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In this work a three-dimensional diffusion model is used to model photopolymers as a recording media. This model allows us to predict the properties of the Diffractive Optical Elements (DOEs) once we recorded into the photopolymer. This model had never been tested with more complex elements, such as multifocal diffractive lenses, as presented in the following in this work. In addition, the model includes; the estimation of the refractive index modulation, the low-pass filtering effect due to the experimental optical setup, and the evolution of the transverse intensity distribution. In this way, the selection of the appropriate material characteristics depending on the intended DOE application is made possible. Specifically, an acrylamide-based PVA/AA photopolymer is simulated using the proposed model. Moreover, coverplating and index matching systems are considered together to avoid the effects of thickness variation. Furthermore, in order to compare their properties using the proposed model, we focus on Fibonacci lenses (FL), a type of bifocal lenses. This allows us to evaluate the dependence of the focii intensity on the polymerisation rate, the diffusivity parameter, low-pass filtering effect and the use of the index matching system for these lenses. This enables us to know the recording parameters in order to produce this type of multifocal diffractive lenses with higher quality and precision. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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.

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 π between the two output waveguides. The signal generator with the insertion loss of −1.43 dB has an ultra-compact footprint of 3.6 μ m × 3.6 μ m . 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. [ABSTRACT FROM AUTHOR]

Vectorial optical fields have garnered significant attention due to their potential applications in areas such as optical nano-fabrication, optical micromachining, quantum information processing, optical imaging, and so on. Traditional compact vectorial optical generators with amplitude modulation perform poorly in terms of diffraction effect reduction. To tackle this problem, the refractive 4f system in amplitude modulation is longitudinally aligned using an optimization approach presented in this research. The phase images used for longitudinal alignment are loaded into the liquid crystal spatial light modulator (SLM), and the distance between the lens and the mirror in the reflective 4f system is adjusted for longitudinal alignment by compensating for the neglected phase in the integrated module for the compact vectorial optical-field generator. The spot images collected by the CCD are processed using the improved eight-direction Sobel operator and Roberts function, and the longitudinal alignment in the reflective 4f system is determined by the sharpness of the image. The sharpness of the edges of the lines and the overall image are both enhanced after optimization compared to before optimization. The results demonstrate that the proposed method can effectively reduce the longitudinal alignment error of the reflective 4f system in the amplitude modulation of the compact vectorial optical-field generator, lessen the diffraction effect, and improve the performance of the system.

Optical neural networks can effectively address hardware constraints and parallel computing efficiency issues inherent in electronic neural networks. However, the inability to implement convolutional neural networks at the all-optical level remains a hurdle. In this work, we propose an optical diffractive convolutional neural network (ODCNN) that is capable of performing image processing tasks in computer vision at the speed of light. We explore the application of the 4f system and the diffractive deep neural network (D2NN) in neural networks. ODCNN is then simulated by combining the 4f system as an optical convolutional layer and the diffractive networks. We also examine the potential impact of nonlinear optical materials on this network. Numerical simulation results show that the addition of convolutional layers and nonlinear functions improves the classification accuracy of the network. We believe that the proposed ODCNN model can be the basic architecture for building optical convolutional networks.

The optical neural network system based on the 4f system (4f-ONN) is a feasible solution for on-orbit real-time target detection and recognition on remote sensing images, as it can directly modulate and encode the two-dimensional image information. However, traditional 4f systems based on spatial light modulators (SLMs) often encounter misalignment errors during assembly due to the reflective optical path used in SLMs. Additionally, implementing electronic SLM in space-based applications introduces problems such as particle number reversal, significantly reducing the reliability of the system. To address these issues, this paper proposes the adoption of diffractive optical elements (DOEs) to construct the 4f-ONN system. The DOE-based design offers a more compact structure, enhanced reliability, and reduced energy consumption, making it highly suitable for on-orbit image processing applications. Due to the expensive and time-consuming nature of the DOE manufacturing process, a design approach for a 4f system based on DOE was pursued through software simulation in this paper. The simulation phase involved the utilization of electronic neural networks to acquire the physical parameters of the DOE mask, while incorporating the array theorem and Fraunhofer diffraction theorem to accurately calculate the physical dimensions of the DOE. The effectiveness of the adopted DOE-based 4f system was initially validated through experiments on a simple pattern dataset. Subsequently, simulation experiments were conducted on three public datasets, namely Mnist, Fashion-mnist, and QuickDraw16, to confirm the efficacy of the DOE-based 4f system in classification tasks. Lastly, target recognition experiments were performed on the GF-2 dataset, and a corresponding hardware system was developed to demonstrate the potential of the DOE-based 4f system in on-orbit image processing. • A structurally more compact and stable DOE-based 4f system is proposed. • The effects of quantization and manufacturing errors on the performance of the DOE-based 4f system are analyzed. • Extensive experiments demonstrate the efficiency of the proposed DOE-based 4f system in ship recognition within remote sensing images. [ABSTRACT FROM AUTHOR]

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.

A light scattering instrument has been designed to allow an investigation of the spatial intensity distribution profile, due to the cells within, a liquid solution, in the near forward direction. The cells are illuminated by the light source, a collimated LED, and the light scattered is imaging with a SCMOS camera. By filtering the unscattered light due to the light source from the light scattering due to the cells suspension, in a detection angular range from 0° to ∼8°, and the experimental results of the angular distribution of scattered light is statistically averaged in order to obtain a good fit. The forward scattered light provides the information to count the number of cells per illuminated volume and their mean size, as well as the corresponding size distribution. The theoretical comparisons have been made with the experimental profiles using Mie theory, leading to the experimental scattering data to show a good agreement with theoretical data. [ABSTRACT FROM AUTHOR]

Knowledge of the focal length of a lens is vital in the construction of all optical instruments, from spectacles to large astronomical telescopes. In this paper, we described a method using Hartmann–Shack sensor to measure the focal lengths of lenses based on the 4F system. The experimental system that we have set up and the experiments which have been done are described, and also the formulas used to calculate the focal lengths of lenses are being given. A clue to improve the measurement accuracy is given. Compared to other methods, it is easy to get a precision value of the focal length using our method, and the relative error will be less than 0.1%; meanwhile, it shows the distribution of wavefront aberrations of imaging information of the detection-area of the lens. [ABSTRACT FROM AUTHOR]

Abstract: Digital shearography based on Mach–Zehnder interferometer suffers from the disadvantage of a small angle of view due to the structure. A novel digital shearography set-up with a large angle of view, which is based on the combination of new CCD technology, a semiconductor laser, a Mach–Zehnder shear interferometer and a 4f system, is demonstrated. Independent control of the shear and the frequency of the spatial carrier can be attained with this set-up. In the optical arrangement, the imaging lens is placed in front of the Mach–Zehnder interferometer instead of behind it as in the traditional digital shearography. So the angle of view is no longer limited by the Mach–Zehnder interferometer. Phase extraction is obtained by both advanced sinusoidal-fitting method and Fourier transform method, which are applied to interference patterns with a spatial carrier in the primary fringes. The experimental implementation of the set-up and the results obtained with it are presented and discussed. [Copyright &y& Elsevier]

A method is reported to simultaneously measure the nonlinear absorption and refraction coefficients of materials using a nonlinear-imaging technique with a phase object. In this technique, the sign and magnitude of both the nonlinear absorption and refraction can be acquired conveniently from the analysis of three experiment images: the linear image, the nonlinear image and the image without sample. In order to validate our approach, we demonstrate this method for ZnSe at 532 nm where two-photon absorption is present and the nonlinear refractive index n 2 is negative. The values of β (nonlinear absorption coefficient) and n 2 we measured are very close to the values found in other literature. [ABSTRACT FROM AUTHOR]

Abstract: The nonlinear absorption can produce a nonlinear image very similar with the one created by the nonlinear refraction when using the nonlinear-imaging technique with phase object to measure the third-order nonlinearity of materials, but the principles of them are different. The formation of the nonlinear absorption image is explained, and the condition that the highest sensitivity of the nonlinear absorption measurement can be reached is deduced. For the materials with both nonlinear absorption and refraction, we find a proper phase shift of the phase object where the effect of the nonlinear refraction to the measured signal can be eliminated. The nonlinear absorption and refraction are numerically simulated when the phase shift of phase object to be π/2 that is normally used. The qualitative tendency of the signal variation is presented. [Copyright &y& Elsevier]

With its unique parallel processing capability, optical neural network has shown low-power consumption in image recognition and speech processing. At present, the manufacturing technology of programmable photonic chip is not mature, and the realization of optical neural network in free-space is still a hot spot of intelligent optical computing. In this article, based on Mixed National Institute of Standards and Technology database (MNIST) datasets and 4 f system, three-layer optical neural networks are constructed, whose recognition accuracy can reach 93.66%. Our network is programmable, high speed, reconfigurable and is better than the existing free-space optical neural network in terms of spatial complexity. [ABSTRACT FROM AUTHOR]

Regenerative amplifiers containing multiple diverse laser heads have the ability of scaling up output power as well as broadening spectral bandwidth. However, the thermal lensing effect will be more complicated. A method using a 4f system to simplify the thermal lensing effect in a multidisk condition is proposed. Two kinds of Yb-dropped sesquioxide materials are chosen as an example. On the basis of calculating the thermal lensing parameters of the thin-disk laser heads, a feasible cavity design that can minimize the fluctuation of beam size when changing the pump power is given out. The 4f system consisting of concave mirrors will introduce astigmatism in the cavity. The influence of astigmatism and the compensation method are discussed. Astigmatism can be compensated by adding extra convex mirrors and controlling the angle of incidence at each mirror. [ABSTRACT FROM AUTHOR]