Determining the absolute value of magnetic penetration depth in small-sized superconducting films

In the previous four decades, a two-coil mutual inductance (MI) technique has been widely employed in characterizing magnetic penetration depth, $\lambda$, of superconducting films. However, conventional methods used to obtain $\lambda$ are not applicable small-sized films with common shapes, which limits application MI superconductivity research. Here, we first fast wavelet collocation (FWC) method system and then proposed possibility directly obtaining absolute polygonal arbitrary sizes. To verify its accuracy advantages, extracted values square NbN different sizes using FWC flux leakage subtraction (FLS) methods. Notably, FLS fails for $5\times 5 \, \rm mm^2$ film, is attributed significant current peak at film edge. contrast, was independent size. Finally, established applicability large coil spacings, may pave way integrating high-accuracy measurements ionic liquid gating technique.