Abstract:A revised formulation of the image light distribution of an incoherent line source proposed by Steel ͓Rev. Opt. 31, 334 -340 ͑1952͔͒ is presented. Analytical and numerical results based on this new representation are given. We explicitly show that a major error in Steel's final expression generates singularities, thereby preventing convenient numerical computation.
“…7(a) and 8(a). The mean value of the target luminance is calculated from the luminance profile the ESF values (Edge Spread Function) [41] using the left section indicated in the graph, Figs. 7(b) and 8(b).…”
“…7(a) and 8(a). The mean value of the target luminance is calculated from the luminance profile the ESF values (Edge Spread Function) [41] using the left section indicated in the graph, Figs. 7(b) and 8(b).…”
“…(8) one needs to substitute the LSF for a more straightforward expression which can be easy to compute. A certain number of exact formulas and approximations are given in the literature [21,22] but we use here the expression recently proposed by us [23]:…”
Section: Degraded Edge-object and Edge-image Intensity Distributionsmentioning
confidence: 99%
“…(10) represents the ESF for blurred edges. The possible oscillations arising from the numerical behavior of the Bessel functions [24,25] are suppressed due to the optimized Bessel functions expansion used in the computation [23]. As an example, Fig.…”
Section: Degraded Edge-object and Edge-image Intensity Distributionsmentioning
We discuss a formalism to characterize degraded edge images formed in a diffraction limited system (with circular pupil of unit radius) under conditions of incoherent illumination. We introduce a novel definition of degraded edges and consider this approach to model a basic optical mechanism involved in the perception of visual depth and edge detection. We introduce a degradation parameter to quantize the degree of edge blur. We present a generalization of such a procedure by assuming the Heaviside function to be a systematic generator of degraded edges. We reproduce experimentally the predictions made by the formalism proposed herein.
“…If the optical system still maintains a circular symmetry but the illumination in the object plane has a well-defined preferential axis, i.e. it has a line shape, the image of a line source should be considered (figure 1): this is the problem of calculating the so-called linespread-function (LSF), which is equivalent to the pointspread-function [11,12].…”
We propose a simplified method to calculate the optical spread function of a paradigmatic system constituted by a pupil-lens with a line-shaped illumination (‘line-spread-function’). Our approach is based on decoupling the two transversal directions of the beam and treating the propagation by means of the Fourier optics formalism. This requires simpler calculations with respect to the more usual Bessel-function-based method. The model is discussed and compared with standard calculation methods by carrying out computer simulations. The proposed approach is found to be much faster than the Bessel-function-based one (CPU time
% of the standard method), while the results of the two methods present a very good mutual agreement.
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