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Electron-optical imaging instruments like Scanning Electron Microscope (SEM) and Transmission Electron Microscope (TEM) use specially designed solenoid electromagnets for focusing of electron beam probe. Indicators of imaging performance of these instruments, like spatial resolution, have strong correlation with focal characteristics of the magnetic lenses which in turn have been shown to be functions of the spatial distribution of axial magnetic field generated by them. Owing to complicated design of practical lenses, empirical mathematical expressions are deemed convenient for use in physics based calculations of their focal properties. So, degree of closeness of such models to the actual field distribution determines accuracy of the calculations. Mathematical models proposed by Glaser[1] and Ramberg[1] have historically been put into extensive use. In this paper the authors discuss one such model with secant-hyperbolic type magnetic field distribution function, and present a comparison among these models, with results from finite element based field simulations as reference.

The sensitivity of a Cherenkov imaging telescope is strongly dependent on the rejection of the cosmic-ray background events. The methods which have been used to achieve the segregation between the gamma-rays from the source and the background cosmic-rays, include methods like Supercuts/Dynamic Supercuts, Maximum likelihood classifier, Kernel methods, Fractals, Wavelets and random forest. While the segregation potential of the neural network classifier has been investigated in the past with modest results, the main purpose of this paper is to study the gamma / hadron segregation potential of various ANN algorithms, some of which are supposed to be more powerful in terms of better convergence and lower error compared to the commonly used Backpropagation algorithm. The results obtained suggest that Levenberg-Marquardt method outperforms all other methods in the ANN domain. Applying this ANN algorithm to $\sim$ 101.44 h of Crab Nebula data collected by the TACTIC telescope, during Nov. 10, 2005 - Jan. 30, 2006, yields an excess of $\sim$ (1141$\pm$106) with a statistical significance of $\sim$ 11.07$\sigma$, as against an excess of $\sim$ (928$\pm$100) with a statistical significance of $\sim$ 9.40$\sigma$ obtained with Dynamic Supercuts selection methodology. The main advantage accruing from the ANN methodology is that it is more effective at higher energies and this has allowed us to re-determine the Crab Nebula energy spectrum in the energy range $\sim$ 1-24 TeV., Comment: Accepted for Publication in Nuclear Instruments Methods in Physics Research A., Dec 2012 ; 36 pages, 11 figures

An Artificial Neural Network-based error compensation method is proposed for improving the accuracy of resolver-based 16-bit encoders by compensating for their respective systematic error profiles. The error compensation procedure, for a particular encoder, involves obtaining its error profile by calibrating it on a precision rotary table, training the neural network by using a part of this data and then determining the corrected encoder angle by subtracting the ANN-predicted error from the measured value of the encoder angle. Since it is not guaranteed that all the resolvers will have exactly similar error profiles because of the inherent differences in their construction on a micro scale, the ANN has been trained on one error profile at a time and the corresponding weight file is then used only for compensating the systematic error of this particular encoder. The systematic nature of the error profile for each of the encoders has also been validated by repeated calibration of the encoders over a period of time and it was found that the error profiles of a particular encoder recorded at different epochs show near reproducible behavior. The ANN-based error compensation procedure has been implemented for 4 encoders by training the ANN with their respective error profiles and the results indicate that the accuracy of encoders can be improved by nearly an order of magnitude from quoted values of ~6 arc-min to ~0.65 arc-min when their corresponding ANN-generated weight files are used for determining the corrected encoder angle., Comment: 16 pages, 4 figures. Accepted for Publication in Measurement Science and Technology (MST)

The energy estimation procedures employed by different groups, for determining the energy of the primary $\gamma$-ray using a single atmospheric Cherenkov imaging telescope, include methods like polynomial fitting in SIZE and DISTANCE, general least square fitting and look-up table based interpolation. A novel energy reconstruction procedure, based on the utilization of Artificial Neural Network (ANN), has been developed for the TACTIC atmospheric Cherenkov imaging telescope. The procedure uses a 3:30:1 ANN configuration with resilient backpropagation algorithm to estimate the energy of a $\gamma$-ray like event on the basis of its image SIZE, DISTANCE and zenith angle. The new ANN-based energy reconstruction method, apart from yielding an energy resolution of $\sim$ 26%, which is comparable to that of other single imaging telescopes, has the added advantage that it considers zenith angle dependence as well. Details of the ANN-based energy estimation procedure along with its comparative performance with other conventional energy reconstruction methods are presented in the paper and the results indicate that amongst all the methods considered in this work, ANN method yields the best results. The performance of the ANN-based energy reconstruction has also been validated by determining the energy spectrum of the Crab Nebula in the energy range 1-16 TeV, as measured by the TACTIC telescope., Comment: 23pages, 9 figures Accepted for publication in NIM A