Universal inverse modeling of point spread functions for SMLM localization and microscope characterization.

The point spread function (PSF) of a microscope describes the image of a point emitter. Knowing the accurate PSF model is essential for various imaging tasks, including single-molecule localization, aberration correction and deconvolution. Here we present universal inverse modeling of point spread functions (uiPSF), a toolbox to infer accurate PSF models from microscopy data, using either image stacks of fluorescent beads or directly images of blinking fluorophores, the raw data in single-molecule localization microscopy (SMLM). Our modular framework is applicable to a variety of microscope modalities and the PSF model incorporates system- or sample-specific characteristics, for example, the bead size, field- and depth- dependent aberrations, and transformations among channels. We demonstrate its application in single or multiple channels or large field-of-view SMLM systems, 4Pi-SMLM, and lattice light-sheet microscopes using either bead data or single-molecule blinking data.

Large-FOV 3D localization microscopy by spatially variant point spread function generation.

Accurate characterization of the microscopic point spread function (PSF) is crucial for achieving high-performance localization microscopy (LM). Traditionally, LM assumes a spatially invariant PSF to simplify the modeling of the imaging system. However, for large fields of view (FOV) imaging, it becomes important to account for the spatially variant nature of the PSF. Here, we propose an accurate and fast principal components analysis-based field-dependent 3D PSF generator (PPG3D) and localizer for LM. Through simulations and experimental three-dimensional (3D) single-molecule localization microscopy (SMLM), we demonstrate the effectiveness of PPG3D, enabling super-resolution imaging of mitochondria and microtubules with high fidelity over a large FOV. A comparison of PPG3D with a shift-variant PSF generator for 3D LM reveals a threefold improvement in accuracy. Moreover, PPG3D is approximately 100 times faster than existing PSF generators, when used in image plane-based interpolation mode. Given its user-friendliness, we believe that PPG3D holds great potential for widespread application in SMLM and other imaging modalities.

Universal inverse modelling of point spread functions for SMLM localization and microscope characterization.

The point spread function (PSF) of a microscope describes the image of a point emitter. Knowing the accurate PSF model is essential for various imaging tasks, including single molecule localization, aberration correction and deconvolution. Here we present uiPSF (universal inverse modelling of Point Spread Functions), a toolbox to infer accurate PSF models from microscopy data, using either image stacks of fluorescent beads or directly images of blinking fluorophores, the raw data in single molecule localization microscopy (SMLM). The resulting PSF model enables accurate 3D super-resolution imaging using SMLM. Additionally, uiPSF can be used to characterize and optimize a microscope system by quantifying the aberrations, including field-dependent aberrations, and resolutions. Our modular framework is applicable to a variety of microscope modalities and the PSF model incorporates system or sample specific characteristics, e.g., the bead size, depth dependent aberrations and transformations among channels. We demonstrate its application in single or multiple channels or large field-of-view SMLM systems, 4Pi-SMLM, and lattice light-sheet microscopes using either bead data or single molecule blinking data.

Near index matching enables solid diffractive optical element fabrication via additive manufacturing.

Diffractive optical elements (DOEs) have a wide range of applications in optics and photonics, thanks to their capability to perform complex wavefront shaping in a compact form. However, widespread applicability of DOEs is still limited, because existing fabrication methods are cumbersome and expensive. Here, we present a simple and cost-effective fabrication approach for solid, high-performance DOEs. The method is based on conjugating two nearly refractive index-matched solidifiable transparent materials. The index matching allows for extreme scaling up of the elements in the axial dimension, which enables simple fabrication of a template using commercially available 3D printing at tens-of-micrometer resolution. We demonstrated the approach by fabricating and using DOEs serving as microlens arrays, vortex plates, including for highly sensitive applications such as vector beam generation and super-resolution microscopy using MINSTED, and phase-masks for three-dimensional single-molecule localization microscopy. Beyond the advantage of making DOEs widely accessible by drastically simplifying their production, the method also overcomes difficulties faced by existing methods in fabricating highly complex elements, such as high-order vortex plates, and spectrum-encoding phase masks for microscopy.

Diffractive optical system design by cascaded propagation.

Modern design of complex optical systems relies heavily on computational tools. These frequently use geometrical optics as well as Fourier optics. Fourier optics is typically used for designing thin diffractive elements, placed in the system's aperture, generating a shift-invariant Point Spread Function (PSF). A major bottleneck in applying Fourier Optics in many cases of interest, e.g. when dealing with multiple, or out-of-aperture elements, comes from numerical complexity. In this work, we propose and implement an efficient and differentiable propagation model based on the Collins integral, which enables the optimization of diffractive optical systems with unprecedented design freedom using backpropagation. We demonstrate the applicability of our method, numerically and experimentally, by engineering shift-variant PSFs via thin plate elements placed in arbitrary planes inside complex imaging systems, performing cascaded optimization of multiple planes, and designing optimal machine-vision systems by deep learning.

Monocular kilometer-scale passive ranging by point-spread function engineering.

Standard imaging systems are designed for 2D representation of objects, while information about the third dimension remains implicit, as imaging-based distance estimation is a difficult challenge. Existing long-range distance estimation technologies mostly rely on active emission of signal, which as a subsystem, constitutes a significant portion of the complexity, size and cost of the active-ranging apparatus. Despite the appeal of alleviating the requirement for signal-emission, passive distance estimation methods are essentially nonexistent for ranges greater than a few hundreds of meters. Here, we present monocular long-range, telescope-based passive ranging, realized by integration of point-spread-function engineering into a telescope, extending the scale of point-spread-function engineering-based ranging to distances where it has never been tested before. We provide experimental demonstrations of the optical system in a variety of challenging imaging scenarios, including adversarial weather conditions, dynamic targets and scenes of diversified textures, at distances extending beyond 1.7 km. We conclude with brief quantification of the effect of atmospheric turbulence on estimation precision, which becomes a significant error source in long-range optical imaging.

Quantitative reconstruction of the complex-valued object based on complementary phase modulations.

In the coherent diffraction imaging (CDI) techniques, a key point is to reconstruct the complex-valued object from the far-field intensity measurements, i.e., solving the phase retrieval problem. However, due to this ill-posed problem, traditional phase retrieval algorithms often encounter some problems associated with the iteration convergence. In this work, complementary phase modulations (CPM) are introduced to generate different far-field intensity measurements. The namely CPM-based method aims to find out the global optimal solution by imposing multi-dimensional constraints, including the diverse intensity images at the Fourier plane and the CPM at the object plane. It is proved by the numerical simulations and the optical experiments that the convergence speed and the recovery accuracy could be greatly improved. Furthermore, the shifting complementary phase modulations (SCPM)-based method is proposed by introducing more CPMs. The reconstruction performance is further improved even when the phase range is larger, and the support constraints are not required. In addition, the SCPM-based method is more robust to the Poisson noise. With the outstanding reconstruction performance, the CPM-based methods may be helpful to phase imaging in the application of visible-light microscopy and X-ray imaging.