How can I decrease the output angle of a fiber to achieve a more collimated beam with a lens / ball lens?

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How can I decrease the output angle of a fiber to achieve a more collimated beam with a lens / ball lens?

A lens with a positive focal length can help reduce the divergence angle of an output beam from an optical fiber. The lens must have a f/# less than or equal to 0.5/NA, where NA is the numerical aperture of the fiber. The f/# of the lens is equal to f/D where f and D are the lens' respective focal length and diameter. This insures that the lens will capture the cone of light exiting the fiber. It should be placed away from the fiber at a distance equal to the lens' focal length. A Ball Lens placed in contact with the fiber can also reduce the divergence angle of the output beam.

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