From the definition, microscope resolution is the shortest distance between two separate points in a microscope’s field of view that can still be distinguished as distinct entities. I imported a picture acquired by a microscopy to a digital image processing software, the picture was calibrated already. By using this software, I zoom in this picture to a point that I can get a length of each pixel on this picture, it shows that length of each pixel is 0.1 um, does it mean that the resolution of this microscopy is 0.1 um?
No. There is not necessarily any relationship between the image that comes out of the microscope ( i.e. the sensor, or data acquisition tool) and the image after processing (the processing being 'signal processing').
You may conceivably have a situation where the data processing has finer granularity than the sensor - in which case you'd have some contiguous pixels reflecting the very same datum), or reversely a situation where the data processing would have coarser granularity, in which case data processing would lead to loss of information.
Any data acquisition chain is made up of a sensor and of a signal processing unit - which are independent.
Jeannie,
as you define microscope resolution is essentially correct. 'can be distinquished' here refers to a mode of observation (eye or camera) which does not reduce the resolving power. If, for intance you observe with your eyes, (and have a little bit of experience with looking through a microscope) it will be evident to you whether problems in recognizing two light-dots as separated result from limitations of your eyes or from limitations of the microscope's image formation capability. If you suspect that your eyes are the limiting factor, simply change a stronger ocular, so that the image you see gets larger and you have less difficulty to regognize all the detail that the image formed by the microscope actually contains. If you choose an even stronger ocular you will see the details even more enlarged, but no more detail will shine up, only everything larger and the unsharpness more evident. This then is called 'dead magnification'.
If you do not observe through the ocular with your eyes but with a CCD camera (or some equivalent), that is properly adjusted to the microscope (e.g. designed for that microscope by the microscope manufacturer) you always work with 'slightly dead' magnification since the resolution of the microscope should not be cut down by the pixel structure of the image sensor.
If one specifies resolution for critical comparison one works typically with line patterns instead of nearby 'points' and gives a 'modulation transfer curve' (MTF) instead of a single number. Given the mature technology of today, a (for most purposes sufficient) indicator of the resolution of a microscope is the 'numerical aperture' (NA) of its objective lens. You should read about its meaning in Wikipedia or an optics textbook.
I could write a novel about microscopy and microscopes since building those as a school boy brought me to physics. Nevertheless I will stop here in order to overload you not too seriously.
Generally the resolution of optical microscopy is lambda by 2. Thats why it gives result of ensemble not single particle
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