Wavefront Information Research Articles

High-precision, real-time wavefront sensing via sparse diffractive deep neural networks

As a key component of adaptive optics systems, wavefront sensing technology is an important way to effectively obtain aberrant phases in optical systems for high-capacity optical communications and high-quality imaging in relevant applications ranging from biological imaging to astronomical observation. To enhance the time efficiency of detection, the wavefront sensing with diffraction deep neural network (D2NN) directly calculates the wavefront information in the optical field. However, the compactness of the D2NN structure and the accuracy of wavefront prediction are important bottlenecks, restricting its practical application. Here, we design a multi-layer compact D2NN based on Bayesian optimization, called sparse D2NN (SD2NN), to achieve high-precision, real-time direct wavefront sensing. The experimental results demonstrated a reduction in the root-mean-square error (RMSE) of the SD2NN wavefront sensing of approximately 45.4%, along with a reduction in the axial length of approximately 82% in comparison to the unoptimized fully connected D2NN. This resulted in the attainment of a minimum layer distance of 8.77 mm. In addition, we additionally explored the effects of network depth and neuron size on the wavefront sensing performance of SD2NN and further summarized the general law of diffraction layer distance and neuron size. The proposed method will provide a reliable means of designing miniaturized integrated wavefront sensing chips.

Comparing the clinical applicability of wavefront phase imaging in keratoconus versus normal eyes

The aim of this work is to quantitatively assess the wavefront phase of keratoconic eyes measured by the ocular aberrometer t·eyede (based on WaveFront Phase Imaging Sensor), characterized by a lateral resolution of 8.6 µm without requiring any optical element to sample the wavefront information. We evaluated the parameters: root mean square error, Peak-to-Valley, and amplitude of the predominant frequency (Fourier Transform analysis) of a section of the High-Pass filter map in keratoconic and healthy cohorts. Furthermore, we have analyzed keratoconic eyes that presented dark–light bands in this map to assess their period and orientation with the Fourier Transform. There are significant statistical differences (p value < 0.001) between healthy and keratoconic eyes in the three parameters, demonstrating a tendency to increase with the severity of the disease. Otherwise, the quantification of the bands reveals that the width is independent of eye laterality and keratoconic stage as orientation, which tends to be oblique. In conclusion, the quantitative results obtained with t·eyede could help to diagnose and monitor the progression of keratoconus.

Exploring Wavefront Detection in Imaging Systems with Rectangular Apertures Using Phase Diversity.

The attainment of a substantial aperture in the rotating synthetic aperture imaging system involves the rotation of a slender rectangular primary mirror. This constitutes a pivotal avenue of exploration in space telescope research. Due to the considerable aspect ratio of the primary mirror, environmental disturbances can significantly impact its surface shape. Active optical technology can rectify surface shape irregularities through the detection of wavefront information. The Phase Diversity (PD) method utilizes images captured by the imaging system to compute wavefront information. In this study, the PD method is applied to rotating synthetic and other rectangular aperture imaging systems, employing Legendre polynomials to model the wavefront. The study delved into the ramifications stemming from the aperture aspect ratio and aberration size.

Alias Transformation of Structured Beam and Holography in Real and Fourier Space Based on Dielectric Metasurface

AbstractStructured beams are analytical solutions to wave equations that possess specific spatial profiles and rigorous transmission properties. Holography enables wavefront reconstruction by recording objective wavefront information. In this study, comprehensive wavefront control by transforming a structured beam in real space is proposed and experimentally verified, and optical holography is reconstructed in Fourier space. To obtain an arbitrary profile of the structured beam, alias transformation is performed to rebuild the coordinate system to form arbitrary user‐defined shapes. Subsequently, the complex amplitude control of the metasurface to encode the alias‐transformed structured beam accordingly is applied. This allows the conventional standard Hermite–Gaussian and Laguerre–Gaussian modes to be transformed into their corresponding shapes while maintaining their distinct features. Holography is realized based on pure phase modulation by interleaving the information with a structured beam, which fully utilizes the space‐bandwidth product of the metasurface. These distinctive optical phenomena in both spaces expand the definition of conventional structured beams and enable further developments in laser fabrication, optical manipulation, and optical displays.

Hexagonal diffractive optical elements.

Diffractive optical elements (DOEs) have widespread applications in optics, ranging from point spread function engineering to holographic display. Conventionally, DOE design relies on Cartesian simulation grids, resulting in square features in the final design. Unfortunately, Cartesian grids provide an anisotropic sampling of the plane, and the resulting square features can be challenging to fabricate with high fidelity using methods such as photolithography. To address these limitations, we explore the use of hexagonal grids as a new grid structure for DOE design and fabrication. In this study, we demonstrate wave propagation simulation using an efficient hexagonal coordinate system and compare simulation accuracy with the standard Cartesian sampling scheme. Additionally, we have implemented algorithms for the inverse DOE design. The resulting hexagonal DOEs, encoded with wavefront information for holograms, are fabricated and experimentally compared to their Cartesian counterparts. Our findings indicate that employing hexagonal grids enhances holographic imaging quality. The exploration of new grid structures holds significant potential for advancing optical technology across various domains, including imaging, microscopy, photography, lighting, and virtual reality.

Fourier ptychographic layer-based imaging of hazy environments

Macroscopic Fourier ptychographic imaging method can significantly improve the resolution of imaging systems. Nevertheless, under far-field complex environment conditions, such as strong scattering medium (e.g.,hazy), the inhomogeneous distribution of the particles inside the hazy cause random interference to the propagation of the photons carrying the target information, resulting in distortion and blurring of the wavefront information. This severely impacts the quality of the final reconstructed image. In this paper, we propose an improved Resnet network to extract and enhance the features from distorted intensity images in hazy environment, and effectively merge information through multi-scale feature fusion. We successfully recover the target intensity information sequences hidden by different concentrations of hazy and even dynamic non-uniform hazy, and present the final Fourier ptychographic reconstruction results. To the best of our knowledge, we are the first to demonstrate the feasibility of far-field Fourier ptychographic imaging through hazy environments using deep learning methods. Experimental results indicate that it can effectively overcome the images blurring and distortion problems caused by the scattering of hazy environment, significantly improving the structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR) of final macroscopic Fourier ptychographic reconstructed images under different hazy levels. This study not only reveals the great value of deep learning in solving the imaging problems of complex scenes such as dynamic non-uniform strong scattering media, but also effectively suppresses the adverse effect of hazy scattering environment on macroscopic Fourier ptychographic imaging, which greatly promotes the progress and development of the application of the Fourier ptychographic imaging technology in the field of imaging complex environments in the long distance.

Highly Stable Spatio-Temporal Prediction Network of Wavefront Sensor Slopes in Adaptive Optics.

Adaptive Optics (AO) technology is an effective means to compensate for wavefront distortion, but its inherent delay error will cause the compensation wavefront on the deformable mirror (DM) to lag behind the changes in the distorted wavefront. Especially when the change in the wavefront is higher than the Shack-Hartmann wavefront sensor (SHWS) sampling frequency, the multi-frame delay will seriously limit its correction performance. In this paper, a highly stable AO prediction network based on deep learning is proposed, which only uses 10 frames of prior wavefront information to obtain high-stability and high-precision open-loop predicted slopes for the next six frames. The simulation results under various distortion intensities show that the prediction accuracy of six frames decreases by no more than 15%, and the experimental results also verify that the open-loop correction accuracy of our proposed method under the sampling frequency of 500 Hz is better than that of the traditional non-predicted method under 1000 Hz.

Multiple image encryption based on multiplexing holography with Kramers–Kronig relations

Multiplexing techniques can store multiple wavefront information of object beams in one hologram, which is a way to realize multi-image encryption. In this paper, an optical multi-image encryption method based on Kramers-Kronig multiplexing digital holography is proposed. In the encryption process, multiple images are subjected to Fresnel diffraction at a certain distance and modulated by a random phase mask. The modulated images then interfere with the reference beam and form a noise-like compound ciphertext. In the decryption process, the information of the original images can be extracted directly from the positive frequency part of the spectrum. Compared to the traditional image encryption based on off-axis digital holography, this method enables the decryption of images in the case of spectrum overlap. The feasibility of our proposed method is demonstrated through numerical simulations, which provide a novel approach for the field of multi-image encryption based on digital holography.

Discrete Multi-Step Phase Hologram for High Frequency Acoustic Modulation

Abstract Acoustic holograms can recover wavefront stored acoustic field information and produce high-fidelity complex acoustic fields. Benefiting from the advantages of the huge spatial information content unmatched by traditional acoustic components, acoustic holograms pursue the realization of high-resolution complex acoustic fields and gradually tend to high-frequency ultrasound applications. However, conventional continuous phase holograms are limited by 3D printing size and the presence of unavoidable small printing errors make it difficult to achieve acoustic field reconstruction at high frequency accuracy. Here, we present an optimized discrete multi-step phase hologram. It can guarantee the reconstruction quality of image with high robustness, and properly lower the requirement of the 3D printing accuracy. Meanwhile, the concept of reconstruction similarity is proposed to refine a measure of acoustic field quality. In addition, the realized complex acoustic field at 20 MHz promotes the application of acoustic holograms in high frequencies and provides a new way to generate high-fidelity acoustic fields.

Lensless masked imaging with self-calibrated phase retrieval.

Lensless imaging with a mask is an attractive topic as it enables a compact configuration to acquire wavefront information of a sample with computational approaches. Most existing methods choose a customized phase mask for wavefront modulation and then decode the sample's wave field from modulated diffraction patterns. Different from phase masks, lensless imaging with a binary amplitude mask facilitates a cheaper fabrication cost, but high-quality mask calibration and image reconstruction have not been well resolved. Here we propose a self-calibrated phase retrieval (SCPR) method to realize a joint recovery of a binary mask and sample's wave field for a lensless masked imaging system. Compared with conventional methods, our method shows a high-performance and flexible image recovery without the help of an extra calibration device. Experimental results of different samples demonstrate the superiority of our method.

Eyebox expansion with accurate hologram generation for wide-angle holographic near-eye display.

Small eyebox in wide-angle holographic near-eye display is a severe limitation for 3D visual immersion of the device. In this paper, an opto-numerical solution for extending the eyebox size in these types of devices is presented. The hardware part of our solution expands the eyebox by inserting a grating of frequency fg within a non-pupil forming display configuration. The grating multiplies eyebox, increasing the possible eye motion. The numerical part of our solution is an algorithm that enables proper coding of wide-angle holographic information for projecting correct object reconstruction at arbitrary eye position within the extended eyebox. The algorithm is developed through the employment of the phase-space representation, which facilitates the analysis of the holographic information and the impact of the diffraction grating in the wide-angle display system. It is shown that accurate encoding of the wavefront information components for the eyebox replicas is possible. In this way, the problem of missing or incorrect views in wide angle near-eye display with multiplied eyeboxes is efficiently solved. Moreover, this study investigates the space-frequency relation between the object and the eyebox and how the hologram information is shared between eyebox replicas. The functionality of our solution is tested experimentally in an augmented reality holographic near-eye display that has maximum field of view of 25.89°. Obtained optical reconstructions demonstrate that correct object view is obtained for arbitrary eye position within extended eyebox.

Improved SNR and super-resolution reconstruction of multi-scale digital holography based on deep learning

Digital holography is one of the key technologies to obtain the wavefront information of three-dimensional objects, and obtaining high quality hologram is the primary condition. Due to the constraints of image sensors and the influence of experimental environment, the digital hologram obtained has the problems of speckle noise and low resolution. In order to overcome this constraint, a method based on deep learning is used to improve the hologram quality and fringe signal-to-noise ratio, and then high-quality reconstructed phase diagrams are obtained as data sets to realize end-to-end superresolution reconstruction. The results show that the obtained high quality hologram has better reconstruction effect, and the effect of speckle noise is suppressed. The performance of three loss functions in the training of the network is compared.

Label-free optical interferometric microscopy to characterize morphodynamics in living plants.

During the last century, fluorescence microscopy has played a pivotal role in a range of scientific discoveries. The success of fluorescence microscopy has prevailed despite several shortcomings like measurement time, photobleaching, temporal resolution, and specific sample preparation. To bypass these obstacles, label-free interferometric methods have been developed. Interferometry exploits the full wavefront information of laser light after interaction with biological material to yield interference patterns that contain information about structure and activity. Here, we review recent studies in interferometric imaging of plant cells and tissues, using techniques such as biospeckle imaging, optical coherence tomography, and digital holography. These methods enable quantification of cell morphology and dynamic intracellular measurements over extended periods of time. Recent investigations have showcased the potential of interferometric techniques for precise identification of seed viability and germination, plant diseases, plant growth and cell texture, intracellular activity and cytoplasmic transport. We envision that further developments of these label-free approaches, will allow for high-resolution, dynamic imaging of plants and their organelles, ranging in scales from sub-cellular to tissue and from milliseconds to hours.

Photon-starved snapshot holography

Digital holography (DH) is a powerful imaging modality that is capable of capturing the object wavefront information, making it very valuable for diverse scientific research applications. Generally, it requires ample illumination to enable good fringe visibility and a sufficient signal-to-noise ratio. As such, in situations such as probing live cells with minimal light interaction and high-speed volumetric tracking in flow cytometry, the holograms generated with a limited photon budget suffer from poor pattern visibility. While it is possible to make use of photon-counting detectors to improve the hologram quality, the long recording procedure coupled with the need for mechanical scanning means that real-time extremely low-light holographic imaging remains a formidable challenge. Here, we develop a snapshot DH that can operate at an ultra-low photon level (less than one photon per pixel). This is achieved by leveraging a quanta image sensor to capture a stack of binary holographic frames and then computationally reconstructing the wavefront through integrating the mathematical imaging model and the data-driven processing, an approach that we termed PSHoloNet. The robustness and versatility of our DH system are demonstrated on both synthetic and experimental holograms with two common DH tasks, namely particle volumetric reconstruction and phase imaging. Our results demonstrate that it is possible to expand DH to the photon-starved regime, and our method will enable more advanced holography applications in various scientific imaging systems.

Study on the decision method of thermal spherical aberration coefficient of single end-pumped Nd:YVO4 Laser

An analytical method which can be used as a guide to determine the thermal spherical aberration in the stable zone is presented. The position factor is numerically simulated with the change of pump power. The method of determining the stable limit by the particular values of the position factor is proposed and explained from the perspective of classical optics. The influence of the shape factor on the thermal spherical aberration coefficient is discussed. The wavefront information measurement experiment of asymmetric flat cavity of single end-pumped Nd:YVO4 is constructed. The thermal spherical aberration and the waist parameters at both ends of the thermal lens in the cavity are measured, and the symmetric cavity is used as the support experiment. The particular values of the position factor could be used as the basis for determining the stable limit. The experimental results of the thermal spherical aberration coefficient are consistent with the theoretical analysis.

Dynamic Chiral Metasurfaces for Broadband Phase‐Gradient Holographic Displays

AbstractNext‐generation holographic displays have promising applications in medical science, augmented/virtual reality, smart security, data encryption, etc. Although metasurfaces emerged as the suitable choice to provide compact holographic displays, multifunctionality in metasurfaces at broadband optical wavelengths is inevitable for the abovementioned applications. Here, a metasurface is demonstrated based on chiral structures to introduce multifunctionality in terms of multiple wavefront information depending upon the polarization of incident light. The proposed metasurface integrated with a liquid crystal (LC) provides fast switching and dynamic optical response at broadband visible wavelengths in transmission mode. To avoid the phase distortion in multiple wavefront information embedded into a single planar metasurface, chiral z‐shaped meta‐atoms are used to provide high diffraction efficiency and phase chirality response for circularly polarized (CP) light illuminations. The phase mask of holographic information is encoded into the metasurface using a combination of dynamic and geometric phase modulation techniques. The experimental validation of the designed metasurface is performed to reproduce the spin‐dependent‐specific information at broadband visible wavelengths for changing the polarization of incident light. This research may pave the way toward designing highly efficient multifunctional metadevices to produce next‐generation holographic displays for promising applications in healthcare, media, smart security, and data encryption.

Adaptive Optics Compensation for Orbital Angular Momentum Optical Wireless Communications

Adaptive optics (AO) can efficiently compensate for turbulence-induced distortion in orbital angular momentum (OAM)-based optical wireless communication (OWC) systems. In this paper, we design a modified phase diversity algorithm (MPDA)-based wavefront sensor to enhance the reconstruction accuracy of distorted OAM wavefront information. Aiming to further strike a compelling trade-off between AO system complexity and compensation accuracy, we first construct a novel AO system that applies a quickly and electronically controlled focus-tunable lens (FTL). It decontaminates distorted OAM signaling beams while having a low systemic complexity and superior convergence performance. Furthermore, we propose the 3-modified phase diversity algorithm (3-MPDA) AO scheme relying upon a Fourier intensity and two defocused intensities as the prior information, which beneficially balances the compensation effect and the number of defocused intensities and exhibits good noise robustness against charge-coupled device (CCD) detectors. In summary, this paper provides new insight for designing AO schemes with high compensation performance in communication links.

Two-dimensional differential null interferometry of transmission wavefront of axicon lens

Axicon lenses are critical in the beam transforming, such as the Bessel beam and hollow beam generation, and its manufacturing accuracy directly affects the quality of the output beam. Aiming at the versatility and high accuracy, we propose a two-dimensional differential null interferometry for measuring transmission wavefront of axicon lens. The method uses a pair of axicon lens to construct a null interferometric setup, with one as the compensator. The two-dimensional difference separates the wavefront information introduced by the compensator and achieves the orthogonal difference of the measured wavefront. Finally, the measured wavefront is reconstructed from the differential wavefront based on the Hudgin slope method. The experiments proved that this method achieves a measurement accuracy of ±0.125 µm with a repeatability of 0.759 nm.

Fast wavefront sensing for X-ray optics with an alternating speckle tracking technique.

Advances in accelerator technologies have enabled the continuous development of synchrotron radiation and X-ray free electron laser (XFEL) sources. At the same time, it has been critical to perform in-situ wavefront sensing to aid delivery of high-quality X-ray beams to the end users of these facilities. The speckle-based scanning technique has obtained popularity due to its high spatial resolution and superior sensitivity compared to other wavefront sensing methods. However, these advantages often come at the expense of longer data acquisition times since multiple images have to be collected to derive the necessary wavefront information. Whereas initial speckle tracking techniques could obtain wavefront information relatively quickly, the installation of additional hardware was routinely required to do so. Here, we propose a novel speckle-based approach, termed Alternating Speckle Tracking (AST), to perform fast wavefront sensing within a conventional beamline setup. The wavefront information derived from the new technique has proven to be valuable for many applications that require temporal resolution. Importantly, both horizontal and vertical wavefront information can be simultaneously derived by moving the speckle generator along the diagonal direction. We expect this method will be widely used by the synchrotron radiation and XFEL community in the future.

Liquid-crystal-polymer binary diffractive optical elements with a sub-micrometer feature size realized by a contact polarization holography.

In this Letter, a contact polarization holographic photoalignment method is proposed. In the holographic recording, a phase mask is contacted with a photoalignment film, making light carrying wavefront information interfere with reference light in the near-field region to realize polarization holographic pattern recording with a sub-micrometer feature size. The relevant theoretical derivation is given, and holographic recording of a 0.4 µm feature-size phase mask is realized. The proposed method can conveniently realize liquid-crystal binary diffractive optical elements with a sub-micrometer feature size. Off-axis diffraction can also be realized by superimposing the grating information by changing the angle between the substrate and the interference light.