In this contribution we present a new algorithm for structured illumination microscopy with incoherent light. Existing algorithms for determining the contrast values of the focal depth response require a high accurate phase shift of the fringe pattern illumination. The presented algorithm, which is robust against inaccurate phase shift of the fringe pattern, reduces significantly the requirements for the phase shift and consequently the costs of the microscope. The new algorithm was tested by a preliminary experiment, whereby the grating was shifted by an elastic guided micro-motion mechanism employing a low-cost stepper motor replacing the conventional expensive piezo drive. The determined focal depth response is very smooth and corresponds very well to the theoretical focal depth response.
In this contribution, the extent to which the Nyquist criterion can be violated in optical imaging systems with a digital sensor, e.g., a digital microscope, is investigated. In detail, we analyze the subpixel uncertainty of the detected position of a step edge, the edge of a stripe with a varying width, and that of a periodic rectangular pattern for varying pixel pitches of the sensor, thus also in aliased conditions. The analysis includes the investigation of different algorithms of edge localization based on direct fitting or based on the derivative of the edge profile, such as the common centroid method. In addition to the systematic error of these algorithms, the influence of the photon noise (PN) is included in the investigation. A simplified closed form solution for the uncertainty of the edge position caused by the PN is derived. The presented results show that, in the vast majority of cases, the pixel pitch can exceed the Nyquist sampling distance by about 50% without an increase of the uncertainty of edge localization. This allows one to increase the field-of-view without increasing the resolution of the sensor and to decrease the size of the setup by reducing the magnification. Experimental results confirm the simulation results.
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