Abbe error

Abstract: The present invention preferably employs non-contact, small-displacement, capacitive sensors to determine Abbe errors due to the pitch, yaw, or roll of a near linear mechanical stage that are not indicated by an on-axis position indicator, such as a linear scale encoder or laser interferometer. The system is calibrated against a precise reference standard so the corrections depend only on sensing small changes in the sensor readings and not on absolute accuracy of the sensor readings. Although the present invention is preferred for use in split-axis positioning systems with inertially separated stages, the invention can be employed in typical split-axis or stacked stage systems to reduce their manufacturing costs.

Abstract: To establish of standard technique of nanolength measurement in a two-dimensional plane, a new (AFM) system has been designed. In this system, measurement uncertainty is dominantly affected by the Abbe error of the XYZ scanning stage. No linear stage is perfectly straight; in other words, every scanning stage is subject to tilting, pitch, and yaw motion. In this article, an AFM system with minimum offset of XYZ sensing is designed. And, the XYZ scanning stage is designed to minimize the rotation angle because Abbe errors occur through the multiply of offset and rotation angle. For XY stage, optimal design is performed to minimize the rotation angle by maximizing the stiffness ratio of motion direction to the parasitic motion direction of each stage. For the Z stage, the optimal design of maximizing the first-resonant frequency is performed. When the resonant frequency increases, the scan speed is improved, thereby reducing errors caused by sensor drift. This article describes the procedures of selecting p...

Abstract: Macromachine design philosophies that may be of use to micromachining designs are reviewed. Definitions are provided for the precision engineering terms accuracy, repeatability, resolution, and Abbe error. Topics covered include predicting errors to mechanical systems, such as linear motion system errors, axis of rotation errors, and thermal growth errors, as well as issues relating to bearings, position measurement systems, and kinematic and elastically averaged design. >

Abstract: A novel linear and angular interferometric heterodyne system, capable of measuring large angular motion, is proposed. The interferometric system has a high linear-displacement resolution of 1.24 nm while the angular-displacement resolution can reach 0.0025 arcsec. By combining the advantages of the interferometer with a retroreflector and the interferometer with a plane-mirror reflector, the proposed interferometric measurement system allows a desirable transverse motion and rotational motion along any of the three orthogonal directions. Using a retroreflector with a diameter of 38.1 mm, the translational range in the transverse directions is no less than 20 mm × 10 mm while the angular range along any axis is no less than 10°. The angular readings can be used to compensate the linear outputs in real time when the Abbe error occurs. This ability has been demonstrated by the experiments.