Image arrays do not contain information about resolution. Image files might contain information about resolution, but unless they are DICOM images (or perhaps PNG produced by scientific microscopes), any resolution information they contain is likely to be wrong.
If you have a DICOM file that contains a number of slices, then the z spacing has to be read from the DICOM metadata. Typically the z spacing is given as a scalar -- the space between slices is a constant typically. The z resolution is really not something you calculate, it is something you read out from the metadata.
However, if there happened to be something of known size that was present in every slice, then you could potentially calculate the resolution from the images themselves. For medical images, this typically only happens if you are running a "phantom" (imaging a non-medical object of known properties.)
