Active-tracking scaling laws using the noise-equivalent angle due to speckle

It is well known to system engineers that speckle imposes a limitation on active-tracking performance, but scaling laws that quantify this limitation do not currently exist in the peer-reviewed literature. Additionally, existing models lack validation through either simulation or experimentation. With these points in mind, this paper formulates closed-form expressions that accurately predict the noise-equivalent angle due to speckle. The analysis separately treats both well-resolved and unresolved cases for circular and square apertures. When compared with the numerical results from wave-optics simulations, the analytical results show excellent agreement to a track-error limitation of (1/3)λ/D, where λ/D is the aperture diffraction angle. As a result, this paper creates validated scaling laws for system engineers that need to account for active-tracking performance.