Theoretical analysis of photon noise limiting axial depth resolution for three-dimensional microscopy by incoherent structured illumination

The influence of photon noise to the signal evaluation of digital microscopy using a sinusoidal fringe pattern illumination with incoherent light is shown. The signal is evaluated by calculating the contrast for every charge coupled device (CCD) pixel when the object is defocused and the fringe pattern illumination shifted by a defined phase over the sample for every z-position. Every CCD pixel gets a certain number of irradiance values for every z-position which allows calculating the contrast. The result is the focal depth response (FDR) for every pixel. The FDR is Gaussian shaped and contains the height information of the specimen in the maximum. To accelerate the signal evaluation it is common to compute a fit curve to detect the maximum of the FDR. Due to the statistical photon noise, every measured irradiance value and every computed contrast value contains an error and thus also the maximum of the three-point-Gauss-curve-fit. The error of the maximum of the three-point-Gauss-curve-fit is the uncertainty of the measured height information. A general and a simplified analytical closed form solution are derived to calculate this uncertainty. An easily manageable equation allows calculating the optimal spatial frequency for an incoherent sinusoidal fringe pattern illumination and the corresponding sampling distance. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI: 10.1117/1.OE.51.10.103203]