Calculation Of Point Spread Function Research Articles

Diagnostic performance of the beam emission spectroscopy system on the National Spherical Torus Experiment

The beam emission spectroscopy system on the National Spherical Torus Experiment measures localized density fluctuations on the ion gyroscale. Optical sightlines provide core to edge radial coverage, and the sightlines are aligned to typical pitch angles to maximize cross-field spatial resolution. Sightline images are 2-3 cm, and point spread function calculations indicate image distortion from pitch angle misalignment and atomic state finite lifetimes is minor with a 15% increase in the image size. New generation photodetectors achieve photon noise limited measurements at frequencies up to 400 kHz with refrigerant cooling at -20 °C. Measurements near the pedestal show broadband turbulence up to 100 kHz, and poloidal correlation lengths are about 10 cm. Plasma turbulence signals can be 2-3 orders of magnitude above photon noise and amplifier thermal noise.

Study of effect of non-central obscuration to obscured circular aperture on third order spherical aberration

In this research we have been studied the 3rd order spherical aberration for an optical system consisted of obscured circular aperture with non central circular obscuration through the calculation of point spread function (P.S.F) in presence of the obscuration in the center and comparing the obtained results with that results of moving obscuration far away from the center, where the results showed significant improvement for(P.S.F) value. The study was done of different obscurities ratios in addition to the different 3rd order spherical aberration values (W40=0.25 ,0.5 ,0.75 ,1 ).

Study of effect of non-central obscuration to obscured circular aperture on third order spherical aberration

In this research we have been studied the 3rd order spherical aberration for an optical system consisted of obscured circular aperture with non central circular obscuration through the calculation of point spread function (P.S.F) in presence of the obscuration in the center and comparing the obtained results with that results of moving obscuration far away from the center, where the results showed significant improvement for(P.S.F) value. The study was done of different obscurities ratios in addition to the different 3rd order spherical aberration values (W40=0.25 ,0.5 ,0.75 ,1 ).

Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment

This paper presents a novel model-based approach of dynamic defocus and occlusion compensation method in a multi-projection environment. Conventional defocus compensation research applies appearance-based method, which needs a point spread function (PSF) calibration when either position or orientation of an object to be projected is changed, thus cannot be applied to interactive applications in which the object dynamically moves. On the other hand, we propose a model-based method in which PSF and geometric calibrations are required only once in advance, and projector’s PSF is computed online based on geometric relationship between the projector and the object without any additional calibrations. We propose to distinguish the oblique blur (loss of high-spatial-frequency components according to the incidence angle of the projection light) from the defocus blur and to introduce it to the PSF computation. For each part of the object surfaces, we select an optimal projector that preserves the largest amount of high-spatial-frequency components of the original image to realize defocus-free projection. The geometric relationship can also be used to eliminate the cast shadows of the projection images in multi-projection environment. Our method is particularly useful in the interactive systems because the movement of the object (consequently geometric relationship between each projector and the object) is usually measured by an attached tracking sensor. This paper describes details about the proposed approach and a prototype implementation. We performed two proof-of-concept experiments to show the feasibility of our approach.

Zernike representation and Strehl ratio of optical systems with variable numerical aperture

We consider optical systems with variable numerical aperture (NA) on the level of the Zernike coefficients of the correspondingly scalable pupil function. We thus present formulas for the Zernike coefficients and their first two derivatives as a function of the scaling factor ε ≤ 1, and we apply this to the Strehl ratio and its derivatives of NA-reduced optical systems. The formulas for the Zernike coefficients of NA-reduced optical systems are also useful for the forward calculation of point-spread functions and aberration retrieval within the Extended Nijboer–Zernike (ENZ) formalism for optical systems with reduced NA or systems that have a central obstruction. Thus, we retrieve a Gaussian, comatic pupil function on an annular set from the intensity point-spread function in the focal region under high-NA conditions.

Calculation of point-spread function for optical systems with finite value of numerical aperture

The scalar theory is described for calculation of the point-spread function (PSF) of optical systems with a large numerical aperture. In our work, we introduced an analytic description of this phenomenon and we derived exact and simple approximate relations that enable to calculate the PSF for a diffraction-limited optical system with a finite value of numerical aperture. The derived relations convert to classical relations that are commonly described in literature for the case that the value of numerical aperture tends to zero. Our derived relation is a generalization of the classical relation for calculation of PSF in the case of a large numerical aperture.

Supergridded cone-beam reconstruction and its application to point-spread function calculation

In cone-beam computed tomography (CBCT), the volumetric reconstruction may in principle assume an arbitrarily fine grid. The supergridded cone-beam reconstruction refers to reconstructing the object domain or a subvolume thereof with a grid that is finer than the proper computed tomography sampling grid (as determined by gantry geometry and detector discreteness). This technique can naturally reduce the voxelization effect, thereby retaining more details for object reproduction. The grid refinement is usually limited to two or three refinement levels because the detail pursuit is eventually limited by the detector discreteness. The volume reconstruction is usually targeted to a local volume of interest due to the cubic growth in a three-dimensional (3D) array size. As an application, we used this technique for 3D point-spread function (PSF) measurement of a CBCT system by reconstructing edge spread profiles in a refined grid. Through an experiment with a Teflon ball on a CBCT system, we demonstrated the supergridded volume reconstruction (based on a Feldcamp algorithm) and the CBCT PSF measurement (based on an edge-blurring technique). In comparison with a postreconstruction image refinement technique (upsampling and interpolation), the supergridded reconstruction could produce better PSFs (in terms of a smaller FWHM and PSF fitting error).

TU-C-I-609-10: Preliminary Study of Pixel Pitch and Effect of Divergence On Thick Cadmium Tungstate Detector

Purpose: To theoretically study the effects of pixel pitch and beam divergence on 1 cm thick crystals for use in megavoltage cone beam computed tomography (MVCBCT). Method and Material: linear array (80-elements, each 0.275 × 0.8 × 1 cm3 in fan beam) has been proven to be a good candidate for MVCT in our lab. For this study, DOSXYZnrc Monte Carlo code was used to find the point spread function (PSF) as the distribution of energy deposited in a theoretical flat detector (30 × 30 × 10 mm3, 0.01 × 0.01 × 10 mm3 voxels). A pencil-beam of 6 MV photons was incident at a range of angles (0°, 5°, 10°, 15°, 20°) with respect to the normal. In each case, the detector PSF (ignoring optical spread) was convolved with a realistic source function to give the system PSF in the plane of the object. A realistic object to detector magnification of 1.4 was used in the system PSF calculations. The PSF at 0.01 mm pitch was re-binned into several pitches (0.5, 0.7, 1.0 mm) and Fourier transformed to obtain the system modulation transfer function (MTF). Results: This analysis suggests an optimum pitch of 0.5 mm which cannot be fabricated using because of the cleavage plane. However, the pre-sampled detector PSF is further degraded due to small optical leakage through reflective coating and scintillator-photodiode interface, and the scattered radiation from the object. So, in practice a pitch of 1 mm may be sufficient. The degradation of the system MTF with the increasing divergence is significant between 0° and 5°, and becomes large at 10°. Conclusion: Practical pitch of 1 mm is not ideal yet maybe sufficient. The use of flat panel photodiode arrays for MVCBCT is precluded due to divergence; instead a focused detector should be used.

Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy

We propose a method for microscope point spread function computation in which both design and actual acquisition parameters are explicitly introduced in the integrals describing the electromagnetic field in the focal region. This model therefore combines the ease of use of the Gibson and Lanni scalar approach with the accuracy of the Torok and Varga method. We also compare some theoretical predictions of this model with those of a scalar model. In particular, the scalar model underestimates the point spread function size. This has practical application, for example when deconvolving microscope images or analyzing point spread functions. The method may also be used for confocal microscopy.

Analytic evaluation of the intensity point spread function

The intensity point spread function (PSF) for geometric imaging such as occurs in a projection electron system like SCALPEL is derived analytically from the ray aberration coefficients. The results show that, as expected, the PSF for ordinary aberrations has a finite radius and is not Gaussian. Hence blur estimates, which are often based on assuming a Gaussian PSF and computing the root-sum-square or “rss” of the separate blur radii will generally overestimate the true aberration blur. Global space charge acts like an electrostatic lens and hence its effects can be included in the PSF calculation as well. The net PSF can be convolved with an object to produce an accurate representation of the image. The convolution integral can also be performed first which yields the image intensity distribution directly in terms of the aberrations.

Monte Carlo calculation of point-spread functions of Compton scatter cameras

A technique has been devised for independently determining the energy and spatial resolution components of the point-spread functions of electronically collimated (Compton scatter) imaging devices using a Monte Carlo method. Monte Carlo runs are performed for the device being examined, and detailed records of exact energy loss and spatial coordinates of each interaction for each particle in the simulation are made. Taking resolution parameters from the known performance of the detectors, measured data is simulated by sampling from Gaussian distributions (for both energy and position) about the exact interaction energy and position in both detectors, for each Monte Carlo history. By back-projecting cones on an event-by-event basis and calculating the closest approach of the cone to the known source point using the simulated measurement data for one of the energy and position variables and the exact interaction data for the rest of the variables, the effect of the variable in question on the point spread can be isolated. In this paper the authors present the calculations of the contribution to the point-spread function of the energy and spatial resolution in each detector for various source positions for a representative Compton camera configuration.

3-D tomographic imaging of near‐surface seismic velocity and attenuation

As a result of the similarity between velocity and attenuation imaging, we have implemented both using the same 3-D tomography software, with simple variable changes. The resulting sets of linear equations are solved by the Simultaneous Iterative Reconstruction Technique (SIRT). The algorithm is applied to 3-D estimation of near‐surface velocity and attenuation distributions from 3-D surface‐survey field data from the Ouachita frontal thrust zone in southeastern Oklahoma; the images obtained correlate well with the known surface geology. Resolution analysis by computation of point spread functions indicates highest resolution in the direction parallel to the densest distribution of survey points (the receiver lines).

Fast point spread function computation from aperture functions in high-resolution positron emission tomography

The problem of extracting point spread functions from detector aperture functions in high-resolution PET is addressed. In the limit of very small size detectors relative to the ring dimensions, assumptions are made that lead to a fast and simple computation model yielding point spread functions with negligible errors due to the reconstruction algorithm. The methods allows one to assess accurately the intrinsic performance of a PET tomograph, and it appears to be adequate to relate the imaging capabilities in every point of the camera reconstruction field to the geometric and physical characteristics of the detection system. The method was developed as an investigation tool to help design the next generation of very-high-resolution PET tomographs.

Point-spread Function Calculation for Optical Systems with Residual Aberrations and a Non-uniform Transmission Pupil

A numerical method for evaluating the intensity at points in the image space of an optical system is developed. This method can be applied to optical systems with any kind of residual aberrations and any pupil transmission function. It is valid for the general case of an axial or extra-axial monochromatic object point. The accuracy of the method is also studied.

The Computation of Diffraction Patterns in the Presence of Aberrations

The diffraction integral for the disturbance produced in the image plane normal to the optical axis by an extra-axial pencil has been shown to lead to a Fourier transform provided the exit pupil surface is taken to be that of the reference sphere. It has been shown also that, except for small aperture and field sizes, the effect on the wave-front aberration of a shift of the image plane is not represented with sufficient accuracy merely by a term proportional to the aperture squared. Both of these results have been respected in formulating a numerical technique for the calculation of point spread functions. The diffraction integral is evaluated in polar coordinates, and is such that no error is made in approximating the domain of the exit pupil in cases where this may be represented by an ellipse. A study of the accuracy obtained has shown that, if each quadrant of the pupil is divided into a 20 × 20 mesh of elementary areas, the error in the intensity is not expected to exceed 0·8 per cent of the intensity at the focus of a diffraction limited system. The method takes account of the first derivatives of the wave aberration at each mesh point, and the results are therefore expected to be more accurate than those obtained by merely replacing the integral by a simple sum. Results are given for a case of primary and secondary coma, and of a study of the influence of secondary spectrum and spherical aberration on the images formed by 2 mm achromatic microscope objectives of numerical aperture equal to 1·40.