Comprehensive tool for a phase compensation reconstruction method in digital holographic microscopy operating in non-telecentric regime

PLOS ONE RESEARCH ARTICLE Comprehensive tool for a phase compensation reconstruction method in digital holographic microscopy operating in non-telecentric regime Brian Bogue-Jimenez ID1, Carlos Trujillo ID2, Ana Doblas ID1* a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Bogue-Jimenez B, Trujillo C, Doblas A (2023) Comprehensive tool for a phase compensation reconstruction method in digital holographic microscopy operating in nontelecentric regime. PLoS ONE 18(9): e0291103. https://doi.org/10.1371/journal.pone.0291103 Editor: Ireneusz Grulkowski, Nicolaus Copernicus University, POLAND Received: May 12, 2023 Accepted: August 22, 2023 Published: September 8, 2023 Peer Review History: PLOS recognizes the benefits of transparency in the peer review process; therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. The editorial history of this article is available here: https://doi.org/10.1371/journal.pone.0291103 Copyright: © 2023 Bogue-Jimenez et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: The raw codes written in MATLAB and Python, a MATLAB GUI, manual, and the non-telecentric holograms are 1 Department of Electrical and Computer Engineering, The University of Memphis, Memphis, Tennessee, United States of America, 2 School of Applied Sciences and Engineering, Universidad EAFIT, Medellin, Colombia * Abstract Quantitative phase imaging (QPI) via Digital Holographic microscopy (DHM) has been widely applied in material and biological applications. The performance of DHM technologies relies heavily on computational reconstruction methods to provide accurate phase measurements. Among the optical configuration of the imaging system in DHM, imaging systems operating in a non-telecentric regime are the most common ones. Nonetheless, the spherical wavefront introduced by the non-telecentric DHM system must be compensated to provide undistorted phase measurements. The proposed reconstruction approach is based on previous work from Kemper’s group. Here, we have reformulated the problem, reducing the number of required parameters needed for reconstructing phase images to the sensor pixel size and source wavelength. The developed computational algorithm can be divided into six main steps. In the first step, the selection of the +1-diffraction order in the hologram spectrum. The interference angle is obtained from the selected +1 order. Secondly, the curvature of the spherical wavefront distorting the sample’s phase map is estimated by analyzing the size of the selected +1 order in the hologram’s spectrum. The third and fourth steps are the spatial filtering of the +1 order and the compensation of the interference angle. The next step involves the estimation of the center of the spherical wavefront. An optional final optimization step has been included to fine-tune the estimated parameters and provide fully compensated phase images. Because the proper implementation of a framework is critical to achieve successful results, we have explicitly described the steps, including functions and toolboxes, required for reconstructing phase images without distortions. As a result, we have provided open-access codes and a user interface tool with minimum user input to reconstruct holograms recorded in a non-telecentric DHM system. Introduction Digital Holographic Microscopy (DHM) is a quantitative phase imaging modality that relies on optical interferometry to record holograms [1–5], and numerical reconstruction PLOS ONE | https://doi.org/10.1371/journal.pone.0291103 September 8, 2023 1 / 18 PLOS ONE publicly available on GitHub, https://github.com/ OIRL/noteleDHM-Tool. Funding: This research was partially funded by the Vicerrectorı́a de Ciencia, Tecnologı́a e Innovación from Universidad EAFIT, and National Science Foundation (NSF) grant number 2042563. The funders had no role in library design, implementation and validation, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. Comprehensive tool for a phase compensation reconstruction method in DHM operating in non-telecentric regime procedures to retrieve amplitude and phase information from micrometric specimens. The phase information encodes the lateral and axial information of the sample, enabling the characterization of both its functional and morphological information. Therefore, DHM has proven to be a powerful metrological tool when non-invasive imaging is desired across various fields and applications [1–5]. In biology, it has been applied to study cells and tissues, offering a powerful tool for developmental biology [6], stem cell research [7], and cancer diagnosis [8]. DHM has also found applications in material science, where it has been used to study the microstructure and mechanical properties of materials such as polymers [9], ceramics [10], and metals [11]. Additionally, DHM has been used for particle analysis in liquids and suspensions, allowing for the determination of particle size, shape, and concentration [12]. DHM has also been applied in microfluidics to study fluid flow and behavior at the microscale, including lab-on-a-chip devices [13]. DHM has also found applications in industrial inspection, where it has been used for non-destructive testing and quality control in industries such as electronics [14] and pharmaceuticals [15]. These applications demonstrate the versatility and potential of DHM as a tool for scientific and industrial applications. Wavefront aberrations can significantly distort the accuracy of the phase measurements provided by DHM during the hologram recording [16]. The most common distortion is phase aberration due to the tilt angle between the interfering object and reference wavefronts inherent in all off-axis DHM systems. This first-order phase aberration is observable on the recorded holograms as interferential fringes. Correction of this linear phase aberration is known as the phase compensation stage in DHM reconstruction algorithms, in which the shifted object spectrum (e.g., the +1-diffraction term) is centered on the frequency origin. Over the last decade, several research groups have proposed automated compensation methods [17, 18]. These methods reconstruct phase images by minimizing the number of phase wrappings in the final reconstructed phase map. However, a significant limitation of these computational approaches is that they are designed for only telecentric-based DHM imaging systems, assuming that the center of the +1-diffraction term is a maximum value. Although telecentric-based DHM systems have been validated as intrinsically linear shiftinvariant imaging sys (...truncated)