Fourier Plane Research Articles

Dark-field super-oscillatory microscopy with high-pass super-oscillatory filters

Super-resolution imaging of transparent objects is particularly challenging due to the interference caused by background light. This interference can significantly degrade image quality by reducing contrast and obscuring fine details. In this work, high-pass super-oscillatory masks are designed to address this issue by filtering out the background light on the Fourier plane. The resolution of the corresponding super-oscillatory point-spread function is 0.66 times the diffraction limit, enabling the resolution of transparent objects with 67% transparency at sub-wavelength scales. Additionally, the high-pass super-oscillatory masks are designed for a 1080 × 1920 liquid-crystal spatial light modulator, making future experimental implementation straightforward. This facilitates easy switching between bright-field and dark-field super-oscillatory microscopy, broadening the range of application scenarios for the system.

Calibration approach of non-modulated pyramid wavefront sensors for improving the dynamic range

The pyramid wavefront sensor (PWFS) can provide high sensitivity in demanding adaptive optics applications. However, its exquisite sensitivity has a limited dynamic range, which relies on the use of beam modulation to improve the dynamic range of the PWFS—despite this task being achieved by moving optical components in the PWFS, increasing the complexity of the system. An attractive idea to simplify the optical and mechanical design of a PWFS is to work without any dynamic modulation. This paper proposes a new method, to the best of our knowledge, called the pyramid wavefront sensor with truncated axicon (TA-PWFS), which is used in the non-modulated PWFS in the closed-loop adaptive optics system with high sensitivity and high dynamic range without the need for cumbersome modulation. The new approach uses a diffractive element placed at a conjugated Fourier plane of the pyramid prism to shape part of the incident light in a ring pattern around the pyramid pin. The radius of the circular-shaped image is identical to that of the modulation radius in the sinusoidal modulation, offering a high dynamic range, while the remaining portion of the light continues un-diffracted, producing high sensitivity through a spot on the pyramid pin. Simulation results with different kinds of aberrations containing large global tilts reveal that the use of the TA-PWFS has a noticeable improvement in the aberration estimation performance. With a highly simplified structure, elements without mechanical modulation, and aberration reconstruction without precorrection of global tilt, the TA-PWFS could present an innovative method for the design of non-modulated pyramid wavefront sensors that can better suit the higher requirements of adaptive optics applications.

Multifunctional multifocal lens for simultaneous edge and polarisation imaging

ABSTRACT The method of inserting ultrathin devices in the Fourier plane of the 4F imaging system can achieve multifunctional imaging. However, such a method generally requires precise alignment in the system, which also makes the system more complex. Here, we present an imaging system that incorporates a multifocal Pancharatnam–Berry (PB) phase liquid crystal (LC) lens capable of achieving simultaneous edge and polarisation imaging. Without placing optical elements in the Fourier plane of the 4F system, the proposed imaging system replace a refracted lens in 4F system by multifocal LC lens, which integrates edge and polarisation imaging modes. The phase distribution of multifocal lens is obtained through manipulating the positions and polarisation states of four foci with holographic principles. Furthermore, the imaging system based on the proposed multifocal lens has been shown to be effective in simultaneously achieving polarisation and edge imaging with broadband characteristics. The proposed optical system effectively reduces the complexity of the imaging system, which is expected to be applied in the fields of biomedical imaging, optical interconnection and microscopic imaging.

Michelson Interferometric Methods for Full Optical Complex Convolution.

Optical real-time data processing is advancing fields like tensor algebra acceleration, cryptography, and digital holography. This technology offers advantages such as reduced complexity through optical fast Fourier transform and passive dot-product multiplication. In this study, the proposed Reconfigurable Complex Convolution Module (RCCM) is capable of independently modulating both phase and amplitude over two million pixels. This research is relevant for applications in optical computing, hardware acceleration, encryption, and machine learning, where precise signal modulation is crucial. We demonstrate simultaneous amplitude and phase modulation of an optical two-dimensional signal in a thin lens's Fourier plane. Utilizing two spatial light modulators (SLMs) in a Michelson interferometer placed in the focal plane of two Fourier lenses, our system enables full modulation in a 4F system's Fourier domain. This setup addresses challenges like SLMs' non-linear inter-pixel crosstalk and variable modulation efficiency. The integration of these technologies in the RCCM contributes to the advancement of optical computing and related fields.

Laser biospeckle method for a fast and reliable microbioassay

Recently, the direct toxicity assessment (DTA) approach or bioassay has attracted much attention, as it can comprehensively evaluate water toxicity without examining a specific/individual chemical component. Bioassays are used to investigate how organisms respond to pollutants compared to controls. In this technique, a microscopic observation is required to know the critical features such as alive/dead, and swimming ability of microorganisms. As the size of the microorganism becomes smaller, observation becomes more difficult due to the narrower focal depth of the imaging system. In our study, to overcome the difficulties, we propose, to our knowledge, a novel technique for the microbioassay utilizing a biospeckle in the diffraction field generated from its movement. We employed Paramecia caudatum sized around 200–300 µm. The sample cell containing Paramecia was illuminated with a laser light with a diameter 15 mm and wavelength 635 nm. The specular component of the transmitted light was filtered out using a spatial filter placed at the Fourier plane and the biospeckle patterns in the diffraction field were acquired using a CCD camera as a movie. It is obvious that the dynamic properties of the biospeckle precisely reflects the movement of the scattering particles or Paramecia. Paramecia were exposed to HCl solutions with pH7.1, control, to 3.7 where all were dead. The swimming abilities of the Paramecia were successfully evaluated based on the crosscorrelation function of the frames of biospeckle patterns. The advantage of the method is that, owing to the non-imaging system, an enormous number of Paramecia can be processed as a whole, and a statistically significant estimation of the swimming ability of Paramecia under the influence of environmental pollution can be derived immediately.

Transformer based deep learning hybrid architecture for phase unwrapping

A deep learning Hybrid architecture for phase unwrapping has been proposed. The hybrid architecture is based on integration of Convolutional Neural Networks (CNN) with Vision Transformer. The performance of Hybrid architecture/network in phase unwrapping is compared against CNN based standard UNET network. Structural Similarity Index (SSIM) and Root Mean Square Error (RMSE) have been used as performance metrics to assess the performance of these deep learning networks for phase unwrapping. To train and test the networks, dataset with high mean Entropy has been generated using Gaussian filtering of random noise in Fourier plane. The Hybrid architecture is tested on test dataset and is found to have superior performance metrics against the UNET network. Their performance is also tested in noisy environment with various noise levels and Hybrid architecture demonstrated better anti-noise capability than UNET network. Hybrid architecture was successfully validated in real world scenario using experimental data from custom built Digital Holographic Microscope. With the advent of newer architectures and hardware, Deep learning networks can further improve the performance in solving inverse problems.

Accurate optical dispersion identification for linear deformable mirror with spatial-spectral interferometry

In ultrashort laser pulse systems, optical dispersion can cause severe distortion of the spectral phase and thus significantly affect the pulse shape. To address this problem, this study places a linear deformable mirror (LDM) at the Fourier plane of a blazed grating for dispersion control, and reconstructs the spectral phase modulated by the LDM using single-shot spatial-spectral interferometry. An iterative algorithm and closed-loop optimization process are used to drive the LDM to generate orthogonal modes of Legendre polynomials with a signal-to-background ratio (SBR) of more than 10 dB. The identified LDM modes are then used as the basis for spectral phase modulation. It is shown that the group delay dispersion (GDD), third order dispersion (TOD), fourth order dispersion (FOD), and fifth order dispersion (5OD) can be accurately obtained by the linear combination of identified Legendre modes. In addition, the maximum phase error between the generated and target dispersions is less than 0.15 rad, while the error between the pulse widths produced by the generated dispersion and the target dispersion, respectively, is less than 3.5 %. Overall, the results confirm that the linear superposition of the generated Legendre modes enables the accurate dispersion modulation of ultrashort laser pulses.

Partially coherent Pearcey-Gauss source with hyperbolic sine correlation of the spatial spectrum.

By designing the intricate coherence structure, we are able to create a desired beam profile and trajectory. Our research focus lies on the Fourier plane, specifically emphasizing the coherence of spatial frequencies, and we find it can be seen as a constant system response. A theoretical framework is developed, and experimental studies are conducted to generate a light field of the spatial spectrum with a complex correlation using the pseudo-mode superposition method. We successfully produce partially coherent Pearcey-Gauss beams whose spatial spectrum is hyperbolic sine correlational. Interestingly, these beams maintain the distinctive propagation properties of the Pearcey pattern while exhibiting the remarkable ability to split the mainlobe into two separate lobes.

Optimal speckle size and signal processing for displacement measurements using a 4f optical setup

Fully developed laser speckle patterns are, due to their high contrast and statistical nature, well suited to measure strain and displacement via an appropriately designed measurement system. Laser speckle patterns are formed when a sufficiently coherent light source, such as a HeNe-laser, illuminates an optically rough surface. Therefore, methods based on laser speckle patterns can be applied to any surface scatterer with a minimum mean surface roughness of about a quarter of the laser’s wavelength. This includes also materials such as thin natural and technical fibres as well as foils, for which the presented measurement system, including the digital signal processing, was designed. In order to achieve the best possible resolution of a speckle-based measurement system, combined with a sufficiently small measurement uncertainty, all available design parameters must be optimised. One of these parameters is the speckle size, which is dependant on the properties of the imaging optics. In this paper a subjective laser speckle-based measurement system based on a so-called 4f-optical setup is presented. This setup allows the speckle size to be controlled in both axial and lateral dimensions separately, which is achieved with the help of an aperture in the Fourier plane of the optics. It is shown that the optimal speckle size for the presented measurement system, not only depends on the physical setup, but also on the signal processing applied. The signal processing routine estimates displacements of the speckle pattern, leading to an estimate for the strain. Additionally, it is demonstrated that the optimal speckle size can be lower than the commonly reported optimum between two and five pixel pitches, necessary to circumvent aliasing in the image data. While this is shown for a measurement setup using 4f-optics, the results are of general importance to speckle-based strain or displacement measurement systems and should thus be taken into account.

Возможность применения метода Гершберга-Папулиса в задаче реконструкции фазовой структуры по малоракурсным гильбертограммам

The possibility of processing small-view hilbertograms by the Gershberg-Papulis method to restore the refractive index of phase objects is discussed. The method consists in iterative transitions from estimating a function in the Fourier plane to estimating it in a coordinate space with an adjustment using a priori information. The spectrum of the function is determined on the entire frequency plane as an iterative process result Numerical simulation of the refractive index reconstruction for various test functions was performed using the Gershberg-Papulis method using Radon data known for four angles. Experimental studies on the Hilbert diagnostics example of reacting media (flames) in a high-speed shooting mode (up to 2000 frames per second) were performed using a four-angle tomographic complex implemented on the basis of an upgraded IAB-463M shadow device.

Wide-field mid-infrared hyperspectral imaging beyond video rate

Mid-infrared hyperspectral imaging has become an indispensable tool to spatially resolve chemical information in a wide variety of samples. However, acquiring three-dimensional data cubes is typically time-consuming due to the limited speed of raster scanning or wavelength tuning, which impedes real-time visualization with high spatial definition across broad spectral bands. Here, we devise and implement a high-speed, wide-field mid-infrared hyperspectral imaging system relying on broadband parametric upconversion of high-brightness supercontinuum illumination at the Fourier plane. The upconverted replica is spectrally decomposed by a rapid acousto-optic tunable filter, which records high-definition monochromatic images at a frame rate of 10 kHz based on a megapixel silicon camera. Consequently, the hyperspectral imager allows us to acquire 100 spectral bands over 2600-4085 cm−1 in 10 ms, corresponding to a refreshing rate of 100 Hz. Moreover, the angular dependence of phase matching in the image upconversion is leveraged to realize snapshot operation with spatial multiplexing for multiple spectral channels, which may further boost the spectral imaging rate. The high acquisition rate, wide-field operation, and broadband spectral coverage could open new possibilities for high-throughput characterization of transient processes in material and life sciences.

Microsphere photolithography with dynamic angular spectra control for metasurface fabrication.

Microsphere photolithography (MPL) is a promising technique for cost-effective fabrication of large-scale metasurfaces. This approach generates an array of photonic jets by the collimated illumination of self-assembled microspheres. The photonic jets can be precisely steered within the unit cell defined by each microsphere by changing the angle of incidence. This allows for the creation of complex metasurface element geometries. Computer controlled articulation of the substrate relative to a static UV source allows the direct-write of different metasurface elements. However, this is time-consuming and requires registration between each exposure for complex features. This paper investigates a single exposure method with the dynamic continuous angle of incidence control provided by a Digital Micromirror Device (DMD) in the front Fourier plane of the projection system. The grayscale values of the DMD pixels can be adjusted to provide optical proximity correction. Larger patterns can be achieved by scanning the substrate relative to the exposure beam. This approach is demonstrated with the creation of hierarchical patterns. This work greatly simplifies the MPL exposure process for complex resonators and provides potential for full light field control.

Light-field imaging from position-momentum correlations

Correlation plenoptic imaging (CPI) is a light-field imaging technique employing intensity correlation measurements to simultaneously detect the spatial distribution and the propagation direction of light. Compared to standard methods, in which light-field images are directly encoded in intensity, CPI provides a significant enhancement of the volumetric reconstruction performance in terms of both achievable depth of field and 3D resolution. In this article, we present a novel CPI configuration where light-field information is encoded in correlations between position and momentum measurements, namely, points on a given object plane and points of the Fourier plane of the imaging lens. Besides the fundamental interest in retrieving the properties of position-momentum correlation, the proposed scheme overcomes practical limitations of previously proposed setups, providing higher axial homogeneity and robustness with respect to the identification of reference planes.

Generation of Perfect Vortex Beams with Complete Control over the Ring Radius and Ring Width

We have experimentally created perfect vortex beams (PVBs) by Fourier transformation of Bessel–Gaussian vortex beams, which are generated by modulating the fundamental Gaussian beam with the spiral phase plates and the axicons, respectively. Although the method has been used many times by other authors, as far as we know, few people pay attention to the quantitative relationship between the control parameters of the PVB and ring width. The effects of the waist radius of the fundamental Gaussian beam wg, base angle of the axicon γ, and focal length of the lens f on the spot parameters (ring radius ρ, and ring half-width Δ) of PVB are systematically studied. The beam pattern of the generated Bessel–Gaussian beam for different propagation distances behind the axicon and the fundamental Gaussian beam wg is presented. We showed experimentally that the ring radius ρ increases linearly with the increase of the base angle γ and focal length f, while the ring half-width Δ decreases with the increase of the fundamental beam waist radius wg, and increases with enlarging the focal length f. We confirmed the topological charge (TC) of the PVB by the interferogram between the PVB and the reference fundamental Gaussian beam. We also studied experimentally that the size of the generated PVB in the Fourier plane is independent of the TCs. Our approach to generate the PVB has the advantages of high-power tolerance and high efficiency.

Optical vortex coronagraphy for high-contrast imaging of femtosecond laser filaments

A high-contrast imaging technique for phase objects based on the optical vortex coronagraph (OVC) is proposed. This method offers the unique advantage of background-free imaging due to the introduction of azimuthal phase in the Fourier plane. We employed the OVC method to detect femtosecond laser-induced air plasma and compared it with the classic diffractometry and fluorescent imaging methods. We achieved a phase sensitivity of ∼0.035 waves that surpassed the capabilities of the other two methods. The combination of this highly sensitive imaging technique with the pump–probe method holds promise for applications in ultrafast imaging of laser–material interactions.

Adjustable accuracy of phase steps in a double-aperture common-path interferometer by rotating and displacing grating at Fourier plane

Detuning errors limit the accuracy of phase extraction in phase-shifting interferometry (PSI). To improve this accuracy, the systems to control the phase shifter dispositive must be highly accurate, involving high technology, exhaustive calibration, high cost, and constant maintenance. This manuscript presents a method for improving the accuracy of the phase step generated at the Fourier plane by rotating and displacing the grating in a double-aperture common-path interferometer. It is demonstrated that both the detuning errors and the phase extraction uncertainty decrease with the grating rotation angle. The experimental implementation is very simple, as it does not require any sophisticated mechanical system to improve the accuracy, no exhaustive calibration, and no additional mechanical and optical dispositive. With the present approach, the PSI method could be achieved very simply and with high accuracy by using a low-accuracy actuator. The theoretical model and experimental results are presented to demonstrate the present proposal.

Diffraction-based nonlinear model for the design of broadband adiabatic up-conversion imaging.

In recent years, mid-infrared parametric upconversion imaging, a nonlinear optical method that involves converting mid-infrared light into visible images, has significantly advanced and has shown considerable potential for various applications, including biomedical imaging and remote sensing. While diffraction-based parametric upconversion imaging modeling in standard thin birefringence crystals have been addressed, the numerical framework developed so far fails to address long aperiodic poled crystals. Specifically, diffraction-based analysis of the recent broadband adiabatic frequency upconversion imaging, which allows simultaneous image upconversion of extremely broadband signals is still lacking. Here, we introduce a diffraction-based numerical simulation framework for predicting the evolution of the nonlinear image/signal generation in upconversion imaging systems. This generalized framework can handle both periodically and aperiodically poled crystal designs. Specifically, the model captures faithfully and addresses the varying image magnification arising from upconversion at a Fourier plane of a multiwavelength object. The numerical simulations are validated by experimental measurements of broadband upconversion 3-5 µm mid-IR images to the visible-NIR, showing a good agreement. Moreover, the model allows the exploration of the trade-offs in the spectral span when moving to the full visible range. Our numerical framework will be useful for the interpretation of experimental results obtained in an imaging setting with nonlinear optical elements.

Intelligent Phase Contrast Meta-Microscope System.

Phase contrast imaging techniques enable the visualization of disparities in the refractive index among various materials. However, these techniques usually come with a cost: the need for bulky, inflexible, and complicated configurations. Here, we propose and experimentally demonstrate an ultracompact meta-microscope, a novel imaging platform designed to accomplish both optical and digital phase contrast imaging. The optical phase contrast imaging system is composed of a pair of metalenses and an intermediate spiral phase metasurface located at the Fourier plane. The performance of the system in generating edge-enhanced images is validated by imaging a variety of human cells, including lung cell lines BEAS-2B, CLY1, and H1299 and other types. Additionally, we integrate the ResNet deep learning model into the meta-microscope to transform bright-field images into edge-enhanced images with high contrast accuracy. This technology promises to aid in the development of innovative miniature optical systems for biomedical and clinical applications.

Fringe projector with submillimeter fringe spacing at a meter-scale field of view.

State-of-the-art fringe projection systems generate fringe patterns using digital light projectors (DLP). The axial uncertainty is limited by the smallest fringe period and is directly related to the pixel count. This results in limited accuracy of current DLP systems that affect applications such as in situ measurements for laser powder bed fusion systems, where a submillimeter fringe period is needed for field-of views larger than 500m m×500m m. This work presents a scalable fringe projection technique that enables the generation of stable fringe patterns over a large field of view spanning several meters while maintaining submillimeter fringe periods. This system uses geometric phase gratings to enable variable fringe spacing and fringe orientation capabilities. The system shears a coherent beam in the Fourier plane using a pair of geometric polarization gratings. The separation between the gratings directly affects the fringe spacing, and the orientation of the gratings affects the fringe orientation. The depth of focus is only limited by the coherence of the light source, enabling high fringe periods even on tilted planes. The system is designed with a single path configuration, making the system more robust to environmental noise. With a rotating linear polarizer, we demonstrate that phase-shifting methods could be employed to acquire phase information about the object. This paper employs a single-shot Fourier transform phase estimation technique to process the intensity maps acquired using projected fringe patterns. Further, we demonstrate the capabilities of the system to produce submillimeter fringe spacing and the ability to project fringes on larger scales for measurements.

Spiral-phase-objective for a compact spiral-phase-contrast microscopy.

Spiral-phase-contrast imaging, which utilizes a spiral phase optical element, has proven to be effective in enhancing various aspects of imaging, such as edge contrast and shadow imaging. Typically, the implementation of spiral-phase-contrast imaging requires the formation of a Fourier plane through a 4f optical configuration in addition to an existing optical microscope. In this study, we present what we believe to be a novel single spiral-phase-objective, integrating a spiral phase plate, which can be easily and simply applied to a standard microscope, such as a conventional objective. Using a new hybrid design approach that combines ray-tracing and field-tracing simulations, we theoretically realized a well-defined and high-quality vortex beam through the spiral-phase-objective. The spiral-phase-objective was designed to have conditions that are practically manufacturable while providing predictable performance. To evaluate its capabilities, we utilized the designed spiral-phase-objective to investigate isotropic spiral phase contrast and anisotropic shadow imaging through field-tracing simulations, and explored the variation of edge contrast caused by changes in the thickness of the imaging object.