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 (?).