Melles Griot Optics Guide

Examples

Numerical Aperture and Magnification

To understand how to use the relationship between magnification and numerical aperture, consider the following example. System with Fixed Input Numerical Aperture Two very common applications of simple optics involve coupling light into an optical fiber or into the entrance slit of a monochromator. Although these problems appear to be quite different, they both have the same limitation � they have a fixed numerical aperture. For monochromators, this limit is usually expressed in terms of the f-number. In addition to the fixed numerical aperture, they both have a fixed entrance pupil (image) size. Suppose it is necessary, using a singlet lens from the Melles Griot catalog, to couple the output of an incandescent bulb with a filament 1 mm in diameter into an optical fiber as shown in the figure below. Assume that the fiber has a core diameter of 100 mm and a numerical aperture of 0.25, and that the design requires that the total distance from the source to the fiber be 110 mm. Which lenses are appropriate?

Optical system geometry for focusing the output of an incandescent bulb into an optical fiber
By definition, the magnification must be 0.1. Letting s + s" total 110 mm (using the thin-lens approximation), we can use equationx for focal length and conjugate distances found in Basic Paraxial Formulae,

and

and find that s = 100 mm and s" = 10 mm. We can now use the relationship NA = f /2s or NA" = f /2s" to derive f, the optimum clear aperture (effective diameter) of the lens. With an image numerical aperture of 0.25 and an image distance (s") of 10 mm,

Accomplishing this imaging task with a single lens therefore requires an optic with a 9.1-mm focal length and a 5-mm diameter. Using a larger diameter lens will not result in any greater system throughput because of the limited input numerical aperture of the optical fiber. The singlet lenses in this catalog that meet these criteria are 01 LPX 003, which is plano-convex, and 01 LDX 003 and 01 LDX 005, which are biconvex. Making some simple calculations has reduced our choice of lenses to just three. The following chapeter, Gaussian Beam Optics, discusses how to make a final choice of lenses based on various performance criteria.

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