Improved Analytic Starting Points for Beam Matching Problems to Be Solved on Digital Computers

Digital computer codes using methods of least squares and linear programming can solve extraordinarily complicated beam matching problems involving many simultaneous parameters provided that they are provided with the starting points "close" to the desired solution. Estimates based on zero-emittance beams frequently are inadequate for this prupose. We here develop some thin lens formulae for finite-emittance beams to provide improved initial values to the variable parameters.