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Test ray

On the planar and solid views you can create a test ray via the options panel. The initial coordinates of the ray are specified in terms of reduced field coordinates (Hx,Hy) and reduced pupil coordinates (Px,Py).

testRay screenshot

After the ray is traced through the system, the results are displayed on the options panel, in the following format:

Position:     0.000     0.000  1102.925
Momentum:  0.000000  0.000000  1.000000
Basis transformation:
 1.000000  0.000000  0.000000
 0.000000  1.000000  0.000000
 0.000000  0.000000  1.000000
Transfer matrix in (px,py,qx,qy) basis:
  -0.2768    0.0000   -0.0045    0.0000
   0.0000   -0.2768    0.0000   -0.0045
  27.2325    0.0000   -3.1737    0.0000
   0.0000   27.2325    0.0000   -3.1737

The ray position and momentum are given in global coordinates. The ray momentum is a vector in the direction of ray propagation (if the refractive index is positive), with length equal to the refractive index in which the ray finds itself. The basis transformation B has columns that are the x, y, and z directions of the ray's own coordinate system. The transfer matrix M is the symplectic matrix describing the propagation of rays near the traced one.

The transfer matrix can be displayed with a basis of your choice. The default basis is (px, py, qx, qy), with ray momentum first. Another basis used in the literature is (qx, qy, px, py); this is the usual ordering used for the ABCD matrix.

If the object and image indexes of refraction are the same, and the test ray is axial (Hx=Hy=Px=Py=0), then the transfer matrix is equal to the ABCD matrix.

Note that upper case P refers to reduced pupil coordinate, and lower case p refers to ray momentum. These quantities are not the same.

Tracing to a particular surface

To trace a test ray to a particular surface, just set the last surface on the Surfaces tab of the options panel.

See also