Point Spread Function Of System Research Articles

Passive Cavitation Mapping by Cavitation Source Localization From Aperture-Domain Signals-Part I: Theory and Validation Through Simulations.

Passive cavitation mapping (PCM) algorithms for diagnostic ultrasound arrays based on time exposure acoustics (TEA) exhibit poor axial resolution, which is in part due to the diffraction-limited point spread function of the imaging system and poor rejection by the delay-and-sum beamformer. In this article, we adapt a method for speed of sound estimation to be utilized as a cavitation source localization (CSL) approach. This method utilizes a hyperbolic fit to the arrival times of the cavitation signals in the aperture domain, and the coefficients of the fit are related to the position of the cavitation source. Wavefronts exhibiting poor fit to the hyperbolic function are corrected to yield improved source localization. We demonstrate through simulations that this method is capable of accurate estimation of the origin of coherent spherical waves radiating from cavitation/point sources. The average localization error from simulated microbubble sources was 0.12 ± 0.12mm ( 0.15 ± 0.14λ0 for a 1.78-MHz transmit frequency). In simulations of two simultaneous cavitation sources, the proposed technique had an average localization error of 0.2mm ( 0.23λ0 ), whereas conventional TEA had an average localization error of 0.81mm ( 0.97λ0 ). The reconstructed PCM-CSL image showed a significant improvement in resolution compared with the PCM-TEA approach.

Ultrasound Image Deconvolution Using Fundamental and Harmonic Images

Ultrasound (US) image restoration from radio frequency (RF) signals is generally addressed by deconvolution techniques mitigating the effect of the system point spread function (PSF). Most of the existing methods estimate the tissue reflectivity function (TRF) from the so-called fundamental US images, based on an image model assuming the linear US wave propagation. However, several human tissues or tissues with contrast agents have a nonlinear behavior when interacting with US waves leading to harmonic images. This work takes this nonlinearity into account in the context of TRF restoration, by considering both fundamental and harmonic RF signals. Starting from two observation models (for the fundamental and harmonic images), TRF estimation is expressed as the minimization of a cost function defined as the sum of two data fidelity terms and one sparsity-based regularization stabilizing the solution. The high attenuation with a depth of harmonic echoes is integrated into the direct model that relates the observed harmonic image to the TRF. The interest of the proposed method is shown through synthetic and in vivo results and compared with other restoration methods.

Multi-frame image restoration method for novel rotating synthetic aperture imaging system

The novel rotating synthetic aperture (RSA) optical imaging system is an important development direction for future high-resolution optical remote sensing satellites in geostationary orbit. However, owing to the rotating rectangular pupil, the point spread function of the RSA system has an asymmetric spatial distribution, and the images obtained using the primary mirror from different rotation angles have nonuniform blur degradation. Moreover, platform vibration and pupil rotation have coupling effects on the RSA imaging, resulting in further radiometric and geometric quality degradation. To address these problems, the image degradation characteristics are first analyzed according to the imaging mechanism. Then, combined with the theory of mutual information, an image registration method is suggested by introducing the orientation gradient information. From this, a multi-frame image restoration model is proposed based on the directional gradient prior of the RSA system image. From the perspective of interpretation and application, when the aspect ratio is less than 3, the proposed inversion restoration method can achieve a satisfactory processing performance. This work can provide engineering application reference for the future space application of RSA imaging technology.

Influence of circular and annular pupil function on Axial Point Spread Function of optical system

The paper presents an analysis of influence of shape and transmissivity of a pupil of an optical system on an axial energy distribution while the optical system images axial point. Therefore, a depth of focus is studied. Specifically, the analysis is done for uniform illumination of a circular pupil, and for the circular and annular pupil in the case of Gaussian amplitude distribution. Analytical formulas for Point Spread Function and Axial Point Spread Function are described, and characteristics of properties of the depth of focus of the optical system are derived. The novel analytic formulas presented in the paper can be used for determination of the value of the depth of focus of the optical system for given threshold limit of normalized axial intensity.

Constrained polynomial fit-based k-domain interpolation in swept-source optical coherence tomography

We propose a [Formula: see text]-domain spline interpolation method with constrained polynomial fit based on spectral phase in swept-source optical coherence tomography (SS-OCT). A Mach–Zehnder interferometer (MZI) unit is connected to the swept-source of the SS-OCT system to generate calibration signal in sync with the fetching of interference spectra. The spectral phase of the calibration signal is extracted by Hilbert transformation. The fitted phase–time relationship is obtained by polynomial fitting with the constraint of passing through the central spectral phase. The fitting curve is then adopted for [Formula: see text]-domain uniform interpolation based on evenly spaced phase. In comparison with conventional [Formula: see text]-domain spline interpolation, the proposed method leads to improved axial resolution and peak response of the axial point spread function (PSF) of the SS-OCT system. Enhanced performance resulting from the proposed method is further verified by OCT imaging of a home-constructed microspheres-agar sample and a fresh lemon. Besides SS-OCT, the proposed method is believed to be applicable to spectral domain OCT as well.

Broadband scattering imaging technology based on common-mode rejection of polarization characteristic

<sec>Owing to the inhomogeneity of the refractive index inside the sample (e.g. biological tissue) or on the surface of the sample(e.g. ground glass), light will be strongly scattered when it propagates through the sample. Therefore, we can hardly obtain the information about the objects behind the scattering medium, except for only a complex speckle pattern. To date, many approaches to realize focusing and imaging through scattering medium have been put forward. The traditional method mainly utilizes ballistic photons for imaging through scattering medium. Since the ballistic light is attenuated exponentially with the increase of depth of propagation in the scattering medium, the reconstruction from the speckle formed by scattered light is more conducive to practicability such as deep biomedical imaging. Typically, the wavefront shaping, optical transmission matrix and speckle correlation techniques which can successfully recover hidden object from the speckle, are valuable in biomedical imaging field. However, both optical transmission matrix and wavefront shaping rely on the coherence of light waves. The physical model of speckle correlation imaging is limited by the similarity of the point spread function of the imaging system. Thus, it is restrictive to achieve imaging through random scattering medium with broadband light illumination by using the current techniques.</sec><sec>In this paper, we present a broadband scattering imaging method based on common-mode rejection of polarization characteristic. In order to solve the problem that current scattering imaging methods are limited by the spectral width of the light source illumination, the polarization characteristic of the speckle field is explored in depth. We qualitatively analyze the difference in polarization information between the hidden object and the background noise in the speckle field. Notably, owing to the differences among autocorrelation functions of the speckle field intensity with different rotate angles of polarization, we can obtain two images where the object information contained in the speckle field and the background noise are dominant. Specifically, two speckle patterns are selected according to the maximum value and minimum value of the peak-to-correlation energy of the different speckles’ intensity autocorrelation. Afterwards, the serious background noise caused by the broadband light illumination is significantly suppressed by using polarization speckle difference imaging, and then the hidden object is reconstructed, with basic phase retrieval algorithm combined.</sec><sec>Comparison with conventional speckle correlation imaging technique, the value of peak signal-to-noise ratio and structural similarity index of reconstructions through using the proposed method are improved significantly, and the fitting curves are stabilized. Emphatically, the background noise item is physically handled by developing a novel physical imaging model. Furthermore, the proposed method is highly efficient and universal to recover different types of the hidden objects with better quality under broadband light illumination. Therefore, the proposed method has more potential applications in scattering imaging and biomedical imaging.</sec>

Adaptive Phase Correction for Phase Measuring Deflectometry Based on Light Field Modulation

The phase measuring deflectometry is a powerful measuring method for complex optical surfaces, which captures the reflected fringe images associated with a displaying screen and calculates the normal vectors of the surface under test (SUT) accordingly. The captured images are usually set conjugate to the SUT, which in turn makes the screen defocused. As a result, the blurring effect caused by the point spread function (PSF) of the off-axis catadioptric imaging system can bias the solved phases. In order to correct the phase errors, a light field is constructed based on the Fourier compressive sensing method to describe the light transmission between the screen and camera pixels. Fringe modulation is conducted to enhance the robustness against noise, and then, space-variant PSFs can be extracted from the light field. The true phases are obtained by solving a Wiener deconvolution problem, with the merit function adaptively regularized by adjusting the damping parameter. The proposed method can correct adaptively the phase errors induced by the complex aberrations. Compared to the reference measurements, the form accuracy can be improved by four times.

A Reference-Free Image Index to Simultaneously Quantify Infrared-Imaging Fixed-Pattern-Noise and Blur Artifacts

A reference-free image index to jointly assess infrared-imaging fixed-pattern-noise and blur artifacts is proposed in this work. The proposed index is based on tuned-spatial-domain filtering, which works by combining two Laplace operators to simultaneously quantify the global infrared-imaging fixed-pattern-noise and the global or local blur artifacts. The index effectiveness is demonstrated by two task-based image-quality assessments to determine the focused and fixed-pattern-noise free images from sequences captured with both a mid-wave-infrared microscope system and a long-wave-infrared plenoptic system. The index quantitative limits are shown on numerical computations over synthetic corrupted images as well as real black-body radiator calibrated infrared images with representative simulated fixed-pattern noise, from six well known infrared focal plane arrays transducer technologies, along with artificial blur added using real infrared imaging system point spread functions.

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

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

Improved GNSS-Based Bistatic SAR Using Multi-Satellites Fusion: Analysis and Experimental Demonstration.

The Global Navigation Satellite System (GNSS)-based Bistatic Synthetic Aperture Radar (SAR) is getting more and more attention in remote sensing for its all-weather and real-time global observation capability. Its low range resolution results from the narrow signal bandwidth limits in its development. The configuration difference caused by the illumination angle and movement direction of the different satellites makes it possible to improve resolution by multi-satellite fusion. However, this also introduces new problems with the resolution-enhancing efficiency and increased computation brought about by the fusion. In this paper, we aim at effectively improving the resolution of the multi-satellite fusion system. To this purpose, firstly, the Point Spread Function (PSF) of the multi-satellite fusion system is analyzed, and focusing on the relationship between the fusion resolution and the geometric configuration and the number of satellites. Numerical simulation results show that, compared with multi-satellite fusion, dual-satellite fusion is a combination with higher resolution enhancement efficiency. Secondly, a method for dual-satellite fusion imaging based on optimized satellite selection is proposed. With the greedy algorithm, the selection is divided into two steps: in the first step, according to geometry configuration, the single-satellite with the optimal 2-D resolution is selected as the reference satellite; in the second step, the angles between the azimuthal vector of the reference satellite and the azimuthal vector of the other satellites were calculated by the traversal method, the satellite corresponding to the intersection angle which is closest to 90° is selected as the auxiliary satellite. The fused image was obtained by non-coherent addition of the images generated by the reference satellite and the auxiliary satellite, respectively. Finally, the GPS L1 real orbit multi-target simulation and experimental validation were conducted, respectively. The simulation results show that the 2-D resolution of the images produced by our proposed method is globally optimal 15 times and suboptimal 8 times out of 24 data sets. The experimental results show that the 2-D resolution of our proposed method is optimal in the scene, and the area of the resolution unit is reduced by 70.1% compared to the single-satellite’s images. In the experiment, there are three navigation satellites for imaging, the time taken to the proposed method was 66.6% that of the traversal method. Simulations and experiments fully demonstrate the feasibility of the method.

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

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

Quantitative assessment of human cervix with correlation length ratio during pregnancy: An in vivo longitudinal study

We recently introduced a novel parameter called the correlation length ratio (CLR), a ratio of lateral to axial correlation lengths for backscattered echo signals, to detect the presence of elongated structures in soft tissues. Here, we look at variation of CLR and presence of elongated structures in human cervix during pregnancy using a longitudinal data from a group of women with normal pregnancy. Thirty women, ages ranging from 19 to 37years, were scanned with ultrasound at five time points beginning at their normal first-trimester screening (8 –13 weeks) through term pregnancy (nominally 40 week). We computed correlation lengths, and CLR. To account for the system point spread function, an empirical cumulative distribution function of the CLR was obtained from a reference phantom. A one-sided threshold of 95% of the CDF was then computed. The difference between CLR in the sample and the threshold was computed and its variation with increasing gestational age was obtained. CLR estimation demonstrated a gradient along the length of the cervix. This longitudinal study also demonstrated an increase of about 0.5% (per week) in lateral correlation length and 0.8% increase in CLR with increasing gestational age, while axial correlation length was almost constant.

Quantum limited source localization and pair superresolution in two dimensions under finite-emission bandwidth

Optically localizing a single quasi-monochromatic source to sub-diffractive precisions entails, in the photon-counting limit, a minimum photon cost that scales as the squared ratio of the width, $w$, of the optical system's point-spread function (PSF) and the sought localization precision, $d$, i.e., as $\alpha(w/d)^2$. For sources with a finite emission-frequency spectrum, while the inverse quadratic scaling is expected to remain unchanged, the coefficient $\alpha$ must increase due to a degrading fidelity of localization as the imaging bandwidth increases and PSF undergoes a frequency-dependent widening. We specifically address how rapidly $\alpha$ must increase with increasing width of a flat-top spectral profile of emission of a point source being localized in two dimensions by an imager with a clear circular aperture by calculating quantum Fisher information (QFI), whose inverse yields the lowest possible unbiased-estimation variance of source-localization error. The novel use of prolate spheroidal wave functions as a basis for obtaining a solution of the eigenvalue problem of the single-photon density operator needed for the QFI calculation helps us develop the notion of an effective dimensionality of the continuous-state problem in terms of the associated space-bandwidth parameter. We subsequently extend our considerations of QFI to treat the finite-bandwidth pair superresolution problem in two dimensions, obtaining similar results. We also consider generalizations to emission power spectra of arbitrary profiles.

Comparison of heuristic and deterministic algorithms in neutron coded imaging reconstruction

Neutron coded imaging is an effective tool for diagnosing the shape, size and symmetry of deuterium (D)–tritium (T) plasma in inertial confinement fusion (ICF). It can provide an important reference for designing and improving the D–T pellet and confinement configuration. Image reconstruction algorithms play a role of reconstructing the source images from the blurred coded images and the point spread functions (PSFs) of imaging systems. Conventionally, the convolution model is used as the mathematical model for neutron coded imaging reconstruction, but it applies only to the spatially invariant PSF. In this paper, the linear equations model is regarded as the mathematical model for the reconstruction, and it can also be suitable for spatially variant PSF. In the reconstruction, the spatially variant PSFs were simulated through Monte Carlo method. Then an improved genetic algorithm (IGA) for the source image reconstruction was proposed. The comparison of its performance with other types of deterministic algorithms (like the algorithm with total variation (TV) minimization) was conducted, and the results showed that the IGA has better performance in source reconstruction regardless of the utilization of TV sparse prior.

Non-invasive single-shot recovery of a point-spread function of a memory effect based scattering imaging system.

Accessing the point-spread function (PSF) of a complex optical system is important for a variety of imaging applications. However, placing an invasive point source is often impractical, and estimating it blindly with multiple frames is slow and requires a complex nonlinear optimization. Here, we introduce a simple single-shot method to noninvasively recover the accurate PSF of an isoplanatic imaging system, in the context of multiple light scattering. Our approach is based on the reconstruction of any unknown sparse hidden object using the autocorrelation imaging technique, followed by a deconvolution with a blur kernel derived from the statistics of a speckle pattern. A deconvolution on the camera image then retrieves the accurate PSF of the system, enabling further imaging applications. We demonstrate numerically and experimentally the effectiveness of this approach compared to previous deconvolution techniques.

Estimation of Ultrasound Echogenicity Map from B-Mode Images Using Convolutional Neural Network.

In ultrasound B-mode imaging, speckle noises decrease the accuracy of estimation of tissue echogenicity of imaged targets from the amplitude of the echo signals. In addition, since the granular size of the speckle pattern is affected by the point spread function (PSF) of the imaging system, the resolution of B-mode image remains limited, and the boundaries of tissue structures often become blurred. This study proposed a convolutional neural network (CNN) to remove speckle noises together with improvement of image spatial resolution to reconstruct ultrasound tissue echogenicity map. The CNN model is trained using in silico simulation dataset and tested with experimentally acquired images. Results indicate that the proposed CNN method can effectively eliminate the speckle noises in the background of the B-mode images while retaining the contours and edges of the tissue structures. The contrast and the contrast-to-noise ratio of the reconstructed echogenicity map increased from 0.22/2.72 to 0.33/44.14, and the lateral and axial resolutions also improved from 5.9/2.4 to 2.9/2.0, respectively. Compared with other post-processing filtering methods, the proposed CNN method provides better approximation to the original tissue echogenicity by completely removing speckle noises and improving the image resolution together with the capability for real-time implementation.

Experimental characterization of a mode-separating photonic lantern for imaging applications.

The point spread function (PSF) of an imaging system has a minimum size, a "diffraction limit," determined by the size of the limiting aperture. Image features smaller than this PSF can be, in a conventional imaging system, resolved only if the intensity noise is low enough to permit deconvolution. Measuring image-plane intensity as a function of spatial mode rather than position has the potential to reduce the quantum noise and thus enable subdiffraction resolution at lower light levels or in shorter measurement times than can be tolerated with conventional imaging. Here we examine experimental measurements of intensity and intensity noise as a function of spatial mode. We characterize the impulse response of a spatial mode coupling measurement at the focal plane of an imaging system to the position of a far-field point source. Our measured intensity noise scales with power in a way that suggests photon shot noise is a significant contributor, and we find that the signal-to-noise ratio of our modal-basis measurement of point source position exceeds that of a conventional image-plane pixel array for subdiffraction objects imaged against dark backgrounds. The mode coupling is measured with a custom mode-separating fiber photonic lantern. Photonic lanterns and equivalent structures constructed from rigid waveguides are simple, passive devices that lend themselves to real-world implementations of this measurement scheme with minimal size, weight, power, and cost.

High axial resolution and long field of view for light-sheet fluorescence microscopy via double-beam aperture

We propose a simple method based on the use of interference of the double-beam aperture to enhance both the axial resolution and field of view of light-sheet fluorescence microscopy. The double-beam aperture placed in the pupil plane generates multiple-spot intensity patterns in which the size of central lobe reduces. By scanning this intensity pattern along x -axis, the light sheet is generated. By satisfactorily choosing the numerical apertures of illumination lens and detection lens, only the central light sheet is used to achieve image, so the axial resolution of light-sheet fluorescence microscopy is enhanced. Both the numerical apertures of the illumination lens and detection lens of 0.3 and 1.1, respectively, are employed to perform the simulation results. The simulation results indicated that both the axial resolution and field of view are improved in comparison to the Gaussian light-sheet. Additionally, in order to remove a small amount of the existing outside lobes, we propose a subtraction method. The simulation results demonstrated that our technique can eliminate the outside lobes in the system point spread function of the double-beam aperture beam light sheet.

Method for Determining the Point Spread Function for a Digital Radiography System

The shape and size of the projection of the focal spot of an x-ray tube largely depend on the direction of the beam, which results in a spatial difference of the point spread function (PSF) of the imaging system. A model developed for determining the PSF at an arbitrary point of the radiation field is presented in this article. The input data for the model are the geometric parameters of the system, the measured magnified projection of the effective focal spot, and the PSF in the internal structure of the detector. The difference in the width of the profiles of the PSF between the experimental and modeled data does not exceed 7.2%. The projection images are reconstructed by means of a deconvolution algorithm using the modeled PSF. The frequency–contrast characteristics of the images show improvement compared with the initial image.

Far-field thermal imaging below diffraction limit.

Non-uniform self-heating and temperature hotspots are major concerns compromising the performance and reliability of submicron electronic and optoelectronic devices. At deep submicron scales where effects such as contact-related artifacts and diffraction limits accurate measurements of temperature hotspots, non-contact thermal characterization can be extremely valuable. In this work, we use a Bayesian optimization framework with generalized Gaussian Markov random field (GGMRF) prior model to obtain accurate full-field temperature distribution of self-heated metal interconnects from their thermoreflectance thermal images (TRI) with spatial resolution 2.5 times below Rayleigh limit for 530nm illumination. Finite element simulations along with TRI experimental data were used to characterize the point spread function of the optical imaging system. In addition, unlike iterative reconstruction algorithms that use ad hoc regularization parameters in their prior models to obtain the best quality image, we used numerical experiments and finite element modeling to estimate the regularization parameter for solving a real experimental inverse problem.