Computational localization microscopy with extended axial range

Optimizing self-interference digital holography for single-molecule localization

Self-interference digital holography (SIDH) can image incoherently emitting objects over large axial ranges from three two-dimensional images. By combining SIDH with single-molecule localization microscopy (SMLM), incoherently emitting objects can be localized with nanometer precision over a wide axial range without mechanical refocusing. However, background light substantially degrades the performance of SIDH due to the relatively large size of the hologram. To optimize the performance of SIDH, we performed simulations to study the optimal hologram radius (Rh) for different levels of background photons. The results show that by reducing the size of the hologram, we can achieve a localization precision of better than 60 nm laterally and 80 nm axially over a 10 µm axial range under the conditions of low signal level (6000 photons) with 10 photons/pixel of background noise. We then performed experiments to demonstrate our optimized SIDH system. The results show that point sources emitting as few as 2120 photons can be successfully detected. We further demonstrated that we can successfully reconstruct point-like sources emitting 4200 photons over a 10 µm axial range by light-sheet SIDH.

Double helix point spread function with variable spacing for precise 3D particle localization

To extend the axial depth of nanoscale 3D-localization microscopy, we propose here a splicing-type vortex singularities (SVS) phase mask, which has been meticulously optimized with a Fresnel approximation imaging inverse operation. The optimized SVS DH-PSF has proven to have high transfer function efficiency with adjustable performance in its axial range. The axial position of the particle was computed by using both the main lobes' spacing and the rotation angle, an improvement of the localization precision of the particle. Concretely, the proposed optimized SVS DH-PSF, with a smaller spatial extent, can effectively reduce the overlap of nanoparticle images and realize the 3D localization of multiple nanoparticles with small spacing, with respect to PSFs for large axial 3D localization. Finally, we successfully conducted extensive experiments on 3D localization for tracking dense nanoparticles at 8µm depth with a numerical aperture of 1.4, demonstrating its great potential.

Point spread function in interferometric scattering microscopy (iSCAT). Part I: aberrations in defocusing and axial localization

Interferometric scattering (iSCAT) microscopy is an emerging label-free technique optimized for the sensitive detection of nano-matter. Previous iSCAT studies have approximated the point spread function in iSCAT by a Gaussian intensity distribution. However, recent efforts to track the mobility of nanoparticles in challenging speckle environments and over extended axial ranges has necessitated a quantitative description of the interferometric point spread function (iPSF). We present a robust vectorial diffraction model for the iPSF in tandem with experimental measurements and rigorous FDTD simulations. We examine the iPSF under various imaging scenarios to understand how aberrations due to the experimental configuration encode information about the nanoparticle. We show that the lateral shape of the iPSF can be used to achieve nanometric three-dimensional localization over an extended axial range on the order of 10 µm either by means of a fit to an analytical model or calibration-free unsupervised machine learning. Our results have immediate implications for three-dimensional single particle tracking in complex scattering media.

Twin-Airy Point-Spread Function for Extended-Volume Particle Localization

The localization of point sources in optical microscopy enables nm-precision imaging of single-molecules and biological dynamics. We report a new method of localization microscopy using twin Airy beams that yields precise 3D localization with the key advantages of extended depth range, higher optical throughput, and potential for imaging higher emitter densities than are possible using other techniques. A precision of better than 30 nm was achieved over a depth range in excess of 7  μm using a 60×, 1.4 NA objective. An illustrative application to extended-depth-range blood-flow imaging in a live zebrafish is also demonstrated.

Precise 3D particle localization over large axial ranges using secondary astigmatism

We propose an analytical pupil phase function employing cropped secondary astigmatism for extended-depth nanoscale 3D-localization microscopy. The function provides high localization precision in all three dimensions, which can be maintained over extended axial ranges, customizable up to two orders of magnitude relative to the conventional, diffraction-limited imaging. This enables, for example, capturing nanoscale dynamics within a whole cell. The flexibility and simplicity in the implementation of the proposed phase function make its adoption in localization-based microscopy attractive. We demonstrate and validate its application to real-time imaging of 3D fluid flow over a depth of 40 µm with a numerical aperture of 0.8.

Investigation of extended depth-of-field f/8 camera with optimized cubic phase mask and digital restoration

An investigation of extended depth-of-field camera with optimized phase mask and digital restoration is presented. The goal of this paper is to implement the wavefront coding technique without affecting much of the original design, and the design has taken the complexity of imaging system into consideration. The optimized strength of cubic phase mask (CPM) is based on the analytical optimal solution for the task-based imaging system [J. Opt. Soc. Am. A 25, 1064 (2008)]. The noisy intermediate images of CPM system with highest spatial frequency of interest can be effectively restored by vector-based Richardson-Lucy algorithm. Restoration from the system with generalized CPM produces precise image position than the system with CPM does. In general, the CPM system procures modulation transfer function higher than 0.195 in the whole depth-of-field, and the mean squared error of the restored images are less than 5 %.

Holistic Monte-Carlo optical modelling of biological imaging

The invention and advancement of biological microscopy depends critically on an ability to accurately simulate imaging of complex biological structures embedded within complex scattering media. Unfortunately no technique exists for rigorous simulation of the complete imaging process, including the source, instrument, sample and detector. Monte-Carlo modelling is the gold standard for the modelling of light propagation in tissue, but is somewhat laborious to implement and does not incorporate the rejection of scattered light by the microscope. On the other hand microscopes may be rigorously and rapidly modelled using commercial ray-tracing software, but excluding the interaction with the biological sample. We report a hybrid Monte-Carlo optical ray-tracing technique for modelling of complete imaging systems of arbitrary complexity. We make the software available to enable user-friendly and rigorous virtual prototyping of biological microscopy of arbitrary complexity involving light scattering, fluorescence, polarised light propagation, diffraction and coherence. Examples are presented for the modelling and optimisation of representative imaging of neural cells using light-sheet and micro-endoscopic fluorescence microscopy and imaging of retinal vasculature using confocal and non-confocal scanning-laser ophthalmoscopes.

Non-diffracting linear-shift point-spread function by focus-multiplexed computer-generated hologram

An Airy beam can be used to implement a non-diffracting self-bending point-spread function (PSF), which can be utilized for computational 3D imaging. However, the parabolic depth-dependent spot trajectory limits the range and resolution in rangefinding. In this Letter, we propose a novel pupil-phase-modulation method to realize a non-diffracting linear-shift PSF. For the modulation, we use a focus-multiplexed computer-generated hologram, which is calculated by multiplexing multiple lens-function holograms with 2D sweeping of the foci. With this method, the depth-dependent trajectory of the non-diffracting spot is straightened, which improves the range and resolution in rangefinding. The proposed method was verified by numerical simulations and optical experiments. The method can be applied to laser-based microscopy, time-of-flight rangefinding, and so on.

High-speed extended-volume blood flow measurement using engineered point-spread function

Experimental characterization of blood flow in living organisms is crucial for understanding the development and function of cardiovascular systems, but there has been no technique reported for snapshot imaging of thick samples in large volumes with high precision. We have combined computational microscopy and the diffraction-free, self-bending property of Airy-beams to track fluorescent beads with sub-micron precision through an extended axial range (up to 600 μm) within the flowing blood of 3 days post-fertilization (dpf) zebrafish embryos. The spatial trajectories of the tracer beads within flowing blood were recorded during transit through both cardinal and intersegmental vessels, and the trajectories were found to be consistent with the segmentation of the vasculature recorded using selective-plane illumination microscopy (SPIM). This method provides sufficiently precise spatial and temporal measurement of 3D blood flow that has the potential for directly probing key biomechanical quantities such as wall shear stress, as well as exploring the fluidic repercussions of cardiovascular diseases. Although we demonstrate the technique for blood flow, the ten-fold better enhancement in the depth range offers improvements in a wide range of applications of high-speed precision measurement of fluid flow, from microfluidics through measurement of cell dynamics to macroscopic aerosol characterizations.

Joint digital-optical design of complex lenses using a surrogate image quality criterion adapted to commercial optical design software

Like classical optical design, joint digital-optical design of complex lenses requires a skilled optical designer helped by powerful optical design software. Consequently, if optimization criteria have to be modified to take into account digital post-processing, the convenient optimization environment provided by commercial optical design software needs to be preserved. For that purpose, we define a joint-design criterion based on a merit function that contains terms classically implemented in optical design software but used in a non-standard way. After validation on a simple design problem, the proposed method is applied to the design of a very fast (f/0.75) complex lens. The obtained joint-designed lens is shown to be superior to a classically designed one in terms of weight and image quality in the field.