Parax Tool

This page is a faithful conversion of Section 4 of the provisional manual (KrakenOS/Docs/USER_MANUAL_KrakenOS_Provisional.pdf, pages 20–21).

Parax is a method on the system class that returns the paraxial quantities needed for matrix ray tracing, evaluated at a chosen wavelength.

Prx = Doublet.Parax(0.4)
SistemMatrix, S_Matrix, N_Matrix, a, b, c, d, EFFL, PPA, PPP, C, N, D = Prx

The fields returned in Prx are:

Total system matrix

SistemMatrix — the cascaded refraction/translation matrix for the whole system. For the doublet example:

SistemMatrix = [[ 8.69329466e-01  -9.80840791e-03]
                [ 1.00167690e+02   2.01470656e-02]]
Per-element surface matrices

S_Matrix — a list of 2×2 matrices, alternating refraction and translation entries:

S_Matrix = [matrix([[1., 0.], [ 0., 1.]]),
            matrix([[1., 0.], [10., 1.]]),
            matrix([[0.65323249, -0.00361793], [0., 1.]]),
            matrix([[1., 0.], [ 6., 1.]]),
            matrix([[0.92657697,  0.00239038], [0., 1.]]),
            matrix([[1., 0.], [ 3., 1.]]),
            matrix([[1.65215474, -0.00833986], [0., 1.]]),
            matrix([[1., 0.], [97.37604743, 1.]]),
            matrix([[1., 0.], [ 0., 1.]]),
            matrix([[1., 0.], [ 0., 1.]])]
Matrix labels

N_Matrix — human-readable labels for each entry in S_Matrix:

N_Matrix = ['R sup: 0', 'T sup: 0 to 1',
            'R sup: 1', 'T sup: 1 to 2',
            'R sup: 2', 'T sup: 2 to 3',
            'R sup: 3', 'T sup: 3 to 4',
            'R sup: 4', 'T sup: 4 to 5']
Total-matrix entries

a, b, c, d are the four entries of the cascaded matrix:

a = 0.8693294662072478
b = -0.009808407908592333
c = 100.16768993870667
d = 0.02014706564149671
Cardinal quantities

  • EFFL — effective focal length

  • PPA — principal anterior plane

  • PPP — principal posterior plane

EFFL = 101.9533454684305
PPA  = -99.89928472490783
PPP  =  13.322298074316684
Per-surface arrays

C — curvatures, N — refractive indices at each medium, D — surface separations:

C = [1.00000000e-12, 1.04332892e-02, -3.25562791e-02, -1.27881671e-02, 1.00000000e-12]
N = [1.0, 1.5308485382492993, 1.6521547400480732, 1.0, 1.0]
D = [10., 6., 3., 97.37604743, 0.]