Discipline: Technology and Engineering
Subcategory: Electrical Engineering
Miu Tamamitsu - University of California, Los Angeles
Co-Author(s): Yibo Zhang, University of California, Los Angeles, CA; Hongda Wang, University of California, Los Angeles, CA; Yichen Wu, University of California, Los Angeles, CA; Aydogan Ozcan, University of California, Los Angeles, CA
Digital holographic imaging relies on the knowledge of the sample-to-hologram distance to reconstruct an accurate image of the sample. Automatic determination of the sample distance (i.e., autofocusing) has been a widely researched topic, and we have recently found that the edge sparsity of the refocused complex optical wavefront serves as a robust autofocusing criterion for a wide variety of samples [1,2], which makes it especially useful for unsupervised holographic autofocusing. The edge sparsity is quantified by a measure called the Sparsity of Gradient (SoG), which is given by a sparsity metric calculated on the spatial gradient modulus of the refocused complex hologram. In this work, we investigated the performance of SoG-based holographic autofocusing across different types of samples, demonstrating its robustness. While various sparsity metrics can be used in SoG, we specifically focused on the Tamura coefficient (TC) and the Gini index (GI) as they satisfy all the desirable attributes of a sparsity metric [2,3]. We term the autofocusing algorithm based on TC of the gradient modulus as ToG, and that based on GI of the gradient modulus as GoG.
We first theoretically compared the performances of TC and GI as sparsity metrics . Our theoretical analysis predicted that TC and GI show similar behavior when the pixel values of the image data are uniformly distributed, while for naturally sparse image data containing few high-valued signal pixels and many low-valued noisy background pixels, TC becomes more robust to background noise and more sensitive to the distribution changes in the signal compared to GI. These predictions were also confirmed by our ToG- and GoG-based holographic autofocusing experiments performed on dense and connected samples (e.g., stained breast tissue sections) and naturally sparse samples (e.g., Giardia lamblia cysts, bovine sperm cells, Yeast cells, and red blood cells). For the dense/connected samples, ToG and GoG offered almost identical autofocusing performance, whereas for naturally sparse samples, GoG needed to be calculated on a relatively small region of interest (ROI) surrounding the object of interest, while ToG offered better flexibility in choosing a larger ROI containing more background pixels. These results suggest that ToG allows for unsupervised holographic autofocusing on a wider range of samples with different degrees of spatial sparsity, boosting the robustness of the presented SoG-based holographic autofocusing method.
References:  Y. Zhang et al., Optics Letters 42, 3824 (2017).  M. Tamamitsu et al., arXiv:1708.08055 (2017).  N. Hurley et al., IEEE Transactions on Information Theory 55, 4723 (2009).Not Submitted
Funder Acknowledgement(s): The Ozcan Research Group at UCLA gratefully acknowledges the support of the National Science Foundation (NSF) CBET Division Biophotonics Program, and the NSF Emerging Frontiers in Research and Innovation (EFRI) Award.
Faculty Advisor: Aydogan Ozcan, firstname.lastname@example.org
Role: I proposed to use TC as a sparsity metric in SoG, performed the theoretical analysis of TC and GI, investigated the performance of ToG and GoG-based holographic autofocusing on various samples, and analyzed the obtained data to derive the presented conclusions.