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

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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.