57th example file.

A quick simulation of a simple system based on one component of one of the systems proposed by G. D. Archard (Proc. Phys. Soc. B68, 817-829, 1955) to cancel chromatic aberration in one plane.

This is what Archard calls a 'two-pole group', consisting of a pair of spheres of radius 0.1, centred at x = 0, y = +/- 0.5, z = -3, followed by an artificial thin lens at z=3.  

The action of the thin lens is given by the User-supplied routine given below (and so the 'scattering' version of CPO3D must be used).

The data file called by the routine is:

3.         = plane of lens

0.94248    = focal length

0.         = cs

-0.0373    = cc (with unconventional definition)

4.         = reference energy 

These are empirical data, designed to give chromatic compensation for the first group of rays (see below) when V = 1 is applied to the spheres.

The 3 groups of rays start at x = 0.02, .1 and .3 respectively and have energies 3.9, 4 and 4.1, and are parallel to the axis.

The output data are:

The only ray data given for the nearly-zero print level (for possible re-use as data input) are values of:  

x, y, z, cx, cy, cz, kinetic energy, time , current at each test plane and ray, where cx, cy and cz are direction cosines.

  4.85505E-07  0.00000E+00  4.00000E+00 -3.17776E-02  0.00000E+00  9.99495E-01  3.90216E+00  1.13147E-05  0.00000E+00

 -4.20898E-09  0.00000E+00  4.00000E+00 -3.14689E-02  0.00000E+00  9.99505E-01  4.00216E+00  1.11712E-05  0.00000E+00

  5.77741E-07  0.00000E+00  4.00000E+00 -3.11749E-02  0.00000E+00  9.99514E-01  4.10216E+00  1.10331E-05  0.00000E+00

 -1.16008E-05  0.00000E+00  4.00000E+00 -1.54742E-01  0.00000E+00  9.87955E-01  3.90216E+00  1.13242E-05  0.00000E+00

 -1.73282E-05  0.00000E+00  4.00000E+00 -1.53318E-01  0.00000E+00  9.88177E-01  4.00216E+00  1.11805E-05  0.00000E+00

 -1.72970E-05  0.00000E+00  4.00000E+00 -1.51960E-01  0.00000E+00  9.88387E-01  4.10216E+00  1.10421E-05  0.00000E+00

 -1.10294E-03  0.00000E+00  4.00000E+00 -3.94024E-01  0.00000E+00  9.19100E-01  3.90214E+00  1.13861E-05  0.00000E+00

 -1.13051E-03  0.00000E+00  4.00000E+00 -3.91489E-01  0.00000E+00  9.20183E-01  4.00214E+00  1.12407E-05  0.00000E+00

 -1.13764E-03  0.00000E+00  4.00000E+00 -3.89058E-01  0.00000E+00  9.21213E-01  4.10214E+00  1.11008E-05  0.00000E+00

When the potentials on the spheres is put to 0 and the test plane is moved to z = 3.9425, the output data are:

 -1.96883E-05  0.00000E+00  3.94250E+00 -2.12363E-02  0.00000E+00  9.99774E-01  3.90000E+00  1.12209E-05  0.00000E+00

 -4.23929E-07  0.00000E+00  3.94250E+00 -2.12158E-02  0.00000E+00  9.99775E-01  4.00000E+00  1.10798E-05  0.00000E+00

  1.88404E-05  0.00000E+00  3.94250E+00 -2.11954E-02  0.00000E+00  9.99775E-01  4.10000E+00  1.09438E-05  0.00000E+00

 -9.91325E-05  0.00000E+00  3.94250E+00 -1.05612E-01  0.00000E+00  9.94407E-01  3.90000E+00  1.12253E-05  0.00000E+00

 -2.12113E-06  0.00000E+00  3.94250E+00 -1.05511E-01  0.00000E+00  9.94418E-01  4.00000E+00  1.10841E-05  0.00000E+00

  9.48892E-05  0.00000E+00  3.94250E+00 -1.05410E-01  0.00000E+00  9.94429E-01  4.10000E+00  1.09480E-05  0.00000E+00

 -3.14399E-04  0.00000E+00  3.94250E+00 -3.03597E-01  0.00000E+00  9.52801E-01  3.90000E+00  1.12606E-05  0.00000E+00

 -6.36584E-06  0.00000E+00  3.94250E+00 -3.03314E-01  0.00000E+00  9.52891E-01  4.00000E+00  1.11189E-05  0.00000E+00

  3.01612E-04  0.00000E+00  3.94250E+00 -3.03031E-01  0.00000E+00  9.52981E-01  4.10000E+00  1.09824E-05  0.00000E+00

Conclusions (looking at the first columns of data):

95% of chromatic aberration removed, but spherical aberration introduced (?).