Advances in Calculus of Variations

Breaking the tradeoff between resolution and field-of-view, while obtaining distortion-free images, can be achieved through computational imaging techniques. A recent approach, Angular Ptychographic Imaging with Close-form method (APIC), has showcased its capability to analytically recover both intricate aberrations and high space-bandwidth product complex optical fields with NA-matching and darkfield illuminations. However, its flat illumination setup limits its ability to efficiently reconstruct a large field-of-view simultaneously with high resolution, owing to the curvature in the wavefront from NA-matching illuminations and the finite beam angle of the Lambertian LED light source. Here, we introduce an illumination framework tailored for APIC consisting of a distant annular LED ring and an LED dome that enables the reconstruction of a larger area with an extended synthetic numerical aperture, consequently enhancing resolution. For a single set of measurements, our new prototype, termed Dome-APIC can reach 620nm resolution with a 10×/0.25 NA objective lens over a field-of-view of 450 µm x 450 µm.

We introduce a compact, all-fiber laser system with a gain-managed nonlinear (GMN) amplified Yb:fiber oscillator and an integrated pulse-picker. The system delivers 39 fs pulses with peak powers of 0.83 MW and adjustable pulse repetition rates (0.3–15 MHz), enabling multiphoton imaging at remarkably low excitation powers (as low as 66 µW). Its design simplifies integration and enhances experimental flexibility. Compatible with two- and three-photon excitation, but also second harmonic generation microscopy, this versatile system offers precise control of imaging parameters, making it an effective tool for advancing multiphoton microscopy and other imaging techniques across various experimental environments.

The optical properties of microscopic turbid media are critical for understanding light-tissue interactions with applications in biomedical imaging and diagnostics. However, traditional scattering coefficient-based methods are limited in their ability to capture topological heterogeneities within tissue structures, which play a crucial role in describing the relationship between microscopic tissue characteristics and their corresponding light propagation behaviors. In this study, we propose using persistent homology-based persistent images (PIs) as a descriptor and optical property of microscopic tissues. As a proof of concept, we analyzed particle-distributed turbid media with uniform and clustered particle distributions by persistent homology analysis, demonstrating that PIs can capture topological characteristics that are not discernible using traditional scattering coefficient-based methods. Light propagation simulations using the beam propagation method (BPM) demonstrated that PIs correlate with optical behaviors, such as beam centroid displacement and distortion, providing a foundation for linking microscopic topological heterogeneities to light propagation behaviors. Our results validate PIs as a meaningful and predictive optical property, bridging microscopic turbid media topology with their light propagation behaviors. This work establishes PIs as a potential optical property of microscopic tissue, capturing its topological characteristics and offering predictive insights into light propagation behaviors.

Reconstruction-based acoustic-resolution photoacoustic microscopy (AR-PAM) has been developed to extend the depth of field (DOF), enabling simultaneous observation of structures at multiple depths. However, conventional AR-PAM systems, which rely on focused transducers, face inherent limitations in effectively increasing the DOF. To address this issue, we developed a needle hydrophone (NH)-based AR-PAM system that enables deep imaging with enhanced resolution and improved DOF. The proposed system was validated using tissue-mimicking phantoms and ex Ovo chick embryo imaging. Our results demonstrated a DOF exceeding 20 mm, a lateral resolution comparable to the NH diameter (∼400 µm) at shallow depth (10 mm) and 870 µm at deep depth (30 mm), and an axial resolution of 250 µm. Furthermore, we investigated the impact of different reconstruction techniques, including the measured impulse response function (MIRF), simulated impulse response function (SIRF), and coherence factor (CF). Our comparative analysis revealed that MIRF-based reconstruction provided superior performance in maintaining resolution and image quality across varying depths, making it the most effective approach for multi-depth imaging.

Terahertz biosensors are employed to detect proteins in cancer cells to facilitate early diagnosis and monitoring of cancer treatments. By optimizing the design and functionality of black phosphorus-based sensors, it is possible to enhance their sensitivity and specificity for specific cancer biomarkers, leading to more accurate diagnostic outcomes. The application of the externally applied magnetic field and the 455 nm continuous-wave laser further augments the sensitivity of cellular responses to THz waves, with magnetic influences typically surpassing those of light fields by 10%-80%. Our results examine the photonic properties of black phosphorus, improve its interaction with terahertz waves, and create prototypes that can selectively identify proteins associated with cancer cells. Additionally, the stability and reproducibility of these sensors have been greatly improved, boosting their potential for widespread use in clinical environments.

Cryo-imaging has the potential to obtain and visualize the metabolic state of the whole kidney without labeling. However, uneven fixation of metabolic information and incomplete organ morphology in three dimensions limit cryo-imaging application. Here, a pipeline of in vivo insulated cryofixation combined with cryo-micro optical sectioning tomography (cryo-MOST) was established to achieve uniform and complete cryofixation and three-dimensional visualization of renal metabolic mapping at a micron-scale resolution. By this pipeline, we discovered an increased renal redox ratio of db/db mice with type 2 diabetes, indicating the presence of metabolic disorders. The results demonstrate that our convenient optical imaging tool provides a micro-resolution, quantitative assessment of the metabolic state of the whole kidney and potentially extends to other organs.

Recent advancements in cellular-resolution optical coherence tomography (OCT) have opened up possibilities for high-resolution and non-invasive clinical diagnosis. This study uses deep learning-based models on cross-sectional OCT images for in vivo human skin layers and keratinocyte nuclei segmentation. With U-Net as the basic framework, a 5-class segmentation model is developed. With deeply supervised learning objective functions, the global (skin layers) and local (nuclei) features were separately considered in designing our multi-class segmentation model to achieve an > 85% Dice coefficient accuracy through 5-fold cross-validation, enabling quantitative measurements for the healthy human skin structure. Specifically, we calculate the thickness of the stratum corneum, epidermis, and the cross-sectional area of keratinocyte nuclei as 22.71 ± 17.20 µm, 66.44 ± 11.61 µm, and 17.21 ± 9.33 µm2, respectively. These measurements align with clinical findings on human skin structures and can serve as standardized metrics for clinical assessment using OCT imaging. Moreover, we enhance the segmentation accuracy by addressing the limitations of microscopic system resolution and the variability in human annotations.

Myopia progression in children can lead to ocular morbidity during adulthood. Spectacle lenses have been developed and commercialized for myopia control (MC), but their imaging properties have only been assessed under monochromatic illumination. In this study, we quantified the chromatic imaging properties (wavelengths, 450, 532 and 635 nm) of four MC lenses and a single vision lens at three retinal eccentricities (0°, 20° and 30°) along the horizontal meridian using spatial light modulation technology. Our results suggest that the design of myopia-control lenses based on simultaneous competing blurring should enhance the quality of images projected in front of the peripheral retina at long wavelengths.

Polarization measurements of tissue in ex vivo and in vivo rigid laparoscopy studies have shown promise for enhancing diagnosis, guiding biopsies, and improving biological contrast compared to conventional imaging. However, a technological gap exists in performing polarization measurements through flexible endoscopes. The depolarization inherent in the coherent fiber bundles commonly used in these endoscopes to relay images from within the body hinders polarization information retrieval. To address this, we propose a simple, compact, and low-cost architecture: a pixelated polarizer placed directly on the tip of the flexible, coherent imaging fiber bundle. We demonstrate this architecture’s ability to retrieve the linear polarization properties of a scene.

A rapid and non-invasive method to identify phenotypes of colorectal malignant tumors is of vital importance for oncological surgery and further development of corresponding anti-tumor drugs. Herein, we demonstrate an approach to detect colorectal adenocarcinoma and colorectal cancer using the quasi-bound state in the continuum (q-BIC) resonance of a metasurface-based terahertz biosensor. We found that the colorectal adenocarcinoma leads to a 40 GHz q-BIC resonance shift compared to healthy colorectal cells. In addition, we found that colorectal cancer results in a q-BIC resonance red-shift of about 60 to 80 GHz. Both colorectal adenocarcinoma and cancer increase the linewidth of q-BIC resonance compared to healthy colorectal cells. The electric permittivity change confirms the aforementioned frequency shift, which is attributed to the water content of different colorectal malignant tumor cells. Our results highlight that the q-BIC resonance of a terahertz photonic biosensor offers a rapid and non-invasive methodology for identifying different colorectal malignant tumors, which accelerates oncological diagnosis.

The influence of hypoxia - a condition where tissues are under oxygen deficiency - on the human brain under functional load has not been fully understood yet. This study aims to analyse the effects of hypoxia on the brain’s haemodynamic response under visual stimulation, using the in-house developed functional near-infrared spectroscopy system and to quantify the hemodynamic response. Our results (median, 25th and 75th percentile) demonstrate the amplitude of the oxygenated haemoglobin functional response during hypoxia 0.30 µM (0.27, 0.41) was lower compared with the normoxia 0.63 µM (0.54, 0.93) and hyperoxia 0.73 µM (0.43, 1.09). No statistical significance is observed for the deoxygenated haemoglobin changes. The hypoxia has a statistically significant effect on the amplitude of the haemodynamic response (p < 0.001).