Modeling Point Spread Function in Fluorescence Microscopy With a Sparse Gaussian Mixture: Tradeoff Between Accuracy and Efficiency

Calculating point spread functions: methods, pitfalls, and solutions

The knowledge of the exact structure of the optical system point spread function (PSF) enables a high-quality image reconstruction in fluorescence microscopy. Accurate PSF models account for the vector nature of light and the phase and amplitude modifications. Most existing real-space-based PSF models fall into a sampling pitfall near the center position, yielding to the violation of energy conservation. In this work, we present a novel, to the best of our knowledge, Fourier-based techniques for computing vector PSF and compare them to the state-of-the-art. Our methods are shown to satisfy the physical condition of the imaging process. They are reproducible, computationally efficient, easy to implement, and easy to modify to represent various imaging modalities.

PSF-Radon transform algorithm: Measurement of the point-spread function from the Radon transform of the line-spread function

In this article, we present a new method called point spread function (PSF)-Radon transform algorithm. This algorithm consists on recovering the instrument PSF from the Radon transform (in the line direction axis) of the line spread function (i.e., the image of a line). We present the method and tested with synthetic images, and real images from macro lens camera and microscopy. A stand-alone program along with a tutorial is available, for any interested user, in Martinez (PSF-Radon transform algorithm, standalone program). RESEARCH HIGHLIGHTS: Determining the instrument PSF is a key issue. Precise PSF determinations are mandatory if image improvement is performed numerically by deconvolution. Much less exposure time to achieve the same performance than a measurement of the PSF from a very small bead. Does not require having to adjust the PSF by an analytical function to overcome the noise uncertainties.

Semi-automated 3D fluorescence speckle analyzer (3D-Speckler) for microscope calibration and nanoscale measurement

The widespread use of fluorescence microscopy has prompted the ongoing development of tools aiming to improve resolution and quantification accuracy for study of biological questions. Current calibration and quantification tools for fluorescence images face issues with usability/user experience, lack of automation, and comprehensive multidimensional measurement/correction capabilities. Here, we developed 3D-Speckler, a versatile, and high-throughput image analysis software that can provide fluorescent puncta quantification measurements such as 2D/3D particle size, spatial location/orientation, and intensities through semi-automation in a single, user-friendly interface. Integrated analysis options such as 2D/3D local background correction, chromatic aberration correction, and particle matching/filtering are also encompassed for improved precision and accuracy. We demonstrate 3D-Speckler microscope calibration capabilities by determining the chromatic aberrations, field illumination uniformity, and response to nanometer-scale emitters above and below the diffraction limit of our imaging system using multispectral beads. Furthermore, we demonstrated 3D-Speckler quantitative capabilities for offering insight into protein architectures and composition in cells.

Structure-Based Analysis of Protein Cluster Size for Super-Resolution Microscopy in the Nervous System

To overcome the diffraction limit and resolve target structures in greater detail, far-field super-resolution techniques such as stochastic optical reconstruction microscopy (STORM) have been developed, and different STORM algorithms have been developed to deal with the various problems that arise. In particular, the effect of the local structure is an important issue. For objects with closely correlated distributions, simple Gaussian-based localization algorithms often used in STORM imaging misinterpret overlapping point spread functions (PSFs) as one, which limits the ability of super-resolution imaging to resolve nanoscale local structures and leads to inaccurate length measurements. The STORM super-resolution images of biological specimens from the cluster-forming proteins in the nervous system were reconstructed for localization-based analysis. Generally, the localization of each fluorophore was determined by two-dimensional Gaussian function fitting. Further, the physical shape of the cluster structure information was incorporated into the size parameter of the localization structure analysis in order to generate structure-based fitting algorithms. In the present study, we proposed a novel, structure-based, super-resolution image analysis method: structure-based analysis (SBA), which combines a structural function and a super-resolution localization algorithm. Using SBA, we estimated the size of fluorescent beads, inclusion proteins, and subtle synaptic structures in both wide-field and STORM images. The results show that SBA has a comparable and often superior performance to the commonly used full width at half maximum (FWHM) parameter. We demonstrated that SBA is able to estimate molecular cluster sizes in far-field super-resolution STORM images, and that SBA was comparable and often superior to FWHM. We also certified that SBA provides size estimations that corroborate previously published electron microscopy data.

Rethinking resolution estimation in fluorescence microscopy: from theoretical resolution criteria to super-resolution microscopy

Resolution is undoubtedly the most important parameter in optical microscopy by providing an estimation on the maximum resolving power of a certain optical microscope. For centuries, the resolution of an optical microscope is generally considered to be limited only by the numerical aperture of the optical system and the wavelength of light. However, since the invention and popularity of various advanced fluorescence microscopy techniques, especially super-resolution fluorescence microscopy, many new methods have been proposed for estimating the resolution, leading to confusions for researchers who need to quantify the resolution of their fluorescence microscopes. In this paper, we firstly summarize the early concepts and criteria for predicting the resolution limit of an ideal optical system. Then, we discuss some important influence factors that deteriorate the resolution of a certain fluorescence microscope. Finally, we provide methods and examples on how to measure the resolution of a fluorescence microscope from captured fluorescence images. This paper aims to answer as best as possible the theoretical and practical issues regarding the resolution estimation in fluorescence microscopy.

Point spread function degradation model of a polarization imaging system for wide-field subwavelength nanoparticles

We propose a comprehensive point spread function (PSF) degradation model, which considers multiple factors consisting of degradation of specimen retardant sampling and polarization angularly anamorphic sampling, to indicate the image degradation characteristics of polarization imaging systems. First, a one-layer optical coherence tomography (OCT) model was established to express the retardancy of medium-loading specimens. Then, a PSF degradation model of angularly anamorphic polarization sampling was deduced through the retrieval of Stokes parameters. Finally, maximum a posteriori probability (MAP) was adopted to assess the distribution of the proposed model. Hypothesis testing using actual data and numerical simulations demonstrated that the error of the system followed an asymmetric generalized Gaussian distribution (AGGD). Finite-difference time-domain (FDTD) simulation results and an actual imaging experiment demonstrate the consistency of the proposed model and the degradation characteristics of the PSF, which provide support for the improved accuracy and enhanced image quality of the optical field retrieval of nanoparticles.

Video-rate lensless endoscope with self-calibration using wavefront shaping

Lensless fiber endoscopes are of great importance for keyhole imaging. Coherent fiber bundles (CFB) can be used in endoscopes as remote phased arrays to capture images. One challenge is to image at high speed while correcting aberrations induced by the CFB. We propose the combination of digital optical phase conjugation, using a spatial light modulator, with fast scanning, for which a 2D galvo scanner and an adaptive lens are employed. We achieve the transmission of laser and image scanning through the CFB. Video-rate imaging at 20 Hz in 2D with subcellular resolution is demonstrated in 3D with 1 Hz. The sub-millimeter-diameter scanning endoscope has a great potential in biomedicine, for manipulation, e.g., in optogenetics, as well as in imaging.