Speckle Phenomena in Optics: Theory and Applications
... The scattering of a coherent wave when transmitting through a random medium or reflecting from a rough surface inflicts a transformation in the complex amplitude and phase of the wave. Multiple scattered partial waves interfere with each other and form a granular structure known as a speckle pattern [1,2]. This phenomenon has been observed in a wide range of waves of different nature [3,4]. ...
... Speckle field is the superposition of a large number of partial waves with random and independent amplitudes and phases, where the phases are distributed over a range of 2 . Under these general conditions, the speckle field is characterized by Rayleigh statistics where the field's amplitude follows a Gaussian distribution, and a negative exponential intensity distribution is observed in the speckle [1,2]. The central limit theorem of random variables dictates the Rayleigh statistics under these circumstances [5]. ...
... For some instances, such as in the weak scattering regime or near field region of the scattering media, where limited scattering waves are detected, random phases are not distributed uniformly in the range of 2 . Therefore, statistical properties follow non-Rayleigh statistics such as the Rician or Rice distribution [1,[5][6][7][8]. Statistical properties deviate from the Rayleigh distribution even in the strong scattering regime if the phase of partial waves is correlated. ...
We analytically derive an expression for a speckle field's intensity probability density function (PDF) in a nonlinear medium. The analytically driven results are in good agreement with the numerical outcomes. In a focusing nonlinear medium, the local intensity of the speckle is enhanced as manifested through the longer tail of the PDF. In contrast, the local intensity of speckle is reduced in the presence of a defocusing nonlinearity, and the tail of the probability density function also reduces. This change in local intensity of the speckles arises due to the cubic Kerr nonlinearity, which eventually modifies the second-order statistics. Hence, the intensity correlation is altered as per the nature of the associated nonlinearity while the field correlation remains invariant of both types of the nonlinear conditions.
... Materials or environments in which light undergoes multiple scattering events are commonly referred to as complex media [1,2]. Many everyday structures fall into this category. ...
... Many everyday structures fall into this category. For instance, white paint reflects most of the incident visible light, yet it cannot serve as a mirror because multiple scattering events randomize the light's direction [1,2]. Similarly, fog scatters light and prevents us from clearly observing distant objects, creating a serious challenge for both human vision and optical sensing technologies like LIDAR [3,4]. ...
... In such conditions, conventional imaging approaches -such as Laser Scanning Microscopy (LSM) -become ineffective. The tightly focused excitation spot, which is crucial for high-resolution imaging, is rapidly degraded by scattering and transforms into a so-called speckle pattern -a random interference pattern formed by multiply scattered light [1]. As a result, the ability to resolve fine structures deep inside the brain is fundamentally limited by the scattering properties of the tissue. ...
Achieving high-resolution optical imaging deep within heterogeneous and scattering media remains a fundamental challenge in biological microscopy, where conventional techniques are hindered by multiple light scattering and absorption. Here, we present a non-invasive imaging approach that harnesses the nonlinear response of luminescent labels in conjunction with the statistical and spatial properties of speckle patterns - an effect of random light interference. Using avalanching nanoparticles (ANPs) with strong photoluminescence nonlinearity, we demonstrate that random speckle illumination can be converted into a single, localized, sub-diffraction excitation spot. This spot can be scanned across the sample using the angular memory effect, enabling high-resolution imaging through a scattering layer. Our method is general, fast, and cost-effective. It requires no wavefront shaping, no feedback, and no reconstruction algorithm, offering a powerful new route to deep, high-resolution imaging through complex media.
... Nevertheless, these models do not properly take into account multiple reflections. 6 To overcome this limit, facets must not be considered in isolation, but rather in pairs. When a light ray hits a facet, it can bounce on another facet, be reflected towards the observer or get lost in the dark. ...
... The number of facets per pixel (n), which is the inverse of the zooming factor (z) , is high ( n > 1 and z < 1) . The variance decreases with n and 6 Torrance and Sparrow's geometrical optics model [19] relies on the following hypothesis: "(5) Only the first reflection of an incident beam is added to the specularly reflected flux. (6) All multiple reflections are assumed to be perfectly diffused." ...
... (6) All multiple reflections are assumed to be perfectly diffused." Shinning points (physical optics) models have same limitations [2,6]. 7 Although it might be closer to Plekszy-Gladz's [8]. ...
Identifying ternary gold alloys by their mere colors appears to be problematic. Surface state induces multiple reflections and creates mixtures of structural colors. Two models stochastic backward raytracing (SBR) and finite asymmetrical dihedral facets (FADF) are explored to compute the color of a given surface state. Assaying gold by its color without a touchstone seems hopeless but using colorimetric microscopy and variable magnification could be a way forward.
... A laser speckle is an interference pattern formed by coherent light reflected from a rough surface. The surface pattern changes over time due to variations in optical properties, scatterer movement, or external influences [1]. A proposed sensitive subpixel correlation method enables the detection of subtle changes undetectable by standard techniques. ...
... [ ] = ∑= 1 ...
... However, low coherence is needed in some special cases, such as projection displays [13], synthetic aperture radar [14], and microscopy [15]. Speckles with random strength and sizes are produced through destructive and constructive interference, when the laser is scattered by a coarse object [16]. The speckle phenomenon obstructs the observer from obtaining information from the image. ...
... where m is the number of the spectral peaks, p i is the normalized intensity of the i-th spectral peak, and w i is the full width at half maximum of the i-th spectral peak. SC is used to evaluate the impact of speckle noise, which is calculated by [16] ...
Laser diodes working at 940 nm are potential in video surveillance systems, but the speckle problem needs to be solved. Both the spectrum and far-field pattern of the broad-area semiconductor lasers (BALs) are important for speckle suppression of multimode fibers, but the relation between them has not been studied. In this paper, the time-averaged spectrum and far-field pattern of the BALs under optical feedback are studied in experiments and simulations. Effective spectral bandwidth and spot fill factor are introduced to evaluate the effective temporal coherence of the BALs and the relative numerical aperture of the coupled light. In-phase change between the effective spectral bandwidth and spot fill factor is observed under different feedback intensities, due to the spatial separation of the longitudinal modes. Low speckle contrast is obtained under 10% to ∼20% optical feedback, while stronger feedback may reduce the speckle suppression efficiency. A spectral bandwidth of 15.3 nm is observed under 10% feedback, but the spectral hole-burning is serious. The spectral hole-burning is partly suppressed by tuning the length of the external cavity. What we believe to be a novel low frequency fluctuation is observed in BALs at a high pump current, which may have some relation with the spatial bistability of the lateral modes. The spatiotemporal dynamic of BALs is simulated by a multimode model of BALs, and the spatial separation of the longitudinal modes is demonstrated. This work provides insight into the spectral and spatial characteristics of the BALs under optical feedback.
... Light field manipulation is traditionally based on fully coherent optics approaches. However, it is known that the light beams produced by these methods introduce some negative effects, such as speckle noise [4], and are very sensitive to external perturbations [5]. Mitigating this vulnerability has been an open challenge and requires in-depth research. ...
Research on the optical coherence manipulation has made significant progress, but the modulation rate of conventional tailoring technology is too low, which has become a key factor hindering its transition from laboratory to practical application. Here, we utilize lithium niobate films (LNF) modulator to achieve high-speed optical coherence manipulation based on its high-speed electro-optical modulation capability. Our experimental modulation rate reaches 350 kHz, which is about 20 times higher than the fastest modulation rate reported so far. This design strategy provides a simple rule for high-speed optical coherence manipulation based on electro-optical modulation, paving the way for further practical applications of optical coherence manipulation technology.
... Illuminating an optically rough surface with coherent light, such as a laser, results in light being scattered on and below the surface [10]. The backscattered light undergoes interference, creating a random pattern of bright and dark spots, known as a laser speckle pattern [11][12][13][14]. However, as the scattering structures are not static instead undergo Brownian motion, the laser speckle pattern fluctuates [15]. ...
The ability to measure protein functionality is critical for the development of plant-based products, particularly with respect to gelation behavior, which is vital for food structure and texture. Small amplitude oscillatory shear (SAOS) tests remain the standard for monitoring protein gelation; however, these methods are costly, time-consuming, and require physical contact with the sample. Laser speckle rheology, an optical-based technique, offers a contactless alternative by assessing rheological properties through speckle pattern fluctuations. In this work, we present a simple laser speckle rheology setup, utilizing a diode laser and a digital camera, to monitor rheological changes during the rennet coagulation of milk. We use a viscoelasticity index (VI), derived from a two-dimensional linear correlation, to quantify speckle pattern fluctuations. The laser speckle rheology method is compared with conventional SAOS rheology. Results demonstrate that key characteristics of the coagulation process, including coagulation and gelation times, are temporally aligned between the two methods. Furthermore, the VI allows for the comparison of the complex modulus in samples with similar compositions under consistent acquisition parameters. These findings underscore the potential of laser speckle rheology as a cost-effective, rapid, and contactless approach for capturing protein gelation, providing an alternative to conventional shear rheological methods.
... If the scatterers on the surface are stationary and static, the scattered light forms stable laser speckle patterns. However, if the scatterers move or change over time, time-varying speckles are produced [1]. The literature data indicate advances and potential applications of laser speckle techniques to evaluate dynamic processes in microbiological media. ...
This study addresses the challenge of rapidly and accurately distinguishing zones of microbial activity from antibiotic inhibition zones in Petri dishes. We propose a laser speckle imaging technique enhanced with subpixel correlation analysis to monitor dynamic changes in the inhibition zone surrounding an antibiotic disc. This method provides faster results compared to the standard disk diffusion assay recommended by EUCAST. To enable automated analysis, we used machine learning algorithms for classifying areas of bacterial or fungal activity versus inhibited growth. Classification is performed over short time windows (e.g., 1 h), supporting near-real-time assessment. To further improve accuracy, we introduce a correction method based on the known spatial dynamics of inhibition zone formation. The novelty of the study lies in combining a speckle imaging subpixel correlation algorithm with ML classification and with pre- and post-processing. This approach enables early automated assessment of antimicrobial effects with potential applications in rapid drug susceptibility testing and microbiological research.
... It was soon discovered that the origin of the observed pattern was the superposition of randomly phased reflected wavetrains and the observed phenomenon became known as speckle. Fast forward to today and speckle has become a fascinating area of modern optics [23] with impact in technology such as sensing and imaging [24,26,40,43,44] while at the same time continuing to provide opportunities for new fundamental understanding in optics. One example of the latter was to understand if speckle supported superoscillatoins and the nature of such wave behavior [16]. ...
This book chapter gives a selective review of physical implementations and applications of superoscillations and associated phenomena. We introduce the field by reviewing simple examples of superoscillations and showing how their existence naturally follows from the real part of the quantum mechanical weak value, which the parallel phenomena of supergrowth naturally follows from the imaginary part. Focusing on electromagnetic applications, we review the topics of superoscillation and supergrowth in speckle, creating superoscillating hot spots with patterned filters, superspectroscopic discrimination of two molecules, noise mitigation and the engineering of super behavior in point spread functions for the purpose of optical superresolution. We also cover a variety of different methods for creating superoscillatory and supergrowing functions, reviewing both mathematical and physical ways to create this class of functions, and beyond. Promising directions for future research, including superoscillations in other wave phenomena, super radar, and generalized super-phenomena in quantum physics, are outlined.
... Speckle noise arises from the rough surface of the object under imaging and is highly non-stationary. It causes localized variations in intensity and phase, making it difficult to remove with conventional filtering and often leading to unwrapping errors [5,6]. On the other hand, Gaussian noise introduces random fluctuations across both smooth and detailed regions, reducing the signal-to-noise ratio (SNR) [7,8]. ...
Phase wrapping is a common phenomenon in optical full-field imaging or measurement systems. It arises from large phase retardations and results in wrapped-phase maps that contain essential information about surface roughness and topology. However, these maps are often degraded by noise, such as speckle and Gaussian, which reduces the measurement accuracy and complicates phase reconstruction. Denoising such data is a fundamental problem in computer vision and plays a critical role in biomedical imaging modalities like Full-Field Optical Interferometry. In this paper, we propose WPD-Net (Wrapped-Phase Denoising Network), a lightweight deep learning-based neural network specifically designed to restore phase images corrupted by high noise levels. The network architecture integrates a shallow feature extraction module, a series of Residual Dense Attention Blocks (RDABs), and a dense feature fusion module. The RDABs incorporate attention mechanisms that help the network focus on critical features and suppress irrelevant noise, especially in high-frequency or complex regions. Additionally, WPD-Net employs a growth-rate-based feature expansion strategy to enhance multi-scale feature representation and improve phase continuity. We evaluate the model’s performance on both synthetic and experimentally acquired datasets and compare it with other state-of-the-art deep learning-based denoising methods. The results demonstrate that WPD-Net achieves superior noise suppression while preserving fine structural details even with mixed speckle and Gaussian noises. The proposed method is expected to enable fast image processing, allowing unwrapped biomedical images to be retrieved in real time.
... However, when the thickness of scattering media significantly exceeds the transport mean free path, , the medium becomes highly diffusive [26][27] . The transport mean free path represents the average distance photons travel before losing directional memory due to successive scattering events [28] , hence, there are no snake photons or ballistic photons in diffusive media (Fig. 1a). In biological tissues, typical absorption and reduced scattering coefficients are approximately = 0.05 −1 and ′ = 10 −1 , respectively, yielding the transport mean free path around = 1 + ′ = 0.1 [29] . ...
Various imaging techniques have significantly enhanced our ability to visualize objects embedded within complex media such as biological tissues, fog, atmosphere, or various turbid media. Optical imaging, in particular, offers multiple advantages, including non-invasive capabilities, absence of ionizing radiation, and high contrast for many biological tissues. However, optical imaging through substantially thick scattering media remains challenging due to extensive photon diffusion, significantly restricting reconstruction quality and achievable resolution. To address these limitations, we introduce Diffuse Optical Ptychography (DOP), a novel imaging method inspired by ptychography technique, which exploits additional spatial information gained from multiple overlapping illumination patterns. The primary technical innovation of DOP lies in its effective use of overlapping yet minimally correlated illuminations, significantly enhancing reconstruction accuracy and image quality. Compared to existing optical imaging methods through thick diffusive media, DOP achieves superior resolution (down to 1 mm) and reliably reconstructs both binary and grayscale objects embedded within media thicker than 100 transport mean free paths. Importantly, DOP demonstrates robust reconstruction performance both with accurately calibrated diffusion properties and even without prior calibration. Furthermore, the experimental setup for DOP remains straightforward, utilizing only a conventional camera and scanning illumination spots. Our demonstrations underscore the broad potential impact of DOP in applications ranging from medical diagnostics to non-destructive testing, thus opening promising avenues for high-resolution imaging in highly scattering environments.
... To overcome these limitations, our group recently introduced a speckle differencing approach that leverages the statistical properties of speckle patterns to image embedded inhomogeneities 23 . Speckle patterns are stochastic intensity patterns with a granular structure that are observed when coherent light illuminates a scattering medium 26 . They result from the interference of light waves with randomized phase delays caused by multiple scattering events within the medium. ...
Non-invasive detection of objects embedded inside an optically scattering medium is essential for numerous applications in engineering and sciences. However, in most applications light at visible or near-infrared wavebands is scattered by the medium resulting in the obscuration of the embedded objects. Existing methods to overcome scattering generally rely on point-by-point scanning strategies, which limit spatial sampling density. In this work, we address the sampling limitations by drawing inspiration from multisensory integration mechanisms observed in nature, wherein distinct sensing modalities work together to enhance the perception of the surroundings. Our multisensory approach leverages the unique advantages of coherent light by combining the sensitivity of an interferometric LiDAR with a wide field neuromorphic sensor to probe objects inside a densely scattering medium. The neuromorphic camera provides wide field spatial cues of the embedded object, by monitoring the fluctuations in the speckle patterns produced by tuning the laser frequency. These spatial cues are used to guide a point-scanning FMCW LiDAR to retrieve high-resolution images. Using this approach, we imaged objects embedded within an 8 cm thick (>100 transport mean free paths), tissue-like scattering medium with a 10x improvement in sampling density compared to traditional uniform sampling.
... Sonar images are generated through the reception and processing of echo signals by sonar systems [17][18][19]. Unlike optical images, sonar images are significantly impacted by the imaging mechanism and marine environment, resulting in substantial speckle noise [20]. This leads to issues such as edge blurring, reduced image contrast, and diminished feature information in side-scan sonar images [21]. ...
Side-Scan Sonar (SSS) is widely used in underwater rescue operations and the detection of seabed targets, such as shipwrecks, drowning victims, and aircraft. However, the quality of sonar images is often degraded by noise sources like reverberation and speckle noise, which complicate the extraction of effective features. Additionally, challenges such as limited sample sizes and class imbalances are prevalent in side-scan sonar image data. These issues directly impact the accuracy of deep learning-based target classification models for SSS images. To address these challenges, we propose a side-scan sonar image classification model based on joint image deblurring–denoising and a pre-trained feature fusion attention network. Firstly, by employing transform domain filtering in conjunction with upsampling and downsampling techniques, the joint image deblurring–denoising approach effectively reduces image noise while preserving and enhancing edge and texture features. Secondly, a feature fusion attention network based on transfer learning is employed for image classification. Through the transfer learning approach, a feature extractor based on depthwise separable convolutions and densely connected networks is trained to effectively address the challenge of limited training samples. Subsequently, a dual-path feature fusion strategy is utilized to leverage the complementary strengths of different feature extraction networks. Furthermore, by incorporating channel attention and spatial attention mechanisms, key feature channels and regions are adaptively emphasized, thereby enhancing the accuracy and robustness of image classification. Finally, the Gradient-weighted Class Activation Mapping (Grad-CAM) technique is integrated into the proposed model to ensure interpretability and transparency. Experimental results show that our model achieves a classification accuracy of 96.80% on a side-scan sonar image dataset, confirming the effectiveness of this method for SSS image classification.
... The average diameter of a speckle can be obtained using the following equation 56 : ...
Cerebral blood flow (CBF) is a crucial indicator of brain function, and its continuous monitoring is critical for diagnosing and treating neurological disorders such as stroke, traumatic brain injury, and neurodegenerative diseases. Diffuse correlation spectroscopy (DCS) is a non-invasive diffuse optical technique to investigate deep tissue microvascular dynamics. However, traditional DCS systems face challenges in real-time applications due to reliance on correlation boards or software autocorrelators for signal acquisition, which limits their practical use. Furthermore, most existing DCS measurements are confined to a source-detector separation, \rho = 20 - 30 mm, with a maximum \rho = 40 mm, potentially reducing cerebral hemodynamics assessment accuracy. To overcome these limitations, we utilized a fully in-house-built 512 x 512 single-photon avalanche diode array (SPAD) called ATLAS, featuring innovative on-chip autocorrelators. The ATLAS-DCS system was evaluated against a commercial correlator board DCS system for liquid phantoms and cuff occlusion studies. Also, we successfully monitored pulsatile blood flow at \rho of 50 mm with a high sampling rate of up to 56.3 Hz in a human forehead in vivo. Our system also demonstrated high fidelity in detecting human pulse and identifying behaviour-induced physiological variations from the subject's prefrontal cortex during video gaming. We show that the ATLAS-DCS system outperforms the commonly used APD-based DCS system, achieving more than 571x SNR improvement in a milk-phantom at \rho of 20 mm. This DCS on-chip design paves the way for high-speed biological signal measurement in real-time applications by significantly enhancing detection sensitivity and speed.
... where CN (., .)denotes a circular complex Gaussian distribution 41 . This shows that the four-step phase-shifting method suffers from complex Gaussian noise with a variance (4ηF) −1 σ 2 . ...
Incoherent digital holography (IDH) is a passive holographic 3D imaging technique under spatially incoherent light. Single-shot recording with high light-utilization efficiency and high spatial resolution is a challenge in IDH. Herein, we propose a single-shot three-step phase-shifting IDH system with a 1D phase grating that has a line-and-space structure. The 0th and ± 1st diffraction orders of the grating are used for simultaneously creating three self-interference holograms, which are then captured using an image sensor at a single exposure. Three-step phase shifts are introduced into the holograms using the geometric phase of circular polarizations. To compensate the intensity variations between the holograms due to grating fabrication errors, we derive and implement a generalised three-step phase-shifting algorithm. We experimentally performed the single-shot recording of reflective objects as a proof-of-principle demonstration. We further examined the theoretical noise tolerances between three- and four-step phase-shifting methods for grating-assisted space-division phase shifting. The results show that the three-step phase-shifting method is superior to the four-step method when the diffraction efficiency of the 1D phase grating is at least four-thirds higher than that of the 2D phase grating used for the four-step method.
Supplementary Information
The online version contains supplementary material available at 10.1038/s41598-025-90793-8.
... In particular, k * (x, y) ⊗ k(x, y) represents the self-correlation of the key k(x, y), which is a random function. This self-correlation can be approximated as a Dirac delta by applying the broadband noise approximation [69]. The decrypted object is then ...
In this paper, we demonstrate a scheme to encrypt multiplane scenes using an experimental joint transform correlator cryptosystem capable of full complex modulation, implemented with a single phase-only spatial light modulator. We use two different encoding algorithms to achieve full complex modulation of the input plane of the joint transform correlator cryptosystem, enabling the encryption of any complex optical field using arbitrary complex-valued encryption keys. Using the capabilities of this proposal, we demonstrate, for the first time to our knowledge, the experimental optical encryption of a multiplane scene composed of up to nine different 2D objects placed at different distances along the optical axis. This scheme is implemented using both double-phase encoding and binary amplitude encoding, and the performance with both encoding approaches is compared both numerically and experimentally. We show that binary amplitude encoding is superior to double-phase encoding, producing results with comparable or higher quality, particularly in the experimental case, and allowing the encryption of larger scenes than what is possible using double-phase encoding.
... Light beams with reduced spatial coherence, known as partially coherent (PC) beams, have become an important class of beams in contemporary optics [8,9]. Traditional fully coherent light beam faces limitations in practical applications, including sensitivity to environmental factors and prone to speckle [10]. The advent of PC beams offers a solution to these issues [8,9]. ...
This paper investigates the evolution of information entropy (IE) in Hermite–Gaussian correlated Schell-model (HGcSM) beams propagating through a gradient-index (GRIN) fiber using Shannon information theory. Our results reveal that the IE of such beams evolves periodically, with the beam order significantly influencing its initial distribution. Compared with traditional Gaussian Schell-model beams, HGcSM beams exhibit more complex IE dynamics, characterized by periodically emerging low-entropy regions whose IE decreases with increasing beam order. Furthermore, the fiber’s central refractive index and core radius strongly affect the evolution period and fluctuation amplitude of IE. These findings provide a theoretical basis for optimizing partially coherent beams in optical fiber applications.
... Illuminating an optically rough surface with coherent light, such as a laser, results in light being scattered on and below the surface [10]. The backscattered light undergoes interference, creating a random pattern of bright and dark spots, known as a laser speckle pattern [11,12,13,14]. However, as the scattering structures are not static but instead undergo Brownian motion, the laser speckle pattern fluctuates [15]. ...
The ability to measure protein functionality is critical for the development of plant-based products, particularly with respect to gelation behavior, which is vital for food structure and texture. Small amplitude oscillatory shear tests remain the standard for monitoring protein gelation; however, these methods are costly, time-consuming, and require physical contact with the sample. Laser speckle rheology, an optical-based technique, offers a contactless alternative by assessing rheological properties through speckle pattern fluctuations. In this work, we present a simple laser speckle rheology setup, utilizing a diode laser and a digital camera, to monitor rheological changes during the rennet coagulation of milk. We use a viscoelasticity index, derived from a two-dimensional linear correlation, to quantify speckle pattern fluctuations. The laser speckle rheology method is compared with conventional small amplitude oscillatory shear rheology. Results demonstrate that key characteristics of the coagulation process, including coagulation and gelation times, are temporally aligned between the two methods. Furthermore, the viscoelasticity index allows for the comparison of the complex modulus in samples with similar compositions under consistent acquisition parameters. These findings underscore the potential of laser speckle rheology as a cost-effective, rapid, and contactless approach for capturing protein gelation, providing a viable alternative to conventional shear rheological methods.
... To generate speckled SAR images, we consider speckles in SAR images as multiplicative noise. According to Goodman et al. [50], who proposed the fully developed speckle model, SAR intensity can be expressed as ...
Deep-learning-based ship detection methods in Synthetic Aperture Radar (SAR) imagery are a current research hotspot. However, these methods rely on high-quality images as input, and in practical applications, SAR images are interfered with by speckle noise, leading to a decrease in image quality and thus affecting detection accuracy. To address this problem, we propose a unified framework for ship detection that incorporates a despeckling module into the object detection network. This integration is designed to enhance the detection performance, even with low-quality SAR images that are affected by speckle noise. Secondly, we propose a Multi-Scale Window Swin Transformer module. This module is adept at improving image quality by effectively capturing both global and local features of the SAR images. Additionally, recognizing the challenges associated with the scarcity of labeled data in practical scenarios, we employ an unlabeled distillation learning method to train our despeckling module. This technique avoids the need for extensive manual labeling and making efficient use of unlabeled data. We have tested the robustness of our method using public SAR datasets, including SSDD and HRSID, as well as a newly constructed dataset, the RSSDD. The results demonstrate that our method not only achieves a state-of-the-art performance but also excels in conditions with low signal-to-noise ratios.
... Consider a stationary stochastic process X = {X i } i∈N , X i ∈ X , observed under a multiplicative noise model, Y i = X i W i , where W i represents the speckle noise. In most coherent imaging applications, the speckle noise process is assumed to be fully developed and is therefore modeled as Gaussian [5]. Here, we assume that {W i } i are independent and identically distributed as standard normal random variables, N (0, 1). ...
Speckle noise is a fundamental challenge in coherent imaging systems, significantly degrading image quality. Over the past decades, numerous despeckling algorithms have been developed for applications such as Synthetic Aperture Radar (SAR) and digital holography. In this paper, we aim to establish a theoretically grounded approach to despeckling. We propose a method applicable to general structured stationary stochastic sources. We demonstrate the effectiveness of the proposed method on piecewise constant sources. Additionally, we theoretically derive a lower bound on the despeckling performance for such sources. The proposed depseckler applied to the 1-Markov structured sources achieves better reconstruction performance with no strong simplification of the ground truth signal model or speckle noise.
... , with D the (translational) diffusion coefficient given by the Stokes-Einstein relation, D = k B T/(6πηR), with R the particle radius R, η the solvent viscosity, T the absolute temperature and k B Boltzmann's constant. A ≲ 1 is a constant that depends on the speckle-to-pixel size ratio 45 and B ≈ 0 is the baseline 39 . Note that, since CMOS cameras are slower detectors compared to the avalanche photodiodes used for DLS, the smallest delay time τ accessible by PCI is here 5 ms, still sufficient to correctly capture the particles' dynamics. ...
Colloidal solids (COLIS) is a state-of-the-art light scattering setup developed for experiments onboard the International Space Station (ISS). COLIS allows for probing the structure and dynamics of soft matter systems on a wide range of length scales, from a few nm to tens of microns, and on time scales from 100 ns to tens of hours. In addition to conventional static and dynamic light scattering, COLIS includes depolarized dynamic light scattering, a small-angle camera, photon correlation imaging, and optical manipulation of thermosensitive samples through an auxiliary near-infrared laser beam, thereby providing a unique platform for probing soft matter systems. We demonstrate COLIS through ground tests on standard Brownian suspensions, and on protein, colloidal glasses, and gel systems similar to those to be used in future ISS experiments.
... The study of small-scale scattering, recognized in the acoustic and ultrasonic fields (Abbott and Thurstone, 1979;Fink and Derode, 1998;Goodman, 2007), has predominantly focused on analyzing and mitigating noise in intensity images at a fixed frequency. However, seismic imaging operates with broadband signals, presenting unique challenges. ...
The complex near-surface scattering introduces significantdistortions in deep reflection data, necessitating effectivenoise mitigation strategies. In this study, we investigate therecovery of signal phase in the presence of multiplicativenoise which is a crucial step for subsequent despecklingalgorithms. Leveraging a stack-based approach, weintroduce the concept of a "phase pilot trace", whichrepresents the trace closest to the signal phase using theminimum number of traces possible. Our analysis focuses onevaluating the quality of the phase pilot by assessing thestandard deviation of the residual phase and its enhancementwith increasing stack size. Through numerical experiments,we demonstrate a consistent reduction in phase spread acrossall frequencies, adhering to the 1/√N rule, indicating auniform reduction in normalized values for all thefrequencies. We propose utilizing the standard deviation ofthe residual phase as a metric for assessing the quality ofphase pilot traces, providing insights into the necessaryensemble size for desired phase recovery quality. However,the pronounced frequency dependency adds complexity todetermining the necessary trace count for broadband data.
Various imaging techniques have significantly enhanced our ability to visualize objects embedded within complex media such as biological tissues, fog, atmosphere, or various turbid media. Optical imaging, in particular, offers multiple advantages, including non-invasive capabilities, absence of ionizing radiation, and high contrast for many biological tissues. However, optical imaging through substantially thick scattering media remains challenging due to extensive photon diffusion, significantly restricting reconstruction quality and achievable resolution. To address these limitations, we introduce Diffuse Optical Ptychography (DOP), a novel imaging method inspired by ptychography technique, which exploits additional spatial information gained from multiple overlapping illumination patterns. The primary technical innovation of DOP lies in its effective use of overlapping yet minimally correlated illuminations, significantly enhancing reconstruction accuracy and image quality. Compared to existing optical imaging methods through thick diffusive media, DOP achieves superior resolution (down to 1 mm) and reliably reconstructs both binary and grayscale objects embedded within media thicker than 100 transport mean free paths. Importantly, DOP demonstrates robust reconstruction performance both with accurately calibrated diffusion properties and even without prior calibration. Furthermore, the experimental setup for DOP remains straightforward, utilizing only a conventional camera and scanning illumination spots. Our demonstrations underscore the broad potential impact of DOP in applications ranging from medical diagnostics to non-destructive testing, thus opening promising avenues for high-resolution imaging in highly scattering environments.
While the spontaneous emission from independent emitters provides spatially uncorrelated photons—a typical manifestation of quantum randomness, the interference of the coherent scattering leads to a well-defined intensity pattern—a feature described by linear optics. We here demonstrate experimentally how the interplay between the two mechanisms in large systems of quantum emitters leads to spatial variations of photon correlations. The implementation with trapped ion crystals in free space allows us to observe the anticorrelation between photon rates and variance of the photon number distributions in chains of up to 18 ions. For smaller crystals of four ions, the transition from antibunching to bunching and super-Poissonian statistics of the scattered light is reported. For higher numbers of scatterers, the photon statistics still display a strong deviation from the fully incoherent scattering case. Our results illustrate how the interference of coherent scattering, combined with spontaneous emission, provides a control mechanism for the light statistics.
Published by the American Physical Society 2025
Partially coherent beams are characterized by the presence of speckle patterns. Modeling the evolution of speckle properties throughout propagation requires solving the beam propagation equation, potentially at the cost of resource-intensive calculations. Here, we derive analytical expressions for the transverse size of speckles by approximating the mean autocorrelation function of the electric field through Wigner function moments. As those moments follow particularly simple propagation laws, this approach allows us to describe the evolution of the mean speckle properties along the beam propagation with the use of a few scalar parameters, hence at a very low computational cost. We highlight the relevance of this approach by plotting the evolution of the speckle size in different examples, including Gaussian-Schell and multiple beam configurations. The formalism we introduce is general and applies to the case of multi-dimensional fields, which is of particular interest for studying the effect, on the speckle characteristics, of space–time couplings in dispersive systems.
Holographic displays hold the promise of providing authentic depth cues, resulting in enhanced immersive visual experiences for near-eye applications. However, current holographic displays are hindered by speckle noise, which limits accurate reproduction of color and texture in displayed images. We present HoloChrome, a polychromatic holographic display framework designed to mitigate these limitations. HoloChrome utilizes an ultrafast, wavelength-adjustable laser and a dual-Spatial Light Modulator (SLM) architecture, enabling the multiplexing of a large set of discrete wavelengths across the visible spectrum. By leveraging spatial separation in our dual-SLM setup, we independently manipulate speckle patterns across multiple wavelengths. This novel approach effectively reduces speckle noise through incoherent averaging achieved by wavelength multiplexing, specifically by using a single SLM pattern to modulate multiple wavelengths simultaneously on one or more SLM devices. Our method is complementary to existing speckle reduction techniques, offering a new pathway to address this challenge. Furthermore, the use of polychromatic illumination broadens the achievable color gamut compared to traditional three-color primary holographic displays.
Our simulations and tabletop experiments validate that HoloChrome significantly reduces speckle noise and expands the color gamut. These advancements enhance the performance of holographic near-eye displays, moving us closer to practical, immersive next-generation visual experiences.
The ability to image blood flow in early-stage avian embryos has significant applications in developmental biology, drug and vaccine testing, as well as determining sex differentiation. In this project, we used our recently developed laser speckle contrast imaging (LSCI) system to non-invasively image extraembryonic blood vessels and used these images to attempt early sex identification of chick embryos. Specifically, we captured images of blood vessels from 1,251 living chicken embryos between day three and day four of incubation. We then applied deep neural network (DNN) models to evaluate whether it is possible to differentiate sex based on vascular patterns. Using ResNetBiT and YOLOv5 models, our results indicate that sex differentiation from extraembryonic blood vessel images was not achievable with sufficiently high accuracy or statistical significance for practical use. Specifically, ResNetBiT had a five-fold cross-validated average accuracy of 59%±5% (fold-wise p-value, p ≤ 0.3) at day 3 and 61%±3% (fold-wise, p ≤ 0.04) at day 4. YOLOv5 had a five-fold cross-validated average accuracy of 55%±3% (fold-wise, p ≤ 0.3) at day 3 and 53%±3% (fold-wise, p ≤ 0.5) at day 4. Our findings suggest that using vascular pattern imaging alone is inconclusive for reliable early sex identification in chicken embryos.
The statistical analysis of electromagnetic scattering is crucial for understanding sea clutter due to various influencing factors such as weather conditions and wave activity, making research in this area particularly challenging. To address this, multiple statistical models have been developed, as no single model can fully meet the requirements for accurate analysis. These models are used to characterize and calculate sea clutter. While traditional models are based on fully polarized electromagnetic waves, which are inherently vectorial, the complex nature of the sea surface means that actual electromagnetic scattering cannot be completely polarized. Therefore, more realistic models should adopt a vector approach. This paper employs the Rayleigh distribution, the K-distribution, the log-normal distribution, and the Weibull distribution to examine the polarization statistical characteristics of sea clutter models. We investigate the probability density functions of the Stokes parameters and analyze the evolution of each model in relation to its respective shape parameters. This research deepens and enhances the understanding of sea clutter properties in the relevant parts of the electromagnetic regime.
Manipulating broadband fields in scattering media is a modern challenge across photonics and other wave domains. Recent studies have shown that complex propagation in scattering media can be harnessed to manipulate broadband light wave packets in space-time for focusing, imaging, and computing applications. Interestingly, while many proposed methodologies operate on intensity-based assessment of scattered fields, often in the spectral domain, from a pure transmission-function perspective, scattering operates as a linear field-level combinatory process, i.e., the superposition of transformation of unit excitations. As a result, we recently demonstrated that gaining experimental access to instantaneous scattered fields, as available through time-domain spectroscopy in the terahertz (THz) spectral range, in conjunction with sparse light excitation typical of ghost imaging, provides a key advantage in enabling the functionalisation of scattering, exposing a novel modelling paradigm. In this paper, we provide experimental proof of reconstructing 1-dimensional object features through a scattering medium using a fully broadband THz time-domain approach.
Optical coherence is a fundamental property of light, playing a key role in understanding interference, propagation, and
light-matter interactions for both classical and quantum light. Measuring the coherence properties of an optical field is
crucial for a wide range of applications. However, despite many proposed measurement schemes, significant challenges
still remain. In this work, we present a protocol to measure the full-dimensional coherence properties of a partially coherent beam. The method is based on tomographing the complex coherent modes of the partially coherent field within its coherence time. Once the complex coherent modes are reconstructed, all coherence properties including field correlation
and its higher-order correlations (e.g., intensity correlation) can be recovered for beams that are either spatially uniformly
or non-uniformly correlated. We perform a proof-of-principle experiment to measure the complex field correlation and intensity correlation of a structured partially coherent beam synthesized by random modes. Additionally, we discuss the application of full-dimensional complex coherence function tomography in coherence-based multi-cipher information security. The robustness of our system in complex environments is also evaluated.
This paper introduces an optical instrument leveraging a defocused speckle pattern for angular measurements of a sample orientation. The technique involves illuminating the sample with the speckle pattern and capturing the reflected pattern using a camera. With an uncertainty level of 0.4 µrad and repeatability of 0.47 µrad, this system is modestly comparable to the traditional autocollimators but with a wider angular range advantage. One of the key innovations of this system is its cost-effectiveness, offering a significant reduction in expense compared to conventional autocollimators. This paper outlines the design, operational principles, and performance evaluation of the instrument, highlighting its potential as a cost-efficient alternative in the field of optical metrology.
Coherent lidar uses a chirped laser pulse for 3D imaging of distant targets. However, existing coherent lidar image reconstruction methods do not account for the system's aperture, resulting in sub-optimal resolution. Moreover, these methods use majorization-minimization for computational efficiency, but do so without a theoretical treatment of convergence. In this paper, we present Coherent Lidar Aperture Modeled Plug-and-Play (CLAMP) for multi-look coherent lidar image reconstruction. CLAMP uses multi-agent consensus equilibrium (a form of PnP) to combine a neural network denoiser with an accurate surrogate forward model of coherent lidar. Additionally, CLAMP introduces a computationally efficient FFT-based method to account for the system's aperture to improve resolution of reconstructed images. Furthermore, we formalize the use of majorization-minimization in consensus optimization problems and prove convergence to the exact consensus equilibrium solution. Finally, we apply CLAMP to synthetic and measured data to demonstrate its effectiveness in producing high-resolution, speckle-free, 3D imagery
Several 3D light-based printing technologies have been developed that rely on the photopolymerization of liquid resins. A recent method, so-called Tomographic Volumetric Additive Manufacturing, allows the fabrication of microscale objects within tens of seconds without the need for support structures. This method works by projecting intensity patterns, computed via a reverse tomography algorithm, into a photocurable resin from different angles to produce a desired 3D shape when the resin reaches the polymerization threshold. Printing using incoherent light patterning has been previously demonstrated. In this work, we show that a light engine with holographic phase modulation unlocks new potential for volumetric printing. The light projection efficiency is improved by at least a factor 20 over amplitude coding with diffraction-limited resolution and its flexibility allows precise light control across the entire printing volume. We show that computer-generated holograms implemented with tiled holograms and point-spread-function shaping mitigates the speckle noise which enables the fabrication of millimetric 3D objects exhibiting negative features of 31 μm in less than a minute with a 40 mW light source in acrylates and scattering materials, such as soft cell-laden hydrogels, with a concentration of 0.5 million cells per mL.
In this paper, we use wave-optics simulations to explore the benefits of hidden-phase compensation for laser systems that employ extended-beacon adaptive optics. Specifically, we create a trade space, where we vary the strength of the scintillation as well as the size of the beacon, and score laser-system performance in terms of no phase compensation, perfect least-squares compensation, and perfect full-phase compensation. Here, “full phase” refers to the least-squares and hidden-phase components of the pupil-plane phase function. The results of this trade space lead to three main conclusions. (1) If the scintillation is weak and we have either a point-source beacon or a very small extended-source beacon, then we see similar performance with perfect least-squares and full-phase compensation; however, both significantly improve performance compared to the no compensation case. On the other hand, if the scintillation is strong and we have either a point-source beacon or a very small extended-source beacon, then we get a significant improvement in performance using perfect full-phase compensation compared to perfect least-squares compensation. (2) If the scintillation is strong, then there will be a large number of turbulence-induced branch points and branch cuts in the hidden-phase component of the pupil-plane phase function. These branch points and cuts will result in a major reduction in performance if left uncompensated. (3) If the extended-source beacon is large, then the associated rough-surface scattering and resultant speckle will corrupt the perfect least-squares and full-phase compensation to the point where performance is on par with or worse than the no compensation case. At large, (1)–(3) will inform the development of future laser systems that need to mitigate the effects of scintillation and speckle to perform extended-beacon adaptive optics.
We consider the Jacobian of a random transverse polarisation field, from the transverse plane to the Poincaré sphere, as a Skyrme density partially covering the sphere. Connected domains of the plane where the Jacobian has the same sign—patches—map to facets subtending some general solid angle on the Poincaré sphere. As a generic continuous mapping between surfaces, we interpret the polarisation pattern on the sphere in terms of fold lines (corresponding to the crease lines between neighbouring patches) and cusp points (where fold lines meet). We perform a basic statistical analysis of the properties of the patches and facets, including a brief discussion of the polarisation analogue to superoscillation in scalar speckle patterns and the percolation properties of the Jacobian domains. Connections with abstract origami manifolds are briefly considered. This analysis combines previous studies of structured skyrmionic polarisation patterns with random polarisation patterns, suggesting a particle-like interpretation of random patches as polarisation skyrmionic anyons.
The paper proposes a method for estimating the average speckle size using experimentally recorded images of speckle fields on a CMOS matrix. This method can be useful when used in speckle interferometry methods when determining their metrological parameters.
Fiber scrambling is integral to high-precision calibration systems for radial velocity (RV) measurements, crucial in the quest for exoplanet discovery. Coherent light sources, like laser frequency combs, often induce laser speckles, a form of modal noise, which can result in spectra calibration errors. The starlight collected in astronomical observations is often polychromatic light. This study investigates the speckle-like mode noise generated under incoherent light, identifying a clear correlation between fiber length and the intensity of this noise. Remarkably, experiments using LED illumination showed that fibers shorter than 2 m exhibit significant speckle-like noise, manifesting as distinctive ripple-like structures, a newly identified phenomenon referred to as modal patterns. Mitigation techniques, including squeezing and vibrating methods, can reduce contrast and suppress modal patterns effectively. To further enhance scrambling performance, a novel fiber scrambling approach, the compound scrambler, is proposed. This design integrates laser polishing, thermal heating, and fiber tapering techniques to enhance near-field uniformity. Utilizing a combination of non-circular and graded index fibers, the compound scrambler achieves notable improvements in scrambling gain (SG). A refined nondestructive fabrication method, leveraging the superior scrambling effect of non-circular fibers and the efficiency of adiabatic taper structures, achieves a high SG of 1064. These findings contribute to advancing high-precision spectrograph design, offering practical solutions to enhance RV measurement accuracy. The compound scrambler's integrity and modular design promise stability, longevity, and scalability, holding immense potential for astronomical instrumentation.
Significance: We present a system to measure and analyze the complete polarization state distribution of speckle patterns generated from in vivo tissue. Accurate measurement of polarization speckle requires both precise spatial registration and rapid polarization state acquisition. A unique measurement system must be designed to achieve accurate images of polarization speckle patterns for detailed investigation of the scattering properties of biological tissues in vivo. Aim and approach: This system features a polarization state analyzer with no moving parts. Two pixel-polarizer cameras allow for the instantaneous acquisition of the spatial Stokes vector distribution of polarization speckle patterns. System design and calibration methods are presented, and representative images from measurements on liquid phantoms (microsphere suspensions) and in vivo healthy and tumor murine models are demonstrated and discussed. Results and Conclusions: Quantitative measurements of polarization speckle from microsphere suspensions with controlled scattering coefficients demonstrate differences in speckle contrast, speckle size, and the degree of polarization. Measurements on in vivo murine skin and xenograft tumor tissue demonstrate the ability of the system to acquire snapshot polarization speckle images in living systems. The developed system can thus rapidly and accurately acquire polarization speckle images from different media in dynamic conditions such as in vivo tissue. This capability opens the potential for future detailed investigation of polarization speckle for in vivo biomedical applications.
Subject of study. This study examines the propagation of Bessel light beams in scattering media under acoustic interaction. Aim of study. The study aims to investigate speckle contrast reduction, or the “enlightenment” of a scattering medium, as Bessel light beams propagate through it, using the acoustic impact on the medium. Method . Speckle structure suppression is achieved by generating multiple statistically independent field realizations through acoustic influence on the scattering media. Main results. The study explores how the properties of the scattering medium and the parameters of acoustic impact affect speckle contrast reduction. A theoretical explanation is provided, suggesting that both a coherent component and additive noise are present in the field of a Bessel light beam traveling through the medium. The coherent component arises from the self-reconstruction effect of the Bessel beam. The study demonstrates that speckle structure reduction is maximized by acoustic impact, which increases the number of statistically independent realizations of the speckle field during image capture. Both pulse and continuous acoustic impacts are shown to effectively suppress the noise component in a Bessel light beam. Experimental results illustrate the enlightenment effect during Bessel beam propagation in liquid scattering media. Practical significance . The acoustically induced speckle contrast reduction observed in scattering media has practical applications for transmitting optical images through scattering environments, enhancing tomographic imaging depth, and enabling optical communication in free space.
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