Relay lens
Encyclopedia
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 periscope
Periscope
A periscope is an instrument for observation from a concealed position. In its simplest form it consists of a tube with mirrors at each end set parallel to each other at a 45-degree angle....

s for the purpose of extending the system, and before eyepiece
Eyepiece
An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is so named because it is usually the lens that is closest to the eye when someone looks through the device. The objective lens or mirror collects light and brings...

s 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
Grin
Grin may refer to:* A facial expression; see Smile* Alexander Grin , Russian novelist* Grin , 1993* Grin , a band formed by Nils Lofgren** Grin , 1971...

 (a GRIN lens). Relay lenses operate by producing intermediate planes of focus. For example, an objective lens such as an SLR
SLR
The initialism SLR can refer to:* Satellite laser ranging* Scalable Linear Recording Tape Drive Backup* Self-Loading Rifle, see semi-automatic rifle.** The UK version of the Belgian FN FAL select fire battle rifle, the L1A1 SLR.* Semi-linear resolution...

 lens produces an image plane where the image sensor would usually go. If you place a lens with focal length
Focal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...

 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 Lens imaging properties). Ideally, this second image plane will be identical to the first, so you could put a sensor there and record the exact 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
Numerical aperture
In optics, the numerical aperture of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one...

 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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