Optical EngineeringTwo-dimensional space-angle product of a Gaussian beam
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Relations for Gaussian beam propagation are expressed in full diameters and full angles. They are also expressed in terms of area and solid angle. The resulting formulas are more elegant than traditional expressions with half diameters and half angles. The space-angle product of a Gaussian beam is derived from the Heisenberg uncertainty principle. The resulting 2-D space-angle product contains only parameters of the beam without any scalar constants. The longitudinal uncertainty is employed to derive the coherence length.