Figure Correction Research Articles

Ultraprecision Machining. Development of Numerically Controlled EEM (Elastic Emission Machining) System.

Ultraprecise figuring systems are needed in many scientific fields. For example the mirrors for synchrotron-radiation X-ray facilities and extreme ultraviolet lithography systems should have atomically smoothed surfaces and extremely high figure accuracy of the order of nanometer range. Furthermore, next-generation semiconductor surfaces should be atomically flat as the substrates for nanometer devices. The EEM (Elastic Emission Machining) system developed by the authors can provide the atomically smoothed surfaces free from any crystallographic damage. A basic research has been performed to evaluate the use of a numerically controlled EEM system for ultraprecise figure corrections. We have constructed an EEM figuring system for ultraprecise scientific components. Testing showed that its performances are sufficient for figuring with nanometer accuracy.

数値制御ＥＥＭ（Ｅｌａｓｔｉｃ Ｅｍｉｓｓｉｏｎ Ｍａｃｈｉｎｉｎｇ）加工システムの開発 ｎｍオーダでの加工精度の評価

To develop the ultraprecision figuring system is very important and strongly required in many scientific fields. The mirrors for synchrotron radiation X-ray facilities or EUV (extreme ultraviolet) lithography system are required to have atomically smoothed surface and extremely high figure accuracy with the order of nanometer range. EEM that has been developed by authors has been known to be able to prepare the many kinds of optical components with the atomically smoothed surface without any crystallographic damage. On the other hand, several basic researches are performed to evaluate the possibilities of the visualization of numerically controlled EEM system for the ultraprecision figure corrections. In this work, a new type of EEM head, that is for the transportation of ultrafine powders, utilizing a jet flow of the ultrapure water has been developed for the numerically controlled figuring system to realize the good controllability and stability of machining properties such as removal rate and the processed surface qualities. A new EEM system for the figuring practically required optical components described above has been constructed, tested and concluded to have sufficiently good performances for the ultraprecision figuring with the nanometer accuracy.

New name for a Middle Cambrian trilobite and a figure correction

New name for a Middle Cambrian trilobite and a figure correction

The Effect of Soller Slit and Monochromator Used for Background Reduction in Texture Measurements

An X‐ray texture goniometer equipped with a vertical Soller slit and a monochromator in the secondary beam in combination with Cu radiation is found to be useful for pole figure measurements on different materials, e.g. Al and Fe, as well as for low incident beam angle measurements on thin coatings. The obtained ODF′s are less sensitive to errors in the procedure used for background correction of the pole figures than obtained with the classical setup used for pole figure measurements. The reason for that is the drastically ameliorated Intensity/Background (I/B) ratio by the use of the monochromator. Examples for cold rolled Fe and Al are presented. One of the merits of the new setup is that pole figures of Al, Cu, Ti, Fe can all be measured by using Cu Kα radiation, thus avoiding frequent and time‐consuming exchanges of X‐ray tubes.

Ion beam figuring of small optical components

Ion beam figuring provides a highly deterministic method for the final precision figuring of optical components with advantages over conventional methods. The process involves bombarding a component with a stable beam of accelerated particles that selectively removes material from the surface. Figure corrections are achieved by rastering the fixed-current beam across the workpiece at appropriate, time-varying yelocities. Unlike conventional methods, ion figuring is a noncontact technique and thus avoids such problems as edge rolloff effects, tool wear, and force loading of the workpiece. This work is directed toward the development of the precision ion machining system at NASA's Marshall Space Flight Center. This system is designed for processing small (≈ 10-cm diam) optical components. Initial experiments were successful in figuring 8-cm-diam fused silica and chemical-vapor-deposited SiC samples. The experiments, procedures, and results of figuring the sample workpieces to shallow spherical, parabolic (concave and convex), and non-axially-symmetric shapes are discussed. Several difficulties and limitations encountered with the current system are discussed. The use of a 1-cm aperture for making finer corrections on optical components is also reported.

Contouring algorithm for ion figuring

Ion beam figuring provides a highly deterministic method for the final precision figuring of optical components with advantages over conventional methods. The ion-figuring process involves bombarding a component with a stable beam of accelerated particles, which selectively removes material from the surface. The specific figure corrections are achieved by rastering the fixed-current beam across the workpiece at varying velocities. Unlike conventional methods, ion figuring is a noncontract technique that avoids such problems inherent in traditional fabrication processes as edge roll-off effects, tool wear, and force loading of the work piece. Other researchers have demonstrated that ion beam figuring is effective for correcting of large optical components. This work is directed toward the development of the precision ion-machining system (PIMS) at NASA's Marshall Space Flight Center (MSFC). This system is designed for processing small (≅ 10 cm diameter) optical components. The ion-figuring process involves obtaining an interferometric error map of the surface, choosing a raster pattern for the beam, and determining the velocities along that path. Because the material removed is the convolution of the fixed ion beam removal and the rastering velocity as a function of position, determining the appropriate velocities from the desired removal map and the known ion beam profile is a deconvolution process. A unique method of performing this deconvolution was developed for the project, which is also applicable to other mathematically similar processes, including computer-controlled polishing. This paper presents the deconvolution algorithm, a comparison of this technique with other methods, and a simulation analysis. Future research will implement this procedure at MSFC.

Correction of Pole Figures Measured on Small Diameter Metallic Wires

Correction of Pole Figures Measured on Small Diameter Metallic Wires

The reflection of road traffic noise

In the U.K. prediction method for L 10 noise levels from road traffic single figure corrections are used to allow for the effects of reflecting facades. In this paper, simple expressions are proposed as improved corrections. These are derived for facades lying parallel to the road by using geometrical reflection theory and the equations for distance and angle of view effects given in the U.K. prediction method. The expressions are functions of the receiver and reflector distance from the road, the angles subtended by the source line and the image of the source line at the receiver and also the type of ground cover. The corrections are compared with the results of computer simulations and show good agreement.

Pole figure correction formulae for the parallel-sided plate

Pole figure correction formulae for the parallel-sided plate

Sur un passage des Definitiones du pseudo-Héron d'Alexandrie (Ed. Heiberg, p. 156, I. 1-5).

SUMMARY. — Section nr. 136,58 of the pseudo-Heronian scholia (Heronis alexandrini... vol. IV Definitiones, éd. Heiberg, 1912, p. 156) has been transmitted in a manner which makes it incomprehensible. In addition, the figure which follows the text is wrong. We present a correction of both text and figure. We also show that the text is a transcription of the reconstituted figure, which originally accompanied one of the scholia of Euclid's Elements, V, def. 5 (Euclidis Elementa, ed. Heiberg, vol. V, 1888, p. 289-290), and which disappeared in the course of a manuscript translation.

A Correction of Figures in the 1935 Report of the Board of Registration in Medicine

A Correction of Figures in the 1935 Report of the Board of Registration in Medicine