Relay lens

Cross-section of relay lens assembly - System 1.
Cross-section of relay lens assembly - System 2.
Image erecting optical system for astronomical telescopes (Erecting eyepiece).

In optics, a relay lens is a lens or lens group that inverts an image and extends the optical tube. Relay lenses are found in endoscopes and periscopes for the purpose of extending the system, and before eyepieces for the purpose of inverting an image. They may be made of one or more conventional lenses or achromatic doublets, or a long cylindrical gradient-index of refraction lens (a GRIN lens). Relay lenses operate by producing intermediate planes of focus. For example, an objective lens such as an SLR lens produces an image plane where the image sensor would usually go. If you place a lens with focal length f a distance 2f from that image plane and then put an image sensor 2f beyond the lens, that lens will relay the first image to the second with 1:1 magnification (see thin lens formula with object distance s=2f, the image distance is calculated to s'=2f). Ideally, this second image plane will be identical to the first, so you could put a sensor there and record exactly the same image. If a longer distance is needed, this can be repeated.

In practice, the lens will be an achromatic doublet. Also, for endoscope applications, where small tube diameter is desirable, most of the tube is filled with glass, with thin air gaps to allow for powered surfaces; because marginal ray angle is smaller at a given numerical aperture the higher the index of refraction, this allows the relay to have higher NA for a given diameter. These are known as Hopkins rod lenses.

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