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

Abstract

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-pointGauss-curve-fit. The error of the maximum of the three-point-Gausscurve-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. © 2012 Society of Photo-Optical Instrumentation Engineers (SPIE).

Fault Tolerant Algorithm for Structured Illumination Microscopy with Incoherent Light

“…The sample and the fringe pattern are simultaneously in focus or blurred. Blurring of the fringe pattern, which is caused by axial displacement of the sample, entails a loss in fringe contrast C. For measuring the contrast C locally, an accurate standard [15][16][17][18][19][20] or sinusoidal [4,[9][10][11][12][13][14] Pattern Grating [1,4,9,[20][21][22][23][24][25] Interference [10] DMD [11,12,16,26] LED Array [19] SLM [27][28][29][30] Color grid [17] phase shifting is applied to the fringe pattern. [20] In the case of three phase shifts, the contrast for each pixel is calculated by…”

“…A result of the theoretical analysis in [20] is that the axial uncertainty caused by photon noise also depends on the spatial frequency of the structured illumination. The spatial frequency of the fringe pattern, which minimizes the axial uncertainty due to photon noise, corresponds to 0.29 Á u c .…”

“…The spatial frequency of the fringe pattern, which minimizes the axial uncertainty due to photon noise, corresponds to 0.29 Á u c . [20] …”

“…The incoherent non-super-resolution SIM systems, which are the focus of our analysis, share all the common operations: projecting a patterned illumination on the sample, phase-shifting the pattern in accurate steps over the specimen, determining the contrast values for all pixels, shifting the specimen in steps of z s through focus, extracting the focal depth response (FDR) for all pixels and determining the focal position of each pixel to generate the topography of the specimen. The different existing SIM systems differ in their shapes of the patterns (sinusoidal, [4,[9][10][11][12][13][14] rectangular [15][16][17][18][19][20] ), their algorithms, their pattern generations (grating, [1,4,9,[20][21][22][23][24][25] digital light modulator (DMD), [10,12,16,26] spatial light modulator (SLM), [27][28][29][30] light emitting diode (LED) array, [19] interference [10] ) and their manners of shifting the pattern over the sample (high precision linear actuator, [1,4,10,15,20] rotational actuator, [24,25] micro mirrors, [11,12,16,…”

An optical platform for the production, trapping, manipulation and visualization of ultra-low interfacial tension emulsion droplets

“…The resulting focal depth resolution and image contrast depend strongly on the chosen grating period and sectioning interval. 12 Fluorescent return is preferred over brightfield output, as the possibility of self-refraction through objects of Proc. of SPIE Vol.…”