Fourier-based structural metric with a CNN-assisted focus decision for robust autofocusing in microscopy

A robust autofocus method for microscopy is presented, combining a Fourier-based structural metric <i>f</i>_FS(<i>z</i>) with a convolutional neural network (CNN)-assisted focus decision. Unlike polynomial fitting, which suffers from boundary oscillations or sensitivity loss, the proposed <i>f</i>_FS(<i>z</i>) stably preserves structural peaks under low-, high-, and overexposed illumination. The <i>f</i>_FS(<i>z</i>) curve exhibits distinguishable patterns-local peaks under low/high intensity and global peaks under overexposure-providing clearer focus signatures that reduce CNN complexity. A CNN-based decision then discriminates between higher-plane, lower-plane, and transparent regions, refining the focal position by local or global peak selection. Validation on metallic Cu-Ni-Al alloys and a Zea mays seed section-covering reflective, textured, and biological tissues-demonstrates that the method consistently yields accurate focal positions where conventional gradient-based measures fail due to background noise, saturation, or transparency. The integration of Fourier-domain analysis with CNN decision thus enables robust, generalizable autofocusing across diverse microscopy samples and imaging conditions.