Oculus radius calculations

Spreadsheet of oculus calculations for theta = 1.5°, R = 2600 m.

A simplistic model for the oculus radius is as follows:

R = fieldRadius, r = focalRadius, x = lampRadius 

focalRadius = fieldRadius * sin(theta) 

phi = arcsin(focalRadius/lampRadius) 

Divergence aspect ratio, AR, at lampRadius 

AR = phi/theta = (arcsin(r/x))/theta 

Oculus aspect ratio, due to foreshortening, is ~2 

gamma = reshaped beam’s angular major axis 

gamma = phi / sqrt(AR/2) 

corresponding oculus radius = xtan(gamma)

Geometrical relations at the focal zone.

As the spreadsheet indicates, the beam-shaping optics needs to operate at the widest possible field angular radius, phi. Phi in the range of 20°-30° permits a land concentration factor (gross field area/oculus area) of 9,000 to 13,000 and a lamp D/H of 1.8-1.3.