Advanced autofocus algorithm for microscopy imaging: counting-based identification of high-intensity, low-intensity, overexposed, and dark regions in metallic samples

This study presents an advanced autofocus method based on a counting approach, where the total count is decomposed into background <i>C</i>_<i>bg</i>(<i>z</i>) and sample <i>C</i>_{<i>sample</i>}(<i>z</i>) components. By leveraging the relationship between <i>C</i>_<i>bg</i>(<i>z</i>) and <i>C</i>_{<i>sample</i>}(<i>z</i>), the proposed algorithm effectively differentiates four imaging conditions: high-intensity non-overexposed, low-intensity, overexposed, and dark regions, while accurately identifying the focal plane. Experimental results demonstrate that the proposed method consistently determines the focal plane across varying intensity conditions and reliably distinguishes these four imaging conditions. In contrast, five conventional autofocus methods-the square gradient, Brenner gradient, energy Laplacian, image power, and maximum intensity-rely on the accumulated sum of grayscale values and fail to differentiate these conditions. Although some conventional methods exhibit robustness under specific intensity conditions, none achieve consistent performance across all scenarios. Therefore, in microscopy imaging, the proposed algorithm provides superior focus determination under high-intensity non-overexposed, low-intensity, and overexposed conditions, while also effectively identifying dark regions.