Please explain with reference to the attached figure. Also,
What does "infinite resolution" of a microscope (optical or electron) imply?
Similarly what do we mean by "zero resolution"? Does having a zero resolution in a microscopy indicate that the two point objects at a finite distance cannot be in focus at the same time?
There are a couple of things to consider.
The image of a (theoretical) point on the object side appears at that location where all the diverging rays, being captured by your optics, are converged into one point on the image side. Having the situation that all object points you want to image are in one plane (object plane) and this plane is perpendicular to the optical axis of your system, all these points are imaged in the image plane (also perpendicular to the optical axis and assuming that the optical system is not desgnied for off-axis imaging).
These two planes have a well defined distance to the optical system. Object points being before or behind this plane are imaged not sufficiently, as the rays before and behind the image plane are not "focussed" as in the image plane (they converge or diverge). Maybe you have a look at Figure 22.13 in the attached file.
The respective depth of field is the range in which the image appears to your eyes as 'sharp'. This depends on magnification, distance of the viewer and other things. Chapter 22.2.4 of the attached file... see "circle of confusion".
The infinite resolution is normally referred to, when talking about a (more or less theoretical) optic, where one can zoom into an object scene at any zoomlevel, still getting an image with a satisfying resolution level.
Some reading on a similar topic might be: https://www.edmundoptics.com/knowledge-center/application-notes/microscopy/understanding-infinity-corrected-objective-resolving-power-and-magnification/ (this is available in various languages.
Not sure about the zero resolution term. This might be interpreted differently in various domains. I could assume, that you have an additional fluorscence detector in your microscope? In this case it could refer to the characteristic, that the signal does not have an 'image resolution', but simply detects the amount of fluorescence coming from a certain area (steradiant). By this it would also detect signals from object aligned behind each other.
Jan
Thanks Prof. Jan Schulz for the nice explanation.
I will also go through the attachment notes and revisit this space.
I assume you understand resolution to be the scale at which objects are discernible from each other. There are a variety of definitions but they ultimately depend on the wavelength of the light. Resolution can be degraded by the quality of the optics.
So if resolution is sigma, you can displace the sample in z by d and not be able to resolve that anything has changed. It still seems to be in focus.
I hope you noticed that the smaller the angle, alpha, the greater d will be for a given sigma. Longer working distances will give you a greater depth of field/focus.
As to "zero resolution" or "infinite resolution", I don't know. In my 40+ years, I have not come across those terms. I would first _guess_ them to be equivalent where you can resolve down to nothing. I would have to google the terms and see if their usage is consistent among scientists. I expect the Edmund link will be be a good source.
The dept of the zone of focus depends on the aperture of the lens. Dept of Field is a function of distance between the lens and the object (doubling the object distance increased Dept of Field by a factor of 4). If the object distance is small the Dept of Field will be limited and two objects at different focal distances will not resolve.
For any lens system there is a hyperfocal distance (dept of field extends from infinity to close to the lens). The combinations of aperture/dept of field needed for the hyperfocal condition of be realized is unlike with the short object distance of microscopy.
There will always be a limit to the resolution set by to the wavelength of the light. I would like to know more of the concept of infinite resolution, could you tell us where you found it?