Tailoring the axial shape of the point spread function using the Toraldo concept

Bifocal flat lens with different imaging characteristics for a dual-sensor imaging system

Wide field of view (FOV) images and magnified images can be taken simultaneously by dual-sensor imaging systems. Here, we propose an approach for creating a bifocal flat lens with different imaging characteristics of its two foci, which makes dual-sensor imaging systems more integrated and miniaturized. That is, two special parts of two different conventional ZP are extracted and then combine the two elements in a specific way. So that there are two foci with different characteristics along the optical axis, one is long focus with higher resolution, the other is short focus with long depth of focus (DOF). Under the proposed approach, a thin and light bifocal diffractive lens (BDL) with thickness of 0.6 μm is developed. The long and short focal lengths of the BDL are ~ 81 mm and ~ 27 mm, respectively, with a diameter of 6 mm. We experimentally demonstrate that the long focus of the BDL is capable of taking high-resolution magnified images, and its resolution is up to 21.90″. The short focus is able to take wide FOV with long DOF images, and two objects spread 2880 mm apart can be imaged clearly. The experiment results demonstrate that all of these metrics are better than those of a conventional refractive lens.

Recent progress in digital holography with dynamic diffractive phase apertures [Invited]

Digital holography with diffractive phase apertures is a hologram recording technique in which at least one of the interfering waves is modulated by a phase mask. In this review, we survey several main milestones on digital holography with dynamic diffractive phase apertures. We begin with Fresnel incoherent correlation holography (FINCH), a hologram recorder with an aperture of a diffractive lens. FINCH has been used for many applications such as 3D imaging, fluorescence microscopy, superresolution, image processing, and imaging with sectioning ability. FINCH has played an important role by inspiring other digital holography systems based on diffractive phase aperture, such as Fourier incoherent single-channel holography and coded aperture correlation holography, which also are described in this review.

Reflective Toraldo pupil for high-resolution millimeter-wave astronomy

A novel, to the best of our knowledge, beam-shaping reflective surface for high-resolution millimeter/submillimeter-wave astronomy instruments is presented. The reflector design is based on Toraldo's super-resolution principle and implemented with annulated binary-phase coronae structure inspired by the achromatic magnetic mirror approach. A thin, less than half a free-space wavelength, reflective Toraldo pupil device operated in the W-band has been fabricated using mesh-filter technology developed at Cardiff University. The device has been characterized on a quasi-optical test bench and demonstrated expected reduction of the beam width upon reflection at oblique incidence, while featuring a sidelobe level lower than -10dB. The proposed reflective Toraldo pupil structure can be easily scaled for upper millimeter and infrared frequency bands as well as designed to transform a Gaussian beam into a flat-top beam with extremely low sidelobe level.

Uncertainty principle for axial power content of highly focused fields

In the analysis of the on-axis intensity for a highly focused optical field, it is highly desirable to deal with effective relations aimed at characterizing the field behavior in a rather simple fashion. Here, a novel and adequate measure for the size of the region where the axial power content mainly concentrates is proposed on the basis of an uncertainty principle. Accordingly, a meaningful relationship is provided for both the spread of the incident beam at the entrance of the highly focused optical system and the size of the region where the on-axis power mainly concentrates.

Spectral image scanning microscopy

For decades, the confocal microscope has represented one of the dominant imaging systems in biomedical imaging at sub-cellular lengthscales. Recently, however, it has increasingly been replaced by a related, but more powerful successor technique termed image scanning microscopy (ISM). In this article, we present ISM capable of measuring spectroscopic information such as that contained in fluorescence or Raman images. Compared to established confocal spectroscopic imaging systems, our implementation offers similar spectral resolution, but higher spatial resolution and detection efficiency. Color sensitivity is achieved by a grating placed in the detection path in conjunction with a camera collecting both spatial and spectral information. The multidimensional data is processed using multi-view maximum likelihood image reconstruction. Our findings are supported by numerical simulations and experiments on micro beads and double-stained HeLa cells.

Design of discrete and continuous super-resolving Toraldo pupils in the microwave range

The concept of super-resolution refers to various methods for improving the angular resolution of an optical imaging system beyond the classical diffraction limit. In optical microscopy, several techniques have been successfully developed with the aim of narrowing the central lobe of the illumination point spread function. In astronomy, however, no similar techniques can be used. A feasible method to design antennas and telescopes with angular resolution better than the diffraction limit consists of using variable transmittance pupils. In particular, discrete binary phase masks (0 or π) with finite phase-jump positions, known as Toraldo pupils (TPs), have the advantage of being easy to fabricate but offer relatively little flexibility in terms of achieving specific trade-offs between design parameters, such as the angular width of the main lobe and the intensity of sidelobes. In this paper, we show that a complex transmittance filter (equivalent to a continuous TP, i.e., consisting of infinitely narrow concentric rings) can achieve more easily the desired trade-off between design parameters. We also show how the super-resolution effect can be generated with both amplitude- and phase-only masks and confirm the expected performance with electromagnetic numerical simulations in the microwave range.

Point-spread function manipulation of the swept-source optical coherence tomography through temporal phase modulation

Recent breakthroughs in microscopy have surpassed Abbe's spatial diffraction limit, especially in the regime of fluorescence imaging. Microcopy's depth-imaging relative tomography is, however, still confined to basic imaging quality, which is limited by the Fourier bandwidth. In this paper, we explore the analogy between spatial microscopy and temporal tomography based on the space-time duality, and hence enlighten the advancement of tomography. As a proof-of-principle demonstration, an all-optical manipulation of the point-spread function (PSF) of a swept-source optical coherence tomography (OCT) is performed based on temporal phase modulation. Although the axial resolving power remains the same, much sharper sketch lines can be obtained from the specimen. In addition, the imaging quality is also improved with suppressed ghost fringes and better sensitivity.

Pareto optimality between width of central lobe and peak sidelobe intensity in the far-field pattern of lossless phase-only filters for enhancement of transverse resolution

Resolution capability of an optical imaging system can be enhanced by reducing the width of the central lobe of the point spread function. Attempts to achieve the same by pupil plane filtering give rise to a concomitant increase in sidelobe intensity. The mutual exclusivity between these two objectives may be considered as a multiobjective optimization problem that does not have a unique solution; rather, a class of trade-off solutions called Pareto optimal solutions may be generated. Pareto fronts in the synthesis of lossless phase-only pupil plane filters to achieve superresolution with prespecified lower limits for the Strehl ratio are explored by using the particle swarm optimization technique.

Spatial filtering nearly eliminates the side-lobes in single- and multi-photon 4pi-type-C super-resolution fluorescence microscopy

Super-resolution microscopy has tremendously progressed our understanding of cellular biophysics and biochemistry. Specifically, 4pi fluorescence microscopy technique stands out because of its axial super-resolution capability. All types of 4pi-microscopy techniques work well in conjugation with deconvolution techniques to get rid of artifacts due to side-lobes. In this regard, we propose a technique based on spatial filter in a 4pi-type-C confocal setup to get rid of these artifacts. Using a special spatial filter, we have reduced the depth-of-focus. Interference of two similar depth-of-focus beams in a 4π geometry result in substantial reduction of side-lobes. Studies show a reduction of side-lobes by 46% and 76% for single and two photon variant compared to 4pi - type - C confocal system. This is incredible considering the resolving capability of the existing 4pi - type - C confocal microscopy. Moreover, the main lobe is found to be 150 nm for the proposed spatial filtering technique as compared to 690 nm of the state-of-art confocal system. Reconstruction of experimentally obtained 2PE - 4pi data of green fluorescent protein (GFP)-tagged mitocondrial network shows near elimination of artifacts arising out of side-lobes. Proposed technique may find interesting application in fluorescence microscopy, nano-lithography, and cell biology.

Optical super-resolution by subtraction of time-gated images

Applying image subtraction strategy together with time-gated detection, we can reveal finer details in a fixed cell sample using moderate light intensities. The subtractive imaging is obtained from the subtraction of a suitably weighted short lifetime intensity-image from a long lifetime one, while the weight coefficient can be selected using the analysis of an optical transfer function. Compared with other subtractive methods, ours is regarded as an optimized variation of gated stimulated emission depletion microscopy and can be implemented in a simpler manner, providing lateral super-resolution, and it is theoretically possible to further expand its application scope.

Toraldo filters with concentric unequal annuli of fixed phase by evolutionary programming

The resolving power of an optical imaging system is limited by residual aberrations and diffraction effects. The Rayleigh-Abbe diffraction limit of resolution corresponds to radius of the central lobe of the point spread function of an aberration free diffraction limited system. An attempt to circumvent this limitation was proposed by Toraldo di Francia, who showed that suitable pupil plane filtering can overcome this resolution limit, albeit over a restricted field. This paper reports results of our investigations on the use of evolutionary programming to obtain globally or quasi-globally optimum solutions in synthesis of lossless Toraldo filters consisting of concentric unequal area zones of fixed phase.

Isotropic single-objective microscopy: theory and experiment

Isotropic single-objective (ISO) microscopy is a recently proposed imaging technique that can theoretically exhibit the same axial and transverse resolutions as 4Pi microscopy while using a classical single-objective confocal microscope. This achievement is obtained by placing the sample on a mirror and shaping the illumination beam so that the interference of the incident and mirror-reflected fields yields a quasi-spherical spot. In this work, we model the image formation in the ISO fluorescence microscope and simulate its point spread function. Then, we describe the experimental implementation and discuss its practical difficulties.

Properties of a laser cavity containing an absorbing ring

This paper considers the transverse optical properties of an absorbing ring when it is lighted by a symmetrical Laguerre-Gauss beam TEM(p0). It is demonstrated that the insertion of an opaque ring having adequate size inside a diaphragmed laser cavity is able to improve greatly (rate of about 100%) the discrimination between the TEM(00) and the TEM(10) modes, while keeping the diffraction losses unchanged or even decreased.

Diffractive superresolution elements for radially polarized light

An optimization method for diffractive superresolution elements (DSEs) for radially polarized light is proposed. Only the longitudinal component of the focused field of radially polarized light is considered for optimization, and the results are 0, pi two-phase distributed DSEs. A series of such DSEs are designed, and the corresponding superresolution performances are calculated with both longitudinal and transverse components of the focused field of radially polarized light. Simulation results show that good superresolution performance can be obtained by the optimization method considering only the longitudinal component of the focused field of radially polarized light. Simulation results also show that such DSEs realize better superresolution performance with radially polarized light than with linearly polarized light.

Particle-swarm optimization of axially superresolving binary-phase diffractive optical elements

A particle-swarm optimization (PSO) algorithm was developed for designing binary-phase-only diffractive optical elements (DOEs) that superresolve the axially focused point-spread function. The method is based on vector diffraction theory to ensure solutions are valid under high-NA conditions. A DOE is identified that superresolves the focal spot by 34% and maintains the sidelobes below 50% of the peak intensity. The algorithm was used to obtain the Pareto front of the fitness-value space, which describes the achievable superresolution versus an allowed upper bound in sidelobe intensity. The results suggest that the algorithm yields solutions that are global in terms of the co-optimized fitness values G and M.

Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms

We present what we believe to be a new application of scanning holographic microscopy to superresolution. Spatial resolution exceeding the Rayleigh limit of the objective is obtained by digital coherent addition of the reconstructions of several off-axis Fresnel holograms. Superresolution by holographic superposition and synthetic aperture has a long history, which is briefly reviewed. The method is demonstrated experimentally by combining three off-axis holograms of fluorescent beads showing a transverse resolution gain of nearly a factor of 2.

Measurement of the spatial response of a detector pixel

In order to measure the internal spatial response of a pixel in a detector, it is scanned by a beam smaller than its size. This becomes difficult as the wave length grows and becomes comparable to the pixel size, such as in the infra red. To overcome this difficulty, a special phase mask which makes the beam narrower was designed, constructed, and tested successfully. The mask was made from five alternating transparent rings, where the rings had half a wave phase difference between them. The beam was scanned with and without the mask in two dimensions in fine steps by a much smaller detector and its response was taken. The spot width dropped by 19% at half its height and by 42% at tenth its height, a significant narrowing. The scan was repeated with the full detector pixel. That beam scan served as a deconvolution kernel and allowed us to find the pixel point spread function (spatial response), the pixel modulation transfer function and the optical cross talk between the pixels.

Reduction of the spherical aberration effect in high-numerical-aperture optical scanning instruments

In modern high-numerical-aperture (NA) optical scanning instruments, such as scanning microscopes, optical data storage systems, or laser trapping technology, the beam emerging from the high-NA objective focuses deeply through an interface between two media of different refractive index. Such a refractive index mismatch introduces an important amount of spherical aberration, which increases dynamically when scanning at increasing depths. This effect strongly degrades the instrument performance. Although in the past few years many different techniques have been reported to reduce the spherical aberration effect, no optimum solution has been found. Here we concentrate on a technique whose main feature is its simplicity. We refer to the use of purely absorbing beam-shaping elements, which with a minimum modification of optical architecture will allow a significant reduction of the spherical aberration effect. Specifically, we will show that an adequately designed reversed-Gaussian aperture permits the production of a focal spot whose form changes very slowly with the spherical aberration.

Walsh filters for tailoring of resolution in microscopic imaging

Walsh functions form a complete set of normal orthogonal functions that take on values either +1 or -1 over a prespecified domain. Corresponding filters can be synthesized as phase filters that take on values either 0 or pi phase. This paper presents different types of Walsh functions in one and two dimensions to demonstrate that a large class of pupil filters can be synthesized from them to cater to the various needs of diffraction pattern for tailoring transverse and/or axial resolution in microscopic applications. Illustrative numerical results are presented.

Design and experimental test of diffractive superresolution elements

By using previously established methods based on linear programming (MLP), we design and fabricate two types of diffractive superresolution element (DSE). The structure parameters and superresolution performances of the fabricated DSEs are tested. The test results agree well with the design results and are applicable to a writable or a read-only optical disk. Thus the application validity of the MLP is experimentally verified.

Quasi-spherical focal spot in two-photon scanning microscopy by three-ring apodization

We present a beam-shaping technique for two-photon excitation (TPE) fluorescence microscopy. We show that by inserting a properly designed three-ring pupil filter in the illumination beam of the microscope, the effective optical sectioning capacity of such a system improves so that the point spread function gets a quasi-spherical shape. Such an improvement, which allows the acquisition of 3D images with isotropic quality, is obtained at the expense of only a small increase of the overall energy in the axial sidelobes. The performance of this technique is illustrated with a scanning TPE microscopy experiment in which the image of small beads is obtained. We demonstrate an effective narrowing of 12.5% in the axial extent of the point spread function, while keeping the 82% of the spot-fluorescence efficiency.

Sidelobe decline in single-photon 4Pi microscopy by Toraldo rings

We demonstrate theoretically the feasibility of single-photon 4Pi-confocal microscopy. By inserting a pair of properly designed multi-ring phase-only pupil filters in the illumination path of a 4Pi microscope the height of the sidelobes of the point spread function substantially reduced, so that there is no ambiguity in the 3D image. Then, an axial resolution up to four times higher than that of single-photon confocal microscope can be effectively achieved.

Optical sectioning by two-pinhole confocal fluorescence microscopy

A two-pinhole axially superresolving confocal fluorescence imaging system is presented. Based on the concept of subtractive incoherent imaging, the system described here is equipped with a zero-focus complex-transmittance pupil filter in one of the collector paths. The optical sectioning capacity of the system is 25% superior to that of a free-pupil one-pinhole instrument.

Resolution enhancement by subtraction of confocal signals taken at different pinhole sizes

Subtractive imaging in confocal fluorescence light microscopy is based on the subtraction of a suitably weighted widefield image from a confocal image. An approximation to a widefield image can be obtained by detection with an opened confocal pinhole. The subtraction of images enhances the resolution in-plane as well as along the optic axis. Due to the linearity of the approach, the effect of subtractive imaging in Fourier-space corresponds to a reduction of low spatial frequency contributions leading to a relative enhancement of the high frequencies. Along the direction of the optic axis this also results in an improved sectioning. Image processing can achieve a similar effect. However, a 3D volume dataset must be acquired and processed, yielding a result essentially identical to subtractive imaging but superior in signal-to-noise ratio. The latter can be increased further with the technique of weighted averaging in Fourier-space. A comparison of 2D and 3D experimental data analysed with subtractive imaging, the equivalent Fourier-space processing of the confocal data only, and Fourier-space weighted averaging is presented.

Design of three-dimensional superresolution filters and limits of axial optical superresolution

Theories to design a three-dimensional superresolution filter (TDSF) for confocal microscopy are proposed that can obtain a globally optimal solution through linear programming. The designed TDSF is proved to be a phase-only element introducing a phase delay of 0 or pi. Five design examples of the TDSF are presented to demonstrate the validity of these theories, Regardless of transverse superresolution, a curve of Seu(Ga+/-) defined as the maximum value of Strehl ratio S under the axial resolving power of Ga+/- is calculated to set the fundamental limits of axial optical superresolution. Finally, what is to our knowledge a novel analytic expression of Seu(Ga+/-) is deduced.