Optical Point Spread Function Research Articles

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.

Super-Resolution Diamond Magnetic Microscopy of Superparamagnetic Nanoparticles.

Scanning-probe and wide-field magnetic microscopes based on nitrogen-vacancy (NV) centers in diamond have enabled advances in the study of biology and materials, but each method has drawbacks. Here, we implement an alternative method for nanoscale magnetic microscopy based on optical control of the charge state of NV centers in a dense layer near the diamond surface. By combining a donut-beam super-resolution technique with optically detected magnetic resonance spectroscopy, we imaged the magnetic fields produced by single 30 nm iron-oxide nanoparticles. The magnetic microscope has a lateral spatial resolution of ∼100 nm, and it resolves the individual magnetic dipole features from clusters of nanoparticles with interparticle spacings down to ∼190 nm. The magnetic feature amplitudes are more than an order of magnitude larger than those obtained by confocal magnetic microscopy due to the narrower optical point-spread function and the shallow depth of NV centers. We analyze the magnetic nanoparticle images and sensitivity as a function of the microscope's spatial resolution and show that the signal-to-noise ratio for nanoparticle detection does not degrade as the spatial resolution improves. We identify sources of background fluorescence that limit the present performance, including diamond second-order Raman emission and imperfect NV charge state control. Our method, which uses <10 mW laser power and can be parallelized by patterned illumination, introduces a promising format for nanoscale magnetic imaging.

Study of Angular Resolution Using Imaging Atmospheric Cherenkov Technique

Angular resolution is crucial for the detailed study of gamma-ray sources and current Cherenkov telescopes (e.g., HESS, MAGIC, and VERITAS) that operate below tens of TeV. Several gamma-ray sources with a photon energy larger than 100 TeV have been revealed by the LHAASO in recent years; the angular resolution of the LHAASO is around 0.3∘. A gamma-ray detector with an angular resolution of less than 0.1∘ operating beyond 100 TeV is needed to study the detailed morphology of ultra-high-energy gamma-ray sources further. The cost-effectiveness is crucial for such large-area detectors. In this paper, the impact of telescope aperture, field of view, pixel size, optical point spread function, and signal integration time window on angular resolution is studied. These results can provide essential elements for the design of telescope arrays.

Contribution of optical resolution to the spatial precision of two-photon optogenetic photostimulation in vivo.

Two-photon optogenetics combines nonlinear excitation with noninvasive activation of neurons to enable the manipulation of neural circuits with a high degree of spatial precision. Combined with two-photon population calcium imaging, these approaches comprise a flexible platform for all-optical interrogation of neural circuits. However, a multitude of optical and biological factors dictate the exact precision of this approach in vivo, where it is most usefully applied. We aimed to assess how the optical point spread function (OPSF) contributes to the spatial precision of two-photon photostimulation in neurobiology. We altered the axial spread of the OPSF of the photostimulation beam using a spatial light modulator. Subsequently, calcium imaging was used to monitor the axial spatial precision of two-photon photostimulation of layer 2 neurons in the mouse neocortex. We found that optical resolution is not always the limiting factor of the spatial precision of two-photon optogenetic photostimulation and, by doing so, reveal the key factors that must be improved to achieve maximal precision. Our results enable future work to focus on the optimal factors by providing key insight from controlled experiments in a manner not previously reported. This research can be applied to advance the state-of-the-art of all-optical interrogation, extending the toolkit for neuroscience research to achieve spatiotemporal precision at the crucial levels in which neural circuits operate.

Poster Session I: Vernier thresholds of a Poisson-noise-limited computational observer with and without fixational eye movements.

Vernier acuity is a fundamental measure of spatial vision. We modeled how stimulus encoding by the cones limits Vernier acuity. We determined Vernier thresholds for a computational observer that had access to the Poisson-distributed cone photopigment excitations. The observer also had access to the cone mosaic layout and the stimulus possibilities on each trial. We varied stimulus contrast (100%, 50%, 22%, 11% Michelson contrast) and duration (2, 4, 9, 18 stimulus frames; frame duration 8.33 ms) while fixing other stimulus properties (foveal viewing; two achromatic vertical bars; length 6.2 arcmin; width 1 arcmin; vertical gap 0.1 arcmin). When the retinal image is stationary, Vernier thresholds depend jointly on contrast and duration through contrast energy: squared contrast times duration. Introducing fixational drift eye movements impairs performance, when the information about eye path is not accounted for by the computational observer. When the path of fixational drift is made available and used ideally, there is no noticeable difference with the stationary case. The lack of improvement when the path of fixational drift is known exactly may reflect the high-density of foveal cones relative to the optical point spread function and the fact that we did not introduce temporal filtering by the visual system. Our results suggest the possibility of a rich interaction between optics, cone sampling, fixational eye movements, post-receptoral filtering and visual performance.

Improved prior for adaptive optics point spread function estimation from science images: Application for deconvolution

Context. Access to knowledge of the point spread function (PSF) of adaptive optics(AO)-assisted observations is still a major limitation when processing AO data. This limitation is particularly important when image analysis requires the use of deconvolution methods. As the PSF is a complex and time-varying function, reference PSFs acquired on calibration stars before or after the scientific observation can be too different from the actual PSF of the observation to be used for deconvolution, and lead to artefacts in the final image. Aims. We improved the existing PSF-estimation method based on the so-called marginal approach by enhancing the object prior in order to make it more robust and suitable for observations of resolved extended objects. Methods. Our process is based on a two-step blind deconvolution approach from the literature. The first step consists of PSF estimation from the science image. For this, we made use of an analytical PSF model, whose parameters are estimated based on a marginal algorithm. This PSF was then used for deconvolution. In this study, we first investigated the requirements in terms of PSF parameter knowledge to obtain an accurate and yet resilient deconvolution process using simulations. We show that current marginal algorithms do not provide the required level of accuracy, especially in the presence of small objects. Therefore, we modified the marginal algorithm by providing a new model for object description, leading to an improved estimation of the required PSF parameters. Results. Our method fulfills the deconvolution requirement with realistic system configurations and different classes of Solar System objects in simulations. Finally, we validate our method by performing blind deconvolution with SPHERE/ZIMPOL observations of the Kleopatra asteroid.

Water-immersion supercritical metalens

Far-field super-resolution lenses are attractive due to their great potential in the application of label-free far-field optical super-resolution. In past decades, there has been a fast development in superoscillatory optical lenses, which allows engineering of optical point-spread functions in the far-field beyond the traditional Abbe diffraction limit. With the decrease of focal spot size, the sidebands will inevitably increase, especially when the spot size is close to 0.358λ/NA, where NA is the numerical aperture. However, it is of critical importance to reduce the spot size while maintaining comparatively small sidelobes for many practical applications. Here, we demonstrate a water-immersion supercritical metalens with a high-numerical aperture of 1.15. Experimental results show the generation of a super-resolution hot spot as small as 0.33λ, which is very close to the superoscillation criterion, at a distance of 60λ from the lens. More importantly, there is no significant sideband on the focal plane, and the strength of the sidelobes near the hot spot is lower than 13.3 % of the central lobe intensity. The deep compression of hot spot and the absence of large sidelobes offer a promising way to further improve the resolution of far-field label-free super-resolution microscopy.

Towards optimal point spread function design for resolving closely spaced emitters in three dimensions.

The past decade has brought many innovations in optical design for 3D super-resolution imaging of point-like emitters, but these methods often focus on single-emitter localization precision as a performance metric. Here, we propose a simple heuristic for designing a point spread function (PSF) that allows for precise measurement of the distance between two emitters. We discover that there are two types of PSFs that achieve high performance for resolving emitters in 3D, as quantified by the Cramér-Rao bounds for estimating the separation between two closely spaced emitters. One PSF is very similar to the existing Tetrapod PSFs; the other is a rotating single-spot PSF, which we call the crescent PSF. The latter exhibits excellent performance for localizing single emitters throughout a 1-µm focal volume (localization precisions of 7.3 nm in x, 7.7 nm in y, and 18.3 nm in z using 1000 detected photons), and it distinguishes between one and two closely spaced emitters with superior accuracy (25-53% lower error rates than the best-performing Tetrapod PSF, averaged throughout a 1-µm focal volume). Our study provides additional insights into optimal strategies for encoding 3D spatial information into optical PSFs.

Relationship between the kernel size of a convolutional layer and the optical point spread function in ghost imaging using deep learning for identifying defect locations.

We explore the contribution of convolutional neural networks to correcting for the effect of the point spread function (PSF) of the optics when applying ghost imaging (GI) combined with deep learning to identify defect positions in materials. GI can be accelerated by combining GI and deep learning. However, no method has been established for determining the relevant model parameters. A simple model with different kernel sizes was built. Its accuracy was evaluated for data containing the effects of different PSFs. Numerical analysis and empirical experiments demonstrate that the accuracy of defect identification improved by matching the kernel size with the PSF of the optics.

Segmentation of visual images: experimental data and modeling

Experimental data on the segmentation of simple geometrical figures surrounded by a frame are compared for the first time to our knowledge with the results of a model of modules that filters the images in local areas of the visual field. It is shown in the experiments that images are perceived as two separate images when they reach a definite spacing between them, depending on their size and shape. When they are small, the distances are comparable with the optical point-spread function and the size of the highest-frequency receptive fields of the neurons in the primary visual cortex, and, when they are large, with the size of modules that optimally describe the images (with the maximum energy conservation in the images when there is a limited number of filters). The images are segmented when the second image (the frame) goes beyond the limits of the module. The results were confirmed by our earlier data on the study of the Oppel–Kundt illusion and by estimating the width of the spatial intervals.

Optical Aberrations Correction in Postprocessing Using Imaging Simulation

As the popularity of mobile photography continues to grow, considerable effort is being invested in the reconstruction of degraded images. Due to the spatial variation in optical aberrations, which cannot be avoided during the lens design process, recent commercial cameras have shifted some of these correction tasks from optical design to postprocessing systems. However, without engaging with the optical parameters, these systems only achieve limited correction for aberrations. In this work, we propose a practical method for recovering the degradation caused by optical aberrations. Specifically, we establish an imaging simulation system based on our proposed optical point spread function model. Given the optical parameters of the camera, it generates the imaging results of these specific devices. To perform the restoration, we design a spatial-adaptive network model on synthetic data pairs generated by the imaging simulation system, eliminating the overhead of capturing training data by a large amount of shooting and registration. Moreover, we comprehensively evaluate the proposed method in simulations and experimentally with a customized digital-single-lens-reflex camera lens and HUAWEI HONOR 20, respectively. The experiments demonstrate that our solution successfully removes spatially variant blur and color dispersion. When compared with the state-of-the-art deblur methods, the proposed approach achieves better results with a lower computational overhead. Moreover, the reconstruction technique does not introduce artificial texture and is convenient to transfer to current commercial cameras. Project Page: https://github.com/TanGeeGo/ImagingSimulation .

Spatial resolution of light field sectioning pyrometry for flame temperature measurement

The light field sectioning pyrometry (LFSP) has proven a significant advancement for in-situ measurement of flame temperature through a single light field camera. However, the spatial resolution of LFSP is limited, which severely inhibits the measurement accuracy. This paper aims to evaluate the spatial resolution of LFSP for flame temperature measurement quantitatively. A theoretical model of the spatial resolution is established based on optical parameters and point spread function of the light field camera. The spatial resolution is then numerically analyzed with different parameters of light field cameras. Based on the theoretical model, a novel cage-typed light field camera with a higher spatial resolution of LFSP is developed and experimentally evaluated. A significant improvement of spatial resolution about 17% and 50% in lateral and depth directions, respectively, is achieved. Results show that the spatial resolution is in good agreement with the theoretical model. The LFSP is then evaluated under different combustion cases and their temperatures are reconstructed.

Joint estimation of atmospheric and instrumental defects using a parsimonious point spread function model

Context. Modeling the optical point spread function (PSF) is particularly challenging for adaptive optics (AO)-assisted observations owing to the its complex shape and spatial variations. Aims. We aim to (i) exhaustively demonstrate the accuracy of a recent analytical model from comparison with a large sample of imaged PSFs, (ii) assess the conditions for which the model is optimal, and (iii) unleash the strength of this framework to enable the joint estimation of atmospheric parameters, AO performance and static aberrations. Methods. We gathered 4812 on-sky PSFs obtained from seven AO systems and used the same fitting algorithm to test the model on various AO PSFs and diagnose AO performance from the model outputs. Finally, we highlight how this framework enables the characterization of the so-called low wind effect on the Spectro-Polarimetic High contrast imager for Exoplanets REsearch (LWE; SPHERE) instrument and piston cophasing errors on the Keck II telescope. Results. Over 4812 PSFs, the model reaches down to 4% of error on both the Strehl-ratio (SR) and full width at half maximum (FWHM). We particularly illustrate that the estimation of the Fried’s parameter, which is one of the model parameters, is consistent with known seeing statistics and follows expected trends in wavelength using the Multi Unit Spectroscopic Explorer instrument (λ6/5) and field (no variations) from Gemini South Adaptive Optics Imager images with a standard deviation of 0.4 cm. Finally, we show that we can retrieve a combination of differential piston, tip, and tilt modes introduced by the LWE that compares to ZELDA measurements, as well as segment piston errors from the Keck II telescope and particularly the stair mode that has already been revealed from previous studies. Conclusions. This model matches all types of AO PSFs at the level of 4% error and can be used for AO diagnosis, post-processing, and wavefront sensing purposes.

Spatial misregistration in hyperspectral cameras: lab characterization and impact on data quality in real-world images

Hyperspectral cameras capture images where every pixel contains spectral information of the corresponding small area of the depicted scene. Spatial misregistration—differences in spatial sampling between different spectral channels—is one of the key quality parameters of these cameras, because it may have a large impact on the accuracy of the captured spectra. Spatial misregistration unifies various factors, such as differences in the position of the optical point spread function (PSF) in different spectral channels, differences in PSF size, and differences in PSF shape. Ideally, there should be no difference in spatial sampling across the spectral channels, but in any real camera, all these factors are present to some degree. Our work shows the magnitude of the spectral errors caused by these spatial misregistration factors of different magnitudes and in various combinations when acquiring hyperspectral images of real scenes. The spectral errors are calculated in Virtual Camera software where high-resolution airborne images of real-world scenes and several PSFs of different hyperspectral cameras are used as the input. The misregistration factors are simulated. Two different methods for quantifying spatial misregistration in the lab are also tested and compared using the correlation with the errors in the real-world scenes as the criterion. The results are used to suggest the best camera characterization approach that would adequately predict spatial misregistration errors and allow reliable comparison of different hyperspectral cameras to each other.

Image restoration of high-energy X-ray radiography with a scintillator blur model

High-energy X-ray radiographic image restoration is performed using a simulated radiation point spread function and an experimentally derived optical point spread function. It is shown that a robust method for removal of thick monolithic scintillator blur can be determined through independent examination of the blur components. We show that the scintillator blur for a 20 MeV end-point X-ray beam and 20 mm thick LYSO scintillator contributes significantly to the system blur. It is also shown that the optical scatter in the monolithic crystal degrades the low-frequency response of the system. The use of a simulated point spread function for image restoration using deconvolution provides a simple method for image restoration, thereby enhancing feature identification and areal density reconstruction.

High‐Numerical‐Aperture Dielectric Metalens for Super‐Resolution Focusing of Oblique Incident Light

AbstractRecently, developments in superoscillatory optical devices have allowed for label‐free far‐field optical super‐resolution technology by allowing engineering of optical point‐spread functions beyond the traditional Abbe diffraction limit. However, such superoscillatory optical devices are optimized for the normal‐incident operation, which inevitably leads to a comparatively slow imaging acquisition rate in the application of super‐resolution microscopy. Here, a super‐resolution metalens is demonstrated with a high numerical aperture that can focus oblique incident light into a hot spot with a size smaller than the diffraction limit at the visible wavelength. This super‐resolution metalens has a numerical aperture of as large as 0.97, a focal length of 38.0 µm, a radius of 151.9 µm, and a field of view of 4° that enables super‐resolution focusing on the focal plane at a wavelength of λ = 632.8 nm. In a 5.6λ × 5.6λ field of view on the focal plane, the size of the focal spot is smaller than 0.45λ, which is only 0.874 times the corresponding Abbe diffraction limit. The super‐resolution metalens offers a promising way toward fast‐scanning label‐free far‐field super‐resolution microscopy.

Application of Superresolution Radial Fluctuation (SRRF) Imaging to Measurement of Single-Molecule DNA Hybridization Kinetics

Superresolution radial fluctuations (SRRF) is a novel algorithm based superresolution imaging technique that incorporates radial intensity gradients and temporal intensity fluctuations to calculate and project SRRF images with resolution up to 2x below the diffraction limit in real time. SRRF, has been used for imaging sub-diffraction intracellular structures and for performing time-resolved superresolution measurements of live cell dynamics. However, no application to single-molecule localization and tracking techniques has been shown. Here, we characterize the capabilities of the SRRF algorithm on measuring DNA hybridization kinetics from a DNA capture surface via single-molecule localization and tracking. We find that SRRF data has some obvious advantages such as a substantial increase in the signal-to-background ratio of single-molecule data. This is a side effect of the image radiality transform which yields low radiality values for regions which contain randomized intensity values on the distance scales of the radiality calculation. This is particularly usefully when measuring hybridization kinetics with slow on rates which necessitate higher solution phase concentrations and resulting in higher background levels. We also find that with sparse data such as these, molecule localization can be performed by calculation of the 1st moment centroids of the SRRF point spread functions (PSF) which can deliver spatial resolution similar to non-linear fitting of the optical PSF but with much faster computational times. Finally, we explore the ability for SRRF to resolve individual molecules in high DNA surface density conditions which result in many overlapping optical PSFs. We find that measuring single-molecule data following the SRRF radiality transform allows for resolving much higher densities of molecules than diffraction limited images thus allowing for faster collection of statistically significant population data.

Effect of point spread function position bias in wavefront coding infrared imaging system

By an experimental finding, for a given radiant point source and a given infrared detector sampling, an optical point spread function (PSF) falling on different positions of an infrared detector focal plane array, will result in different measured PSFs. Those measured PSFs known as decoding kernels will further produce different decoded images. Therefore, this work explores the effect of PSF position bias on decoded images in a wavefront coding infrared imaging system. This paper theoretically analyzes the effect of PSF position bias on decoded images. A simulation is conducted for qualitatively evaluating the effect of PSF position bias on decoded images by mean structural similarity (MSSIM) index. Simulated results prove that the probability for MSSIM index greater than 0.75 is 91.38%, and that for less than 0.5 is only 1.22% but this minority seriously degrades the decoded images. We construct an experimental setup for capturing the raw PSF image at a random position and proposes a procedure to reduce the noise of a raw PSF image. The experimental result demonstrates the feasibility for measuring a PSF to achieve a decoded image with good quality.

Characterising the size and shape of metallic nano-structures by their acoustic vibrations.

The characterisation of metallic nano-structures is of great importance as their optical properties are strongly dependent on their size and shape. Inaccurate size or shape characterisation can result in misleading measurements in applications such as bio-imaging and sensing. Characterisation techniques such as dynamic light scattering, electron microscopy or atomic force microscopy are commonly used; however, performing sub-surface measurements (inside semi-transparent objects) or in liquid media are very challenging. Here, we use time-resolved pump-probe spectroscopy to characterise the size and shape of metallic nano-structures in a water surrounding medium by using their vibrational modes. We show that this technique can achieve size measurements with a precision of 3 nm for the largest nano-structures which are in agreement with electron microscopy images. Furthermore, we demonstrate the ability to probe individual nano-structures despite being located in the same optical point spread function (PSF). Combining the high precision and sub-optical measurements provided by this technique with the ability to insert metallic nano-structures inside biological samples might open a way to perform 3D characterisation measurements.

Deep Super-Resolution Imaging Technology: Toward Optical Super-Vision

Spatially variant optical blur is inevitable in real optical imaging systems with imperfect camera lenses since each object has a different depth in a real scene. Unfortunately, existing super-resolution imaging techniques may not achieve satisfactory performance on images acquired from practical optical imaging systems, where the optical blur is unknown. This is because a predefined global point spread function is adopted for every spatial coordinate without any optical blur estimation in the existing models. To address the challenging issue in recent video technologies, in this article, we propose an optimal super-resolution imaging network based on object-adaptive optical point spread function estimation. In technical, a new object sharpness consistency cost is suggested in the dark channel domain to estimate the point spread function, which is optimal to the super-resolution imaging. In addition, an object image sharpening network is proposed and adaptively combined with the point spread function estimation. The performance of the proposed network is also validated via experiments in terms of various quantitative metrics such as the peak signal-to-noise ratio, S3 index, and BRISQUE values.