A reference-defining criterion for light focusing through scattering media based on circular Gaussian distribution of speckle background intensity

This paper investigates the reference-defining-criterion problem in the field of light focusing through scattering media. In many analogous light focusing experiments, the enhancement values differ greatly from each other. By analyzing the focusing picture after optimizations, we concluded that the discrepancy in enhancement originates from the unclear definition of reference boundary. By averaging multiple speckle backgrounds, we found that the intensity of speckle background obeys circular Gaussian distribution. Based on the intensity statistics and Gaussian-function fitting to the speckle background, we proposed a clear reference-defining criterion– 1/e(2) criterion. With this reference-defining criterion, we have carried out light focusing experiments with the speckle backgrounds possessing different shape and size. The enhancements obtained from the repetitive experiments for both weakly scattering medium and strongly scattering medium were all in the reasonable range, demonstrating its validity and universality. This criterion will provide a comparison standard for light focusing experiments in wavefront-shaping field.