How is microscope resolution measured?

The resolution of a microscope is a measure of the smallest detail of an object that can be observed as separate, typically expressed in linear units such as micrometres ($\mu m$).1

The limit of resolution is fundamentally determined by the wavelength of the light used and the numerical aperture (N.A.) of the objective lens. The N.A. serves as the primary measure of an objective's ability to collect diffracted light from an object, which is essential for reconstructing fine details in an image. It is calculated as the sine of half the angle of the cone of light accepted by the objective, multiplied by the refractive index of the medium between the specimen and the lens.23

To improve resolution, one must either increase the N.A. or use light with a shorter wavelength. Because the aperture of an objective is limited, it cannot transmit all diffracted waves; therefore, the greater the number of diffracted waves an objective can collect, the finer the detail that can be resolved. If an objective has an insufficient N.A., the details will not be resolved, regardless of any further magnification.23