Back Focal Plane Research Articles

Investigating Polarisation Effects in a Confocal Total Internal Reflection-Supercritical Angle Fluorescence (TIR-SAF) Geometry with Sample Scanning

Total internal reflection microscopy is a technique ideal for imaging the cell membrane, as it allows for selective excitation of fluorophores at or near the coverglass. When a beam enters a high NA objective off-axis, it produces an evanescent field, the penetration depth of which is dependent on the refractive index difference between the glass substrate and sample. A pitfall of this method is that sample refractive index varies across a cell surface and organelles, causing unwanted light refraction and scattering. By introducing a Bertrand lens into the detection optics, the critical angle on the back focal plane can be imaged, which allows to calculate the sample refractive angle, and emission from near-membrane and deeper fluorophores can be separated, too. Here, we use a scanning TIR-SAF system to measure the local cellular refractive index across the cell's “footprint” region. The excitation path contains a radial polarizer, and two axicon lenses to form evanescent Bessel beam illumination, allowing for an excitation “needle”. Tightly focused radially and azimuthally polarized Bessel beams are desirable as they allow for a smaller excitation spot size. However, neither effects of azimuthally nor radially polarized excitation on evanescent field formation have been characterized. We built and characterized a confocal TIR-SAF system, and the effects of polarization were assessed.

Rapid determination of fluorescent molecular orientation in leakage radiation microscopy

We demonstrate an efficient and convenient method to recognize the orientation of fluorescent molecules through back focus imaging technology in leakage radiation microscopy. In the common structure of this microscope, the resonant energy transfer from a fluorescent emitter will be modulated and coupled into various waveguide modes. The specific intensity and angular distribution of all modes can be obtained clearly from the back focal plane. This energy transfer is strongly distance-dependent and the axial distribution information can be uniquely determined through the intensity ratio of transverse electric modes. When using the intensity ratio between transverse magnetic modes simultaneity, we find that the three-dimensional spatial orientations of the fluorescent molecules can be obtained directly.

Spatially resolved light field analysis of the second-harmonic signal of χ(2)-materials in the tight focusing regime

In this work, the second-harmonic (SH) signal generated by nonlinear optical crystals is studied in the tightly focused regime. The experimental approach is based on an adapted focal imaging technique, which allows the mapping of the SH intensity distribution in the back focal plane via a traversable pinhole in the confocal operation mode. On the theoretical side, a vectorial treatment of the involved optical fields enables the description and interpretation of the occurring interactions by taking into account the applied experimental parameters. The theoretical results are exemplarily validated by comparison to the acquired experimental data gained by the examination of LiNbO3 and KTiOPO4. It is shown how the phase and amplitude of vector components of the incoming electromagnetic field in the focus as well as the local optical properties of the nonlinear optical crystals determine the characteristic nonlinear signals in the back focal plane.

Direct and Practical Identification for Back Focal Plane Based Surface Plasmon Microscopy

We propose a practical approach to identify plasmonic absorption profile on back focal plane (BFP) of surface plasmon microscopy (SPM). Compared to previous morphology approaches, the proposed one features: i) it is applicable in BFP images with non-concentricity; ii) the algorithm of Fourier Correlation Analysis (FCA) maximizes SPP while minimizes random coherent noises, which makes it extremely suited for BFP images with significant low-quality; (iii) it takes much less time for one identification process and the entire identification can be operated automatically.

Photodynamics and quantum efficiency of germanium vacancy color centers in diamond

Color centers in diamond—especially group IV defects—have been advanced as a viable solid-state platform for quantum photonics and information technologies. We investigate the photodynamics and characteristics of germanium-vacancy (GeV) centers hosted in high-pressure high-temperature diamond nanocrystals. Through back-focal plane imaging, we analyze the far-field radiation pattern of the investigated emitters and derive a crossed-dipole emission, which is strongly aligned along one axis. We use this information in combination with lifetime measurements to extract the decay rate statistics of the GeV emitters and determine their quantum efficiency, which we estimated to be ∼ ( 22 ± 2 ) % . Our results offer further insight into the photodynamic properties of the GeV center in nanodiamonds and confirm its suitability as a desirable system for quantum technologies.

Fourier ptychography via wavefront modulation with a diffuser

Aperture-scanning Fourier ptychography is a configuration of Fourier ptychgraphy by scanning an aperture at the back focal plane of the objective lens. It has been a useful tool for measuring the complex scattering field exited from a sample. However, in this method the intensity of dark images at the charge coupled device (CCD) plane is of same order or even lower than the noise when the high frequency of the Fourier spectrum is filtered by the aperture. Therefore, the recorded dark field images suffer from low signal-to-noise ratio (SNR), which results in poor reconstruction. In this paper, we report a modified Fourier ptychographic imaging method by wavefront modulation. Instead of an aperture, a diffuser is used to modulate the spectrum in the presented method. The complex distribution of the sample and the diffuser are reconstructed simultaneously via iterative phase retrieval. Numerical simulations and proof-of-concept experiments have been carried out to demonstrate the feasibility of the presented method.

Effect of Catadioptric Component Postposition on Lens Focal Length and Imaging Surface in a Mirror Binocular System.

The binocular vision system is widely used in three-dimensional measurement, drone navigation, and many other fields. However, due to the high cost, large volume, and inconvenient operation of the two-camera system, it is difficult to meet the weight and load requirements of the UAV system. Therefore, the study of mirror binocular with single camera was carried out. Existing mirror binocular systems place the catadioptric components in front of the lens, which makes the volume of measurement system still large. In this paper, a catadioptric postposition system is designed, which places the prism behind the lens to achieve mirror binocular imaging. The influence of the post prism on the focal length and imaging surface of the optical system is analyzed. The feasibility of post-mirror binocular imaging are verified by experiments, and it is reasonable to compensate the focal length change by changing the back focal plane position. This research laid the foundation for the subsequent research on the 3D reconstruction of the novel mirror binocular system.

Structured Back Focal Plane Interferometry (SBFPI)

Back focal plane interferometry (BFPI) is one of the most straightforward and powerful methods for achieving sub-nanometer particle tracking precision at high speed (MHz). BFPI faces technical challenges that prohibit tunable expansion of linear detection range with minimal loss to sensitivity, while maintaining robustness against optical aberrations. In this paper, we devise a tunable BFPI combining a structured beam (conical wavefront) and structured detection (annular quadrant photodiode). This technique, which we termed Structured Back Focal Plane Interferometry (SBFPI), possesses three key novelties namely: extended tracking range, low loss in sensitivity, and resilience to spatial aberrations. Most importantly, the conical wavefront beam preserves the axial Gouy phase shift and lateral beam waist that can then be harnessed in a conventional BFPI system. Through a series of experimental results, we were able to tune detection sensitivity and detection range over the SBFPI parameter space. We also identified a figure of merit based on the experimental optimum that allows us to identify optimal SBPFI configurations that balance both range and sensitivity. In addition, we also studied the resilience of SBFPI against asymmetric spatial aberrations (astigmatism of up to 0.8 λ) along the lateral directions. The simplicity and elegance of SBFPI will accelerate its dissemination to many associated fields in optical detection, interferometry and force spectroscopy.

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures.

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by local enhancement of electric field intensity that strengthens light-matter interactions, enabling applications such as surface-enhanced Raman scattering (SERS) and surface plasmon enhanced sensing. In the presence of magneto-optically active materials, the local field enhancement gives rise to anomalous magneto-optical activity. Typically, the confined modes of a given photonic crystal depend strongly on the wavelength and incidence angle of the incident electromagnetic radiation. Thus, spectral and angular-resolved measurements are needed to fully identify them as well as to establish their relationship with the magneto-optical activity of the crystal. In this article, we describe how to use a Fourier-plane (back focal plane) microscope to characterize magneto-optically active samples. As a model system, here we use a plasmonic grating built out of magneto-optically active Au/Co/Au multilayer. In the experiments, we apply a magnetic field on the grating in situ and measure its reciprocal space response, obtaining the magneto-optical response of the grating over a range of wavelengths and incident angles. This information enables us to build a complete map of the plasmonic band structure of the grating and the angle and wavelength dependent magneto-optical activity. These two images allow us to pinpoint the effect that the plasmon resonances have on the magneto-optical response of the grating. The relatively small magnitude of magneto-optical effects requires a careful treatment of the acquired optical signals. To this end, an image processing protocol for obtaining magneto-optical response from the acquired raw data is laid out.

Light-sheet engineering using the Field Synthesis theorem

Recent advances in light-sheet microscopy have enabled sensitive imaging with high spatiotemporal resolution. However, the creation of thin light-sheets for high axial resolution is challenging, as the thickness of the sheet, field of view and confinement of the excitation need to be carefully balanced. Some of the thinnest light-sheets created so far have found little practical use as they excite too much out-of-focus fluorescence. In contrast, the most commonly used light-sheet for subcellular imaging, the square lattice, has excellent excitation confinement at the cost of lower axial resolving power. Here we leverage the recently discovered Field Synthesis theorem to create light-sheets where thickness and illumination confinement can be continuously tuned. Explicitly, we scan a line beam across a portion of an annulus mask on the back focal plane of the illumination objective, which we call C-light-sheets. We experimentally characterize these light-sheets and demonstrate their application on biological samples.

Elucidating optical field directed hierarchical self-assembly of homogenous versus heterogeneous nanoclusters with femtosecond optical tweezers.

Insights into the morphology of nanoclusters would facilitate the design of nano-devices with improved optical, electrical, and magnetic responses. We have utilized optical gradient forces for the directed self-assembly of colloidal clusters using high-repetition-rate femtosecond laser pulses to delineate their structure and dynamics. We have ratified our experiments with theoretical models derived from the Langevin equation and defined the valid ranges of applicability. Our femtosecond optical tweezer-based technique characterizes the in-situ formation of hierarchical self-assembled clusters of homomers as well as heteromers by analyzing the back focal plane displacement signal. This technique is able to efficiently distinguish between nano-particles in heterogeneous clusters and is in accordance with our theory. Herein, we report results from our technique, and also develop a model to describe the mechanism of such processes where corner frequency changes. We show how the corner frequency changes enables us to recognize the structure and dynamics of the coagulation of colloidal homogeneous and heterogeneous clusters in condensed media over a broad range of nanoparticle sizes. The methods described here are advantageous, as the backscatter position-sensitive detection probes the in-situ self-assembly process while other light scattering approaches are leveraged for the characterization of isolated clusters.

Stable stimulated emission depletion imaging of extended sample regions

Stimulated emission depletion (STED) nanoscopy has become one of the most used nanoscopy techniques over the last decade. However, most recordings are done in specimen regions no larger than 10–30 × 10–30 μm2 due to aberrations, instability and manual mechanical stages. Here, we demonstrate automated 2D and 3D STED nanoscopy of extended sample regions up to 0.5 × 0.5 mm2 by using a scanning system that maintains stationary beams in the back focal plane. The setup allows up to 80–100 × 80–100 μm2 field of view (FOV) with uniform spatial resolution, a mechanical stage allowing sequential tiling to record larger sample areas, and a feedback system keeping the sample in focus at all times. Taken together, this allows automated recording of theoretically unlimited-sized sample areas and volumes, without compromising the achievable spatial resolution and image quality.

OPTICAL METHOD FOR QUALITY CONTROL OF TRANSPARENT FABRICS

Background. The main element of optical information processing systems is a coherent optical spectrum analyzer (COSA). In the textile industry in the manufacture and use of thin transparent fabrics (gauze, bandages, etc.) there is a problem of controlling the shape and geometric dimensions of transparent cells. For this purpose, microscopes are used with the help of which the geometrical parameters of many transparent cells are measured. Such process is time consuming, requires a considerable amount of time for measurement. Using COSA allows you to directly measure the average cell size.Objective. The purpose of the paper is development of an optical model of a transparent fabric, on the basis of which a laser method and an experimental stand for measuring the average geometric dimensions of transparent fabrics cells are proposed.Methods. The proposed method of quality control of transparent fabrics is based on the use of COSA. If a transparent fabric is positioned in the front focal plane of a Fourier lens, then diffraction maximums are formed in the back focal plane, the position of which depends on the size of the transparent fabric cells.Results. The geometric model of the structure of a transparent fabric, which describes the amplitude transmittance coefficient of the fabric depending on the period and the size of the transparent fabrics cells, is proposed. An analytical formula is obtained for calculating the spatial spectrum of the transmittance of such a model. The COSA laboratory stand was developed, which allows measuring the geometric dimensions of transparent fabric cells.Conclusions. The research of the transmission model of transparent fabric showed that the fabric structure can be viewed as a two-dimensional diffraction grating, the period of which is determined by the thickness of the filament and the transparent part of the fabric cell. To measure the size of the cells of the transparent fabric, it is proposed to use the COSA, which allows you to directly measure the spatial frequencies of the diffraction peaks and calculate the average values of the fabric cell sizes. To validate the proposed method, an experimental stand of digital COSA has been developed.

Effect of partial coherence on dimensional measurement sensitivity for DUV scatterfield imaging microscopy.

Optical scatterfield imaging microscopy technique which has the capability of controlling scattered fields in the imaging mode is useful for quantitative nanoscale dimensional metrology that yields precise characterization of nanoscale features for semiconductor device manufacturing process control. To increase the sensitivity in the metrology using this method, it is required to optimize illumination and collection optics that enhance scatterfield signals from the nanoscale targets. Partial coherence of the optical imaging system is used not only for enhancing image quality in the traditional microscopy or lithography but also for increasing the sensitivity of the scatterfield imaging microscopy. This paper presents an empirical investigation of the effect of partial coherence on measurement sensitivity using a deep ultraviolet scatterfield imaging microscope platform that uses a 193 nm excimer laser as a source and a conjugate back focal plane as a unit for controlling partial coherence. Dimensional measurement sensitivity is assessed through analyzing scatterfield images measured at the edge area of periodic multiline structures with nominal linewidths ranging 44-80 nm on a Molybdenum Silicide (MoSi) photomask. Intensities scattered from the targets under the illuminations with various partial coherence factors and two orthogonal polarizations are assessed with respect to sensitivity coefficient. The optimization of partial coherence factor for the target dimension is discussed through the sensitivity coefficient maps.

Direct Observation of Gate-Tunable Dark Trions in Monolayer WSe2.

Spin-forbidden intravalley dark excitons in tungsten-based transition-metal dichalcogenides (TMDCs), because of their unique spin texture and long lifetime, have attracted intense research interest. Here, we show that we can control the dark exciton electrostatically by dressing it with one free electron or free hole, forming the dark trions. The existence of the dark trions is suggested by the unique magneto-photoluminescence spectroscopy pattern of the boron nitride (BN)-encapsulated monolayer WSe2 device at low temperature. The unambiguous evidence of the dark trions is further obtained by directly resolving the radiation pattern of the dark trions through back focal plane imaging. The dark trions possess a binding energy of ∼15 meV, and they inherit the long lifetime and large g-factor from the dark exciton. Interestingly, under the out-of-plane magnetic field, dressing the dark exciton with one free electron or hole results in distinctively different valley polarization of the emitted photon, as a result of the different intervalley scattering mechanism for the electron and hole. Finally, the lifetime of the positive dark trion can be further tuned from ∼50 ps to ∼215 ps by controlling the gate voltage. The gate-tunable dark trions usher in new opportunities for excitonic optoelectronics and valleytronics.

Identification of waveguide mode and surface plasmon resonance mode using Fourier cross-correlation analysis.

The light reflected into the back focal plane of a microscope objective allows one to gather a great deal of information about the resonant modes excited on a sample. These dips represent modes excited on the sample, which are related to both the material properties and the structure. Automatic identification of these resonances is a vital stage in developing automated machine-learning techniques for high-throughput sample characterization. In previous work, identification of a single isolated mode was demonstrated; here we show how multiple modes can be separately identified using an automated centering procedure in a process we call radial thresholding. Once the center was determined, the radial thresholding process was modified and combined with interpolation to locate the precise modal positions. We show that this method is capable of resolving very closely spaced modes and is sensitive to nanometric changes in sample dimensions. The processing time for the method is sufficiently fast to ensure that it is suited for rapid sample identification.

Avenue for apertometer using spectral plane and Fourier correlation analysis.

This Letter proposes a simple and practical approach for numerical aperture measurement of immersion objectives. The basic concept is to generate a reference on the spectral plane and then apply the Abbe sine condition to evaluate the numerical aperture. An extremely cheap, simple but effective and practical example is to locate a coverslip on the focal plane and then record the resulting back focal plane, on which the total internal reflection ring is applied as the reference. To achieve higher repeatability and impose fewer requirements on both the operation procedure and experiment conditions, we propose an algorithm mainly consisting of two-dimensional Fourier correlation analysis and grayscale statistics to automatically identify the radii of total internal reflection and clear aperture. The proposed approach is further applied in the measurement of an objective lens with adjustable pupils when surface plasmon is employed as reference. Experimental verification is provided.

Fresnel and Fraunhofer diffraction of (l,n)th-mode Laguerre–Gaussian laser beam by a fork-shaped grating

ABSTRACTWe study theoretically the problem of diffraction of a Laguerre-Gaussian (LG) laser beam with radial mode number n and azimuthal mode number l, by a fork-shaped grating (FG) with integer topological charge (TC) p. The diffracted wave field amplitude and intensity are calculated at any distance behind the FG and in the back focal plane of a convergent lens. The zeroth diffraction order is obtained as an (l,n)th-mode LG beam. The higher, mth diffraction order beam is described in the radial direction through a product of the Gauss-doughnut function of order by the finite sum of hypergeometric Kummer functions. It can be a vortex beam with increased or reduced TC compared to that of the incident beam, or it can be a non-vortex beam. The obtained results are specialized for two particular cases: when the incident LG beam is with zeroth radial mode number and azimuthal mode number l, and when the incident beam is with zeroth azimuthal mode number and radial mode number n. The presented research results can find interest in optical trapping experiments, fibre-optic multiplexing and quantum information processing.

A simple determination approach for zero-padding of FFT method in focal spot calculation

FFT is a widely utilized method to calculate focal spot, in which zero padding is needed to adjust the sampling interval on the focal plane. This work is to apply Abbe limit of resolution to determining of the number of padded zeros when sampling interval on focal plane is given. We specifically investigate the correlation of digitized Fraunhofer diffraction and discrete Fourier transform (DFT) in a lens model. The theoretical support for zero padding on the back focal plane (BFP) is illustrated based on a hypothesis of lens with finite numerical aperture. The proposed hypothesis and the zero padding approach are verified by focal spots calculation, where lights polarized linearly and radially are used as samples.

Three-dimensional subnanoscale imaging of unit cell doubling due to octahedral tilting and cation modulation in strained perovskite thin films

Determining the 3-dimensional crystallography of a material with sub-nanometre resolution is essential to understanding strain effects in epitaxial thin films. A new scanning transmission electron microscopy imaging technique is demonstrated that visualises the presence and strength of atomic movements leading to a period doubling of the unit cell along the beam direction, using the intensity in an extra Laue zone ring in the back focal plane recorded using a pixelated detector method. This method is used together with conventional atomic resolution imaging in the plane perpendicular to the beam direction to gain information about the 3D crystal structure in an epitaxial thin film of LaFeO3 sandwiched between a substrate of (111) SrTiO3 and a top layer of La0.7Sr0.3MnO3. It is found that a hitherto unreported structure of LaFeO3 is formed under the unusual combination of compressive strain and (111) growth, which is triclinic with a periodicity doubling from primitive perovskite along one of the three <110> directions lying in the growth plane. This results from a combination of La-site modulation along the beam direction, and modulation of oxygen positions resulting from octahedral tilting. This transition to the period-doubled cell is suppressed near both the substrate and near the La0.7Sr0.3MnO3 top layer due to the clamping of the octahedral tilting by the absence of tilting in the substrate and due to an incompatible tilt pattern being present in the La0.7Sr0.3MnO3 layer. This work shows a rapid and easy way of scanning for such transitions in thin films or other systems where disorder-order transitions or domain structures may be present and does not require the use of atomic resolution imaging, and could be done on any scanning TEM instrument equipped with a suitable camera.