Long range image enhancement

A Kelvin probe force microscopy (KPFM) image is sometimes difficult to interpret because it is a blurred representation of the true surface potential (SP) distribution of the materials under test. The reason for the blurring is that KPFM relies on the detection of electrostatic force, which is a long-range force compared to other surface forces. Usually, KPFM imaging model is described as the convolution of the true SP distribution of the sample with an intrinsic point spread function (PSF) of the measurement system. To restore the true SP signals from the blurred ones, the intrinsic PSF of the system is needed. In this work, we present a way to experimentally calibrate the PSF of the KPFM system. Taking the actual probe shape and experimental parameters into consideration, this calibration method leads to a more accurate PSF than the ones obtained from simulations. Moreover, a nonlinear reconstruction algorithm based on total variation (TV) regularization is applied to KPFM measurement to reverse the blurring caused by PSF during KPFM imaging process; as a result, noises are reduced and the fidelity of SP signals is improved.

3-D optical fluorescent microscopy becomes now an efficient tool for volume investigation of living biological samples. Developments in instrumentation have permit to beat off the conventional Abbe limit, in any case the recorded image can be described by the convolution equation between the original object and the Point Spread Function (PSF) of the acquisition system. If the goal is 3-D quantitative analysis, whether you improve the instrument capabilities, or (and) you restore the data. These last is until now the main task in our laboratory. Based on the knowledge of the optical Transfer Function of the microscope, deconvolution algorithms were adapted to automatic determine the regularisation threshold in order to give less subjective and more reproducible results. The PSF represents the properties of the image acquisition system; we have proposed the use of statistical tools and Zernike moments to describe a 3-D system PSF and to quantify the variation of the PSF. This first step toward standardization is helpful to define an acquisition protocol optimizing exploitation of the microscope depending on the studied biological sample. We have pointed out that automating the choice of the regularization level; if it facilitates the use, it also greatly improves the reliability of the measurements. Furthermore, to increase the quality and the repeatability of quantitative measurements a pre-filtering of images improves the stability of deconvolution process. In the same way, the PSF pre-filtering stabilizes the deconvolution process. We have shown that Zernike polynomials can be used to reconstruct experimental PSF, preserving system characteristics and removing the noise contained in the PSF. Fluorescent microscopes suffer from limitations; photobleaching and phototoxicity effects, or influence of the sample optical properties to 3-D observation. Amplitude and phase of the object can be reached with optical tomography based on a combination of microholography with a tomographic illumination. So indices cartography of the specimen can be obtained, and combined with fluorescence information it will open new possibilities in 3-D optical microscopy.

An accurate measurement of the point spread function (PSF) for the extended depth of field (EDoF) cell phone camera with CMOS sensor is very important for image processing and image restoration. But due to the coarse sampling of the PSF by CMOS sensor, the overall system including the imaging subsystem and sampling subsystem is a shift-variant system with respect to the sample-scene phase parameter within sub-pixel range. In this paper, we present the sub-pixel digital algorithm to estimate the overall camera PSF based on the measurement of a high resolution PSF of the imaging lens. The sub-pixel digital algorithm averages the shifted high resolution PSFs of the lens over one active pixel area with the assumption of uniform random distribution of point source location within one active pixel area. Then the averaged high resolution PSF is down sampled onto Bayer plane to obtain the shift-invariant overall system PSF. We applied this shift-invariant PSF for image restoration of blurred images captured with an extended depth of field camera. The processed images are compared with originally captured images. Improvement of image quality is seen.

The point spread function (PSF) of imaging system with coded mask is generally acquired by practical measure- ment with calibration light source. As the thermal radiation of coded masks are relatively severe than it is in visible imaging systems, which buries the modulation effects of the mask pattern, it is difficult to estimate and evaluate the performance of mask pattern from measured results. To tackle this problem, a model for infrared imaging systems with masks is presented in this paper. The model is composed with two functional components, the coded mask imaging with ideal focused lenses and the imperfection imaging with practical lenses. Ignoring the thermal radiation, the systems PSF can then be represented by a convolution of the diffraction pattern of mask with the PSF of practical lenses. To evaluate performances of different mask patterns, a set of criterion are designed according to different imaging and recovery methods. Furthermore, imaging results with inclined plane waves are analyzed to achieve the variation of PSF within the view field. The influence of mask cell size is also analyzed to control the diffraction pattern. Numerical results show that mask pattern for direct imaging systems should have more random structures, while more periodic structures are needed in system with image reconstruction. By adjusting the combination of random and periodic arrangement, desired diffraction pattern can be achieved.

The Ingenuity time-of-flight (TF) PET/MR is a recently developed hybrid scanner combining the molecular imaging capabilities of PET with the excellent soft tissue contrast of MRI. It is becoming common practice to characterize the system's point spread function (PSF) and understand its variation under spatial transformations to guide clinical studies and potentially use it within resolution recovery image reconstruction algorithms. Furthermore, due to the system's utilization of overlapping and spherical symmetric Kaiser-Bessel basis functions during image reconstruction, its image space PSF and reconstructed spatial resolution could be affected by the selection of the basis function parameters. Hence, a detailed investigation into the multidimensional basis function parameter space is needed to evaluate the impact of these parameters on spatial resolution. Using an array of 12 × 7 printed point sources, along with a custom made phantom, and with the MR magnet on, the system's spatially variant image-based PSF was characterized in detail. Moreover, basis function parameters were systematically varied during reconstruction (list-mode TF OSEM) to evaluate their impact on the reconstructed resolution and the image space PSF. Following the spatial resolution optimization, phantom, and clinical studies were subsequently reconstructed using representative basis function parameters. Based on the analysis and under standard basis function parameters, the axial and tangential components of the PSF were found to be almost invariant under spatial transformations (~4 mm) while the radial component varied modestly from 4 to 6.7 mm. Using a systematic investigation into the basis function parameter space, the spatial resolution was found to degrade for basis functions with a large radius and small shape parameter. However, it was found that optimizing the spatial resolution in the reconstructed PET images, while having a good basis function superposition and keeping the image representation error to a minimum, is feasible, with the parameter combination range depending upon the scanner's intrinsic resolution characteristics. Using the printed point source array as a MR compatible methodology for experimentally measuring the scanner's PSF, the system's spatially variant resolution properties were successfully evaluated in image space. Overall the PET subsystem exhibits excellent resolution characteristics mainly due to the fact that the raw data are not under-sampled/rebinned, enabling the spatial resolution to be dictated by the scanner's intrinsic resolution and the image reconstruction parameters. Due to the impact of these parameters on the resolution properties of the reconstructed images, the image space PSF varies both under spatial transformations and due to basis function parameter selection. Nonetheless, for a range of basis function parameters, the image space PSF remains unaffected, with the range depending on the scanner's intrinsic resolution properties.

The distribution of the ray density of the spot diagram formed in the image plane is called the geometric point spread function (PSF). It plays an important role in the image formation theory, since it describes the impulse response of an optical system to a source point. However, the literature contains very few techniques for deriving the PSF of optical systems. Accordingly, this study presents a method based on an irradiance model for computing the geometric PSF of an optical system by considering the energy conservation along a single light ray. It is shown that the proposed method obtains a reliable and accurate estimate of the PSF and enables the computation of the centroid and root-mean-square radius of the focus spot on the image plane. In addition, compared to existing ray-counting methods presented in the literature, in which the quality of the PSF solution depends on the number of rays traced and the grid size used to mesh the image plane, the proposed irradiance-based method requires just one tracing operation. Overall, the results presented in this study confirm that the proposed method provides an ideal solution for calculating the merit function and modulation transfer function of an optical system.

Linear systems theory combined with Fourier transform techniques provides a powerful means to characterize electro-optical systems. We present the description and analysis of a particular scanning IR system whose characteristic Point Spread Function (PSF) is space-variant. This peculiarity of the PSF arises from the scanning geometry; the IR sensor spins as it drops toward the ground. A system impulse response, or Point Spread Function (PSF), is derived from effects including diffraction, motion blur, chromatic aberration and detector area. Other effects may be taken into account by cascading PSF's. Once the system PSF is determined, the output of the system is the convolution of the input irradiance with the PSF. Alternatively, the output is the familiar inverse Fourier transform of the product of transforms. However, the space-variance of the PSF makes the latter option impossible and the former difficult. The convolution progresses in a spiral manner, with the PSF width changing continuously. The method is tested using Fortran programs and a digital image processor. The digital images produced show expected results, revealing a marked increase in resolution as the sensor nears the ground.

3-D optical fluorescent microscopy becomes now an efficient tool for volumic investigation of living biological samples. The 3-D data can be acquired by Optical Sectioning Microscopy which is performed by axial stepping of the object versus the objective. For any instrument, each recorded image can be described by a convolution equation between the original object and the Point Spread Function (PSF) of the acquisition system. To assess performance and ensure the data reproducibility, as for any 3-D quantitative analysis, the system indentification is mandatory. The PSF explains the properties of the image acquisition system; it can be computed or acquired experimentally. Statistical tools and Zernike moments are shown appropriate and complementary to describe a 3-D system PSF and to quantify the variation of the PSF as function of the optical parameters. Some critical experimental parameters can be identified with these tools. This is helpful for biologist to define an aquisition protocol optimizing the use of the system. Reduction of out-of-focus light is the task of 3-D microscopy; it is carried out computationally by deconvolution process. Pre-filtering the images improves the stability of deconvolution results, now less dependent on the regularization parameter; this helps the biologists to use restoration process.

In an incoherent imaging system using the liquid crystal active lens, a point spread function can be controlled electrically. Since the liquid crystal active lens is a lens attached to an electrically addressable liquid crystal phase modulator, and the point spread function is an intensity distribution of the Fourier transform of the modulator's phase distribution. In this study, an electro-optical learning system is employed to produce a desirable point spread function by optimizing the phase distribution. Th phase distribution is controlled by a computer and the point spread function of the optical system is captured and fed into the computer. The point spread function is evaluated by the computer to optimize the phase distribution. The optimization method is based on the simulated annealing. The experimentally obtained point spread functions are closer to the desired ones compared to those generated only using a computer, becuase the electro-optical system learns the characteristics of the optical system during the optimization process. The performance of the electro-optical system is discussed.

During spatial remote sensing imaging procedure, combined degradation factors conduce to Gaussian image blurring. The precondition of restoring the degraded image is to estimate point spread function (PSF) of the imaging system as precisely as possible. Because the depredating processes are quite complex, the transfer function of the degraded system is often completely or partly unknown, which makes it quite difficult to identify the precise PSF. Considering the similarity between the quantum process and imaging process in the probability and statistics fields, a novel algorithm is proposed by using multilayer feed-forward back-propagation quantum neural network (QBPNN) to estimate PSF of the Gaussian degraded imaging system. Different from the classical artificial neural network (ANN), 2 adjustable parameters of weight connection coefficient and phase coefficient are introduced in its quantum neurons used in learning stage. By establishing different training sets, this estimation method can overcome the limitation in the dependence on initial values and large amount of computation. Test results show that this method can achieve higher precision, faster convergence and stronger generalization ability comparing with the traditional PSF estimation results.

Optical imaging usually suffers from aberrations that are induced by various structures when imaging biological samples. Usually aberrations degrade the imaging system performances by broadening the point spread function (PSF). Unexpectedly we show that in spatially incoherent interferometry like full-filed optical coherence tomography (FFOCT), the system PSF width is almost insensitive to aberrations. Instead of considering the PSF of a classical imaging system such as a microscope, we specifically pay attention to the system PSF of interferometric imaging systems for which an undistorted wavefront from a reference beam interferes with the distorted wavefront of the object beam. By comparing the cases of scanning OCT with spatially coherent illumination, wide-field OCT with spatially coherent illumination and FFOCT with spatially incoherent illumination, we found that in FFOCT with spatially incoherent illumination the system PSF width is almost independent of the aberrations and only its amplitude varies. This is demonstrated by theoretical analysis as well as numerical calculations for different aberrations, and confirmed by experiments with a FFOCT system. It is the first time to the best of our knowledge that such specific merit of incoherent illumination in FFOCT has been demonstrated. Based on this, the signal level is used as metric in our adaptive optics FFOCT system for retinal imaging. Only the main aberrations (defocus and astigmatism) that are dominating in eye are corrected to improve the signal to noise ratio and the high order aberrations are skipped. This would increase the correction speed thus reducing the imaging time.

Wavefront coding technology can extend the depth of field of the iris imaging system, but the iris image obtained through the system is coded and blurred and can't be used for the recognition algorithm directly. The paper presents a fuzzy iris image restoration method used in the wavefront coding system. After the restoration, the images can be used for the following processing. Firstly, the wavefront coded imaging system is simulated and the optical parameter is analyzed, through the simulation we can get the system's point spread function (PSF). Secondly, using the blurred iris image and PSF to do a blind restoration to estimate a appropriate PSFe. Finally, based on the return value PSFe of PSF, applying the regularization filter on the blurred image. Experimental results show that the proposed method is simple and has fast processing speed. Compared with the traditional restoration algorithms of Wiener filtering and Lucy-Richardson filtering, the recovery image that got through the regularization filtering is the most similar with the original iris image.

The Ingenuity TF PET/MR is a newly developed hybrid scanner combining the molecular imaging capabilities of PET with the excellent soft tissue contrast of MRI. Due to the magnetic field, spatial resolution in PET could potentially be affected. As such, it is important to characterize the system's point spread function (PSF) and understand its variation under spatial transformations to guide clinical studies. An array of 12×7 printed point sources was scanned for 120 minutes to sample the spatially variant PSF with the MR magnet on and the reconstructed data (blob-based LOR-RAMLA) were fitted in image space with a double 3-D Gaussian mixture model to derive parameters of interest. Based on the analysis, the axial resolution was found to be the least variant (up to 5.7mm) followed by the tangential (up to 6.4mm) and the radial (up to 6.9mm). The radial and tangential components were found to be variant under radial transformations and almost invariant under axial transformation. However, this radial dependency was found to be minimal with the resolution degrading only by 2.5mm towards the edge of the radial FOV. Overall the PET subsystem exhibits excellent resolution characteristics mainly due to the fact that the raw data are not under-sampled/re-binned enabling the spatial resolution to be dictated by the scanner's intrinsic resolution and the image reconstruction parameters. To this extent, blob parameters used during image reconstruction could be further optimized to improve the system's resolution characteristics.

Ground-based solar observations enable unprecedented spatial, spectral, and temporal resolution of the lower solar atmosphere, yet Earth’s turbulent atmosphere imposes significant limitations, requiring advanced post facto image reconstruction. State-of-the-art reconstruction methods are based on restoring a burst of short exposure frames to a single observation. Limitations of these techniques arise due to the sparse information available concerning the atmospheric point spread function (PSF), which degrades the observations and, consequently, the quality of reconstructions. Developing new reconstruction methods is essential for providing high-quality data products for the study of the lower solar atmosphere on the smallest scales. We aim to develop a novel image-reconstruction method to achieve unprecedented spatial resolution from short exposure image bursts. This can provide high-quality reconstructions and therefore advance the study of the smallest spatial scales from the solar photosphere to the chromosphere. In this paper, we present a novel approach for high-resolution solar-image reconstruction based on physics-informed neural networks. In the training process, the neural network maps coordinate points $(x,y)$ directly to their corresponding intensity values o(x,y), while simultaneously updating the PSF parameters. The method convolves the "true" object from the neural network with the estimated PSFs and optimizes the network by minimizing the loss between the synthesized and real short-exposure image burst. This approach enabled the simultaneous estimation of both the degrading PSF and the real high-resolution intensity distribution. We demonstrate the method on synthetic intensity data derived from a radiative magnetohydrodynamics (MHD) simulation, where we applied PSF convolution and noise to obtain a realistic synthetic input data set, similar to observational short-exposure observations. Quantitative comparisons using image quality metrics, histograms, and power spectral analysis confirm that the model can reliably reconstruct the original image from the stack of synthetic short-exposure frames. Finally, we applied our method to high-resolution observations from GREGOR and DKIST and compare to state-of-the-art speckle reconstructions and multi-frame blind deconvolutions. Our results demonstrate the ability to reconstruct small-scale solar features that exceed the reconstruction performance of state-of-the-art reconstruction methods. With this approach, we lay the foundation for future spatially varying PSFs.

The nature of the image produced by an optical system depends upon the point spread function (PSF) of the imaging system. It is thus necessary to modify the PSF of the system in order to change its imaging quality. This may be achieved by a number of ways. The usual practice is to modify the phase and amplitude transmission of different zones of ihu pupil. In the present paper, we have shown that the effect of various phase and semi-transparent coatings may be simulated by making-the lens aperture by suitably oriented polarisation devices. Besides, the effective PSF of the lens may be continuously varied by changing the orientation of the analyser at the output.