Collaborative Research: Wavelet Analysis of Periodic Error for Improved Displacement Metrology

这笔赠款将使位移测量干涉测量的新的基础研究成为可能。在这里要研究的外差或双频率系统中，在需要亚纳米定位精度的应用中，使用从移动目标反射的一个频率的激光相对于从固定目标反射的第二频率的激光的相移来确定位移。这项研究的目的是应用小波分析技术来表征由两个光频混合引起的周期性误差，并导致几个纳米量级的非累积定位误差。小波为周期性误差的信号分析提供了一种新的方法；它们以前曾被用于图像压缩、语音识别和医疗应用。由于在变速条件下，周期误差随时间变化，因此需要使用小波而不是更传统的傅立叶变换方法。此外，当偏振保持光纤被用于将激光传输到干涉仪光学元件时，误差幅度是时变的。这是一种常见的情况，因为通常希望将产生热的激光源与测量平台隔离。如果成功，这项研究将提高计量能力，从而推动纳米科学领域的新技术进步。这项研究承诺改进在精度、分辨率和范围方面提供最高性能的测量技术(位移测量干涉法)。例如，这种换能器对半导体制造行业至关重要，在该行业中，它被用在反馈控制系统中，以相对于光刻光学元件定位硅片。可实现的线宽(以及最终的芯片处理速度)的一个限制是平台定位精度。其他应用包括传感器校准和材料去除机器。

This grant will enable new fundamental research into displacement measuring interferometry. In the heterodyne, or two-frequency, systems to be studied here, the phase shift in laser light of one frequency reflected from a moving target relative to laser light of a second frequency reflected from a fixed target is used to determine displacement in applications requiring sub-nanometer positioning accuracy. The objective of the research is to apply wavelet analysis techniques to characterize periodic error, which is caused by mixing of the two light frequencies and leads to non-cumulative positioning errors on the order of several nanometers. Wavelets provide a new approach to signal analysis for periodic error; they have previously been used in image compression, voice recognition, and medical applications. The use of wavelets, rather than the more traditional Fourier transform approach, is required because periodic error varies with time under non-constant velocity conditions. Additionally, the error amplitude is time-varying when polarization-maintaining fibers are used to deliver the laser light to the interferometer optics. This is a common occurrence because it is generally desired to isolate the heat-generating laser source from the measurement platform. If successful, this research will enable improved metrology capabilities and, subsequently, new technological advancements in the nano-science field. This research promises to improve the measurement technique (displacement measuring interferometry) that offers the highest performance in terms of accuracy, resolution, and range. This transducer is critical to the semiconductor manufacturing industry, for example, where it is used in a feedback control system to position the silicon wafer relative to the lithographic optics. One limitation on the achievable linewidth (and, ultimately, the chip processing speed) is the stage positioning accuracy. Other applications include transducer calibration and machines for material removal.