Geometric phase analysis based on the windowed Fourier transform for the deformation field measurement

• The geometric phase analysis basing on the windowed Fourier transform is proposed, referred to as WFT–GPA.
• The fast Fourier transform is performed first to locate the integration limits for the WFT.
• The influence factors for the accuracy of WFT–GPA are discussed.
• The machining distortion incurred in the soft UV-nanoimprint lithography process is measured by WFT–GPA.

The geometric phase analysis (GPA), an important image-based deformation measurement method, has been used at both micro- and nano-scale. However, when a deformed image has apparent distortion, non-ignorable error in the obtained deformation field could occur by using this method. In this paper, the geometric phase analysis based on the windowed Fourier transform (WFT) is proposed to solve the above-mentioned issue, defined as the WFT–GPA method. In WFT–GPA, instead of the Fourier transform (FT), the WFT is utilized to extract the phase field block by block, and therefore more accurate local phase information can be acquired. The simulation tests, which include detailed discussion of influence factors for measurement accuracy such as window size and image noise, are conducted with digital deformed grids. The results verify that the WFT–GPA method not only keeps all advantages of traditional GPA method, but also owns a better accuracy for deformation measurement. Finally, the WFT–GPA method is applied to measure the machining distortion incurred in soft ultraviolet nanoimprint lithography (UV-NIL) process. The successful measurement shows the feasibility of this method and offers a full-field way for characterizing the replication quality of UV-NIL process.