Off-axis Imaging Research Articles

Analysis and experiment of polarization characteristics of Off-axis freeform optical system

As freeform surfaces are widely used in off-axis optical systems with large apertures, large fields of view, and long focal lengths, the polarization effect caused by the system cannot be ignored. For this in mind, a polarization aberration analysis method for freeform optical system with fringe Zernike polynomial is proposed. An analytical model for the polarization aberration in this case is constructed. The influence of the surface shape on the polarization aberration is investigated. Our analysis shows that the distribution of phase aberration, diattenuation and retardance at the exit pupil introduced by the freeform surface in the system is related to the entrance pupil, incident field angle, and also closely dependent on the surface sag of the freeform surface. The introduction of freeform surfaces causes the system polarization aberration distribution to lose rotational symmetry. Finally, a freeform surface multi-angle polarization characteristic test platform was built to test the validity of the theoretical model. The polarization aberration characteristic data of the incident mirror at different angles of view at different positions were obtained and analyzed. The measured results show that the relative errors of phase aberration, diattenuation and retardance are all less than 7.2%, which is basically consistent with the theoretical simulation analysis results. The research in this paper provides a theoretical basis for guiding the design of an off-axis freeform surface polarization imaging optical system, and provides theoretical guidance for improving the polarization aberration calibration of a freeform surface optical system.

Fractional Fourier-transform filtering and reconstruction in off-axis digital holographic imaging.

An off-axis digital holographic reconstruction method with fractional Fourier transform domain filtering is proposed. The theoretical expression and analysis of the characteristics of fractional-transform-domain filtering are given. It is proven that the filtering in a lower fractional-order transform domain can utilize more high-frequency components than that in a conventional Fourier transform domain under the same size of filtering regions. In simulation and experiment, the results demonstrate that the reconstruction imaging resolution can be improved by filtering in the fractional Fourier transform domain. The presented fractional Fourier transform filtering reconstruction provides a novel (to our knowlede) optional way for off-axis holographic imaging.

A New Approach to Evaluate 3D Flow Fields Using an Off-Axis 2D PIV System: Investigation of a Tubular Reactor Equipped with Kenics Static Mixers

In this work, an off-axis 2D Particle Image Velocimetry system is used to obtain the 3D flow field at the outlet of a tubular reactor equipped with Kenics static mixers. The 3D flow fields are obtained exploiting the out-of-plane velocity component and considering the symmetrical features of the flow generated by the static mixers. The raw results show that the velocity vectors, measured on a cross section perpendicular to the tube axis by 2D-PIV with the camera located at 24° from the measurement plane, are affected by the axial component of the flow. However, taking into account the symmetry of the flow field with respect to the tubular reactor axis and evaluating the effect of the out of plane velocity component, the correct 2D velocity vectors on the plane and also the velocity component in the axial direction can be calculated from the raw 2D PIV data. The consistency of the methodology is demonstrated by comparison of the results with the flow field measured in a smaller tubular reactor of similar geometry and Reynolds number with a symmetrical 2D-PIV system, with the camera located perpendicularly to the laser plane. Then, the 3D features of the flow are analyzed to characterize the effects of the different combinations of static mixer configurations on the fluid dynamics of the system in turbulent conditions. The results show that, as the pressure drop increases, a more uniform velocity distribution is achieved.Graphical

Characterization of interfacial waves in stratified turbulent gas-liquid pipe flow using Particle Image Velocimetry and controlled disturbances

The work reports an experimental investigation on stratified gas-liquid pipe flow characteristics in the presence of controlled interfacial waves. Studies of this flow regime with controlled interfacial waves are scarce in the literature. Here, the disturbances are excited at the liquid interface by an oscillating paddle. The waves are synchronized with image acquisitions, enabling the utilization of phase-locked measurements and ensemble averaging techniques. Off-axis Particle Image Velocimetry (PIV) and Shadowgraph techniques were applied to provide information about mean and wave-induced modifications on the velocity fields. Results show that mean flow velocities in the liquid and gas phases close to the pipe walls adhere well to the single-phase flow log-law profile. In the liquid layer, this agreement was observed up to half of the water depth. Controlled disturbances enabled the estimation of the wave amplitude thresholds for the appearance of relevant nonlinear wave effects on the flow field. Results suggest that such a threshold can be fairly represented by a constant value of the non-dimensional parameter proposed in the work of Kirby (2008). Within the non-linear wave regimes investigated, noticeable changes in the flow field were observed close to the interface. However, near the wall the flow was weakly affected by the presence of waves, suggesting that interfacial wave effects are weakly coupled with near-wall disturbances and might be modelled independently. Moreover, contributions to interfacial shear stress due to the presence of waves were obtained experimentally. The results presented here are useful for validation and improvement of models used to predict flow characteristics in stratified flows. In addition, they contribute to shed further light on the physical mechanisms involved in the phenomenon.

3D head-up display with a multiple extended depth of field based on integral imaging and holographic optical elements.

We propose a 3D head-up display with a multiple extended depth of field based on integral imaging and holographic optical elements (HOEs). The system consists of two components, an integral imaging module for generating 3D target objects and a holographic combiner for off-axis diffraction and image magnification. By recording HOEs with different optical powers at different locations on the same recording material, 3D imaging at multiple depth ranges is achieved. The designed and built HUD prototype verifies the feasibility of the method. The center depth planes of the red and green 3D images are at 600 mm and 2200 mm. The theoretical depth magnifications of the red and green channels are 1.5 and 5.5, and the measured depth ranges are approximately 250 mm and 850 mm. In addition, the influencing factors and improvement methods of resolution in LED illumination or laser illumination are analyzed.

Generalized Scale Factor Calibration Method for an Off-Axis Digital Image Correlation-Based Video Deflectometer.

When using off-axis digital image correlation (DIC) for non-contact, remote, and multipoint deflection monitoring of engineering structures, accurate calibration of the scale factor (SF), which converts image displacement to physical displacement for each measurement point, is critical to realize high-quality displacement measurement. In this work, based on the distortion-free pinhole imaging model, a generalized SF calibration model is proposed for an off-axis DIC-based video deflectometer. Then, the transversal relationship between the proposed SF calibration method and three commonly used SF calibration methods was discussed. The accuracy of these SF calibration methods was also compared using indoor rigid body translation experiments. It is proved that the proposed method can be degraded to one of the existing calibration methods in most cases, but will provide more accurate results under the following four conditions: (1) the camera's pitch angle is more than 20°, (2) the focal length is more than 25 mm, (3) the pixel size of the camera sensor is more than 5 um, and (4) the image y-coordinate corresponding to the measurement point after deformation is far from the image center.

Design of off-axis reflective optical system based on planar linkage mechanism

In this paper, we propose a straightforward and dynamic approach to design unobstructed off-axis reflective image systems using a planar linkage mechanism. Objective: The advantage of this design is that it simplifies the process of modeling and optimizing the optical system. Method: The center of the surface is placed at the hinge point, and its tilt angle and position are determined by the adjacent hinge coordinates, and then the curvature of each reflector is determined by the relationship of the optical power. Result: In order to verify the feasibility and convenience of the method, an off-axis four-mirror free-form system is designed, with field of view of 5° × 5°, and the results of the optimized system show that the MTFs greater than 0.8 at 30 lp /mm.

3D Interconnected Magnetic Nanowire Networks as Potential Integrated Multistate Memristors.

Interconnected magnetic nanowire (NW) networks offer a promising platform for three-dimensional (3D) information storage and integrated neuromorphic computing. Here we report discrete propagation of magnetic states in interconnected Co nanowire networks driven by magnetic field and current, manifested in distinct magnetoresistance (MR) features. In these networks, when only a few interconnected NWs were measured, multiple MR kinks and local minima were observed, including a significant minimum at a positive field during the descending field sweep. Micromagnetic simulations showed that this unusual feature was due to domain wall (DW) pinning at the NW intersections, which was confirmed by off-axis electron holography imaging. In a complex network with many intersections, sequential switching of nanowire sections separated by interconnects was observed, along with stochastic characteristics. The pinning/depinning of the DWs can be further controlled by the driving current density. These results illustrate the promise of such interconnected networks as integrated multistate memristors.

Digital-holography efficiency measurements using a heterodyne-pulsed configuration

A digital-holography (DH) system is created in a heterodyne-pulsed configuration, meaning that the reference and signal pulses are nondeterministically correlated in time. Using the off-axis image plane recording geometry, two performance metrics are measured: (1) the total-system efficiency and (2) the ambiguity efficiency. These metrics are compared against the same measured efficiencies for a DH system in a homodyne-pulsed configuration, which uses deterministically correlated reference and signal pulses. The total-system efficiency of both systems is found to be consistent with one another, showing that no new component efficiencies are required when switching from a homodyne- to a heterodyne-pulsed configuration. Additionally, an instantaneous phase modulation model is used to characterize system performance in terms of nonideal pulse overlap. Such a model validates the use of the ambiguity efficiency for future efforts.

In-Line and Off-Axis Hybrid Digital Holographic Imaging Method Based on Off-Axis Hologram Constraints

We put forward a novel hybrid iterative algorithm to improve the imaging quality of digital holography. An off-axis hologram is added to the iteration process via interference and inverse interference process and becomes part of the constraints. A frequency domain filter varying with the number of iterations is used to improve the competitive advantage of low frequency information in the early iterations, while retaining the high frequency information. In practical applications, an additional iterative process is used after averaging filtering to suppress the influence of the imperfect consistency between the reconstructed reference wave and the actual reference wave. Numerical simulations and experiments show that image reconstruction may be significantly improved compared to the conventional method.

High-throughput artifact-free slightly off-axis holographic imaging based on Fourier ptychographic reconstruction

Slightly off-axis digital holographic microscopy (DHM) has recently gained considerable attention due to its unique ability to improve the space-bandwidth product (SBP) of the imaging system while separating the object information from the background intensity to a certain extent. In order to obtain a decent image reconstruction, the spectral aliasing problem still needs to be addressed, which, however, is difficult to be achieved by the conventional linear Fourier domain filtering. To this end, in this paper, we propose a high-throughput artifact-free slightly off-axis holographic reconstruction method based on Fourier ptychographic microscopy (FPM). Inspired by the nonlinear optimized phase reconstruction algorithm of FPM, we perform constrained updates between the real and Fourier domains in an iterative manner to reconstruct the complex amplitude by the hologram intensity. Experimental results on live HeLa cell samples show that the proposed method can provide higher reconstruction accuracy and better image quality compared with the conventional Fourier method and the Kramers–Kronig (KK) relation-based method.

Wide field-of-view Fourier Ptychography microscopy based on Fresnel propagation scheme

Fourier ptychographic microscopy (FPM) is a computational imaging method that gives a significantly increased space-bandwidth product, in practice high resolution combined with a wide field of view. In this article, we propose an improved Fourier Ptychography algorithm based on Fresnel wave propagation integral for wide field-of-view coherent imaging while correcting for the misalignment of the illuminating LED board and calibration of system parameters. In addition, the wave emanating from the LEDs is taken to be parabolic instead of plane wave as done by others. The advantage of this scheme is that it enables to simulate the transition regions between bright and dark field in wide image patches, and hence this feature can be used to estimate the LED misalignment as well as the distortion of the imaging lens. Experimental results are presented for a USAF resolution target and a biological sample for on-axis and off-axis image patches over a wide sample area showing excellent performance of this scheme when compared to the traditional Fraunhofer-model based Fourier Ptychography algorithm. The article summarizes with high technical detail our experiences with developing and implementing improved FPM methods and will hopefully assist other scientists entering this scientific field.

Convex optimization for additive noise reduction in quantitative complex object wave retrieval using compressive off-axis digital holographic imaging

Abstract Image denoising is one of the important problems in the research field of computer vision, artificial intelligence, 3D vision, and image processing, where the fundamental aim is to recover the original image features from a noisy contaminated image. The camera sensor additive noise present in the holographic recording process reduces the quality of the retrieved image. Even though various techniques have been developed to minimize the noise in digital holography, the noise reduction still remains a challenging task. This article presents a compressive sensing (CS) technique to minimize the additive noise in the digital holographic reconstruction process. We demonstrate the reduction of additive noise using complex wave retrieval method as a sensing matrix in the CS model. The proposed CS method to suppress the noise during the reconstruction process is illustrated using numerical simulations. Only 50% of the pixel measurements are considered in the noisy hologram, which is far less than the original complex object pixels. The impact of additive gaussian noise in the recording plane on the reconstruction accuracy of both intensity and phase distribution is analysed. The CS method denoises and estimates the complex object information accurately. The numerical simulation results have shown that the proposed CS method has effectively minimized the noise in the reconstructed image and has greatly improved the quality of both intensity and phase information.

Designing reflective imaging systems with multiple-surfaces-integrated elements using a Gaussian function freeform surface.

We propose a design scheme and method of a freeform off-axis reflective imaging system with multiple mirrors integrated into one element. The use of a multiple-surfaces-integrated element, described by the Gaussian basis functions freeform surface with local and nonsymmetric properties, significantly decreases the system complexity, as well as reduces the assembly and fabrication difficulty, and achieves high imaging performance. The design theory and process including the initial system design, surface conversion, and system optimization are demonstrated in detail. Three design examples are demonstrated to validate the effect and feasibility of the proposed method, and good imaging performance is obtained.

Pulsed laser source digital holography efficiency measurements.

In this paper, a 1064 nm pulsed laser source and a short-wave IR (SWIR) camera are used to measure the total system efficiency associated with a digital holography system in the off-axis image plane recording geometry. At a zero path-length difference between the signal and reference pulses, the measured total system efficiency (15.9%) is consistent with that previously obtained with a 532 nm continuous-wave laser source and a visible camera [Appl. Opt.58, G19 (2019)APOPAI0003-693510.1364/AO.58.000G19]. In addition, as a function of the temporal delay between the signal and reference pulses, the total system efficiency is accurately characterized by a component efficiency, which is formulated from the ambiguity function. Even with multimode behavior from the pulsed laser source and substantial dark current noise from the SWIR camera, the system performance is accurately characterized by the resulting ambiguity efficiency.

Design of off-axis reflective imaging systems based on freeform holographic elements.

Holographic optical element (HOE) can be used in many areas in optics due to its characteristics of thin structure, flexible wavefront reconstruction/control ability and angular/wavelength selectivity. In this paper, we propose a design method of off-axis reflective imaging systems based on freeform HOEs, which are fabricated by freeform wavefronts. The freeform HOEs offer many degrees of design freedom and can correct the aberrations in nonsymmetric imaging systems. The initial imaging system with freeform HOEs is generated using a point-by-point design approach, and is used for the preliminary design of the imaging system and the freeform recording system of each HOE. Then a joint optimization is conducted for all the systems, simultaneously considering the imaging performance, the diffraction efficiency, the system constraints and fabrication to get the final design results. To validate the feasibility and effectiveness of the proposed method, an off-axis reflective head-up display system with good performance based on freeform HOEs is designed and fabricated. Detailed procedures of the design and development process of the prototype are demonstrated.

Common-path off-axis single-pixel holographic imaging.

Common-path off-axis single-pixel holographic imaging (COSHI) is proposed to obtain complex amplitude information using an in-line interferometer and a single-pixel (point-like) detector. COSHI is more robust to disturbances such as vibration than the conventional single-pixel digital holography technique because of its common-path configuration. In addition, the number of measurements can be reduced due to COSHI's reconstruction process based on the Fourier fringe analysis. In COSHI, an off-axis digital hologram can be obtained using the structured patterns composed of Hadamard basis patterns and stationary tilted phase distribution. Interestingly, COSHI's space bandwidth is larger than of the conventional off-axis digital holography because COSHI does not reconstruct the self-correlation term of an object. The proposed method is theoretically confirmed and numerical and experimental results show its feasibility.

Off-axis reflective imaging system design with a conicoid-based freeform surface.

In this paper, we propose an off-axis reflective system design method based on a non-rotational symmetric conicoid-based freeform (CBF) surface description. The base description avoids complicated calculation of decenter and tilt when using the conventional conic expression, thus simplify the system modeling and optimization process, and it can reduce the number of coefficients that needed to represent mild freeform surfaces. A design method that includes the automatic initial system searching, preliminary optimization with rotationally symmetric surface deviation and fine-tuning with non-symmetric surface deviation is proposed. Two three-mirror systems have been designed to demonstrate the feasibility and conveniences of the proposed method.

Automatic design method of starting points of freeform off-axis reflective imaging systems of small volume.

For off-axis reflective systems, there is no effective method that can obtain a small-volume starting point automatically. Reducing system volume using the optimization method is usually a difficult and cumbersome process, which usually takes the designer a long time. This paper proposes a method of designing small-volume starting points of freeform off-axis reflective imaging systems, which does not require human involvement after inputting a planar system, specifications and constraints. In the design example presented in this paper, it took only about ten minutes to obtain a small-volume starting point. The starting point obtained by this method makes the optimization process easier, takes less time of designers and more likely to succeed. In the design example, it is also demonstrated that the method has the ability of establishing small-volume starting points with different specifications, which can be used to quickly estimate the minimum volumes that systems with different specifications can achieve and provide guidance for determination of specifications and optimization.

Robust, accurate, and improved measurement of structural deformation based on off-axis digital image correlation.

We propose a noncontact method for measuring structural deformation using off-axis digital image correlation. An efficient and high-precision algorithm that is insensitive to the accuracy of the initial guess is proposed and validated through numerical simulation. Image displacements in pixels are converted to physical displacements in millimeters using a calibration model based on a new method of measuring the objective distance. A new image-based structural deformation measurement system is proposed and validated using laboratory test results. The proposed method is easy to implement and accurate for structural deformation measurements.