Ewald Construction

P. P. Ewald was responsible for interpreting Laue's results in terms of reciprocal lattices.  He devised a simple geometric construction that demonstrates the relationship in quite elegant but simple terms.

He separated the origins of direct and reciprocal space placing the crystal at the center of a sphere of radius 1/l.  The origin of reciprocal space is placed on the surface of the sphere where S0 (the incident beam) exits the sphere.