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We propose a novel method called compressed sensing with linear-in-wavenumber sampling (k-linear CS) to retrieve an image for spectral-domain optical coherence tomography (SD-OCT). An array of points that is evenly spaced in wavenumber domain is sampled from an original interferogram by a preset k-linear mask. Then the compressed sensing based on l1 norm minimization is applied on these points to reconstruct an A-scan data. To get an OCT image, this method uses less than 20% of the total data as required in the typical process and gets rid of the spectral calibration with numerical interpolation in traditional CS-OCT. Therefore k-linear CS is favorable for high speed imaging. It is demonstrated that the k-linear CS has the same axial resolution performance with ~30 dB higher signal-to-noise ratio (SNR) as compared with the numerical interpolation. Imaging of bio-tissue by SD-OCT with k-linear CS is also demonstrated.

We demonstrate an optical Fourier processing method to quantify object texture arising from subcellular feature orientation within unstained living cells. Using a digital micromirror device as a Fourier spatial filter, we measured cellular responses to two-dimensional optical Gabor-like filters optimized to sense orientation of nonspherical particles, such as mitochondria, with a width around 0.45 μm. Our method showed significantly rounder structures within apoptosis-defective cells lacking the proapoptotic mitochondrial effectors Bax and Bak, when compared with Bax/Bak expressing cells functional for apoptosis, consistent with reported differences in mitochondrial shape in these cells. By decoupling spatial frequency resolution from image resolution, this method enables rapid analysis of nonspherical submicrometer scatterers in an under-sampled large field of view and yields spatially localized morphometric parameters that improve the quantitative assessment of biological function.Fundamental biological processes, such as programmed cell death (apoptosis), involve timedependent dynamic alterations in the morphology and subcellular organization of submicrometer scale organelles. As in any structure-function relationship, these morphological changes are controlled by important molecular pathways and must be quantified objectively to gain a more complete understanding of cellular function. Electron microscopy (EM) can directly image these structures but suffers from low throughput and cannot track dynamic structure changes. Such limitations motivate the development of high throughput optical methods that quantify time-dependent changes in morphology on very small-length scales and over a large field of view.To assess morphological changes with subwave-length sensitivity in unstained living cells, we developed an optical scatter imaging (OSI) technique based on Fourier spatial filtering using an iris with a variable diameter as a Fourier filter in a dark-field microscope [1]. In this Letter, we demonstrate how the assessment of sample morphology can be greatly extended by utilizing a spatial light modulator (SLM) as a Fourier filter. As a proof of concept, we used the SLM to implement 2D Gabor-like filters that can characterize particle orientation and roundness. Gabor filters have been used extensively in texture analysis of digital images. In the space domain, a Gabor filter corresponds to a sinusoidal wavelet with Light from a ~5 mW He-Ne laser (λ o =632.8 nm) was passed through a spinning diffuser and coupled into a multimode fiber whose output was collimated and launched into the microscope's condenser aligned in central Köhler illumination (NA < 0.05) to provide a spatially coherent plane wave. Image acquisition consisted of collecting on the CCD a stack of spatially filtered dark-field images using a spatial filter bank generated by the DMD. The DMD is a 1024×768 array of individually addressable 13.7 μm×13.7 μm mirrors, which can be programmed to deflect the light toward or away from the CCD detect...

We present an endoscopic probe for optical coherence tomography (OCT) equipped with a miniaturized hollow ultrasonic motor that rotates the objective lens and provides an internal channel for the fiber to pass through, enabling 360 deg unobstructed circumferential scanning. This probe has an outer diameter of 1.5 mm, which is ultra-small for motorized probes with an unobstructed view in distal scanning endoscopic OCT. Instead of a mirror or prism, a customized aspheric right-angle lens is utilized, leading to an enlargement of the numerical aperture and thus high transverse resolution. Spectral-domain OCT imaging of bio-tissue and a phantom are demonstrated with resolution of 7.5  μm(axial)×6.6  μm(lateral) and sensitivity of 96 dB.

The outbreak of COVID-19, caused by the SARS-CoV-2 coronavirus, has been declared a pandemic by the World Health Organization (WHO) in March, 2020 and rapidly spread to over 210 countries and territories around the world. By December 24, there are over 77M cumulative confirmed cases with more than 1.72M deaths worldwide. To mathematically describe the dynamic of the COVID-19 pandemic, we propose a time-dependent SEIR model considering the incubation period. Furthermore, we take immunity, reinfection, and vaccination into account and propose the SEVIS model. Unlike the classic SIR based models with constant parameters, our dynamic models not only predicts the number of cases, but also monitors the trajectories of changing parameters, such as transmission rate, recovery rate, and the basic reproduction number. Tracking these parameters, we observe the significant decrease in the transmission rate in the U.S. after the authority announced a series of orders aiming to prevent the spread of the virus, such as closing non-essential businesses and lockdown restrictions. Months later, as restrictions being gradually lifted, we notice a new surge of infection emerges as the transmission rates show increasing trends in some states. Using our epidemiology models, people can track, timely monitor, and predict the COVID-19 pandemic with precision. To illustrate and validate our model, we use the national level data (the U.S.) and the state level data (New York and North Dakota), and the resulting relative prediction errors for the infected group and recovered group are mostly lower than 0.5%. We also simulate the long-term development of the pandemic based on our proposed models to explore when the crisis will end under certain conditions.