Fisher-active residual nulls for dark-field sensing in diffusive optical cloaking

Abstract An object can become externally indistinguishable from its background without becoming 2 uninformative. We examine this possibility in diffusive optical cloaking by separating uniform, 3 simple local, and flat local residual nulls. At a simple local null, the nominal residual vanishes, 4 yet the Fisher information remains finite when the first derivative with respect to the parameter 5 of interest is still observable. We derive this result for both Gaussian measurements and photon 6 counts, examine the loss of identifiability caused by uncertainty in the cloak, and replace a 7 regularized information-to-residual ratio with a constrained design criterion. In a coated-cylinder 8 model, the null retains 62.0% of the Fisher information available from the corresponding bare 9 inclusion. An independent photon-diffusion calculation, including absorption, optical boundary 10 conditions, and Poisson noise, exhibits the same behavior. These results provide a practical dark- 11 field principle for diffuse optics: suppress the calibrated background response while preserving a 12 measurable parameter-sensitive channel.