Rectangular Scanning Research Articles

Binary matrices under the microscope: A tomographical problem

A binary matrix can be scanned by moving a fixed rectangular window (sub-matrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1 s visible in the window, which might be thought of as the luminosity of the window. The rectangular scan of the binary matrix is then the collection of these luminosities presented in matrix form. We show that, at least in the technical case of a smooth m × n binary matrix, it can be reconstructed from its rectangular scan in polynomial time in the parameters m and n , where the degree of the polynomial depends on the size of the window of inspection. For an arbitrary binary matrix, we then extend this result by determining the entries in its rectangular scan that preclude the smoothness of the matrix.

Estimation for the Distribution of Two-dimensional Discrete Scan Statistics

This paper concerns the application of the method introduced in (Haiman, Extremes, 3:349–361, 2000) to estimate the distribution of two-dimensional discrete scan statistics. This method makes it possible to establish sharp bounds for the estimation errors. The method involves the estimation by simulation of the distribution of scan statistics for the particular rectangle sets of size 2×2, 2×3, 3×3, where the unit is the (m1×m2) dimension of the rectangular scanning window, m1, m2 ∈ℕ. We perform several numerical applications and compare our results with results obtained by other authors.

Anterior chamber width measurement by high-speed optical coherence tomography

To measure anterior chamber (AC) width and other dimensions relevant to the sizing of phakic intraocular lenses (IOLs) with a high-speed optical coherence tomography (OCT) system. Cross-sectional observational study. Both eyes of 20 normal volunteers. A novel high-speed (4000 axial scans/second) OCT prototype was developed for anterior segment scanning. The system uses long wavelength (1310 nm) for deeper angle penetration, rectangular scanning for undistorted imaging, and short image acquisition time (0.125 seconds) to reduce motion error. Three horizontal cross-sectional OCT images (15.5 mm wide and 6 mm deep) of the anterior segment were obtained from each eye with real-time image display to guide centration on the corneal apex. Image processing software was developed to correct for image warping resulting from index transitions. Anterior chamber dimensions were measured using computer calipers by 3 expert raters (ophthalmologists). Analysis of variance was used to determine interrater, interimage, right versus left eye, and intersubject standard deviation (SD) of OCT measurements. Anterior chamber width (recess to recess), AC depth, and crystalline lens vault as measured by OCT; external white-to-white (WTW) corneal diameter (CD) as measured by Holladay-Godwin gauge. The mean AC width was 12.53+/-0.47 mm (intereye SD), and the mean corneal diameter was 11.78+/-0.57 mm. Optical coherence tomography measurement of AC width has good repeatability from image to image (SD, 0.134 mm), but there was significant difference between raters (SD, 0.215 mm). Estimation of AC width from WTW CD by linear regression was relatively inaccurate (residual SD, 0.41 mm). The mean AC depth was 2.99+/-0.323 mm (intereye SD), with repeatability of less than 0.001 mm (interimage SD), and the mean crystalline lens vault was 0.39+/-0.27 mm with 0.023 mm repeatability. Reproducible OCT AC biometry was demonstrated using a high-speed OCT prototype. Further improvement in reproducibility may be achieved by automating the measurements with a computer. Direct OCT AC width measurement may improve sizing of angle-supported AC IOLs over conventional estimation by WTW CD. The measurement of AC depth and lens vault also may be useful for other types of phakic AC IOLs.

Photoastigmatic Refractive Keratectomy in Myopes

Photoastigmatic refractive keratectomy (PARK) was studied in a multi-center clinical trial. The Nidek EC-5000 excimer laser was evaluated for its effect on refraction, visual acuity, and safety measures as part of a U.S. Food and Drug Administration (FDA) regulated study. Eight U.S. centers enrolled adults with eyes having refractive astigmatism up to 4.00 D and a myopic spherical equivalent refraction up to -8.00 D. Results are reported for 749 eyes of 486 patients with at least 6 months follow-up. The rectangular beam scanning Nidek EC-5000 used a 5.5-mm-diameter treatment zone, a 7.0-mm-diameter peripheral blend zone, and a 40 Hz pulse rate for surface treatment of myopic astigmatism. Nomogram corrections to machine settings were required to achieve the desired results. Preoperative average spherical equivalent refraction of -4.90+/-1.74 D was reduced to -0.02+/-0.79 D at 6 months. Refractive stability was established at 3 months. Over 62% of eyes were within +/-0.50 D of desired correction at 6 months, with over 86% within +/-1.00 D. Uncorrected visual acuity improved by an average of 10 Snellen lines; over 64% of eyes saw 20/20 or better uncorrected and over 93% saw 20/40 or better uncorrected at 6 and 12 months. PARK treatment effectively reduced astigmatism with little average axis error or magnitude error. Corneal haze and safety concerns were minimal. Photoastigmatic refractive keratectomy using the Nidek EC-5000 excimer laser provided significant reduction of myopia and astigmatism, with minimal complications.

Approximation and Simulation of the Distributions of Scan Statistics for Poisson Processes in Higher Dimensions

Given a Poisson process in two or three dimensions, we are interested in the scan statistic, i.e. the largest number of points contained in a translate of a fixed scanning set restricted to lie inside a rectangular area. The distribution of the scan statistic is accurately approximated for rectangular scanning sets, using a technique that is also extended to higher dimensions. The accuracy of the approximation is checked through simulation.

The scanning micro-sclerometer: a new method for scratch hardness mapping

A new surface engineering research tool, called a scanning microsclerometer (SMS), has been developed. It uses nano-indentation technology and a piezoelectric transducer positioning system to generate high-precision scratch patterns on the surfaces of metals and, by monitoring the instantaneous displacement of the stylus tip, can generate scratch hardness and scratching force maps of the surface. A dual-stroke process is used. The first stroke at low load profiles the surface to establish a reference datum and the second pass, in the opposite direction and at higher load, produces the indentation scratch. Examples of micro-scratch hardness mapping experiments, using scratch spacings of 1·0 μm, on a silicon carbide-based ceramic composite are used to illustrate the capabilities of the SIVIS. Using end-on fibers in the rectangular stylus scanning area, the difference in scratch hardnesses of the fibers, the matrix, and even the thin carbon coatings in the fiber-matrix interface could be detected. The SMS was originally developed to produce scratch hardness maps, but it is also useful for conducting accurately controlled, single-point micro-machining patterns and in studies of differential material abrasion.

On the Distributions of Scan Statistics of a Two-Dimensional Poisson Process

Given a two-dimensional Poisson process, X, with intensity λ, we are interested in the largest number of points, L, contained in a translate of a fixed scanning set, C, restricted to lie inside a rectangular area.The distribution of L is accurately approximated for rectangular scanning sets, using a technique that can be extended to higher dimensions. Reasonable approximations for non-rectangular scanning sets are also obtained using a simple correction of the rectangular result.

On the Distributions of Scan Statistics of a Two-Dimensional Poisson Process

Given a two-dimensional Poisson process, X, with intensity λ, we are interested in the largest number of points, L, contained in a translate of a fixed scanning set, C, restricted to lie inside a rectangular area. The distribution of L is accurately approximated for rectangular scanning sets, using a technique that can be extended to higher dimensions. Reasonable approximations for non-rectangular scanning sets are also obtained using a simple correction of the rectangular result.

An integrated computer system for Fudan nuclear microprobe

With the help of modern personal computer (PC) and object oriented programming (OOP) technology, we have recently developed a compact, integrated, user-friendly computer system for Fudan nuclear microprobe, which was originally modeled after the SUNY/Albany system. The system software has been thoroughly rewritten so as to take advantage of today's high-performance PC and facilitate easy upgrading and expansion in the case of future development of both hardware and software. Most functions of this system such as sample searching, scanning control, data acquisition, image processing and displaying, are based on a single 80386 IBM style PC with a 1-MB DRAM TVGA high-resolution monitor. Data from up to 4 ADCs, 4 sensors and a CCD camera can be acquired simultaneously. Two stepper motors are employed to move the target; a CCD camera system is also included to locate the area of interest on the sample; the secondary electron image could act as a reference to fine adjustment. Rectangular raster scanning or irregular scanning is facilitated with beam motion triggered either by a timer or by pulses from a current integrator. A variety of built-in image displaying, processing and printing methods have also been implemented in order to make the maps easier to interpret for the eyes. All of these functions are administrated by an integrated, completely menu-driven software package-MBSYS.

A Universal Microphotometer and Solar Corona Polarimetry

Realization of solar corona polarimetry pertains to astrophysical centre-symmetrical problems. Usual ways of digitization are not optimum for this task. Coronal images obtained during solar eclipse at different angles of the polarizer should be digitized symmetrically in relation to the centre of the solar disk. Unfortunately, digitization of such centre-symmetrical images is usually performed by rectangular scanning with a firmly oriented digitization slit. Corresponding pixels in different images have to be found by methods of shifting the centres of the relevant images and a necessary rotation of the images. When the images are almost identical, or at least very similar each to other, the final fitting of the images can be tested by calculating the best correlation. As a rule, this is not the case for solar corona images obtained with different angle of the polarizer. In addition, after rotation of the digitized image, the digitisation rectangular networks become incompatible and thus some information is changed or even lost.

A preprocessor for geotomographic imaging of irregular geometric scans

An algorithm that acts as a preprocessor to the straight ray algebraic reconstruction technique (ART) algorithm, for the purpose of dealing with nonrectangular scanning geometries, is described. The mathematics of ART in its elementary form is reviewed, showing how the discretization of the rectangular scanning space defines quantities in the projection matrix of the algorithm. A triangular discretization approach for the scanning space that allows nonrectangular or twisted plane geometries to be addressed is proposed, and the effect of this approach on the projection matrix is discussed. An algorithm for determining the projection matrix under these discretization conditions is described, followed by some commentary on its computer implementation. The performance of this preprocessor algorithm, working with standard ART, in reconstructing various synthetic images is demonstrated. >

Mapping of Electrostatic Charge Using a Robot Controlled by a Computer

This paper is intended to fulfill two purposes. The first objective is to describe a particular laboratory system which maps the distribution and decay of residual electric fields around flat or curved insulating surfaces. Such a system may have applications in the noudestructive testing of insulation in the form of boards, cylinders, cones, and other shapes. The second objective is to point out the general usefulness of a system consisting of one or more sensors positioned by a robot controlled by a computer for reliably mapping in detail many kinds of fields in three dimensions. The particular implementation described uses a modified Microbot Teachmover robot to move the measuring head of a Monroe Type 230A field meter through a two-dimensional rectangular scanning grid over a flat sheet specimen. A DEC 11/23 MINC laboratory computer is used to both control the robot's movements, and to digitize and store in memory the readings of the field meter. The computer also plots a field map on the video screen during the scan, and stores field data on disk for later retrieval and processing. Results of scans of residual field are given for a typical plastic (polypropylene). Plots of the rate of change of residual field (obtained by taking the difference between scans) are also given. The significance of these results for nondestructive testing is discussed. The combination of one or more sensors, robot, and a computer, forms a flexible and convenient bench top system for the measurement, processing, real-time display, and storage of large amounts of data on two- and three-dimensional specimens.

Unified theory of near-field analysis and measurement: Nonmathematical discussion

A new unified theory of near-field analysis and measurement emphasizes highly accurate, extremely efficient data processing to yield, e.g., radiation, receiving, and scattering patterns, and absolute gain values. The theory includes 17 types of plane rectangular and plane radial scanning, a more accurate and efficient plane polar scanning, spherical scanning, various types of circular cylindrical scanning, many procedures for determining complex dyadic scattering patterns, the extrapolation method for gain and effective area, and application of symmetry analysis to scattering and inverse scattering analysis. High accuracy is obtained by expressing the fields as linear combination of exact solutions of the differential equations involved (Maxwell's in the electromagnetic (EM) cases) and by using exact expressions for their transformations under coordinate changes. High efficiency is obtained with natural orthogonalities of both the solutions and transformation coefficients with respect to integration, especially summation, and implemented with the fast Fourier transform (FFT) as an approximation-free symmetry decomposition. The unified theory is based upon relativistic and gauge invariances, symmetry analysis, and the scattering matrix theory; it yields all the preceding facets and systems, both electromagnetic and scalar, and the single unified notation, general equations, and explicit expressions for the quantities which vary with the physical or scanning system. A nonmathematical discussion of other papers on the theory is provided. Many of the conceptual errors of the literature are corrected. The advantages and limitations of near-field measurements are described, and scanning systems are compared.

Surface Temperatures Produced In Silicon Using Large Diameter Scanning Cw Sources

ABSTRACTThe temperature induced at the surface of a silicon wafer is calculated for both circular and rectangular scanning beams, assuming both a thermally isolated and heat sunk back surface. In the former case, the problem is one of simple uniform heating with radiative cooling at slow scan speeds. A significant thermal gradient is produced across the wafer at high scan speeds. In the latter case, a one-dimensional analysis suffices except for beam diameters less than about twice the wafer thickness, when lateral heat diffusion effects are present.

The oscillatory velocity field observed in a unipolar sunspot region

The velocity field has been mapped for 42 min in an area 80″ by 85″ containing a unipolar sunspot. Apparent shifts of Fe iλ5233 were measured photoelectrically using a rectangular scanning aperture 1.6″ × 4.0″. The sunspot did not exert a marked influence on the generally random pattern of oscillations at a period of 300 s. Discrete periods of oscillation both longer and shorter than 300 s were excited within the enhanced magnetic field boundaries of this spot. Umbral oscillations at periods near 180 s were detected in agreement with independent observations of the same spot during the previous solar rotation.

The "working region" of distance-independence for pointsensitivity in air of moving and stationary scanners

A unified theoretical approach is presented for moving and stationaryscanners, together with experimental evidence which supports the theory. The lawsof variation of point sensitivity in air with position in the field of view are shown to besimilar for both the types of scanner. The "working region" is defined as that partof the field of view in which the point sensitivity in air is independent of position.For points within the working region, the scanning system behaves as though thehole-septum discontinuities in the collimator were absent and as if the totalresponsiveness were "smeared out" uniformly over the detection plane. The shapeof the working region for a circular multi-parallel-hole camera collimator is a "rightcircular cone". For a rectilinear scanner the working region for a square scan areais a "regular square pyramid"; that for a rectangular scan area is extended along thelonger side to an extent equal to the difference of two sides - geometrically it is a"laterally tapering wedge" resting on the rectangular face.

Pseudorandom rectangular scan system with uniform frame density

A new method for pseudorandom scanning of a rectangular frame is described. The system employs feedback shift registers and reversible counters. The scanning density is uniform over the whole area. The scan path is a dotted line that can be changed from relatively smooth to more warped configurations. The periodicity of this pseudorandom line can be made as long as desired and can be repeated starting from any preselected initial condition.

Realisation of HPD systems at three laboratories

The basic feature of the HPD system is the use of a spot of light to execute a regular rectangular scan over the whole bubble chamber picture. Indvidual bubbles are digltized to an accuracy of about 450 deg C in a 3 . These digitizings are transmitted directly to an on-line general purpose digital computer. Production versions of this machine were built and are beginning to operate at CERN, Brookhaven, and Berkeley. The three machines are based on the same principles but have different layouts-and accordingly have different advantages and inconveniences. Special scanning tables are being developed, and steps are being taken to incorporate ionization density measurements into the program. (A.G.W.)