4f Imaging System Research Articles

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.

A spatial carrier dynamic quantitative differential phase imaging method

Differential interference contrast (DIC) microscopy is an important method for quantitative phase imaging (QPI) due to its high compatibility regarding to partial coherent light illumination and excellent optical sectioning ability. However, limited by the on-axis interferometric configuration of Nomarski DIC microscopic imaging system, it is difficult to achieve single-shot phase retrieval. Here, we propose a simple and efficient method for dynamic quantitative differential phase imaging (QDPI) by introducing a spatial carrier device into DIC microscope. A Wollaston prism (WP) is placed on the imaging plane of DIC microscope and then projected by a 4f imaging system, so two orthogonally polarized imaging beams with a certain shearing amount will interfere on the conjugate plane of the 4f imaging system and form a spatial carrier DIC image, thus the QDPI can be conveniently realized. Importantly, the system not only possesses high temporal phase stability provided by the common-path geometries and low spatial phase noise due to partially coherent light illumination, but also the advantages of simple optical implementation, no additional phase distortion, high light energy utilization efficiency, and high signal-to-noise ratio. The experimental result demonstrates that using the proposed method, the phase measurement sensitivity reaches 0.003 rad, the corresponding applicability is verified by a polystyrene microsphere crown and biological cells.

Simultaneous chiral polarization and edge enhancement imaging enabled by a single geometric-phase-based element.

In this Letter, we propose a multifunctional imaging system enabled by a single geometric-phase-based liquid crystal (LC) element, which integrates chiral polarization and edge enhancement imaging. The element is located at the frequency domain plane in a 4F imaging system, and the phase profile of the element consists of a fork grating in the x direction and a grating in the y direction, which provide edge enhancement and chiral polarization imaging capabilities. Benefiting from the tunable property of the LC, the system can be switched from a polarization and edge imaging mode to the normal conventional imaging mode which is capable of conveniently acquiring the needed image information. Experiments demonstrate that the system can easily achieve multifunctional and switchable imaging, which agrees well with our design, and our LC element can work in the broadband spectrum because of the geometric phase modulation. The multifunctional strategy used here can effectively avoid the need to increase the size of the original microscopic system and the need for additional mechanical rotation of components. We believe that the proposed system with the additional advantages of electric control and tunability can find applications in biological imaging, medical detection, and optical computing.

Optical convolutional neural network with atomic nonlinearity.

Due to their high degree of parallelism, fast processing speeds and low power consumption, analog optical functional elements offer interesting routes for realizing neuromorphic computer hardware. For instance, convolutional neural networks lend themselves to analog optical implementations by exploiting the Fourier-transform characteristics of suitable designed optical setups. However, the efficient implementation of optical nonlinearities for such neural networks still represents challenges. In this work, we report on the realization and characterization of a three-layer optical convolutional neural network where the linear part is based on a 4f-imaging system and the optical nonlinearity is realized via the absorption profile of a cesium atomic vapor cell. This system classifies the handwritten digital dataset MNIST with 83.96% accuracy, which agrees well with corresponding simulations. Our results thus demonstrate the viability of utilizing atomic nonlinearities in neural network architectures with low power consumption.

Sensitivity optical non-linear measurement based on wide-band phase objects

On the basic that the phase object (PO) is the key optical device in the 4f imaging system, a modified high sensitivity optical nonlinear measurement technique with an absorptive homemade phase object (HPO) is reported in order to characterize the value of weak nonlinear refraction material. The absorptive HPO used in this technique is two transparent glass plates on which a liquid film between two pieces of transparent glasses is deposited and added a rotating object at the below HPO to modulate the phase of a PO. The measuring sensitivity can be improved by changing the transmittance of the absorptive HPO. Meanwhile, because the phase retardation of HPO can be continuously adjustable by modulate the rotating object, it makes the sensitivity of measurement at different wavelengths of laser optimal. Results show that the measuring sensitivity is improved 2-4 times compare with the conventional 4f imaging technique. Furthermore, the modified technique can be used to measure the spectrum of nonlinear refraction coefficients of materials at the continuous wavelength. This method further expands the 4f phase coherent imaging measurement technology, not only solves the deficiencies of the conventional phase object, but also improves the accuracy of the measurement. Experiment and theoretical analysis results are presented to validate our technique.

Large-scale phase retrieval from coded diffraction patterns with electrically tunable lens

General optical detection devices rely on converting photons to electrons (current), and do not allow for direct recording of the phase due to the high oscillation frequency. As so, the missing phase can only be recovered from the intensity measurements. The emerging non-convex phase retrieval algorithm, represented by the Wirtinger Flow (WF) algorithm requires multiple-shot coded diffraction patterns (CDPs) for accurate recovery. To achieve the real-time acquisition for multiple CDPs, this paper proposes a 4f imaging system based on an electrically tunable lens (ETL), which can be used for real-time acquisition of multiple-shot CDPs, and can take the advantages of highspeed, high-resolution, extended depth-of-field, high-sensitivity and low-cost imaging. In this paper, the performance of 4f-ETL based imaging system for phase retrieval with multiple CDPs is compared under different iteration times, different object size, different numbers of masks and different noise levels. Numerical experiments demonstrate the effectiveness and superiority of our proposed ETL-based imaging system, and ETL allows variable-distance focusing of imaging and display systems without mechanical structures, which reduces the mechanical complexity and power consumption, improves acquisition speed.

Back to sources – the role of losses and coherence in super-resolution imaging revisited

Photon losses are intrinsic for any translationally invariant optical imaging system with a non-trivial Point Spread Function, and the relation between the transmission factor and the coherence properties of an imaged object is universal – we demonstrate the rigorous proof of this statement, based on the principles of quantum mechanics. The fundamental limit on the precision of estimating separation between two partially coherent sources is then derived. The careful study of the role of photon losses allows to resolve conflicting claims present in previous works. We compute the Quantum Fisher Information for the generic model of optical 4f imaging system, and use prior considerations to validate the result for a general, translationally invariant imaging apparatus. We prove that the spatial-mode demultiplexing (SPADE) measurement, optimal for non-coherent sources, remains optimal for an arbitrary degree of coherence. Moreover, we show that some approximations, omnipresent in theoretical works about optical imaging, inevitably lead to unphysical, zero-transmission models, resulting in misleading claims regarding fundamental resolution limits.

Characterizations and Use of Recycled Optical Components for Polarizing Phase-Shifting Interferometry Applications

In this research, we report using optical components such as cubic beam splitters, lenses, diffraction gratings, and mirrors from broken, obsolete, or disused electronic devices to implement a simultaneous polarization-based phase-shifting interferometric system. The system is composed of a polarized Mach–Zehnder interferometer (PMZI) which generates a sample pattern coupled to a 4f imaging system with a diffraction grating placed on its Fourier plane. Such a diffractive element replicates the pattern generated by the PMZI, and each replica is centered and modulated by each diffraction order generated by the grating. The corresponding individual phase shifts are controlled by placing linear polarizers with known angles in front of each replica. Experimental results are presented using several phase samples such as an oil drop, a pseudoscorpion claw, a microarthropod, and red blood cells. In addition, a comparison of the retrieved phase was conducted by employing two different phase demodulation algorithms.

Switchable imaging between edge-enhanced and bright-field based on a phase-change metasurface.

Edge-enhanced imaging and bright-field imaging extract different morphological information from an object, and hence a system capable of switching dynamically between them is of vital importance for various applications. By incorporating an elaborately designed meta-device with a 4f imaging system, we demonstrate dynamic switching between 2D edge-enhanced imaging and bright-field imaging. The dynamically switchable characteristic results from the composed phase-change material meta-atoms, which are optimized to provide two independent phase profiles in amorphous and crystalline states. For dynamically switchable imaging, the meta-device functions as either a high-pass or a low-pass filter in the Fourier frequency spectrum, relying on its phase state. In addition, the dynamically switchable imaging is polarization independent. The proposed meta-device owns ultra-thin architecture and polarization-insensitive dynamically switchable functionality, holding potential applications in integrated biomedical imaging and defect detection.

Optical image reconstruction in 4f imaging system: Role of spatial coherence structure engineering

We examine the effect of spatial coherence on the image quality of a classic 4f imaging system when its Fourier plane is partially blocked by an opaque obstacle. We find that although reducing the degree of spatial coherence of the source results in the improved image quality, the concurrent distortions in the image plane are inevitable. Employing a suitable decomposition of a partially coherent light source into a set of coherent pseudo-modes with a multitude of linear phase shifts, we demonstrate that the distortions are primarily induced by the modes whose maxima are located at the obstacle edges. We show that by tailoring spatial coherence of the source we can enable all the coherent modes to circumnavigate the obstacle, ensuring the same image quality as if the obstacle were absent from the Fourier plane. We expect our findings to be instrumental in high-contrast optical microscopy with coherence structured light.

Edge detection by spiral phase contrast imaging at terahertz frequencies

This paper proposes the spiral phase contrast (SPC) imaging at terahertz (THz) frequencies to achieve the target edge detection. The THz SPC imaging is built based on a classical 4f imaging system, and a spiral phase plate is placed in the Fourier plane to generate the spiral phase. Owing to the unique nature of the spiral phase, edge detection can be achieved. The THz SPC imaging mechanism is analysed by the scalar diffraction theory, and its corresponding analytic expression is derived. A circle target is simulated and the resultant image shows a remarkable edge detection. A proof-of-principle experiment is carried out using our designed THz SPC imaging system and the effectiveness of target edge extraction on the THz images is validated. A circle same as the simulation is imaged firstly, which is consistent with the simulated result. And the letter “Z” with more edges is imaged later. All edges in experiments are extracted perfectly, which are extremely consistent with the THz SPC imaging theory.

High-resolution multi-planar coherent diffraction imaging with multimode fiber source

Coherent diffractive imaging (CDI) is a lensless, high-resolution imaging method. In order to overcome the problems of poor-quality image and slow convergence of iterative algorithm in traditional CDI, an innovative setup for the multimode-based phase retrieval method is proposed. Here the multimode fiber source was selected as the light source to replace the traditional plane-wave incidence. Due to the nature of the multimode fiber, a speckle light field can be generated on the output fiber facet and then is used to illuminate the object. Thus the diffraction field can be rapidly changed at a very short distance so as to realize much higher resolution and consume less iteration time. Then a phase-only spatial light modulator (SLM) is used as a negative lens instead of a positive lens in a 4f imaging system for the advantage of larger detection space. This proposed setup has many advantages such as a simpler structure and static recording. The comparison experiments with plane waves confirm that our proposed method has higher reconstruction resolution and smaller iteration errors.

Lens-based phase retrieval under spatially partially coherent illumination—Part I: Theory

We present a novel approach of phase retrieval using a 4f-imaging system, for the specific case of spatially partially coherent illumination. The theoretical investigation presented in Part I is based on scalar diffraction theory in combination with a heuristic approach. We find that the intensity of the de-focused speckle fields across the image plane shows sufficient contrast for phase retrieval, as long as the radius of the point spread function of the imaging system is well below the radius of the correlation area (spatial coherence) in the object plane. We also derive a useful relation, which allows to determine the requirements towards the essential parameters of an experimental setup, such as maximum propagation distance, diameter of the source, illumination distance and the numerical aperture of the imaging system. The consecutive paper, Part II, describes shape measurement based on the present treatise.

Lens-based phase retrieval under spatially partially coherent illumination - Part II: Shape measurements

We experimentally demonstrate the shape measurement of micro objects by means of phase retrieval under spatially partially coherent illumination. This approach offers an extended depth of focus, vibration insensitivity, short measurement time and precise shape measurements, enables the use of spatially extended light sources such as LEDs and thus significantly improves the eye safety of the method. The employed setup is based on a telecentric 4f-imaging system with a tunable lens across the common Fourier plane. Based on the theoretical investigation presented in Part I, we verify that 4f-based phase retrieval is feasible if the radius of the point spread function of the imaging system is smaller than that of the correlation (spatial coherence) area across the object plane. In this case, a light field with a defined complex amplitude can be assigned to the measured intensity distributions. As a proof of principle towards industrial applications, the 3D shape of a cold-formed micro-cup is reconstructed by combining phase retrieval with two-wavelength contouring. A depth of focus in the range of few millimeters and the measurement time and uncertainty of 0.4 s, and 2μm, respectively, can be achieved.

Non-local edge enhanced imaging with incoherent thermal light

Spiral phase contrast imaging is an effective technique for the edge enhancement of a phase object. The spiral phase filter is the core component of the system and it provides sensitivity to the phase and amplitude gradients of the object. General spiral phase contrast imaging depends on the 4f imaging system in a single light beam with the coherent light source of visible or infrared wavelengths. Here, we constructed a non-local edge enhanced imaging system using an incoherent thermal light source. The detected object and the adopted spiral phase filter were non-locally placed in two separated light beams. The edge enhanced ghost image of the phase object can then be achieved through second-order intensity correlation measurements. The classical nature of the spatial degree of freedom of our proposed edge enhanced ghost imaging system was also demonstrated through the measurement of Bell-type inequality.

Cylindrically polarized perfect optical vortex: Generation and focusing properties

In this paper we extend the concept of perfect optical vortex to the vector case and investigate its focusing properties in the high numerical aperture regime. We show that simultaneous phase encoding of orthogonal components can be realized by means of a 4f imaging system incorporating a phase only liquid-crystal spatial light modulator whose director axis is rotated 45° with respect to the horizontal axis. As an example of application, we demonstrate theoretically and experimentally that a ring-shaped field with inner radius of 0.15 λ can be obtained by focusing a radially polarized perfect vortex and a tight spot of 0.34 λ FWHM can be obtained by focusing an azimuthally polarized perfect vortex.

Diffraction and interference pattern by 4f imaging system to determine the thin film magnetic properties

Determine the magnetic properties of thin film material using X-ray has been attracting enormous attention in recent years. In this work, we propose a simple method to determine base on 4F imaging system. The narrow slit is applied to produce diffraction pattern in the X-ray scale. The slit width variation is applied to numerically obeserve the Fraunhofer diffraction pattern sequential changes. To demonstrate the sensitivity of the method, the power distribution of the temporal observed patterns was also measured. The selection of the object shape also discussed for comprehensive discussion.

32 W high-beam-quality long pulse green laser operating in a wide range of temperature from −19 °C to 27 °C

Abstract We report a high-beam-quality long pulse 532 nm laser, which can operate in wide range of temperature. By using a master-oscillator power amplifier (MOPA) system and LBO extracavity-frequency-doubling, we achieved 532 nm laser with the maximum output power of 32 W, the pulse frequency of 12 kHz, and the pulse width 90.2 ns. In addition, the beam quality factors reached M2 x = 1 . 31 , M2 y = 1 . 36 , respectively. In order to get long pulse, apart from choosing suitable transmissivity of output coupler, we also spreaded the cavity length with a 4f imaging system. The laser was proved to be stable when the ambient temperature changed from −19 °C to 27 °C. Compared to other green lasers, this laser can be applied in Rayleigh beaconing because of its long pulse and wide range of working temperature.

Fourier processing with partially coherent fields.

We describe how Fourier signal processing techniques can be generalized to partially coherent fields. Using standard coherence theory, we first show that focusing of a partially coherent beam by a lens modifies its coherence properties. We then consider a 4f imaging system composed of two lenses and discuss how spatial filtering in the Fourier plane allows one to tune the coherence properties of the beam. This, in turn, provides control over the beam's directionality, spectrum, and degree of polarization.

Effects of illumination on image reconstruction via Fourier ptychography

Abstract The Fourier ptychographic microscopy (FPM) technique provides high-resolution images by combining a traditional imaging system, e.g. a microscope or a 4f-imaging system, with a multiplexing illumination system, e.g. an LED array and numerical image processing for enhanced image reconstruction. In order to numerically combine images that are captured under varying illumination angles, an iterative phase-retrieval algorithm is often applied. However, in practice, the performance of the FPM algorithm degrades due to the imperfections of the optical system, the image noise caused by the camera, etc. To eliminate the influence of the aberrations of the imaging system, an embedded pupil function recovery (EPRY)-FPM algorithm has been proposed [Opt. Express 22, 4960–4972 (2014)]. In this paper, we study how the performance of FPM and EPRY-FPM algorithms are affected by imperfections of the illumination system using both numerical simulations and experiments. The investigated imperfections include varying and non-uniform intensities, and wavefront aberrations. Our study shows that the aberrations of the illumination system significantly affect the performance of both FPM and EPRY-FPM algorithms. Hence, in practice, aberrations in the illumination system gain significant influence on the resulting image quality.