Depth-dependent Point Spread Function Research Articles

Extended depth of field for Fresnel zone aperture camera via fast passive depth estimation.

The lensless camera with incoherent illumination has gained significant research interest for its thin and flexible structure. However, it faces challenges in resolving scenes with a wide depth of field (DoF) due to its depth-dependent point spread function (PSF). In this paper, we present a single-shot method for extending the DoF in Fresnel zone aperture (FZA) cameras at visible wavelengths through passive depth estimation. The improved ternary search method is utilized to determine the depth of targets rapidly by evaluating the sharpness of the back propagation reconstruction. Based on the depth estimation results, a set of reconstructed images focused on targets at varying depths are derived from the encoded image. After that, the DoF is extended through focus stacking. The experimental results demonstrate an 8-fold increase compared with the calibrated DoF at 130 mm depth. Moreover, our depth estimation method is five times faster than the traversal method, while maintaining the same level of accuracy. The proposed method facilitates the development of lensless imaging in practical applications such as photography, microscopy, and surveillance.

Reconstructing a Deblurred 3D Structure in a Turbid Medium from a Single Blurred 2D Image-For Near-Infrared Transillumination Imaging of a Human Body.

To provide another modality for three-dimensional (3D) medical imaging, new techniques were developed to reconstruct a 3D structure in a turbid medium from a single blurred 2D image obtained using near-infrared transillumination imaging. One technique uses 1D information of a curvilinear absorber, or the intensity profile across the absorber image. Profiles in different conditions are calculated by convolution with the depth-dependent point spread function (PSF) of the transillumination image. In databanks, profiles are stored as lookup tables to connect the contrast and spread of the profile to the absorber depth. One-to-one correspondence from the contrast and spread to the absorber depth and thickness were newly found. Another technique uses 2D information of the transillumination image of a volumetric absorber. A blurred 2D image is deconvolved with the depth-dependent PSF, thereby producing many images with points of focus on different parts. The depth of the image part can be estimated by searching the deconvolved images for the image part in the best focus. To suppress difficulties of high-spatial-frequency noise, we applied a noise-robust focus stacking method. Experimentation verified the feasibility of the proposed techniques, and suggested their applicability to curvilinear and volumetric absorbers such as blood vessel networks and cancerous lesions in tissues.

Spatially adaptive blind deconvolution methods for optical coherence tomography

Optical coherence tomography (OCT) is a powerful noninvasive imaging technique for detecting microvascular abnormalities. Following optical imaging principles, an OCT image will be blurred in the out-of-focus domain. Digital deconvolution is a commonly used method for image deblurring. However, the accuracy of traditional digital deconvolution methods, e.g., the Richardson-Lucy method, depends on the prior knowledge of the point spread function (PSF), which varies with the imaging depth and is difficult to determine. In this paper, a spatially adaptive blind deconvolution framework is proposed for recovering clear OCT images from blurred images without a known PSF. First, a depth-dependent PSF is derived from the Gaussian beam model. Second, the blind deconvolution problem is formalized as a regularized energy minimization problem using the least squares method. Third, the clear image and imaging depth are simultaneously recovered from blurry images using an alternating optimization method. To improve the computational efficiency of the proposed method, an accelerated alternating optimization method is proposed based on the convolution theorem and Fourier transform. The proposed method is numerically implemented with various regularization terms, including total variation, Tikhonov, and l1 norm terms. The proposed method is used to deblur synthetic and experimental OCT images. The influence of the regularization term on the deblurring performance is discussed. The results show that the proposed method can accurately deblur OCT images. The proposed acceleration method can significantly improve the computational efficiency of blind demodulation methods.

Near-infrared fundus imaging system with light illumination from an electronic contact lens

As for the diagnosis and treatment of eye diseases, an ideal fundus imaging system is expected to be portability, low cost, and high resolution. Here, we demonstrate a non-mydriatic near-infrared fundus imaging system with light illumination from an electronic contact lens (E-lens). The E-lens can illuminate the retinal and choroidal structures for capturing the fundus images when voltage is applied wirelessly to the lens. And we also reconstruct the images with a depth-dependent point-spread function to suppress the scattering effect that eventually visualizes the clear fundus images.

Lensless Fiber Imaging With Long Working Distance Based on Active Depth Measurement

Lensless fiber endoscopes allow noncontact imaging in narrow spaces without lenses or scanning devices at the distal tip. In this work, an active depth measurement module based on a Fabry–Perot interferometer is integrated onto the imaging fiber bundles. An accurate depth-dependent point spread function can be constructed for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> deconvolution in image deblurring. We have demonstrated that the working distance of a lensless fiber endoscope can be increased from the end face to several tens of micrometers, or even up to more than double for certain spatial frequencies. The contrast of the reconstructed image is also significantly improved. Furthermore, the proposed device can be implemented rapidly without precalibration and is resilient to fiber bending; thus, it can be used for real-time monitoring applications.

Depth estimation of the absorbing structure in a slab turbid medium using point spread function

Nowadays, transillumination imaging is more popular used in the medical field with the development of the vein finder and the non-invasive diagnosis applications. Near-infrared light with a wavelength of 700 - 1200 nm has relatively high transmission through biological tissue. Using near-infrared light, we can able to obtain a two dimensional (2D) transillumination image of the internal absorption structure such as blood vessel structure, liver ... in the body noninvasively. Even with a simple system (light-emitting diode (LED)'s array and low-cost camera), we could obtain the blood vessel transillumination image of human arm. However, the image is severely blurred due to the strong scattering in the tissue. We have devised the depth-dependent point spread function (PSF) to suppress the scattering effect in fluorescent imaging. In previous studies, we successfully applied this principle and developed a technique to reconstruct the absorbing structure in a turbid medium without using fluorescent material. The feasibility and effectiveness of the proposed technique were verified in experiments. However, this point spread function (PSF) is depth dependence, so that the depth information is required in practice. In order to make this method more practical, the new techniques for estimating the parameters of absorbing structure (depth and width) in the turbid medium by convolution and de-convolution with the point spread function (PSF) were devised. This paper presents a new technique for the estimation depth of an absorber in 2D transillumination image. This new technique was developed to estimate the depth of the absorber in turbid medium by convolution operation with the point spread function (PSF). By observing images with two-wavelength selected at which the scattering property of the medium is different. The transillumination image at one of the wavelengths is convolved with the PSF of another wavelength. Two images of alternative wavelengths are compared while changing the depth of the PSF. We can obtain the correct depth that gives a minimum difference between the two convoluted images. This technique does not require the repetition of the unstable deconvolution operation. The effectiveness of the proposed technique was verified in simulation and experiment.

Addressing systematic errors in axial distance measurements in single-emitter localization microscopy.

Nanoscale localization of point emitters is critical to several methods in optical fluorescence microscopy, including single-molecule super-resolution imaging and tracking. While the precision of the localization procedure has been the topic of extensive study, localization accuracy has been less emphasized, in part due to the challenge of producing an experimental sample containing unperturbed point emitters at known three-dimensional positions in a relevant geometry. We report a new experimental system which reproduces a widely-adopted geometry in high-numerical aperture localization microscopy, in which molecules are situated in an aqueous medium above a glass coverslip imaged with an oil-immersion objective. We demonstrate a calibration procedure that enables measurement of the depth-dependent point spread function (PSF) for open aperture imaging as well as imaging with engineered PSFs with index mismatch. We reveal the complicated, depth-varying behavior of the focal plane position in this system and discuss the axial localization biases incurred by common approximations of this behavior. We compare our results to theoretical calculations.

Depth-dependent PSF calibration and aberration correction for 3D single-molecule localization.

Three-dimensional single molecule localization microscopy relies on the fitting of the individual molecules with a point spread function (PSF) model. The reconstructed images often show local squeezing or expansion in z. A common cause is depth-induced aberrations in conjunction with an imperfect PSF model calibrated from beads on a coverslip, resulting in a mismatch between measured PSF and real PSF. Here, we developed a strategy for accurate z-localization in which we use the imperfect PSF model for fitting, determine the fitting errors and correct for them in a post-processing step. We present an open-source software tool and a simple experimental calibration procedure that allow retrieving accurate z-positions in any PSF engineering approach or fitting modality, even at large imaging depths.

Performance evaluation of 18 F radioluminescence microscopy using computational simulation.

Radioluminescence microscopy can visualize the distribution of beta-emitting radiotracers in live single cells with high resolution. Here, we perform a computational simulation of 18 F positron imaging using this modality to better understand how radioluminescence signals are formed and to assist in optimizing the experimental setup and image processing. First, the transport of charged particles through the cell and scintillator and the resulting scintillation is modeled using the GEANT4 Monte-Carlo simulation. Then, the propagation of the scintillation light through the microscope is modeled by a convolution with a depth-dependent point-spread function, which models the microscope response. Finally, the physical measurement of the scintillation light using an electron-multiplying charge-coupled device (EMCCD) camera is modeled using a stochastic numerical photosensor model, which accounts for various sources of noise. The simulated output of the EMCCD camera is further processed using our ORBIT image reconstruction methodology to evaluate the endpoint images. The EMCCD camera model was validated against experimentally acquired images and the simulated noise, as measured by the standard deviation of a blank image, was found to be accurate within 2% of the actual detection. Furthermore, point source simulations found that a reconstructed spatial resolution of 18.5 μm can be achieved near the scintillator. As the source is moved away from the scintillator, spatial resolution degrades at a rate of 3.5 μm per μm distance. These results agree well with the experimentally measured spatial resolution of 30-40 μm (live cells). The simulation also shows that the system sensitivity is 26.5%, which is also consistent with our previous experiments. Finally, an image of a simulated sparse set of single cells is visually similar to the measured cell image. Our simulation methodology agrees with experimental measurements taken with radioluminescence microscopy. This in silico approach can be used to guide further instrumentation developments and to provide a framework for improving image reconstruction.

Recovering Inner Slices of Layered Translucent Objects by Multi-Frequency Illumination.

This paper describes a method for recovering appearance of inner slices of translucent objects. The appearance of a layered translucent object is the summed appearance of all layers, where each layer is blurred by a depth-dependent point spread function (PSF). By exploiting the difference of low-pass characteristics of depth-dependent PSFs, we develop a multi-frequency illumination method for obtaining the appearance of individual inner slices. Specifically, by observing the target object with varying the spatial frequency of checker-pattern illumination, our method recovers the appearance of inner slices via computation. We study the effect of non-uniform transmission due to inhomogeneity of translucent objects and develop a method for recovering clear inner slices based on the pixel-wise PSF estimates under the assumption of spatial smoothness of inner slice appearances. We quantitatively evaluate the accuracy of the proposed method by simulations and qualitatively show faithful recovery using real-world scenes.

Correction of depth-dependent aberrations in 3D single-molecule localization and super-resolution microscopy

Single-molecule switching based super-resolution microscopy techniques have been extended into three dimensions through various 3D single-molecule localization methods. However, the localization accuracy in z can be severely degraded by the presence of aberrations, particularly the spherical aberration introduced by the refractive index mismatch when imaging into an aqueous sample with an oil immersion objective. This aberration confines the imaging depth in most experiments to regions close to the coverslip. Here we show a method to obtain accurate, depth-dependent z calibrations by measuring the point spread function (PSF) at the coverslip surface, calculating the microscope pupil function through phase retrieval, and then computing the depth-dependent PSF with the addition of spherical aberrations. We demonstrate experimentally that this method can maintain z localization accuracy over a large range of imaging depths. Our super-resolution images of a mammalian cell nucleus acquired between 0 and 2.5 μm past the coverslip show that this method produces accurate z localizations even in the deepest focal plane.

SPECT Imaging With Resolution Recovery

Single-photon emission computed tomography (SPECT) is a method of choice for imaging spatial distributions of radioisotopes. Applications of this method are found in medicine, biomedical research and nuclear industry. This paper deals with improving spatial resolution in SPECT by applying correction for the point-spread function (PSF) in the reconstruction algorithm and optimizing the collimator. Several approaches are considered: the use of a depth-dependent PSF model for a parallel-beam collimator derived from experimental data, the extension of this model to a fan-beam collimator, a triangular approximation of the PSF for reconstruction acceleration, and a method for optimal fan-beam collimator design. An unmatched projector/backprojector ordered subsets expectation maximization (OSEM) algorithm is used for image reconstruction. Experimental results with simulated and physical phantom data of a micro-SPECT system show a significant improvement of spatial resolution with the proposed methods.

Depth-Dependent Hemoglobin Analysis From Multispectral Transillumination Images

Multispectral transillumination imaging is a promising modality for noninvasive imaging of living tissue. Multispectral Nevoscope imaging is directed toward the imaging of skin lesions for the detection and characterization of skin cancers through the volumetric analysis of selected chromophores, such as melanin, oxy-, and deoxyhemoglobin. In this letter, we present a novel method of recovering depth-dependent measurements from transillumination images obtained through the Nevoscope. A method for estimating the depth-dependent point spread function is presented and used in recovering multispectral transillumination images of a skin phantom or lesion through blind deconvolution. A method for ratiometric analysis for the quantification of oxy- and deoxyhemoglobin is then presented and evaluated on a skin phantom. The presented methods would allow reliable quantitative analysis of multispectral Nevoscope images for early detection of angiogenesis leading to early diagnosis of skin cancers.

Improvement of transcutaneous fluorescent images with a depth-dependent point-spread function

The point-spread function (PSF) for transcutaneous fluorescent imaging was obtained as an analytical solution in a closed form. It is applicable to cases in which the optical property of the image-blurring turbid medium is considered to be fairly homogeneous. We proposed a technique to improve a transcutaneous image by using depth-dependent PSF. Contrast of the fluorescent image was improved for depths of 1-15 mm in a scattering medium (micro(s)' = 1/mm). The visible depth was more than doubled with this technique. An experiment with a rat demonstrated considerable improvement of a transcutaneous image of the cerebral vein at a specified depth. The spread image of the heart was reduced to the correct size by use of the PSF with the actual depth of the heart.

Maximum-Likelihood Reconstruction for Single-Photon Emission Computed-Tomography

A mathematical model is formulated for a gamma camera used to observe single-photon emissions from multiple view angles. The model accounts for the statistics of radioactive decays, nonuniform attenuation, and a depth-dependent point-spread function. The maximum-likelihood method of statistics is used with the model to derive an algorithm for estimating the distribution of radioactivity.