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Oversampling

Oversampling is the contrary to undersampling, i.e., measuring with a sampling distance smaller than the critical sampling distance determined by the Nyquist rate.

In theory oversampling is an excess of information, and therefore a waste of storage and computing resources. Still, taking more samples with the same number of photons per pixel improves the Signal to Noise Ratio (SNR). Vice versa, taking more samples allows you to achieve the same quality in the deconvolution result at lower intensities per pixel.

One more reason to oversample is that with sparse objects and good SNR it is often possible to achieve a Half Intensity Width resolution on the objects corresponding with a bandwidth in excess of the microscope's bandwidth. The objects are then said to be super resolved. The Shannon theorem says it doesn't matter whether you get the supersampled image during sampling or afterwards by interpolation, but it is more practical to get it during sampling, if only to improve the SNR situation.

A different matter is two-point resolution: separating two objects. It is very hard to separate two objects reliably at distances smaller than the Nyquist distance.