Complex Field Images Research Articles

All-optical complex field imaging using diffractive processors.

Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However, conventional image sensors are intensity-based and inherently lack the capability to directly measure the phase distribution of a field. This limitation can be overcome using interferometric or holographic methods, often supplemented by iterative phase retrieval algorithms, leading to a considerable increase in hardware complexity and computational demand. Here, we present a complex field imager design that enables snapshot imaging of both the amplitude and quantitative phase information of input fields using an intensity-based sensor array without any digital processing. Our design utilizes successive deep learning-optimized diffractive surfaces that are structured to collectively modulate the input complex field, forming two independent imaging channels that perform amplitude-to-amplitude and phase-to-intensity transformations between the input and output planes within a compact optical design, axially spanning ~100 wavelengths. The intensity distributions of the output fields at these two channels on the sensor plane directly correspond to the amplitude and quantitative phase profiles of the input complex field, eliminating the need for any digital image reconstruction algorithms. We experimentally validated the efficacy of our complex field diffractive imager designs through 3D-printed prototypes operating at the terahertz spectrum, with the output amplitude and phase channel images closely aligning with our numerical simulations. We envision that this complex field imager will have various applications in security, biomedical imaging, sensing and material science, among others.

Analytical solution for single-pixel ptychography through linear modeling

Amplitude-modulated single-pixel ptychography (SPP) enables non-interferometric complex-field imaging of objects. However, the conventional iterative and nondeterministic reconstruction methods, based on the ptychography algorithm, pose challenges in fully understanding the role of critical optical parameters. In response, this paper introduces an innovative analytical approach that establishes a theoretical foundation for the uniqueness of SPP reconstruction results. The proposed method conceptualizes SPP as a system of linear equations in the frequency domain, involving both object and modulated illumination. Solving this equation system reveals a determined solution for the complex object, providing an alternative to iterative and nondeterministic techniques. Through a series of simulations, this approach not only validates the uniqueness of SPP reconstruction, but also explores key properties influencing accuracy.

Crop plant automatic detecting based on in-field images by lightweight DFU-Net model

Efficiently and accurately extracting crop plants from authentic and complex field images is essential to ensure the economic efficiency of agricultural production and enhance farming operations. However, many existing deep Convolutional Neural Networks (CNNs) prioritize accuracy over efficiency in crop detection, often lacking real-time capabilities. Therefore, this study aims to investigate the automated detection of various crops, such as cotton plants and seed melons, in natural environments using a U-Net established with a Double-depth convolutional and Fusion block (DFU-Net). This involves exploring compound loss functions for improved accuracy. The DFU-Net model combines the strengths of lightweight CNNs and the U-Net model, constructing a Lightweight Crop with a Double-Depth Convolution backbone (LC-DDC). This is achieved by introducing a Double-Depth Convolutional block (DDC block) and incorporating initial and fusion blocks at the first and last positions of the encoder, respectively. The effectiveness of these designs is confirmed through ablation experiments and interpretability analyses. The experimental results indicate that the DFU-Net model achieved Pixel Accuracy (PA), mean Intersection over Union (mIoU), and F1 metrics exceeding 92.0 % for the cotton plant, seed melon, and Chloroplast Viability Prediction in Plant Phenotyping (CVPPP) dataset. Particularly, on the CVPPP dataset, DFU-Net outperformed the Pyramid Scene Parsing Network (PSPNet) model, demonstrating 16.4 %, 17.2 %, and 13.2 % higher PA, mIoU, and F1 scores, respectively. In addition, DFU-Net demonstrated efficient model space utilization, requiring only 0.975 MB and 1.68 GB for parameters and floating-point operations (FLOPs), respectively. The performance of low-performance computers is impressive, achieving a detection speed of 10.5 Frames Per Second (FPS), which is 6.9 times faster than that of the Deeplabv3 + model. This achievement demonstrates a balanced compromise between detection speed and accuracy. This study provides novel approaches for optimizing crop-detection algorithms, providing valuable technical support for intelligent crop management.

∂H$\bm{\partial }\mathbf {H}$: Differentiable Holography

AbstractOver the past decade, the field of holography has gained significant ground due to advances in computational imaging. However, the utilization of computational tools is hampered by the mismatch between experimental setups and the conceptual model. Differentiable holography (), a novel framework for automatically self‐calibrating experimental imperfections in inverse holographic imaging, is presented here. The technique is demonstrated on auto‐focused complex field imaging from a single intensity‐only inline hologram.

Single-shot complex field imaging through a diffuser by in-line holography with polarization multiplexing

The imaging of complex-amplitude objects that are hidden behind scattering media by single frame detection has faced challenges. Here, we propose, and experimentally demonstrate, a novel complex-field imaging technique through a scattering medium by utilizing the in-line holography scheme in combination with polarization multiplexing. The imaging is achieved by using a polarization multiplexing assisted four-step phase shifting scheme and by designing a compact in-line holographic configuration. Moreover, the randomness associated with the speckle pattern generation of the object transmission through the diffuser is removed after an imaging system in accordance with the shower-curtain effect is employed. We experimentally demonstrate the potential of the technique by single-shot measurement of multiple phase-shifting holograms acquired with a polarization camera and illustrate the dominance of the approach over traditional phase-shifting holography-based imaging through diffusers. Finally, the efficacy of the approach is demonstrated with complex field imaging of nervures in the honeybee wing.

Matching an immersion medium's refractive index to a cell's cytosol isolates organelle scattering.

Angularly-resolved light scattering has been proven to be an early detector of subtle changes in organelle size due to its sensitivity to scatterer size and refractive index contrast. However, for cells immersed in media with a refractive index close to 1.33, the cell itself acts as a larger scatterer and contributes its own angular signature. This whole-cell scattering, highly dependent on the cell's shape and size, is challenging to distinguish from the desired organelle scattering signal. This degrades the accuracy with which organelle size information can be extracted from the angular scattering. To mitigate this effect, we manipulate the refractive index of the immersion medium by mixing it with a water-soluble, biocompatible, high-refractive-index liquid. This approach physically reduces the amount of whole-cell scattering by minimizing the refractive index contrast between the cytosol and the modified medium. We demonstrate this technique on live cells adherent on a coverslip, using Fourier transform light scattering to compute the angular scattering from complex field images. We show that scattering from the cell: media refractive index contrast contributes significant scattering at angles up to twenty degrees and that refractive index-matching reduces such low-angle scatter by factors of up to 4.5. This result indicates the potential of refractive index-matching for improving the estimates of organelle size distributions in single cells.

Single-Shot On-Axis Fizeau Polarization Phase-Shifting Digital Holography for Complex-Valued Dynamic Object Imaging

Digital holography assisted with inline phase-shifting methods has the benefit of a large field of view and a high resolution, but it is limited in dynamic imaging due to sequential detection of multiple holograms. Here we propose and experimentally demonstrate a single-shot phase-shifting digital holography system based on a highly stable on-axis Fizeau-type polarization interferometry. The compact on-axis design of the system with the capability of instantaneous recording of multiple phase-shifted holograms and with robust stability features makes the technique a novel tool for the imaging of complex-valued dynamic objects. The efficacy of the approach is demonstrated experimentally by complex field imaging of various kinds of reflecting-type static and dynamic objects. Moreover, a quantitative analysis on the robust phase stability and sensitivity of the technique is evaluated by comparing the approach with conventional phase-shifting methods. The high phase stability and dynamic imaging potential of the technique are expected to make the system an ideal tool for quantitative phase imaging and real-time imaging of dynamic samples.

Single-Shot Complex Field Imaging Through a Diffuser by In-Line Holography with Polarization Multiplexing

Single-Shot Complex Field Imaging Through a Diffuser by In-Line Holography with Polarization Multiplexing

A modified U-Net with a specific data argumentation method for semantic segmentation of weed images in the field

Weeds are harmful to crop yield. The segmentation of weeds in images is of great significance for precise weeding and reducing herbicide pollution. However, in the field environment, crops and weeds are similar, so it is difficult to accurately segment weed from complex field images. In this paper, an algorithm based on deep learning was proposed to segment weeds from images. This algorithm can segment weeds from the soil and crops in images. This semantic segmentation algorithm was developed with a simplified U-net. Due to the difficulty of image labeling for the semantic segmentation of weeds, an image augmentation method was proposed. The semantic segmentation network was trained by a two-stage training method composed of pre-training and fine-tuning. After training, the intersection over union (IoU) of this method was 92.91% and the average segmentation time of a single image (ST) was 51.71 ms. The results demonstrated that the modified U-Net was able to effectively segment weeds from images with a significant amount of other plants. The weed-targeted image segmentation method proposed in this paper can accurately segment weeds in complex field environments. It has a relatively wide range of applicability.

Single-pixel ptychography.

Ptychography is a predominant non-interferometric technique to image large complex fields but with quite a narrow working spectrum, because diffraction measurements require dense array detection with an ultra-high dynamic range. Here we report a single-pixel ptychography technique that realizes non-interferometric and non-scanning complex-field imaging in a wide waveband, where 2D dense detector arrays are not available. A single-pixel detector is placed in the far field to record the DC-only component of the diffracted wavefront scattered from the target field, which is illuminated by a sequence of binary modulation patterns. This decreases the measurements' dynamic range by several orders of magnitude. We employ an efficient single-pixel phase-retrieval algorithm to jointly recover the field's 2D amplitude and phase maps from the 1D intensity-only measurement sequence. No a priori object information is needed in the recovery process. We validate the technique's quantitative phase imaging nature using both calibrated phase objects and biological samples and demonstrate its wide working spectrum with both 488-nm visible light and 980-nm near-infrared light.

Coded coherent diffraction imaging with reduced binary modulations and low-dynamic-range detection.

Conventional coherent diffraction imaging (CDI) suffers from inherent phase retrieval ambiguity due to limited intensity-only measurements. Coded illumination with multiple modulations has been introduced to tackle the underdetermination challenge, which however slows down imaging speed. In addition, the required high-dynamic-range acquisition at the Fourier plane is also time consuming. To increase imaging speed, we report an accelerated coded CDI method in this Letter. It requires only three binarized intensity patterns to illuminate the full field, which can be implemented at ∼22kHz using a digital micromirror device. Each diffraction pattern at the Fourier plane is acquired in a single shot without high-dynamic-range synthesis, resulting in three intensity-only images corrupted with underexposed pixels. We develop an adaptive phase retrieval algorithm to adaptively remove the negative influence of underexposure and recover both the object's amplitude and phase. Both simulations and experiments validate that the method enables fast and high-fidelity complex-field imaging.

Speckle-field digital polarization holographic microscopy.

We present a new polarization holographic microscopy technique based on speckle-field illumination with enhanced spatial resolution and controlled coherent noise reduction. The proposed technique employs a spatial light modulator for the generation of a sequential speckle pattern for the illumination of the sample. The developed microscope is capable of simultaneous extraction of orthogonal polarization components of the field emanating from the sample. We demonstrate the potential features of the technique by presenting spatially resolved images of the known samples and the inhomogeneous anisotropic samples. The technique has substantial significance in biomedical imaging with digital auto-focusing and complex field imaging.

Noise-robust pixel-super-resolved multi-image phase retrieval with coherent illumination

Multi-image phase retrieval (MPR) algorithms play a significant role in the success of coherent diffractive imaging and in-line lensfree digital holographic imaging. However, they still suffer from the pixelation problem. By using them in combination with pixel super-resolution algorithms, the problem could be partially alleviated. But the existing pixel-super-resolved MPR method requires delicate parameter tuning and additional de-noising techniques. In this paper, we propose a new noise-robust pixel-super-resolved MPR scheme. It obviates the need for the mechanical movement of traditional pixel super-resolution methods and needs no extra measurements so that it can be directly applied in the existing system or dataset. Compared with the existing reconstruction method, it requires no sophisticated parameter selection and exhibits higher noise robustness, especially under laser illumination. Also, a new and effective focus measure is put forward so as to locate the object plane with higher precision and robustness. As a whole, our scheme provides a new label-free way of complex field imaging with a large field of view and high spatial resolution.

Single-shot digital holographic microscopy for quantifying a spatially-resolved Jones matrix of biological specimens.

Field-based polarization measurements are essential for the completeness of information when exploiting the complex nature of optical responses of target objects. Here, we demonstrate digital holographic microscopy for quantifying a polarization-sensitive map of an object with a single-shot measurement. Using the image-splitting device generating four different copies of an object image and a separate reference beam of an off-axis configuration enables single-shot and multi-imaging capability. With the use of two polarization filters, four complex field images containing an object's polarization response are obtained simultaneously. With this method, we can construct a complete set of 2-by-2 Jones matrix at every single point of the object's images, and thus clearly visualize the anisotropic structures of biological tissues with low level of birefringence. This method will facilitate the high-precision measurements for fast dynamics of the polarization properties of biological specimens.

Cell imaging beyond the diffraction limit using sparse deconvolution spatial light interference microscopy

We present an imaging method, dSLIM, that combines a novel deconvolution algorithm with spatial light interference microscopy (SLIM), to achieve 2.3x resolution enhancement with respect to the diffraction limit. By exploiting the sparsity of the phase images, which is prominent in many biological imaging applications, and modeling of the image formation via complex fields, the very fine structures can be recovered which were blurred by the optics. With experiments on SLIM images, we demonstrate that significant improvements in spatial resolution can be obtained by the proposed approach. Moreover, the resolution improvement leads to higher accuracy in monitoring dynamic activity over time. Experiments with primary brain cells, i.e. neurons and glial cells, reveal new subdiffraction structures and motions. This new information can be used for studying vesicle transport in neurons, which may shed light on dynamic cell functioning. Finally, the method is flexible to incorporate a wide range of image models for different applications and can be utilized for all imaging modalities acquiring complex field images.

Phase and amplitude imaging from noisy images by Kalman filtering

We propose and demonstrate a computational method for complex-field imaging from many noisy intensity images with varying defocus, using an extended complex Kalman filter. The technique offers dynamic smoothing of noisy measurements and is recursive rather than iterative, so is suitable for adaptive measurements. The Kalman filter provides near-optimal results in very low-light situations and may be adapted to propagation through turbulent, scattering, or nonlinear media.

Optical diffraction tomography for high resolution live cell imaging

We report the experimental implementation of optical diffraction tomography for quantitative 3D mapping of refractive index in live biological cells. Using a heterodyne Mach-Zehnder interferometer, we record complex field images of light transmitted through a sample with varying directions of illumination. To quantitatively reconstruct the 3D map of complex refractive index in live cells, we apply optical diffraction tomography based on the Rytov approximation. In this way, the effect of diffraction is taken into account in the reconstruction process and diffraction-free high resolution 3D images are obtained throughout the entire sample volume. The quantitative refractive index map can potentially serve as an intrinsic assay to provide the molecular concentrations without the addition of exogenous agents and also to provide a method for studying the light scattering properties of single cells.

Phase sensitive optical near-field mapping using frequency-shifted laser optical feedback interferometry

The use of laser optical feedback Imaging (LOFI) for scattering-type scanning near-field optical microscopy (sSNOM) is proposed and investigated. We implement this sensitive imaging method by combining a sSNOM with optical heterodyne interferometry and the dynamic properties of a B class laser source which is here used both as source and detector. Compared with previous near field optical heterodyne experiments, this detection scheme provides an optical amplification that is several orders of magnitude higher, while keeping a low noise phase-sensitive detection. Successful demonstration of this complex field imaging technique is done on Silicon on Insulator (SOI) optical waveguides revealing phase singularities and directional leakage.