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653. DIFSA: A Program to Simulate a Set of Experimental
Diffraction Efficiencies
by Michael B. Sponsler, Department of Chemistry, Syracuse University, Syracuse, New York 13244 DIFSA is a FORTRAN program that simulates a set of experimental diffraction efficiencies, providing the best refractive index profile that would produce most nearly the experimental data. The program is intended for optically thin (Raman-Nath), unslanted gratings. Optimization of the refractive index profile, expressed as a Fourier series, is achieved through simulated annealing. The diffraction calculation algorithm was taken from the literature (R. Magnusson and T. K. Gaylord, Opt. Commun., 25, 129-132 (1978)). This calculation is done in the subroutine FCN. The rest of the program was adapted from SIMANN. The original comments from SIMANN have been retained or slightly modified where appropriate and are marked with a single "c" or "C". All new comments are marked with "CC". All input to the program is contained in the file, dif.inp. The input format can be determined from the READ and FORMAT statements in the main program, following this comment block. The current limit of 16 on the number of diffraction orders may be changed in the PARAMETER statements in FCN, SA, and the main program. The limit of 8 on the number of Fourier terms may not be changed without additional lines of code in FCN. Usage Notes: DIFSA has been run on several platforms: PCs (486) and mainframe (VMS and UNIX). The execution time depends on the number of Fourier terms (N), the number of diffraction orders (NORD), and on a number of optimization variables. Further, larger coefficient values (X) lead to quite significant increases in computation time due to the larger number of terms that must be evaluated in FCN. Therefore, even if all other aspects are equal, two different data sets may differ markedly in required CPU time. With this caveat, however, here is a benchmark: an optimization with N = 6, NORD = 9, NS = 20, NT = 5, T = 0.4, RT = 0.5, and EPS = 1.0E-3 took 294 seconds of CPU time on a UNIX mainframe. The program was compiled with optimization for run-time speed, cutting the CPU time about in half. A Word of Caution: Although simulated annealing is one of the best ways to achieve global minimization, the results are still function dependent. The simulation "function" in FCN takes enough computation time that one must often cut down the optimization variables (primarily NS and NT) from their recommended values. This decreases the probability that the global minimum will be found. Therefore, multiple runs are suggested, varying either the random number seeds or the starting coefficients, in order to see whether multiple solutions will be found. Remember that the true solution is not necessarily the global minimum (or even a local minimum), since there is error in the experimental values. Multiple solutions are encountered more frequently when more Fourier terms are used, so it is recommended that the minimum number of terms required to achieve a good fit be used. Lines of Code: 1191 FORTRAN 77 (RS/6000) |