Astronomical Applications Department, U.S. Naval Observatory Beam Comp Example Page 5

beam_intersect[251]: Calculating path length...

reflect[301]: Expanding intersection point...

reflect[309]: Simplifying intersection point...

reflect[343]: Finding surface normal...

reflect[345]: Expanding normal vector...

reflect[350]: Simplifying normal vector...

reflect[368]: Calculating reflected beam...

reflect[430]: Expanding reflection vector...

reflect[778]: Simplifying reflection vector...

reflect[1076]: Transforming output beam to GLOBAL frame...

reflect[1076]: ...direction...

reflect[1077]: ...position...

reflect[1078]: Expanding position...

reflect[1082]: Simplifying position...

reflect[1112]: Expanding direction...

reflect[1116]: Simplifying direction...

reflect[1142]: Calculating optical path...

reflect[1142]: Expanding optical path...

reflect[1144]: Simplifying optical path...

raytrace[1149]: Simplifying beam...

raytrace[1207]: Calculating detector intersection point...

beam_intersect[1208]: Equation substitutions...

beam_intersect[1210]: Expanding and simplifying substitution result.

..

beam_intersect[1227]: Solving for t...

beam_intersect[1227]: Calculating intersection point...

beam_intersect[1227]: Trying solution 1...

intersect_findpoint[1229]: Expanding in series...

intersect_findpoint[1234]: Adding vector to previous position and si

mplifying...

intersect_findpoint[1257]: Expanding in series...

beam_intersect[1267]: Checking for small divisors...

beam_intersect[1276]: Transforming to GLOBAL frame...

beam_intersect[1279]: Expanding in series...

beam_intersect[1287]: Calculating path length...

raytrace[1301]: Simplifying...

raytrace[1348]: Calculating and simplifying total path length...

BeamComp[1363]: Calculating OPD...

BeamComp[1390]: Calculating aperture averaged OPD...

annular_average[1390]: Calculating average over annulus...

BeamComp[1406]: Done!

We're finished with the ray trace. This run took 1,406 seconds on a 90 MHz Pentium with

48 M of RAM. An insignificant amount of that time was used in virtual swap file access;

hence the calculation was CPU bound. Peak memory usage, as reported on the Maple

status bar, was 22.1 M. Resources required scale nonlinearly with the expansion orders

used. For example, expanding to 10th order in radius instead of 12th order cuts peak

memory to ~13 M. The OPD and the aperture-averaged OPD are now stored in the global

variables *OPD* and *OPD_avg. *

**The Optical Path Difference (i.e., the Wavefront)**