Spatial Frequency Domain Research Articles

Discrimination tasks in simulated low-dose CT noise.

This study reports the results of a set of discrimination experiments using simulated images that represent the appearance of subtle lesions in low-dose computed tomography (CT) of the lungs. Noise in these images has a characteristic ramp-spectrum before apodization by noise control filters. We consider three specific diagnostic features that determine whether a lesion is considered malignant or benign, two system-resolution levels, and four apodization levels for a total of 24 experimental conditions. The goal of the investigation is to better understand how well human observers perform subtle discrimination tasks like these, and the mechanisms of that performance. We use a forced-choice psychophysical paradigm to estimate observer efficiency and classification images. These measures quantify how effectively subjects can read the images, and how they use images to perform discrimination tasks across the different imaging conditions. The simulated CT images used as stimuli in the psychophysical experiments are generated from high-resolution objects passed through a modulation transfer function (MTF) before down-sampling to the image-pixel grid. Acquisition noise is then added with a ramp noise-power spectrum (NPS), with subsequent smoothing through apodization filters. The features considered are lesion size, indistinct lesion boundary, and a nonuniform lesion interior. System resolution is implemented by an MTF with resolution (10% max.) of 0.47 or 0.58 cyc/mm. Apodization is implemented by a Shepp-Logan filter (Sinc profile) with various cutoffs. Six medically naïve subjects participated in the psychophysical studies, entailing training and testing components for each condition. Training consisted of staircase procedures to find the 80% correct threshold for each subject, and testing involved 2000 psychophysical trials at the threshold value for each subject. Human-observer performance is compared to the Ideal Observer to generate estimates of task efficiency. The significance of imaging factors is assessed using ANOVA. Classification images are used to estimate the linear template weights used by subjects to perform these tasks. Classification-image spectra are used to analyze subject weights in the spatial-frequency domain. Overall, average observer efficiency is relatively low in these experiments (10%-40%) relative to detection and localization studies reported previously. We find significant effects for feature type and apodization level on observer efficiency. Somewhat surprisingly, system resolution is not a significant factor. Efficiency effects of the different features appear to be well explained by the profile of the linear templates in the classification images. Increasingly strong apodization is found to both increase the classification-image weights and to increase the mean-frequency of the classification-image spectra. A secondary analysis of "Unapodized" classification images shows that this is largely due to observers undoing (inverting) the effects of apodization filters. These studies demonstrate that human observers can be relatively inefficient at feature-discrimination tasks in ramp-spectrum noise. Observers appear to be adapting to frequency suppression implemented in apodization filters, but there are residual effects that are not explained by spatial weighting patterns. The studies also suggest that the mechanisms for improving performance through the application of noise-control filters may require further investigation.

Model for the diffuse reflectance in spatial frequency domain imaging.

In spatial frequency domain imaging (SDFI), tissue is illuminated with sinusoidal intensity patterns at different spatial frequencies. For low spatial frequencies, the reflectance is diffuse and a model derived by Cuccia etal. (doi 10.1117/1.3088140) is commonly used to extract optical properties. An improved model resulting in more accurate optical property extraction could lead to improved diagnostic algorithms. To develop a model that improves optical property extraction for the diffuse reflectance in SFDI compared to the model of Cuccia etal. We derive two analytical models for the diffuse reflectance, starting from the theoretical radial reflectance for a pencil-beam illumination under the partial current boundary condition (PCBC) and the extended boundary condition (EBC). We compare both models and the model of Cuccia etal. to Monte Carlo simulations. The model based on the PCBC resulted in the lowest errors, improving median relative errors compared to the model of Cuccia etal. by 45% for the reflectance, 10% for the reduced scattering coefficient and 64% for the absorption coefficient. For the diffuse reflectance in SFDI, the model based on the PCBC provides more accurate results than the currently used model by Cuccia etal.

Laguerre Gaussian mode holography and its application in optical encryption.

Holography provides an approach to reconstructing both intensity and phase information, and has many applications for microscopic imaging, optical security, and data storage. Recently, the azimuthal Laguerre-Gaussian (LG) mode index, orbital angular momentum (OAM), has been implemented in holography technologies as an independent degree of freedom for high-security encryption. The radial index (RI) of LG mode, however, has not been implemented as an information carrier in holography. Here we propose and demonstrate the RI holography by using strong RI selectivity in the spatial-frequency domain. Furthermore, the LG holography is realized theoretically and experimentally with the (RI, OAM) spanning from (1, -15) to (7, 15), which leads to a 26bit LG-multiplexing hologram for high-security optical encryption. Based on LG holography, a high-capacity holographic information system can be constructed. In our experiments, a LG-multiplexing holography with a span of 217 independent LG channels has been realized, which is inaccessible at present for the OAM holography.

Analysis of the D-shaped PCF-based SPR sensor using Resonance Electron Relaxation and Fourier domain method

Since the D-shaped photonic crystal fiber (PCF) based Surface Plasmon Resonance (SPR) sensor is an important tool in scientifical research and applications, a new concept of Resonance Electron Relaxation (RER) is defined to investigate its detection property. It successfully explains the ‘S-shape’ profile in the dispersion and the wavelength delay between the dispersion intersection and loss peak. The birefringence interference has also been analyzed with the RER phenomenon. Then we experimentally demonstrated the SPR sensing performance. A fast Fourier transform (FFT) algorithm is applied in the experiment to separate each component signal in the spatial frequency domain. Then using a band passing filter of 0.001–0.006 nm−1 together with inverse FFT algorithm, the distinguished SPR spectrum shows a significant agreement with theoretical simulations, with differences of only 14.3 nm and 1.48% in resonance wavelength and intensity. This study facilitates a high precision analysis and data process approach for the SPR sensor based on D-shaped PCF and presents greatly promising application prospects in SPR sensors.

Single-shot ultrafast terahertz photography

Multidimensional imaging of transient events has proven pivotal in unveiling many fundamental mechanisms in physics, chemistry, and biology. In particular, real-time imaging modalities with ultrahigh temporal resolutions are required for capturing ultrashort events on picosecond timescales. Despite recent approaches witnessing a dramatic boost in high-speed photography, current single-shot ultrafast imaging schemes operate only at conventional optical wavelengths, being suitable solely within an optically-transparent framework. Here, leveraging on the unique penetration capability of terahertz radiation, we demonstrate a single-shot ultrafast terahertz photography system that can capture multiple frames of a complex ultrafast scene in non-transparent media with sub-picosecond temporal resolution. By multiplexing an optical probe beam in both the time and spatial-frequency domains, we encode the terahertz-captured three-dimensional dynamics into distinct spatial-frequency regions of a superimposed optical image, which is then computationally decoded and reconstructed. Our approach opens up the investigation of non-repeatable or destructive events that occur in optically-opaque scenarios.

Orbital Angular Momentum Multiplexing Holography for Data Storage

In the letter, we propose a holographic data storage method based on orbital angular momentum (OAM). In the proposed method, the OAM holography by discovering strong OAM selectivity in the spatial-frequency domain without a theoretical helical mode index limit is used to label different data pages. Each data page’s points and intensity levels are used to store the information. The data page can be reconstructed by using an OAM reading beam with an inverse helical mode illuminating the OAM-recording hologram. To further increase the density, different OAM-recording holograms are multiplexed. The experimental results show that we can store and read out the data by using the OAM hologram, and the density can be greatly improved by using the OAM-multiplexing hologram.

Analytical solution for the single scattered radiance of two-layered turbid media in the spatial frequency domain. Part 2: Vector radiative transfer equation

In this work, the analytical solution in the spatial frequency domain based on the vector radiative transfer equation is derived for the single scattered radiance of a scattering medium. A two-layer model with spherical scatterers is assumed as the scattering medium, where the second layer is infinitely extended and there is no refractive index mismatch between the two scattering layers. In contrast, a refractive index mismatch to the surrounding non-scattering medium is considered. The time-resolved and time-independent solutions are given and are verified using a self-implemented electrical field Monte Carlo method. Excellent agreement between the analytical solution and the Monte Carlo method is demonstrated. Possible errors due to discretizations in the Monte Carlo method are reduced, for example, by using the polarized last flight variance reduction method.

Application of state equations approach to solve the classical Kubelka-Munk differential equations in turbid environment

The Kubelka-Munk (KM) model is frequently used to describe the optical properties (absorption and scattering) of inhomogeneous media in terms of the measured reflection and transmittance. The classical KM is modeled by two fluxes which counterpropagate in the media and can be described by system of differential equations. This system, on the other hand, can also be rewritten in the form of state equations, widely used in many areas of engineering such as electrical circuits, control systems and more. Here, we describe the simple mathematical expression of light reflectance and transmittance in turbid media based on the KM light propagation model via a system of state equations. To this end, we demonstrate the use of the state equations to solve KM differential equations in a simple and straightforward manner. To validate the solution of our model against the KM solution, different turbid media including tissue phantoms, milk with varying concentrations of sugar, human hands, and mouse brain were tested. We used a spatial frequency domain imaging system to recover the absorption and scattering properties of each of the media. These measured properties were then introduced into both models to obtain diffuse light reflectance and transmittance information. Experimental results demonstrate significant concurrence between the two approaches within a minute difference in all tested cases. The results presented in this study demonstrate the validity of our alternative strategy to the traditional KM solution.

An FFT-based beam profile denoising method for beam profile distortion correction

The accurate verification of beam parameters is mandatory for treatment safety in particle therapy, therefore, the systematic uncertainties of the segmented ionization chambers and detector arrays used as beam monitors, must be measured. In this study, a Fast Fourier Transform (FFT) based denoising method is proposed to remove noise from the pencil beam profile signal in both the spatial and spatial-frequency domains. In the spatial domain, the bias caused by noise was corrected, and the noise outside the 4 σ range of the spot center was discarded. Then, in the spatial-frequency domain, thanks to the Gaussian shape of the signal’s magnitude spectrum, the 4 σ range of frequency components was extracted to eliminate the signal fluctuation caused by noise. In addition, low amplitude high-frequency components are finely removed by thresholding to reduce the distortion of beam profile signals. The performance of the proposed method was verified through simulation experiments in terms of the coefficient of determination ( R 2 ) and signal-to-noise ratio (SNR). Results show that SNRs of the denoised signals are more than six times higher than those of the original signals and R 2 of the denoised signals is larger than 0.9. The denoising capability of the presented method was verified by an X-ray radiation experiment. R 2 of the denoised signal achieves 0.96 from 0.60, and the fitting errors of beam parameters ( μ and σ ) also decrease by denoising without increasing the radiation intensity and the integration time.

Comparison of Transverse With Axial Excitation Modes Cross Correlation Flowmeters in High Water-Cut Oil–Water Flow Measurement

Due to long-term exploitation of oil wells, high water-cut oil–water two-phase flow has become one of the most common flow types in offshore oil fields. In this work, two cross correlation flowmeters for this type of flow, i.e., the newly proposed transverse excitation mode flowmeter and the conventional axial excitation mode flowmeter, are theoretically analyzed, numerically solved, and experimentally compared. By building theoretical models, the resolutions and sensitivities of the sensors are systematically compared to demonstrate their abilities to detect oil bubbles in water. From the numerical solutions by the finite-element method (FEM) models, the resolutions of the sensors are analyzed in the spatial frequency domain, and more accurate analysis of sensitivities can be made. Results show that the resolution of the transverse excitation mode flowmeter is approximately three times higher, and the sensitivity is at most 3.47 times higher than the axial excitation mode one. Experiments with 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{{3}}$ </tex-math></inline-formula> /d, 90%-water-cut oil–water two-phase flow are carried out to demonstrate the dynamic performances of the two flowmeters. It can be concluded that the transverse excitation mode flowmeter has higher accuracy and reliability in flow rate measurement.

A Hybrid Method of Frequency and Spatial Domain Techniques for TFT-LCD Circuits Defect Detection

Defect detection is a crucial but challenging task in thin film transistor liquid crystal display (TFT-LCD) manufacturing. Existing vision-based methods focus on either spatial domain or frequency domain with unsatisfactory detection. In view of that, this paper proposes a hybrid template matching method by drawing benefits from both frequency and spatial domain techniques. Under proposal, frequency domain template matching method and saliency detector method are firstly adopted separately to obtain two candidate frequency components associated with defects. In template matching process, a novel selection criterion is taken to improve identifying components associated with local spatial anomaly. Subsequently, the inverse Fourier transform is applied on the intersection of the two candidates to reconstruct the defect regions. In final steps, image entropy in the spatial domain is employed to filter out false detection regions to improve accuracy. To meet industry’s real-time inspection requirement, image partition and multi-threading calculation techniques are introduced into the proposed methodology. Experimental results have shown practical viability of the proposed approach to increase the yield rate of panels through robust defect detection in TFT-LCD manufacturing.

ICSI: an improved contrast source inversion method for electromagnetic inverse scattering problems.

An improved contrast source inversion method (ICSI) is proposed to solve the problem of electromagnetic inverse scattering. Specifically, we first resort Fourier bases to represent contrast source, so that we can solve contrast source in the frequency domain, which can accelerate the solution of contrast source. Then, a spatial-frequency domain constraint is designed to ensure that the spanned-domain calculation is synchronous optimal. Afterwards, a multi-round optimization combined with SVD (the singular value decomposition) is developed to alleviate the reliance on initial guesses. Finally, we utilize a frequency-domain filter to eliminate redundant inversion information and narrow the search scope of the solution. Extensive experiments on the synthetic and real data show that ICSI holds a faster computing speed, a better inversion ability of relative permittivities, and a stronger anti-noise ability.

Cooperated Moving Target Detection Approach for PA-FDA Dual-Mode Radar in Range-Ambiguous Clutter

This paper proposes a cooperated range ambiguous clutter suppression method for moving target detection in the background of range-ambiguous clutter with a phased array (PA)–frequency diverse array (FDA) dual-mode radar. With the FDA mode, the range-ambiguous clutters are discriminated in the transmit spatial frequency domain, and thus the clutter covariance matrixes (CCMs) corresponding to unambiguous and ambiguous regions can be independently estimated. Therefore, the enhanced CCM can be reconstructed by using a linear combination of these distinguished CCMs from different range regions. With the PA mode, the enhanced CCM is applied, thus taking advantages of its high beampattern gain as well as alleviating the range ambiguous clutter suppression problem. Simulation results are presented to verify the effectiveness of the proposed method in range-ambiguous clutter scenarios.

Improving diameter measurement from Fraunhofer diffraction with fringe segment splicing.

Fraunhofer diffraction is an easy but powerful method for measuring the diameter of a thin filament. In practice, however, the diffraction pattern attainable is always subject to limits imposed by various imperfections in real systems, such as small angle approximation and sensor threshold, thus degrading the measurement resolution. In this Letter, we propose a method of fringe segment splicing for improving the diameter measurement from Fraunhofer diffraction. The fringe segment is chosen from a real diffraction pattern and is used to reproduce an ideal diffraction fringe, where the theoretical estimates give the best approximation to the observations. The problem of diameter measurement is solved in the spatial frequency-domain with an ideal diffraction fringe. Our results show that the relative error in this method is less than 0.1% and is far superior to that of previous methods.

Alternative deep learning method for fast spatial-frequency shift imaging microscopy.

Spatial-frequency shift (SFS) imaging microscopy can break the diffraction limit of fluorescently labeled and label-free samples by transferring the high spatial-frequency information into the passband of microscope. However, the resolution improvement is at the cost of decreasing temporal resolution since dozens of raw SFS images are needed to expand the frequency spectrum. Although some deep learning methods have been proposed to solve this problem, no neural network that is compatible to both labeled and label-free SFS imaging has been proposed. Here, we propose the joint spatial-Fourier channel attention network (JSFCAN), which learns the general connection between the spatial domain and Fourier frequency domain from complex samples. We demonstrate that JSFCAN can achieve a resolution similar to the traditional algorithm using nearly 1/4 raw images and increase the reconstruction speed by two orders of magnitude. Subsequently, we prove that JSFCAN can be applied to both fluorescently labeled and label-free samples without architecture changes. We also demonstrate that compared with the typical spatial domain optimization network U-net, JSFCAN is more robust to deal with deep-SFS images and noisy images. The proposed JSFCAN provides an alternative route for fast SFS imaging reconstruction, enabling future applications for real-time living cell research.

Improved topographic reconstruction of turbid media in the spatial frequency domain including the determination of the reduced scattering and absorption coefficients.

The separation of scattering and absorption is of great importance for studying the radiative transfer in turbid media. Obtaining the corresponding coefficients for non-flat objects is difficult and needs special consideration. Building on our previous work [J. Opt. Soc. Am. A39, 1823 (2022)JOAOD60740-323210.1364/JOSAA.464007], we present an approach that takes the changing incident and detection angles relative to the surface normal of curved surfaces into account to improve the determination of the reduced scattering and absorption coefficients with measurements in the spatial frequency domain (SFD). The optical coefficients are reconstructed using a pre-calculated lookup table generated with Monte Carlo simulations on graphical processing units. With the obtained values, the error in the captured surface geometry of the object, which is due to the volume scattering, is compensated and reduced by 1 order of magnitude for measurements in the SFD. Considering the approximate surface geometry, the absorption and reduced scattering are accurately resolved for moderate object curvatures, with very low dependence on the tilt angle. In contrast to models that only correct the amplitudes of the SFD signal, our approach, in addition to the optical properties, predicts the phase values correctly, which is the reason why it can be used to correct the surface geometry.

MRLA-Net: A tumor segmentation network embedded with a multiple receptive-field lesion attention module in PET-CT images

The tumor image segmentation is an important basis for doctors to diagnose and formulate treatment planning. PET-CT is an extremely important technology for recognizing the systemic situation of diseases due to the complementary advantages of their respective modal information. However, current PET-CT tumor segmentation methods generally focus on the fusion of PET and CT features. The fusion of features will weaken the characteristics of the modality itself. Therefore, enhancing the modal features of the lesions can obtain optimized feature sets, which is extremely necessary to improve the segmentation results. This paper proposed an attention module that integrates the PET-CT diagnostic visual field and the modality characteristics of the lesion, that is, the multiple receptive-field lesion attention module. This paper made full use of the spatial domain, frequency domain, and channel attention, and proposed a large receptive-field lesion localization module and a small receptive-field lesion enhancement module, which together constitute the multiple receptive-field lesion attention module. In addition, a network embedded with a multiple receptive-field lesion attention module has been proposed for tumor segmentation. This paper conducted experiments on a private liver tumor dataset as well as two publicly available datasets, the soft tissue sarcoma dataset, and the head and neck tumor segmentation dataset. The experimental results showed that the proposed method achieves excellent performance on multiple datasets, and has a significant improvement compared with DenseUNet, and the tumor segmentation results on the above three PET/CT datasets were improved by 7.25%, 6.5%, 5.29% in Dice per case. Compared with the latest PET-CT liver tumor segmentation research, the proposed method improves by 8.32%.

Zero-order-removal off-axis digital holographic reconstruction using different beam-ratio holographic recordings

A method of the zero-order-removal off-axis digital holographic reconstruction by recording three holograms with different beam ratios is presented. The zero-order-removal hologram can be constituted using two fitting coefficients in the combination of three holograms, in which the three off-axis holograms with different intensity ratios of the object and reference beams are recorded via arbitrarily turning a half-wave plate. The validity of the zero-order removal of the resultant hologram is proved by expression. The filtering region for the zero-order-removal hologram can extend to the center of its spatial-frequency spectrum domain, which makes higher spatial frequencies on the positive first-order intercepted. In the experiments, the reconstructed amplitude and phase images demonstrate the effectiveness of this zero-order-removal approach and the improvement on imaging resolution.

Extracting Tissue Optical Properties and Detecting Bruised Tissue in Pears Quickly and Accurately Based on Spatial Frequency Domain Imaging and Machine Learning.

Recently, Spatial Frequency Domain Imaging (SFDI) has gradually become an alternative method to extract tissue optical properties (OPs), as it provides a wide-field, no-contact acquisition. SFDI extracts OPs by least-square fitting (LSF) based on the diffuse approximation equation, but there are shortcomings in the speed and accuracy of extracting OPs. This study proposed a Long Short-term Memory Regressor (LSTMR) solution to extract tissue OPs. This method allows for fast and accurate extraction of tissue OPs. Firstly, the imaging system was developed, which is more compact and portable than conventional SFDI systems. Next, numerical simulation was performed using the Monte Carlo forward model to obtain the dataset, and then the mapping model was established using the dataset. Finally, the model was applied to detect the bruised tissue of 'crown' pears. The results show that the mean absolute errors of the absorption coefficient and the reduced scattering coefficient are no more than 0.32% and 0.21%, and the bruised tissue of 'crown' pears can be highlighted by the change of OPs. Compared with the LSF, the speed of extracting tissue OPs is improved by two orders of magnitude, and the accuracy is greatly improved. The study contributes to the rapid and accurate extraction of tissue OPs based on SFDI and has great potential in food safety assessment.

Target Imaging Using Compressed Sampling in Synthetic Aperture Interferometric Radiometer

The target imaging application is significant to various sensing systems, such as radiometers, radars, and infrared. However, high system complexity impedes the application of interferometric radiometers to target imaging tasks to some extent. Specifically for an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -element interferometric radiometer with aperture synthesis technique, complex correlators are of the order of O( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), giving rise to the great difficulty of system hardware implementation. In this paper, we propose a new compressed interferometric radiometer (CIR) concept for target imaging applications, which exploits the sparsity property of targets in the spatial domain. The CIR target imaging framework mainly adopts the compressive measurement method to acquire partial visibility function samples in the spatial-frequency domain via a proper sparse sampling pattern. Then, these partially observed visibility samples are inverted to image the target contrast information by sparse recovery methods. For the above image recovery process, we propose two novel algorithms named local regional information-based reweighted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> 1-norm minimization (LRRL1) and local regional convolution-based reweighted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> 1-norm minimization (LRCRL1). The experiments using simulated and real data demonstrate the validity and effectiveness of the proposed CIR target imaging framework, showing superiority in both imaging performance and system complexity compared with conventional algorithms used in interferometric radiometers.