# Microscopy Nyquist rate and PSF calculator

Please make sure you have the correct values for the Microscopy Parameters necessary for calculating the Nyquist rate. Additional parameters appear if you check the option to calculate the Theoretical PSF. Note that the pinhole size doesn't alter the bandwidth of the detection system.

The Huygens Theoretical PSF page contains more information and interactive examples on the impact of RI mismatch on the PSF shape.

The Pinhole Radius and Pinhole Distances parameters are not physical sizes, but rather BackProjected sizes, i.e. divided by the total magnification of the system. To compute these backprojected values, see the Backprojected Pinhole Calculator. For further details, see below.

## Explanation: proper images

The ideal Sampling Density (or inversely, Voxel Size) for image acquisition depends on the optics of the microscope. It is recommended to sample the image at a rate close to the ideal Nyquist Rate. Images obtained with sampling distances (voxel dimensions) larger than those established by this rate will suffer from undersampling. See the examples on anti aliasing and aliasing artifacts, and some consequences in Quality Vs Sampling.

With the form on this page you can calculate the Ideal Sampling from your optical conditions to acquire a well sampled image. (To see what equations are used in this calculator and some theory behind the scenes read the Nyquist rate background article). The data will be returned in nanometers (nm). You have also the option to generate an image of the Point Spread Function (PSF) which only takes a few seconds more. The size of the PSF image will be given in µm. The images are shown as Maximum Intensity Projections along Z and Y, and upscaled for a better display. The pixelation corresponding to the Nyquist rate will be clearly seen.

A common rule of thumb defines the ideal sampling in terms of spatial resolution ("sample with half of the resolution") but this is not exactly correct, and in some cases will lead to undersampling. The correct Nyquist rate is defined in terms of the system Bandwidth (in the frequency domain) which is determined by the Point Spread Function.

## Exceptions in practice

While sampling at the Nyquist rate is a very good idea, it is in many practical situations hard to attain. In these cases larger sampling distances may be used and a good job can still be done when deconvolving these images. For Confocal Microscope images, sampling distances may be up to 1.7 times the Nyquist ones. When large pinholes are used, up to 2 times larger even. Widefield microscopy data is more sensitive to undersampling, so it is better to stay below a factor of 1.5. In case of low Numerical Apertures, like 0.4, we recommend not to undersample in the axial direction.

Hint: If you have a data stack that is dramatically undersampled in Z (not fulfilling the Nyquist Criterion by a large factor) it is better to interpret the different planes as independent images (i.e. as 2D images) and do 2D deconvolution in the Huygens Software planewise. See Convert the Data Set.

You can use the PSF calculator option in the form to see the expected size of the PSF of your imaging setup and accordingly, of a distilled Experimental PSF from bead images.