Image-plane speckle contrast and Fλ/d in active imaging systems

Coherent illumination of an optically rough surface creates random phase variations in the reflected electric field. Free-space propagation converts these phase variations into irradiance variations in both the pupil and image planes, known as pupil- and image-plane speckle. Infrared imaging systems are often parameterized by the quantity Fλ∕d, which relates the cutoff frequencies passed by the optical diffraction MTF to the frequencies passed by the detector MTF. We present both analytical expressions and Monte-Carlo wave-optics simulations to determine the relationship between image-plane speckle contrast and the first-order system parameters utilized in Fλ∕d (focal length, aperture size, wavelength, and detector size). For designers of active imaging systems, we provide input on speckle mitigation using Fλ∕d to consider in system design.