A study of the point spread function in scintillation camera collimators based on Fourier analysis

Abstract

A new technique for evaluating the point spread function of parallel hole collimators in scintillation cameras is studied. The collimator function is developed into a Fourier series and the intensity distribution in the detector plane for a point source is given by a mathematical expression that depends on the object position and on the collimator parameters. The septal penetration effect is considered. The technique is applied to obtain the general formulae for collimators with hexagonal holes and the PSF is evaluated.

Implementation and preliminary investigation of analytical methods for correction of distance-dependent resolution variation and uniform attenuation in 3D brain SPECT

“…Figure 20 shows the result after correction by the first method [11], [29], where the measured kernel of the Picker collimators was used. In the presence of noise, the approximation of the resolution kernel results in the same reconstruction artifacts as in the noise-free case, see Figures 4,5,18,and 19. The necessity of accurate consideration of the measured resolution kernel is seen again.…”

“…Spatial resolution variation as a function of distance from the collimator surface is one of the major obstacles for quantitative imaging, in addition to photon attenuation (absorption and scatter) in the body [25]. The cause of the variation and its effect on image degradation have been extensively studied, as shown in [6],[10], [16], [17], [18],[331. Correction methods in iterative algorithms can be seen, for example, in [27], [35].…”

Three-dimensional iterative reconstruction algorithms with attenuation and geometric point response correction

“…In (13) the summation over k is the projection operation and the summation over j is the backprojection operation. Therefore each iteration requires one projection and one backprojection operation.…”

“…Even though we develop the structure that can also include the scatter response, we do not include it in the work presented here, but we await studies that can better characterize the response function for distributed sources in an attenuating medium [12]. Here we use analytical expressions for the collimator geometric response function that have been derived for parallel [13,14], fan [15], and cone beam [15] collimators and calculate attenuation factors by integrating the known distribution of attenuation coefficients along the cone of rays that emanate from each detector bin using a method first described in [ 161.…”

Evaluation and Comparison Between the Collimator and the Detector Responses in a Scintillation Camera

“…In a previous paper [7] we proposed a new theoretical method to evaluate the response of collimators with parallel holes . This method, based on Fourier analysis, leads to a mathematical expression for the point spread function .…”