Optical Sectioning Enhancement Using Higher-Order Moment Signals in Random Speckle-Structured Illumination Microscopy

The optical sectioning capability of structured illumination using random speckle patterns is shown by simulations to improve when cumulants beyond the traditional second order are used as the image-forming signals. The improvement scales with the cumulant order, asymptotically approaching confocal performance. As actual experiments operate with finite-size sample estimators instead of true cumulants, purely statistical (nonoptical) effects can result in nonideal behavior. We analyze the finite ensemble effects along with the experimental effects of detector dynamic range through Monte Carlo simulations. Despite these real-world factors, we show when the third-order-derived signal can demonstrate improved sectioning at good signal-to-noise levels set by finite-sample effects.