The better sampled the PSF, the better the deconvolution result?

Am I correct to think that the ideal sampling rate is infinite, and anything else represents a compromise? The formula in the manual seems to imply that there are physical limits to one's ability to deconvolve that are solidly based on optics--not on photobleaching, detector sensitivity, numbers of photons emitted or the size of the bead.

Indeed, the better your PSF, the better the resolution to which you can deconvolve the object and the fewer artifacts. But as to the resolution, there is a limit. Signal To Noise Ratio (SNR) plays a crucial role there.

The Nyquist Rate (similar to the Shannon theorem) says that if a signal is bandlimited, see our FAQ What's a bandlimited system?, it is sufficient to sample it at twice the highest frequency. Then, it is possible to reconstruct the signal at ALL locations, perfectly. So in principle it is sufficient to sample at the Nyquist rate. Taking more samples does not get you more information about the object. In short, the ideal sampling rate is not infinite. Still, taking more samples with the same number of photons per pixel will improve the quality of the deconvolution result. Vice versa, taking more samples allows you to achieve the same quality in the deconvolution result at lower photon counts per pixel. BTW: If you sample below the Nyquist rate you get Aliasing Artifacts (moire patterns, straircasing).

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 Band Width 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 Spatial Resolution: separating two objects. It is very hard to separate two objects reliably at distances smaller than the Nyquist distance.

To see what is the ideal sampling for your setup see Nyquist Calculator.

Keywords: sampling nyquist psf SNR noise superresolution super-resolution Categories: Faq Deconvolution, Faq Microscopy, Huygens Faq, Imported Faqs Platforms: Linux Windows Mac Related products: Hu Ess Hu Pro