Nanoscale displacement measurement by a digital nano-moiré method with wavelet transformation

A digital nano-moiré method with wavelet transformation is explored to measure nanoscale in-plane displacement fields. By applying e-beam lithography, a periodic PMMA nanostructure array is fabricated directly on the specimen and used as the specimen grating. Moiré patterns are generated by overlapping the images of the PMMA specimen grating obtained from AFM scanning and the virtual reference grating produced by a digital image generating process. Then, the overlapped images are filtered by the 2D wavelet transformation (WT) to capture the target moiré patterns. Existing methods, by overlapping the monitor-generated scanning lines with the image of the specimen grating, cause a mismatch problem. Previously, the carrier moiré method was explored with the aim of curing the mismatch problem. Unfortunately, the carrier moiré method, in addition to suffering from increased complexity of mathematical calculations, is incapable of directly obtaining the displacement field. Thus, the mismatch problem will result in inconveniences and restrictions in the practical application. Instead of using monitor-generated scanning lines, the proposed method applies the virtual reference grating, and thus puts the mismatch problem to rest. Nevertheless, the resultant moiré image suffers from low contrast which, if left untreated, might distort the measurement result. Therefore, the WT, known for its sharpened abilities of characteristic and edge detection, is used to capture the target moiré patterns and improve the measurement accuracy. The proposed method has been carried out in the laboratory. Experimental results have shown that the proposed method is convenient and efficient for nanoscale displacement measurement.