OTF compensation in structured illumination superresolution images

The lateral resolution of an imaging system is limited by its numerical aperture and the wavelength. Structured illumination incident on the object heterodynes the higher spatial frequencies of the object with the spatial frequency of the sinusoidal illumination into the passband of the imaging system providing lateral superresolution. This idea has been implemented in microscopy. Multiple images of an object are taken, with distinct phase shifts in the sinusoidally patterned illumination. They are processed to separate the conventional, un-aliased object spatial frequencies from the aliased ones, which contain superresolution information. The separated aliased terms are de-aliased (i.e. the spatial frequencies in them are moved to their correct locations in Fourier space) giving superresolution along the direction perpendicular to the orientation of the sinusoidal fringe pattern. This process is repeated with, say, 60° and 120° rotation of the sinusoidal fringe illumination to obtain superresolution in all directions. The final reconstructed image can be obtained by appropriate combination of the de-aliased superresolution components with the conventional, un-aliased components. We discuss the signal-to-noise ratio (SNR) and optical transfer function (OTF) compensation in the combination of all these components to obtain an image with lateral superresolution.

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