How did Ernst Abbe’s theory explain the importance of numerical aperture?

In 1873, German physicist Ernst Abbe established a modern theory of image formation, which identified diffraction as the fundamental process limiting a microscope's ability to resolve fine detail.

Abbe explained that when light illuminates an object, the structure of that object diffracts the light at angles proportional to the fineness of its details. Because a microscope objective has a limited aperture, it can only collect a portion of these diffracted waves. Abbe demonstrated that the ability to reconstruct fine detail in an image depends directly on the number of these diffracted waves that the objective can capture.

To quantify this, he designated the term numerical aperture (N.A.) as a measure of an objective's capacity to collect diffracted light. His theory established that:

• A higher N.A. allows for the collection of more diffracted waves, thereby increasing the power to resolve finer details.
• If an objective's N.A. is too low to collect the necessary diffracted light, the details will not be resolved, regardless of how much the image is magnified (a condition known as empty magnification).1