On the accuracy bounds of high-order image correlation spectroscopy

High-order image correlation spectroscopy (HICS) or related image-based cumulant analysis of emitter species are important for identifying properties and concentrations of biomolecules or nanoparticles. However, lack of a thorough parameter space test limits its use in full potential. The current study focused on mapping accuracy bounds of bimodal species concentration space by simulating and analysing more than 2 × 10⁵ images (∼10¹¹ data points). Concentration space maps for four values of quantum yield contrast ratio between two species in a mixture and two sampling spaces (834 and 13357 beam areas in an image) were created, which showed clear accuracy bounds governed by two factors, Poisson fluctuation and quantum yield ratio. Typically, brighter species concentration was 1-3 orders of magnitude lower than that of dimmer species, and higher brightness contrast allowed higher concentration difference. Upper limit of accuracy bounds was governed by resolvable Poisson fluctuation, where this condition was violated for emitter density beyond 10 particles per beam area. The accuracy bounds are shown to be largely invariant under noise correction or the calculation method, and are compared against previous experimental results, showing consistent agreement. This study shows that concentration limit needs to be observed when using HICS or related image moment or cumulant analysis techniques. As a rule of thumb, a large quantum yield contrast and large sampling points allow more concentration difference between two species to be resolved in an analysis.