Download A Unitary Principle of Optics, Catoptrics, and Dioptrics by Leibniz Gottfried Wilhelm PDF

By Leibniz Gottfried Wilhelm

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APPLYING THE JANSSON ALGORITHM FIG. 0. APPLYING THE JANSSON ALGORITHM 47 We have used the function « „ ( L » - i ( ' ) ) = «,vi max [L„_,(0(1-£„_,(,))]" (96) most often with η = 1 [a factor of 4 different from Eq. (95)], but also with η = {, for example. The an(Ln_x) functions in Eqs. 00. An an(Ln_x) function that allows one to set minimum and maximum allowed values of Ln{i) is given by Frieden [12] as «„(A,-i(0) - c[\ - 2(B - Ayx\Ln_x{t) - {(A + B)\], (97) where A is the minimum value and Β is the maximum value.

18 Sample DECO test case for two Gaussians. 88 ΛΛ ΛΑ bb cc PS: ORIC , dd ee PS OCNV ff gg FIG. 18 (Continued) — 52 7. DECONVOLUTION EXAMPLES TABLE II Input Data for DECO Example Case Data Line #5 A Β C D Ε F G Η I J Κ -2 150 168 1 1 1 0 0 -4 -8 25 L Μ Ν 0 Ρ Q -3 -1 -5 -4 -2 -6 #10 #15 #20 5. 5. 9. 22. 1. 1. 2. 1 1 1. 1. 1. Comments Read 2 positions and intensities Position, Intensity, line # 1 Position, Intensity, line # 2 Line type = Gaussian, width is 9 points Convert to absorption Response function = Gaussian; 22 points wide No noise No smoothing Power spectrum, original data Power spectrum, convolved data Do 25 iterations, set a = 2, interpolate every other data point, use a = α0(γ — 1)/ as weight parameter Plot original data Plot current result Plot difference between original and current Power spectrum, original Power spectrum, convolved Power spectrum, difference Repeat K-> Q with Κ replaced by 50 3.

45 APPLYING THE JANSSON ALGORITHM C. Apply convergence/termination tests. If satisfactory, the current Lj is the estimator of L(t) and the procedure is completed. If tests are not satisfactory, set j = j + 1 and return to step B. On exiting from the preceding iterative procedure an estimator of the desired true data set L(t) has been found. Notice that at each step, a j(y)(S ~~ Lj_x θ Τ) is the current correction to the previous iteration. Forming ι " j, Σ 2 (93) [«,O0(s-z,_,er)]2 all points essentially the rms correction to the previous estimator of L{t) yields some idea of convergence of the deconvolution process.

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