Resolution limit in opto-digital systems revisited.

The resolution limit achievable with an optical system is a fundamental piece of information when characterizing its performance, mainly in case of microscopy imaging. Usually this information is given in the form of a distance, often expressed in microns, or in the form of a cutoff spatial frequency, often expressed in line pairs per mm. In modern imaging systems, where the final image is collected by pixelated digital cameras, the resolution limit is determined by the performance of both, the optical systems and the digital sensor. Usually, one of these factors is considered to be prevalent over the other for estimating the spatial resolution, leading to the global performance of the imaging system ruled by either the classical Abbe resolution limit, based on physical diffraction, or by the Nyquist resolution limit, based on the digital sensor features. This estimation fails significantly to predict the global performance of opto-digital imaging systems, like 3D microscopes, where none of the factors is negligible. In that case, which indeed is the most common, neither the Abbe formula nor the Nyquist formula provide by themselves a reliable prediction for the resolution limit. This is a serious drawback since systems designers often use those formulae as design input parameters. Aiming to overcome this lack, a simple mathematical expression obtained by finely articulating the Abbe and Nyquist formulas, to easily predict the spatial resolution limit of opto-digital imaging systems, is proposed here. The derived expression is tested experimentally, and shows to be valid in a broad range of opto-digital combinations.

Machine Learning-Based View Synthesis in Fourier Lightfield Microscopy.

Current interest in Fourier lightfield microscopy is increasing, due to its ability to acquire 3D images of thick dynamic samples. This technique is based on simultaneously capturing, in a single shot, and with a monocular setup, a number of orthographic perspective views of 3D microscopic samples. An essential feature of Fourier lightfield microscopy is that the number of acquired views is low, due to the trade-off relationship existing between the number of views and their corresponding lateral resolution. Therefore, it is important to have a tool for the generation of a high number of synthesized view images, without compromising their lateral resolution. In this context we investigate here the use of a neural radiance field view synthesis method, originally developed for its use with macroscopic scenes acquired with a moving (or an array of static) digital camera(s), for its application to the images acquired with a Fourier lightfield microscope. The results obtained and presented in this paper are analyzed in terms of lateral resolution and of continuous and realistic parallax. We show that, in terms of these requirements, the proposed technique works efficiently in the case of the epi-illumination microscopy mode.

Fourier lightfield microscopy: a practical design guide.

In this work, a practical guide for the design of a Fourier lightfield microscope is reported. The fundamentals of the Fourier lightfield are presented and condensed on a set of contour plots from which the user can select the design values of the spatial resolution, the field of view, and the depth of field, as function of the specifications of the hardware of the host microscope. This work guides the reader to select the parameters of the infinity-corrected microscope objective, the optical relay lenses, the aperture stop, the microlens array, and the digital camera. A user-friendly graphic calculator is included to ease the design, even to those who are not familiar with the lightfield technology. The guide is aimed to simplify the design process of a Fourier lightfield microscope, which sometimes could be a daunting task, and in this way, to invite the widespread use of this technology. An example of a design and experimental results on imaging different types of samples is also presented.

Handheld and Cost-Effective Fourier Lightfield Microscope.

In this work, the design, building, and testing of the most portable, easy-to-build, robust, handheld, and cost-effective Fourier Lightfield Microscope (FLMic) to date is reported. The FLMic is built by means of a surveillance camera lens and additional off-the-shelf optical elements, resulting in a cost-effective FLMic exhibiting all the regular sought features in lightfield microscopy, such as refocusing and gathering 3D information of samples by means of a single-shot approach. The proposed FLMic features reduced dimensions and light weight, which, combined with its low cost, turn the presented FLMic into a strong candidate for in-field application where 3D imaging capabilities are pursued. The use of cost-effective optical elements has a relatively low impact on the optical performance, regarding the figures dictated by the theory, while its price can be at least 100 times lower than that of a regular FLMic. The system operability is tested in both bright-field and fluorescent modes by imaging a resolution target, a honeybee wing, and a knot of dyed cotton fibers.

Three-dimensional real-time darkfield imaging through Fourier lightfield microscopy.

We report a protocol that takes advantage of the Fourier lightfield microscopy concept for providing 3D darkfield images of volumetric samples in a single-shot. This microscope takes advantage of the Fourier lightfield configuration, in which a lens array is placed at the Fourier plane of the microscope objective, providing a direct multiplexing of the spatio-angular information of the sample. Using the proper illumination beam, the system collects the light scattered by the sample while the background light is blocked out. This produces a set of orthographic perspective images with shifted spatial-frequency components that can be recombined to produce a 3D darkfield image. Applying the adequate reconstruction algorithm high-contrast darkfield optical sections are calculated in real time. The presented method is applied for fast volumetric reconstructions of unstained 3D samples.

Fast and robust phase-shift estimation in two-dimensional structured illumination microscopy.

A method of determining unknown phase-shifts between elementary images in two-dimensional Structured Illumination Microscopy (2D-SIM) is presented. The proposed method is based on the comparison of the peak intensity of spectral components. These components correspond to the inherent structured illumination spectral content and the residual component that appears from wrongly estimated phase-shifts. The estimation of the phase-shifts is carried out by finding the absolute maximum of a function defined as the normalized peak intensity difference in the Fourier domain. This task is performed by an optimization method providing a fast estimation of the phase-shift. The algorithm stability and robustness are tested for various levels of noise and contrasts of the structured illumination pattern. Furthermore, the proposed approach reduces the number of computations compared to other existing techniques. The method is supported by the theoretical calculations and validated by means of simulated and experimental results.

Improvement of two-dimensional structured illumination microscopy with an incoherent illumination pattern of tunable frequency.

In two-dimensional structured illumination microscopy (2D-SIM), high-resolution images with optimal optical sectioning (OS) cannot be obtained simultaneously. This tradeoff can be overcome by using a tunable-frequency 2D-SIM system and a proper reconstruction method. The goal of this work is twofold. First, we present a computational approach to reconstruct optical-sectioned images with super-resolution enhancement (OS-SR) by using a tunable SIM system. Second, we propose an incoherent tunable-frequency 2D-SIM system based on a Fresnel biprism implementation. Integration of the proposed computational method with this tunable structured illumination (SI) system results in a new 2D-SIM system that is advantageous compared to other 2D-SIM systems with comparable complexity, because it provides high-resolution OS images independent of the objective lens used, without the presence of coherent noise and without reducing the contrast of the structured pattern, as in other incoherent implementations. Evaluation of our proposed system is demonstrated with comparative studies of simulated and experimental reconstructed images to validate our theoretical findings. Our experimental results show a simultaneous improvement of the lateral resolution by a factor of 1.8× with the desired OS capability achieved in the resulting OS-SR combination image. Our experimental results also verify that our system can provide better OS capability than the commercial Zeiss ApoTome-SIM system in the investigated study.

Mapping electron-beam-injected trapped charge with scattering scanning near-field optical microscopy.

Scattering scanning near-field optical microscopy (s-SNOM) has been demonstrated as a valuable tool for mapping the optical and optoelectronic properties of materials with nanoscale resolution. Here we report experimental evidence that trapped electric charges injected by an electron beam at the surface of dielectric samples affect the sample-dipole interaction, which has direct impact on the s-SNOM image content. Nanoscale mapping of the surface trapped charge holds significant potential for the precise tailoring of the electrostatic properties of dielectric and semiconductive samples, such as hydroxyapatite, which has particular importance with respect to biomedical applications. The methodology developed here is highly relevant to semiconductor device fabrication as well.

Free-depths reconstruction with synthetic impulse response in integral imaging.

Integral Imaging provides spatial and angular information of three-dimensional (3D) objects, which can be used both for 3D display and for computational post-processing purposes. In order to recover the depth information from an integral image, several algorithms have been developed. In this paper, we propose a new free depth synthesis and reconstruction method based on the two-dimensional (2D) deconvolution between the integral image and a simplified version of the periodic impulse response function (IRF) of the system. The period of the IRF depends directly on the axial position within the object space. Then, we can retrieve the depth information by performing the deconvolution with computed impulse responses with different periods. In addition, alternative reconstructions can be obtained by deconvolving with non-conventional synthetic impulse responses. Our experiments show the feasibility of the proposed method as well as its potential applications.

Resolution enhancement in integral microscopy by physical interpolation.

Integral-imaging technology has demonstrated its capability for computing depth images from the microimages recorded after a single shot. This capability has been shown in macroscopic imaging and also in microscopy. Despite the possibility of refocusing different planes from one snap-shot is crucial for the study of some biological processes, the main drawback in integral imaging is the substantial reduction of the spatial resolution. In this contribution we report a technique, which permits to increase the two-dimensional spatial resolution of the computed depth images in integral microscopy by a factor of √2. This is made by a double-shot approach, carried out by means of a rotating glass plate, which shifts the microimages in the sensor plane. We experimentally validate the resolution enhancement as well as we show the benefit of applying the technique to biological specimens.

Off-axis digital holographic microscopy: practical design parameters for operating at diffraction limit.

The utilization of microscope objectives (MOs) in digital holographic microscopy (DHM) has associated effects that are not present in conventional optical microscopy. The remaining phase curvature, which can ruin the quantitative phase imaging, is the most evident and analyzed. As phase imaging is considered, this interest has made possible the development of different methods of overcoming its undesired consequences. Additionally to the effects in phase imaging, there exist a set of less obvious conditions that have to be accounted for as MOs are utilized in DHM to achieve diffraction-limit operation. These conditions have to be considered even in the case in which only amplitude or intensity imaging is of interest. In this paper, a thorough analysis of the physical parameters that control the appropriate utilization of MOs in DHM is presented. A regular DHM system is theoretically modeled on the basis of the imaging theory. The Fourier spectrum of the recorded hologram is analyzed to evaluate the performance of the DHM. A set of the criteria that consider the microscope features and the recording parameters to achieve DHM operation at the diffraction limit is derived. Numerical modeling and experimental results are shown to validate our findings.

Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy.

The advantages of using a telecentric imaging system in digital holographic microscopy (DHM) to study biological specimens are highlighted. To this end, the performances of nontelecentric DHM and telecentric DHM are evaluated from the quantitative phase imaging (QPI) point of view. The evaluated stability of the microscope allows single-shot QPI in DHM by using telecentric imaging systems. Quantitative phase maps of a section of the head of the drosophila melanogaster fly and of red blood cells are obtained via single-shot DHM with no numerical postprocessing. With these maps we show that the use of telecentric DHM provides larger field of view for a given magnification and permits more accurate QPI measurements with less number of computational operations.

Enhancing spatial resolution in digital holographic microscopy by biprism structured illumination.

A novel and efficient architecture of a structured-illumination digital holographic microscope (DHM) is presented. As the DHM operates at the diffraction limit, its spatial resolution on label-free imaging of transparent samples is improved by illuminating the sample with a structured illumination produced by a Fresnel's biprism. The theoretical analysis of the method forecasts a twofold improvement of the spatial resolution. The proposed method requires only two images to improve the spatial resolution, which eases the process of unmixing the high-resolution components by means of an unknown phase-shift procedure. Numerical modeling and experimental results validate the theoretical findings.

Aberration compensation for objective phase curvature in phase holographic microscopy: comment.

In a recent Letter by Seo et al. [Opt. Lett.37, 4976 (2012)], the numerical correction of the quadratic phase distortion introduced by the microscope objective in digital holographic microscopy (DHM) has been presented. In this comment, we would like to draw to the attention of the authors and the readers in general that this approach could not be the optimal solution for maintaining the accuracy of the quantitative phase via DHM. We recall that the use of telecentric imaging systems in DHM simplifies the numerical processing of the phase images and produces more accurate measurements.

Shift-variant digital holographic microscopy: inaccuracies in quantitative phase imaging.

Inaccuracies introduced in quantitative phase digital holographic microscopy by the use of nontelecentric imaging systems are analyzed. Computer modeling of the experimental result shows that even negligible errors in the radius and center of curvature of the numerical compensation needed to get rid of the remaining quadratic phase factor introduce errors in the phase measurements; these errors depend on the position of the object in the field-of-view. However, when a telecentric imaging system is utilized for the recording of the holograms, the numerical modeling and experimental results show the shift-invariant behavior of the quantitative-phase digital holographic microscope.

Axial resonance of periodic patterns by using a Fresnel biprism.

This paper proposes a method for the generation of high-contrast localized sinusoidal fringes with spatially noncoherent illumination and relatively high light throughput. The method, somehow similar to the classical Lau effect, is based on the use of a Fresnel biprism. It has some advantages over previous methods for the noncoherent production of interference fringes. One is the flexibility of the method, which allows the control of the fringe period by means of a simple axial shift of the biprism. Second is the rapid axial fall-off in visibility around the high-contrast fringe planes. And third is the possibility of creating fringes with increasing or with constant period as the light beam propagates. Experimental verifications of the theoretical statements are also provided.

Multispectral integral imaging acquisition and processing using a monochrome camera and a liquid crystal tunable filter.

This paper presents an acquisition system and a procedure to capture 3D scenes in different spectral bands. The acquisition system is formed by a monochrome camera, and a Liquid Crystal Tunable Filter (LCTF) that allows to acquire images at different spectral bands in the [480, 680]nm wavelength interval. The Synthetic Aperture Integral Imaging acquisition technique is used to obtain the elemental images for each wavelength. These elemental images are used to computationally obtain the reconstruction planes of the 3D scene at different depth planes. The 3D profile of the acquired scene is also obtained using a minimization of the variance of the contribution of the elemental images at each image pixel. Experimental results show the viability to recover the 3D multispectral information of the scene. Integration of 3D and multispectral information could have important benefits in different areas, including skin cancer detection, remote sensing and pattern recognition, among others.

Subtractive imaging in confocal scanning microscopy using a CCD camera as a detector.

We report a scheme for the detector system of confocal microscopes in which the pinhole and a large-area detector are substituted by a CCD camera. The numerical integration of the intensities acquired by the active pixels emulates the signal passing through the pinhole. We demonstrate the imaging capability and the optical sectioning of the system. Subtractive-imaging confocal microscopy can be implemented in a simple manner, providing superresolution and improving optical sectioning.

Digital holographic microscopy with pure-optical spherical phase compensation.

Telecentric architecture is proposed for circumventing, by the pure-optical method, the residual parabolic phase distortion inherent to standard configuration of digital holographic microscopy. This optical circumvention produces several important advantages. One is that there is no need for computer compensation of the parabolic phase during the phase map recovering procedure. The other is that in off-axis configuration, the spatial frequency useful domain is enlarged. The validity of the method is demonstrated by performing quantitative measurement of depth differences with high axial resolution.