Automatic Focusing of Off-Axis Digital Holographic Microscopy by Combining the Discrete Cosine Transform Sparse Dictionary with the Edge Preservation Index

Automatic focusing is a crucial research issue for achieving high-quality reconstructed images in digital holographic microscopy. This paper proposes an automatic focusing method that combines the discrete cosine transform (DCT) sparse dictionary with edge preservation index (EPI) criteria for off-axis digital holographic microscopy. Specifically, within a predefined search range, Fresnel transform is utilized to reconstruct the off-axis digital hologram, yielding reconstruction images at various reconstruction distances. Synchronously, the DCT sparse dictionary is employed to reduce speckle noise, and the EPI is calculated between the denoised image and original image. The value of EPI is used as an indicator for assessing the focal position. A single-peak focusing curve is obtained within the search range 10 mm, with a step size of 0.1 mm. Once the optimal focus position is determined, a focused and noise-reduced reconstructed image can be simultaneously achieved.