LENS PROPERTIES AND SPECTROMETER COEFFICIENTS

The 2D programs have an option for evaluating lens properties. These programs output the focal lengths f1 and f2 (for the object and image spaces respectively) and the mid-focal lengths F1 and F2 (which are the distances of the principal focal points from the position z=0). Spherical and chromatic aberration coefficients can also be requested, together with the Petzval integral, to give a complete specification of all the third-order aberrations of an electrostatic lens.

All the programs have an option for obtaining lens or spectrometer coefficients by direct ray tracing. In the 2D programs the dependence of 4 final ray parameters (r, z, r_angle and z_angle) on 5 initial parameters (r,z, r_angle, z_angle and kinetic energy, where r is rho or x, for cylindrical or planar symmetry respectively) can be requested. The 'optic axis' is defined by a median ray, and so can be straight or curved. The User also specifies the `order' of the coefficients.

For example if the 'order' is 1 for rho and 3 for z_angle, the program will find the dependence of each of the 4 final parameters r, z, r_angle and z_angle on rho_initial and on the cube of z_angle_initial. In other words the program would give the coefficients in the expansion

p - p_median = (p/r)*dr + (p/aaa)*da*da*da

where p represents a final parameter, and dr and da are the changes in the initial values of rho_initial and z_angle. In this example, the coefficient r/r is the linear magnification, and r/aaa gives the spherical aberration coefficient. A third term (p/raaa)*dr*da*da*da is excluded because it is a fourth order term (and the maximum order is 3).

As another example the order 1 could be chosen for z_angle and for the energy. Then the program would give the coefficients in the expansion

p - p_median = (p/a)*da + (p/e)*de + (p/ae)*da*de

where de is the change in the initial value of the energy. In this example the coefficient r/ae is the Cc*M, where Cc is the chromatic aberration coefficient.

The program can be asked to give any first order coefficient p/u, second order coefficient p/uv or third order coefficient p/uvw, except that the energy is treated only to first order.

In the 3D programs the coefficients give the dependence of 6 final ray parameters (x, y, z, cosx, cosy, cosz) on 7 initial parameters (x, y, z, cosx, cosy, cosz, en), where cosx etc are the direction cosines and en is the initial kinetic energy.