Numerical Aperture and Magnification
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To understand the importance of the numerical aperture, consider its relation to magnification. Referring to the figure below: |
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| Numerical aperture and magnification |
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| which can be rearranged to show |
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| and | |
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| leading to |
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| Since s"/s
is simply the magnification of the system, we arrive at |
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The magnification of the system is therefore equal to the ratio of the numerical
apertures on the object and image sides of the system. This powerful and useful
result is completely independent of the specifics of the optical system, and it can
often be used to determine the optimum lens diameter in situations involving aperture
constraints. When a lens or optical system is used to create an image of a source, it is natural to assume that, by increasing the diameter (f) of the lens, we will be able to collect more light and thereby produce a brighter image. However, because of the relationship between magnification and numerical aperture, there can be a theoretical limit beyond which increasing the diameter has no effect on light-collection efficiency or image brightness. Since the numerical aperture of a ray is given by f/2s, once a focal length and magnification have been selected, the value of NA sets the value of f. Thus, if one is dealing with a system in which the numerical aperture is constrained on either the object or image side, increasing the lens diameter beyond this value will increase system size and cost but will not improve performance (i.e., throughput or image brightness). This concept is sometimes referred to as the optical invariant. |
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| Optics Guide Copyright 2002 Melles Griot Inc. |