction coordinate system, is differentiable almost everywhere, and does not change too fast with respect to the rotation angle. The derivative-free noncircular fan-beam reconstruction formula is the same as the circular one, except that the source-to-origin distance is a function of the rotation angle. A typical simulation result for the noncircular fan-beam formula is given.