4f System Research Articles

Single-pixel phase microscopy without [formula omitted] system

We present single-pixel phase microscopy (SPPM) without 4f system, as a novel common-path quantitative phase imaging method, to acquire the amplitude and phase of any transmissive object. To get rid of the 4f system and make the experimental setup more compact and practical, SPPM adopts the phase-modulated detection mode. A single microscopy objective is employed for image magnification, and a collecting lens is used to circumvent the quadratic phase factor introduced by the objective. A phase-only liquid crystal on silicon is utilized to modulate the phase of object light to achieve Hadamard basis scan phase imaging and Fourier basis scan phase imaging with a single photomultiplier tube. We apply SPPM to observe several different types of objects, from simple artificial objects to complex biological specimens. The experimental results show that SPPM provides clear imaging, accurate phase, and spatial resolution up to 2.19 µm (a spatial frequency of 456 lp/mm). Without the 4f system, SPPM can be implemented as an add-on module to existing optical microscopy, which facilitates its adoption in biomedical science and optical metrology.

An aperture of 21 cm telescope with polarized coaxial for satellite laser ranging

With the development of aerospace and space scientific research, satellite laser ranging (SLR) has put forward higher requirements for response speed, data density, and measurement accuracy. In coaxial common optical path laser ranging, the emitted laser and the received laser echoes pass through the same optical system. Due to the reversibility of the optical path, the laser emission, monitoring, and laser echoes’ optical path all pass through the same optical system structure, and the response speed and ranging ability of the laser ranging system have been greatly improved. Based on the SLR system of the Shanghai Astronomical Observatory (SHAO), the laser transmitting telescope with an aperture of 21 cm was used to build a polarized coaxial SLR system. It uses a picosecond pulsed laser with a pulse repetition frequency of 2 kHz and a single-pulse energy of 2 mJ. Also, a 4f system was applied to shrink the laser echo beam and filter out noise, the measurements of low-Earth orbit and long-distance high-orbit satellites were realized, and the ranging accuracy was ∼2 cm. As far as we know, this is currently the smallest aperture telescope for SLR globally, which is conducive to the miniaturization and integrated development of SLR systems.

Self-healing of holographically generated moiré lattice wave fields

Self-healing in optics generally refers to the ability to reconstruct itself and restore the original state after encountering obstacles in the propagation of the light field. In this research, we observe the processes of the wave fields from perfect to defect in front of the focal plane of the 4f system, finally returning to an intact situation after the plane. According to simulations and experimental results, there is a minimum self-healing distance for the moiré lattice field that positively associates with the radius of the defect (obstacle) in the nondiffracting transmission range. Furthermore, it is observed that the defect self-healing is a process of “repairing the center and then repairing the edges.” These findings can be applied in areas such as optical imaging, capture, and information processing.

A Simultaneous Multi-Directional Defects Measurement Based on Polarization-Multiplexed Four-Directional Digital Shearography With Large Field of View

Since the sensitivity of digital shearography (DS) is related to its shearing direction and the anomaly of the relative deformation is sensitive to the defect direction in non-destructive testing (NDT), traditional single or two direction DS systems may miss defects in some directions. To avoid missing defects, a polarization-multiplexed four-directional digital shearography for simultaneous measurement of multi-directional defects is proposed in this paper. Four object beams whose relative shearing amount and spatial carrier frequency can be adjusted independently are constructed, with which four shearograms can be obtained simultaneously in one recorded interferogram. And by embedding a 4f system in front of the interferometers to transmit the captured image, the measurement field of view (FOV) is doubled. To verify the performance of the proposed four-directional DS system, an experimental setup was constructed, and two experiments of central force loading and non-destructive thermal loading were performed. Experimental results verify that the proposed system can effectively detect the defects in multiple directions simultaneously.

Implementing a non-4f relay system for Hartmann-Shack wavefront sensing.

Hartmann-Shack wavefront sensors (HSWSs) are used in many disciplines to measure optical aberrations. Conventionally, the wavefront of interest is transferred onto the lenslet array of the HSWS with a telescopic 4f relay system. However, the 4f relay design restricts the choice of focal lengths and distances used for the relay system. In this paper, we describe a non-4f variant and demonstrate both theoretically and experimentally that its wavefront relaying properties equal that of a 4f system. We also present an alignment method for conjugating the wavefront with the lenslet array of the HSWS for both 4f and non-4f systems.

Study on processing synthetic aperture radar data based on an optical 4f system for fast imaging.

Due to the huge amount of collected echo data caused by the working principle of synthetic aperture radar (SAR), the use of digital processing relies heavily on the performance of digital chips. Because of the limitation of Moore's law, the technology of digital signal processing exposes the limitation of computing speed and power consumption in the face of SAR processing. Against this background, the optical processing method based on the optical 4f system is introduced into SAR imaging. A spatial light modulator (SLM) is placed on the input surface and spectrum surface of the 4f system to load the echo data of the SAR and the matched filter function of the SAR. Using optical Fourier transform to realize the core calculation of SAR data processing can solve the difficulty of processing time-consuming due to the large amount of calculation. In the process of Fourier transform, instead of using a solid glass lens, we use a phase-type Fresnel lens diagram in the SLM to realize the function of Fourier, which avoids the need for special design of Fourier lens. It also greatly reduces the volume and weight of the whole machine, which provides a reference method for real-time imaging of spaceborne SAR.

On-Chip Optical Adder and Differential-Equation-Solver Based on Fourier Optics and Metasurface.

Analog optical computing (AOC) has attracted great attention over the past few years, because of its ultra-high speed (potential for real-time processing), ultra-low power consumption, and parallel processing capabilities. In this article, we design an adder and an ordinary differential equation solver (ODE) on chip by Fourier optics and metasurface techniques. The device uses the 4f system consisting of two metalenses on both sides and one middle metasurface (MMS) as the basic structure. The MMS that performs the computing is the core of the device and can be designed for different applications, i.e., the adder and ODE solver in this article. For the adder, through the comparison of the two input and output signals, the effect of the addition can be clearly displayed. For the ODE solver, as a proof-of-concept demonstration, a representative optical signal is well integrated into the desired output distribution. The simulation result fits well with the theoretical expectation, and the similarity coefficient is 98.28%. This solution has the potential to realize more complex and high-speed artificial intelligence computing. Meanwhile, based on the direct-binary-search (DBS) algorithm, we design a signal generator that can achieve power splitting with the phase difference of between the two output waveguides. The signal generator with the insertion loss of −1.43 dB has an ultra-compact footprint of 3.6 × 3.6 . It can generate a kind of input signal for experimental verification to replace the hundreds of micrometers of signal generator composed of a multi-mode interference (MMI) combination used in the verification of this type of device in the past.

Color dynamic holographic display based on complex amplitude modulation with bandwidth constraint strategy.

In this Letter, we introduce a multiplexing encoding method with a bandwidth constraint strategy to realize a color dynamic holographic display based on complex amplitude modulation (CAM). The method first uses the angular spectrum method (ASM) with a bandwidth constraint strategy to calculate the diffracted wavefronts of red, green, and blue channels. Then the diffracted wavefronts of three channels are synthesized into a color-multiplexed hologram (CMH) based on the double-phase method after they interfere with off-axis reference lights. The color 3D objects can be reconstructed when the combination of red, green, and blue lights is used to illuminate the double-phase CMH, and a 4f system with a slit filter is introduced to extract the desired spectrums. Numerical simulations and optical experiments are performed to verify the effectiveness of the proposed method and the results show that it can achieve a color holographic display with high quality. Our proposal is simple and fast, and the display system is compact. It is expected that our proposed method could in future be widely used in the holographic field.

FISI: frequency domain integration sequential imaging at 1.26×1013 frames per second and 108 lines per millimeter.

High spatial resolution on the image plane (intrinsic spatial resolution) has always been a problem for ultrafast imaging. Single-shot ultrafast imaging methods can achieve high spatial resolution on the object plane through amplification systems but with low intrinsic spatial resolutions. We present frequency domain integration sequential imaging (FISI), which encodes a transient dynamic by an inversed 4f (IFF) system and decodes it using optical spatial frequencies recognition (OFR), which overcomes the limitation of the spatial frequencies recognition algorithm. In an experiment on the process of an air plasma channel, FISI achieved shadow imaging of the channel with a framing rate of 1.26×1013 fps and an intrinsic spatial resolution of 108 lp/mm (the spatial resolution on the image plane). Owing to its excellent framing time and high intrinsic spatial resolution, FISI can probe both repeatable and unrepeatable ultrafast phenomena, such as laser-induced damage, plasma physics, and shockwave interactions in living cells with high quality.

Off-axis common-path digital holography using a cube beam splitter.

An off-axis common-path digital holography is built up by inserting a 45° tilted cube beam splitter (CBS) into a 4f system that is described in this paper. Two apertures are set as the input of the 4f system, where one supports the object, and the other is vacant. The CBS divides the incoming beam into two copies, which are symmetrical with each other along the semi-reflecting layer. Due to the separation of two beams in a Fourier plane and the flipping of the field of view induced by the CBS, an off-axis hologram can be captured. Moreover, the carrier frequency can be easily modulated by translating the CBS perpendicular to the optical axis. The new proposed scheme has high light utilization, a compact setup, and high temporal stability. The experiments are carried out to demonstrate the validity and stability of the proposed method.

Programmable high-order mode control method based on acoustically induced fiber grating.

We demonstrate a programmable high-order mode control method that can be implemented in high-power fiber lasers. 2 W average-power mode-locked pulses are obtained based on a mode-locked fiber laser working in dissipative soliton resonance regime. The fundamental mode (LP01) is fully or partially converted to the high-order modes (LP11a/b) via an acoustically-induced fiber grating. The mode-superposition fields are recorded using an optical 4f system, and mode components are subsequently analyzed by a mode decomposition algorithm. Our experiments suggest that the mode patterns are stable and dynamically switchable. The method is expected to possess good application value in optical tweezers, fiber communication, laser material processing and other research fields.

Heterometallic decanuclear [Fe6–Ln4] coordination clusters with enzymatic mimic activity: Synthesis, structures, magnetic properties, and evaluation of catecholase activity

AbstractThree [Fe6‐Ln4] clusters are isolated throughN‐methyldiethanolamine (H2mdea) and 3,5‐dinitrobenzoic acid (Hdnbz) acting as ligands together with sodium azide. The X‐ray study demonstrates that these compounds are isostructural formulated as [Fe6Ln4(μ4‐O)2(μ3‐OH)2(mdea)6(dnbz)8(N3)4]·MeCN·aH2O·bCH2Cl2(where Ln = Tb (1),a = 2,b = 3; Ho (2),a = 2,b = 2; Er (3),a = 1,b = 1). All these compounds are centrosymmetric in structure. The catecholase activity for the clusters (1–3) was also studied in methanol by ultraviolet–visible spectrophotometry via 3,5‐di‐tertiarybutyl catechol (3,5‐DTBC) employed as a model substrate for the identification of the compounds as a functional model for metalloenzymes. During this study, the parameters for catecholase activity are estimated asKcat = 1022.12 (1), 827.76 (2), 562.36 (3) h−1; KM = 0.6858 (1), 0.6467 (2), 0.4872 (3) M; andVmax = 0.2840 (1), 0.2291 (2), 0.1556 (3) M min−1. In the Fe–4fsystem, such a type of activity is determined for the first time. The magnetic studies indicate the antiferromagnetic (AF) interactions between the metal centers.

An Optical Image Encryption Method Using Hopfield Neural Network.

In this paper, aiming to solve the problem of vital information security as well as neural network application in optical encryption system, we propose an optical image encryption method by using the Hopfield neural network. The algorithm uses a fuzzy single neuronal dynamic system and a chaotic Hopfield neural network for chaotic sequence generation and then obtains chaotic random phase masks. Initially, the original images are decomposed into sub-signals through wavelet packet transform, and the sub-signals are divided into two layers by adaptive classification after scrambling. The double random-phase encoding in 4f system and Fresnel domain is implemented on two layers, respectively. The sub-signals are performed with different conversions according to their standard deviation to assure that the local information’s security is guaranteed. Meanwhile, the parameters such as wavelength and diffraction distance are considered as additional keys, which can enhance the overall security. Then, inverse wavelet packet transform is applied to reconstruct the image, and a second scrambling is implemented. In order to handle and manage the parameters used in the scheme, the public key cryptosystem is applied. Finally, experiments and security analysis are presented to demonstrate the feasibility and robustness of the proposed scheme.

Compact Computational Holographic Display

Holographic display is an ultimate three-dimensional (3D) display technique that can produce the wavefront of 3D objects. The dynamic holographic display usually requires a spatial light modulator (SLM) with a following 4f system to eliminate the unnecessary orders produced by the grating structure of the SLM. We present a technique that displays the images without the 4f system. We detect the unnecessary wavefield by phase-shifting holography and suppress it using computational optimization. Experimental results are presented to verify the proposed method.

Measuring the orbital angular momentum mode of vortex beam based on phase matching sequence

Measuring the orbital angular momentum(OAM) mode of vortex beams is of great significance in applications based on vortex beams.we propose a method of phase matching characteristics of vortex beams to measure the OAM mode. The method first use a high-speed spatial light modulator(SLM) to sequentially load a set of helical phase sequence images, so that the vortex beam is modulated by this SLM. Then obtain the modulated optical field through pinhole filtering, and then the synchronized tilt phase modulation is performed by the 4f system and high-speed SLM. When the OAM mode of vortex beam is opposite to the topological charge of helical phase image, that is, the incident vortex beam degenerates to the fundamental Gaussian mode beam,and through our optical system, the output plane obtained a indicating spot with the position related to the OAM mode. The Simulation and experimental results show that the method obtains a clear OAM mode indicating spot on the final output plane, which verifies the theoretical derivation.

Simplified dual-channel two-wavelength interferometer using a polarized cube beam splitter.

Two-wavelength interferometers can extend an unambiguous measurement range; however, they suffer from complex optical configurations. To simplify the optical setup for a two-wavelength common-path off-axis interferometer, we propose a dual-channel two-wavelength interferometer using a polarized cube beam splitter. In contrast with the previously presented two-wavelength common-path off-axis interferometer, the proposed method has a simple setup, in which only one polarized cube beam splitter is inserted into the 4f system. With the help of polarization modulation, two single-wavelength interferograms can be captured simultaneously. Several experimental results are presented to demonstrate the advantages and effectiveness of the proposed method.

Conversions of linear-circular polarizations and spin-orbital angular momentums in a focused vector vortex beam with fractional topological charges

We perform theoretical and experimental studies on the tight focusing properties of a vector vortex beam with fractional order topology charges. The fractional-order vector vortex optical fields (FO-VVOF) are experimentally generated by using the 4f system and the hologram technology. In comparison to the integral-order vortex, the 3-dimensional (3D) field distributions of FO-VVOF in the focal volume exhibit unique vectorial structure characteristics. The conversions between the linear and the circular polarizations (spin angular momentum) occur in a tight focusing fractional vortex. Furthermore, the hybrid spin-orbital angular momentum conversions in the longitudinal component in a tight focusing FO-VVOF lead to the interesting distributions of the orbital angular momentum. The dynamic conversions closely depend on the initial topology charge numbers and polarization distributions. The underlying physics of this unique phenomenon is discussed in detail. These results may have potential applications in particle micro-manipulation, quantum information processing and optical field manipulation.

Hydrogen impact on magnetic properties of metallic systems

A brief overview of the impact of presence of hydrogen in metallic systems on magnetic properties is given. Respective differences between the 4f, 5f, and 3d system are emphasized using examples of materials with similar crystal structure. The analysis is based on general aspects of H bonding in metallic environment, H expanding volume and polar bonding of H. Electronegativity is used as a convenient indicator quantifying the polar bonding character.

Telephoto-lens-based Optical Differentiation Wavefront Sensor for freeform metrology.

We report an Optical Differentiation Wavefront Sensor based on a telephoto lens system and binary pixelated filters. It provides a five-fold reduction in the system length compared to a 4f system with identical effective focal length. Measurements of phase plates with this system are compared to measurements performed with a commercial low-coherence interferometer. The telephoto-lens-based system can measure wavefronts with accuracy better than λ/10 Root Mean Squared (RMS) at λ=633 nm. Experimental investigation shows that the system has a high tolerance to components alignment errors.

Coherent imaging of objects through thin-layer highly scattering medium based on optical encryption

In this paper, we declare that the scattering system of coherence light passing through a thin-layer highly scattering medium can be treated as a 4f system of single random phase encoding (SRPE). Assuming no energy loss, the target image behind a thin-layer highly scattering medium can be recovered by using an attack method in a SRPE-4f encryption system. The idea originates from the analysis of speckle field and theoretical model of the system. On the one hand, the statistical distribution of the speckle in the scattering system is consistent with that of the cyphertext in the corresponding SRPE-4f encryption system, which provides the base for equivalent replacement. On the other hand, the point spread function of a thin-layer highly scattering medium is equivalent to the Fourier transform of random phase mask of the SRPE-4f system, which can be used for key estimation in scattering imaging. Both the theory analysis and results of the experiment verify the validity and feasibility of our proposed, and we believe this contribution will open up a novel way to deepen the research of imaging through scattering medium.