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APPENDIX I – DERIVATION OF SEARCH SOLID ANGLE EQUATION R cos dr, d R ds, d Figure 1 – Geometry for Computing Solid Angle We can write the area of the small square in the figure above as dA dsdr R cos d Rd or dA R 2 cos d d . If we want the total area over the angles 1,2 0 2,0 2 and 0 A 2, 0 2 we can integrate the above over these angle ranges, viz. 0 2 0 2 0 2 0 R 2 cos d d . 2 Performing the integral results in A R 2 sin 0 2 sin 0 2 . After some trigonometric manipulations this reduces to A 2R2 cos 0 sin 2 . Finally, dividing by R 2 yields the solid angle, viz. 2 cos0 sin 2 . ©2005 M. C. Budge, Jr