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Relay Trains and Periscopes

This is a continuation from the previous tutorial - galilean and inverse galilean afocal lenses.


There are many applications where it is necessary to perform remote viewing because the object to be viewed is in an environment hostile to the viewer, or because the object is inaccessible to the viewer without unacceptable damage to its environment. Military applications fall into the former category, and medical applications fall into the latter.

For these applications, instrumentation is needed to collect light from the object, transport the light to a location more favorable for viewing, and dispense the light to the viewing instruments or personnel.

Collecting and dispensing optical images is done with focusing lenses, typically. There are three image transportation techniques in common use today: (1) sense the image with a camera and transport the data electronically, (2) transport the light pattern with a coherent fiber optics bundle, and (3) transport the light pattern with a relay lens or train of relay lenses.

The first two techniques are outside the scope of this tutorial. Relay trains, however, are commonly made up of a series of unit power afocal lenses, and are one of the most important applications of finite conjugate afocal lenses. 


Unit Power Afocal Relay Trains

Several factors are important in designing relay trains.

  1. It is desirable to minimize the number of relay stages in the relay train, both to maximize transmittance and to minimize the field curvature caused by the large number of positive lenses.
  2. The outside diameter of the relay train is typically restricted (or a single relay lens could be used), so the choice of image and pupil diameter within the relay is important.
  3. Economic considerations make it desirable to use as many common elements as possible, while minimizing the total number of elements.
  4. It is desirable to keep internal images well clear of optical surfaces where dust and scratches can obscure portions of the image.
  5. The number of relay stages must be either odd or even to insure the desired output image orientation.

Figure 16 shows thin-lens models of the two basic afocal lens designs which can be applied to relay train designs.


Figure 16  Basic unit power afocal relay designs.


Central to both designs is the use of symmetry fore and aft of the central stop to control coma, distortion, and lateral color, and matching the image diameter \(D_i\) and stop diameter \(D_s\) to maximize the stage length to diameter ratio.

In paraxial terms, if \(D_i=D_s\), then the marginal ray angle \(u\) matches the principal ray angle \(u_p\), in accordance with the optical invariant. If the relay lens is both aplanatic and distortion free, a better model of the optical invariant is


and either the field of view \(2u_p\) or the numerical aperture \(\text{NA}=n\sin{u}\) must be adjusted to match pupil and image diameters. For some applications, maximizing the optical invariant which can pass through a given tube diameter \(D_t\) in a minimum number of stages is also critical.

If maximizing the ratio \(D_i\sin{u}/D_t\) is not critical, Fig. 16a shows how the number of elements can be minimized by using a keplerian afocal lens with the stop at the common focus, eliminating the need for field lenses between stages. The required tube diameter in this example is at least twice the image diameter.

If maximizing \(D_i\sin{u}/D_t\) is critical, field lenses FL must be added to the objectives OB as shown in Fig. 16b, and the field lenses should be located as close to the image as possible within limits set by obstructions due to dirt and scratches on the field lens surfaces. Symmetry fore and aft of the central stop at 1 is still necessary for aberration balancing. If possible within performance constraints, symmetry of OB and FL with respect to the planes 2a and 2b is economically desirable, making OB and FL identical.

For medical instruments, where minimizing tube diameter is critical, variants of the second approach are common. The rod lens design developed by H . H . Hopkins can be considered an extreme example of either approach, making a single lens so thick that it combines the functions of OB and FL. Figure 17 a shows an example from the first of two patents by McKinley.

The central element in each symmetrical cemented triplet is a sphere. Using rod lenses does maximize the optical invariant which can be passed through a given tube diameter, but it does not eliminate field curvature. It also maximizes weight, since the relay train is almost solid glass, so it is most applicable to small medical instruments.


Figure 17  Improved unit power afocal relays.


If larger diameter relays are permissible, it is possible to correct field curvature in each relay stage, making it possible to increase the number of stages without adding field curvature.

Baker has patented the lens design shown in Fig. 17b for such an application. In this case, field lens and objective are identical, so that an entire relay train can be built using only three different element forms. Pupil and image diameters are the same, and pupil and image are interchangeable.

For purposes of comparison, the two designs shown in Fig. 17 have been scaled to have the same image diameter (2.8 mm) and numerical aperture (0.10), with component focal lengths chosen so that \(D_s=D_i\).

Minimum tube diameter is 4.0 mm for the rod lens and 5.6 mm for the Baker relay. The image radius of curvature is about 20 mm for the rod relay and about -368 mm for the Baker relay (i.e., field curvature is overcorrected).

Image quality for the rod relay is 0.011 waves rms on axis and 0.116 waves rms at full field, both values for best focus, referenced to 587 nm wavelength. For the Baker relay, the corresponding values are 0.025 and 0.056 waves rms, respectively.

The Baker design used for this comparison was adapted from the cited patent, with modern glasses substituted for types no longer available. No changes were made to the design other than refocusing it and scaling it to match the first order parameters of the McKinley design.

Neither design necessarily represents the best performance which can be obtained from its design type, and both should be evaluated in the context of a complete system design where, for example, the field curvature of the McKinley design may be compensated for by that of the collecting and dispensing objectives. Comparing the individual relay designs does, however, show the price which must be paid for either maximizing the optical invariant within a given tube diameter or minimizing field curvature.



Periscopes are relay trains designed to displace the object space reference point \(RO\) a substantial distance away from the eye space reference point \(RE\). This allows the observer to look over an intervening obstacle, or to view objects in a dangerous environment while the observer is in a safer environment. The submarine periscope is the archetypical example. Many other examples can be found in the military and patent literature.

The simplest form of periscope is the pair of fold mirrors shown in Fig. 18a, used to allow the viewer to see over nearby obstacles. Figure 18b shows the next higher level of complexity, in the form of a rear-view vehicle periscope patented by Rudd.

This consists of a pair of cylindrical mirrors in a roof arrangement. The cylinders image one axis of object space with the principal purpose of compensating for the image inversion caused by the roof mirror arrangement. This could be considered to be a keplerian anamorphoser, except that it is usually a unit power magnifier, producing no anamorphic compression. Beyond these examples, the complexity of periscopes varies widely.


Figure 18  Basic reflecting periscopes.


The optics of complex periscopes such as the submarine periscope can be broken down into a series of component relays. The core of a submarine periscope is a pair of fold prisms arranged like the mirrors in Fig. 18a. The upper prism can be rotated to scan in elevation, while the entire periscope is rotated to scan in azimuth, typically.

The main optics is composed of keplerian afocal relays of different magnification, designed to transfer an erect image to the observer inside the submarine, usually at unit net magnification.

Galilean and inverse galilean power changers can be inserted between the upper prism and main relay optics to change the field of view. Variants of this arrangement will be found in other military periscopes, along with accessories such as reticles or image intensifiers located at internal foci. Optical design procedures follow those for other keplerian afocal lenses.


The next tutorial discusses in detail about optical fiber coatings

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