# eyepiece

Plössl eyepiece (32 mm) for use on a telescope

An eyepiece is the optically effective part of an optical system on the eye side (Latin oculus = eye) , such as binoculars , telescopes , telescopes or light microscopes . An eyepiece consists of a single lens or a lens system. An object-side optical part is called an objective accordingly . However, as in the case of an electronic viewfinder , for example , it can also be a screen that is viewed with an eyepiece.

The function of the eyepiece is usually to virtually map a real intermediate image of an optical image for the human eye . In the Galileo telescope , the eyepiece is still in front of the focal plane of the lens, so that no real intermediate image is created. For this purpose, the intermediate image is projected into infinity, so that the virtual image can be observed by an eye accommodated to infinity .

In afocal photography, special projection eyepieces, which are optimized for an image at a finite distance, are used to project the image onto a film or camera chip.

The exit pupil (AP) of an optical system should be matched to the entry pupil (EP) of the eye . Ideally, their size is not larger than that of the entrance pupil, otherwise light is wasted because the emerging light bundle only partially reaches the eye. In addition, the exit pupil focal length (the interpupillary distance) of the eyepiece should be large enough that the eye pupil can be positioned at this point. Older eyepiece designs did not allow full adaptation to the eye. Either the exit pupil was too close behind the last lens, making it unsuitable for people who wear glasses, or they did not make full color correction . Permanently built-in eyepieces often allow a diopter compensation to adapt the varying refractive powers of the eyes of different viewers to the eyepiece.

As a side effect, if the exit pupil is small (short focal length), the inhomogeneities of the eye located in the beam path are projected particularly clearly onto the retina. These entoptic phenomena can be divided into floaters or scotoma .

## Components

### Eyecup

Most eyepieces have a rubber ring on the edge of the eye, which can often be folded back. It has two purposes: it prevents stray light from entering, which interferes with observation, and it helps to keep the head steady by touching it. Some of these eyecups are designed asymmetrically in order to better protect the outside of the eye from stray light.

### Field stop

The field stop of an eyepiece lies in the focal plane of the objective and thus limits the size of the image viewed through the eyepiece. Depending on the construction of the eyepiece, the field stop is in front of or inside the optics of the eyepiece. With simple eyepiece designs such as the common Kellner, Plössl or Erfle eyepieces or their modifications, the field stop is in front of the lenses of the eyepiece. The field stop is usually designed as a ring in the eyepiece socket and (as seen from the objective) is visible in front of the lenses of the eyepiece. The field stop serves, on the one hand, to conceal image areas in which imaging errors of the eyepiece are present and, on the other hand, to prevent stray light from these areas from entering the lens system of the eyepiece. If the field stop of an eyepiece is removed, the field of view can increase. The edge of the enlarged field of view is then darkened by vignetting and is usually no longer sharply delimited. In order to achieve the maximum field of view in the case of eyepieces with a long focal length in relation to the plug diameter, the field stop is sometimes omitted by the manufacturer and the plug-in sleeve is used as a field stop. In this construction, the maximum size of the field diaphragm results from the plug-in dimension minus twice the material thickness of the receptacle. Vignetting at the edge of the field of view has to be accepted, however, since the cone of light from the lens is conical and the outer area of ​​the cone of light is then cut off. Modern eyepiece designs since the Nagler eyepiece have a field stop that sits inside the eyepiece.

On the field side of almost all eyepieces in sizes 1.25 and 2 inches, there is a filter thread on the inside at the front end of the receptacle , which can accommodate filter adapters. A Barlow lens can also be screwed in there without its rear receptacle. This reduces the extension factor of the focal length, as the distance to the eyepiece is now much smaller than intended. With the field lens of a Barlow with 2x magnification , you can achieve a factor of approx. 1.4x.

However, since there is no real standard in thread diameter and even more in thread pitch, it can sometimes happen that a filter or other accessories do not fit or can only be screwed on approx. 1 to 2 turns.

### Receptacle

The receptacle is the field-side, front part of the eyepiece. The receptacle ideally disappears completely in the focuser and is held there by one or two knurled screws or a clamping ring. The outside of the receptacle is smooth to enable the eyepiece to be swapped with little clamping. The inside, however, is intentionally rough; Often it is provided with the filter thread throughout and it is darkened with a matt black color. Both measures reduce the stray light that always occurs .

### Attachment to the telescope: focuser

The focuser takes the eyepiece of a telescope. It is attached to the tube of a telescope where the bundled light has its focal point and emerges from the telescope. With the Newton telescope this is on the top side of the tube, with the Cassegrain telescope and with telescopes at the rear end. The eyepieces are inserted into the focuser. The eyepiece can then be focused on a setting wheel so that the possibly virtual field plane of the eyepiece coincides with the focal plane of the telescope.

## properties

Beam path in the telescope with eyepiece and dimensions
Various eyepieces for amateur telescopes ;
v. l. n. r: 5 mm, 9 mm, 20 mm, 50 mm with 2 ″ dimensions

### Back focus

The back focus is the distance from the contact surface of the eyepiece to its possibly virtual field plane . Eyepieces from different manufacturers or types have different dimensions. In practice this means that the focus must be readjusted after changing the eyepiece. Sufficient back focus is necessary for this.

### Pupillary distance

The interpupillary distance is defined by the distance from the point of intersection of all emerging bundles of parallel rays (exit pupil intercept) to the eye lens of the eyepiece. If the eye relief is very short, z. B. Eyeglass wearers with glasses attached can no longer see the full image of the eyepiece. In the case of eyepieces with a small eye relief, the eyelashes can also touch the lens of the eye and contaminate them. Too great a distance between the eyes makes it difficult to keep the head still, as contact with the eyepiece can be lost and the image wanders back and forth with the slightest movement of the viewer. Some eyepieces therefore offer an adjustment option; the rear edge of the eyepiece can be unscrewed so that the eye can touch the eyepiece.

The distance to the eye lens of the eyepiece must not be confused with the biological eye distance .

### Exit pupil

The exit pupil (AP) is a measure of the apparent size of the image of the aperture diaphragm in the focus point. If the exit pupil of the eyepiece is larger than the opening of the iris of your own eye , “light is lost” because not all of the light that is collected by the objective can enter the eye. If the AP is too small, the diffraction at the exit pupil limits the resolution of the optical system. One speaks of “empty magnification” because the nominal magnification factor of the optical system is greater than the smallest magnification factor at which the same resolution is achieved. If the exit pupil of the eyepiece is too small, the diffraction phenomena due to the low AP become dominant over the image information in the spatial area . The minimum useful AP is around 0.5 mm.

The entrance pupil of the human eye is the maximum opening of the iris and it decreases with age. Children still have an entrance pupil of approx. 8 mm, adults around 40 years often only have an EP of 6 mm.

### Focal length and magnification

The focal length of an eyepiece is specified in millimeters and, together with the focal length of the lens, determines the magnification of the optical device in which it is used (the smaller the focal length, the higher the magnification). For example, if a telescope has a focal length of 2000 mm and the eyepiece of 20 mm, the result is a magnification of 100 × (one hundred times). This formula results for the magnification calculation:

${\ displaystyle v = {\ frac {F _ {\ text {Lens}}} {F _ {\ text {eyepiece}}}}}$

With magnification and the lens and eyepiece focal length. ${\ displaystyle v =}$${\ displaystyle F _ {\ text {Lens}}}$${\ displaystyle F _ {\ text {eyepiece}}}$

If the focal length is not known, because z. B. If no information can be found on the eyepiece, it can be determined. You need:

• the entrance pupil of the instrument. In the case of telescopes, this is the free diameter of the front lens or the main mirror.${\ displaystyle EP}$
• The exit pupil ( measuring the AP )${\ displaystyle AP}$
• and the focal length of the instrument.${\ displaystyle F _ {\ text {Lens}}}$

All details in the same unit of length , millimeters are common.

${\ displaystyle F _ {\ text {eyepiece}} = {\ frac {F _ {\ text {lens}} \ cdot AP} {EP}}}$

### True field of view or field of view number

From the diameter d of the field diaphragm and the focal length f of the telescope, the true field of view of a telescope-eyepiece combination, i.e. the section in the sky, can easily be calculated:

${\ displaystyle {\ text {wGF}} \ lbrack ^ {\ circ} \ rbrack = 2 \ cdot \ arctan \ left ({\ frac {d} {2 \ cdot f}} \ right)}$

The formula does not apply to Huygens and Mittenzwey eyepieces, as there is an optical system in front of the field diaphragm which changes the size of the image created by the telescope optical system.

In light microscopy , the size of the observable area is indicated by the number of fields of view .

### Apparent field of view

By definition, the apparent field of view is the angle at which the image appears to an observer - i.e. the angle formed by the rays from the upper and lower edge of the image. The apparent field of view determines how “tunnel-like” the view through the optical instrument is. The field of view is given in degrees . A large field of view apparently allows the observer to penetrate deeper into the image because it depicts objects at the edge that would be cut off with a smaller field of view. From a field of view of approx. 60 ° one speaks of a wide-angle eyepiece. Eyepieces with fields of view of approx. 30 ° to 120 ° are currently available for amateur telescopes.

For a field stop with the diameter, the following applies - assuming a distortion-free image - analogous to the formula for the true field of view: ${\ displaystyle \ textstyle d}$

${\ displaystyle \ tan {\ frac {sGF} {2}} = {\ frac {d} {2 \ cdot F}}}$

and thus:

${\ displaystyle \ tan {\ frac {sGF} {2}} = {\ frac {f} {F}} \ cdot \ tan {\ frac {wGF} {2}}}$

This is the focal length of the eyepiece and the focal length of the lens. ${\ displaystyle F}$${\ displaystyle f}$

At small angles, i.e. for objects close to the optical axis, the magnification of the system is therefore approximate . For large angles, however, the relationship applies ${\ displaystyle \ textstyle {\ frac {f} {F}}}$

${\ displaystyle sGF = 2 \ cdot \ arctan \ left \ lbrack {\ frac {f} {F}} \ cdot \ tan {\ frac {wGF} {2}} \ right \ rbrack \ quad.}$
Barlow element on the eyepiece

### Plug dimension or diameter

The plug dimension is the outer diameter of the receptacle of the eyepiece. This dimension is given in inches . Three dimensions are common in amateur astronomy:

• 0.96 ″, is either from a very simple telescope in the lowest price range or out of date,
• 1.25 ″ is a very common measurement; it is often used for eyepieces with smaller focal lengths, focal lengths up to 32 mm for Plössls or 25 mm for Erfles are useful,
• 2 ″, is a plug-in size for eyepieces, usually with a particularly long focal length from 28 mm and higher.

In the case of focusers with a 2 ″ connector, the focuser is often supplied with an adapter to reduce it to 1.25 inches.

With a plug-in dimension of 1.25 inches, the inner diameter of the receptacle is approx. 30 mm; this is at the same time the maximum possible field diaphragm with this plug dimension. Since the field stop required to achieve a certain apparent field of view increases with longer focal length, the inner diameter limits sensible focal lengths of the eyepiece to the 32 mm mentioned above (based on a minimum desired apparent field of view of 50 °). A Plössl with a focal length of 40 millimeters can, however, be used sensibly if, with a shorter focal length, the exit pupil that can be achieved on a telescope would be too small for an object with low surface brightness.

Occasionally you can still find eyepieces with a 31 mm socket diameter, the old German plug size.

Spotting scopes and some older telescopes have screw connections instead of plug systems.

## Eyepiece types

### Single lens eyepieces

Galileo: only virtual field stop
• Galilean eyepiece
The Galilean eyepiece consists of only a single biconcave lens and does not allow pupil imaging (and therefore no crosshairs). It was first practically implemented (1608 in Holland) and re-invented by Galileo.
Today it is mostly used in cheap equipment to maintain an upright image. But it is also used in optics where only a weak magnification is required - for example with opera glasses (“
opera gazers”).
Kepler eyepiece: real field stop
• Kepler eyepiece
The Kepler eyepiece consists of a simple biconvex or plano-convex converging lens and allows pupil imaging (real image in the focal point of the lens, thus the possibility of a crosshair ). However, the picture is upside down. The image field is limited by the errors of a single lens, there is no color correction. This is only possible with a combination of at least two lenses:

### Multi-lens eyepieces

Huygens eyepiece
• Huygens eyepiece
Huygens proved through calculations around 1670 that the color errors ( chromatic aberration ) in the areaclose tothe axis can be reduced significantly if the simple eyepiece lens is replaced by a system of two plano-convex lenses at a suitable distance. This type of eyepiece is still used in inexpensive devices.
Mittenzwey eyepiece
• Mittenzwey eyepiece
by Moritz Mittenzwey , 18th century. It is similar to the Huygens eyepiece, but instead of the plane lenses it has two menisci. This enlarges the field of view up to 50 °.
Ramsden eyepiece
• Ramsden eyepiece
The Ramsden eyepiece was developed by Jesse Ramsden (1735–1800), probably without any knowledge of the Huygens eyepiece. Like this one, it has two plano-convex lenses, but the first lens is turned upside down, its flat side points towards the objective . The eyepiece has similar properties to the Huygens eyepiece, but there is an intermediate image area on the flat side of the first lens, so thatline marks can be used for measuring purposes ina crosshair eyepiece . The exit pupil lies on the flat side of the eye lens, which is why the field of view cannot be seen completely. This can be changed by moving the lenses together, but the achromatic condition is no longer met. The Kellner eyepiece offers a remedy.

### Kellner and monocentric eyepieces

Waiter's eyepiece
• Kellner's eyepiece
The Ramsden eyepiece was improved by Carl Kellner in 1847 by replacing the lens on the eye side with a cemented pair of lenses ( achromatic lenses ) for color correction. The field lens remained a simple, biconvex convergent lens. In addition to reducing the color fringes, the lens combination also reduced the distortions that were normal in microscopes at the time . In amateur astronomy , the inexpensive eyepiece was part of the basic equipment of simple telescopes until the 1970s and is still in cardboard kits today.
Monocentric eyepiece
• Monocentric eyepiece
The monocentric eyepiece was invented by Steinheil around 1880. It consists of a symmetrical biconvex barium crown glass lens that is enclosed by two flint glass menisci. As with the Steinheil Aplanat , the lens surfaces have a common center point. Here the color error is completely corrected. Since the lenses are cemented, this eyepiece is very low in stray light and reflection. The eye relief is 0.85 times the focal length , the apparent field of view is 28 °. It is unsuitable for powerful telescopes.

### Orthoscopic eyepieces

Orthoscopic means "seeing correctly". The term is used for eyepieces that have fewer image errors than simpler variants. Carl Kellner also called his new development, which is now named after him, "orthoscopic eyepiece". However, it is no longer referred to in today's language.

Abbe orthoscopic eyepiece
• Orthoscopic eyepiece according to Ernst Abbe
This eyepiece consists of a field stop , a cemented group of three and a plano-convex lens. The eyepiece corrects very well thanks to the four glass-air surfaces. The group of three consists of a biconcave lens enclosed by two biconvex lenses. This eyepiece is considered the standard for astronomical observations.
König orthoscopic eyepiece
• Orthoscopic eyepiece according to Albert König
It also consists of a field stop and a plano-convex lens on the side of the eye. The cemented pair consists of a plano-concave and a biconvex lens. The construction saves a lens, but requires higher quality glasses. Otherwise the properties are comparable with those of the construction according to Abbe.

### Plössl and Erfle eyepieces

Plössl eyepiece
• Plössl eyepiece
The
Plössl eyepiece inventedby Simon Plössl consists of two achromatic lenses facing each other, i.e. two cemented groups of two for color correction. The color errors are completely corrected. The performance is comparable to that of the Abbe orthoscopic eyepiece, while the cost may be lower. Most eyepieces today are of this type.

Erfles tend to astigmatism , an elliptical distortion of light sources , at the edge of the field of view . Internal reflections ("ghosting") can also occur easily . This makes Erfle eyepieces for observing bright objects, e.g. B. of planets , less suitable in observational astronomy . On the other hand, they are well suited for faint, extended objects such as open star clusters and reflection nebulae .

Erfle eyepieces are comparatively cheap to manufacture. They are therefore still produced today for amateur astronomy or wide-angle binoculars.

### Six-lens eyepiece

Another six-lens eyepiece consists of a Plössl that has been expanded to include a cemented eye group. The last group consists of a plano-convex and a plano-concave lens, the latter only having a very weak refractive power .

### Nagler eyepiece

Ultra-wide Nagler eyepiece, type 2
Nagler eyepieces
The nailer consists of 3 cemented pairs and a planoconvex lens. The Nagler eyepieces are built as wide-angle eyepieces with an apparent field of view of 82 °. High image quality can only be achieved with variants with an aspherical surface or an additional 8th lens. These eyepieces can also be used on very bright telescopes, even more so than the Panoptic from the same manufacturer.

### Zoom eyepieces

Due to their variable focal length, zoom eyepieces do not image as well as eyepieces with a fixed focal length. This is due to the fact that lenses that produce aberrations and corrective lenses only work together optimally at certain distances from one another. With variable focal lengths, however, the distances between the lenses - and thus the effectiveness of the error correction - are also variable. Zoom eyepieces offered for astronomy have a largest zoom factor of up to 3, so with the minimum focal length you have three times the magnification as with the maximum.
However, most zoom eyepieces have a very small field of view, which gradually increases with decreasing focal length, i.e. with increasing magnification. Another disadvantage is the lack of homofocality, so you have to readjust the focus after changing the focal length.
There are also extended types with aspherical surfaces. Due to the manufacturing process, the hyperbolic surfaces drive up the costs.

## More lens elements

### Barlow lens

Barlow lens (1.25 inch) without spacer tube

The Barlow lens is mounted between the focuser and the eyepiece and extends the focal length of the objective. With regard to the magnification and exit pupil, this amounts to shortening the focal length of the eyepiece, but not with regard to the interpupillary distance.

### Shaple lens

The shape lens is the opposite of the Barlow lens: it shortens the focal length of the lens. See: Barlow lens

### Field flattening lens

Field flattening lens with M-48 thread

It is also called a flattener and is a lens that is mainly used for astrophotography. With telescopes it flattens the field of view, which is usually slightly curved. Due to this curvature, stars are shown more and more blurred towards the edge. The flattener removes this blurring; it itself has no enlarging or reducing effect, but merely corrects the image field. However, the distance to the film or sensor plane of the camera is specified and is generated with intermediate rings.

2 inch coma corrector lens

### Coma corrector

The coma corrector is like the flattener (field flattening lens) a corrective lens, but especially for Newtonian telescopes . In parabolic mirrors, it corrects the imaging error coma , which occurs off the optical axis and looks like the tail of a comet (hence the name). There are K. with and without a focal length extension, depending on the design.

### Binocular approach

Binocular attachment
1  eyepiece, 2  compensation piece, 3  prism, 4  beam  path splitter , 5  housing, 6 Barlow lens
Binocular approach

A binocular approach is a beam splitter for viewing an object with both eyes. Two identical eyepieces are used at its rear end. Binocular vision has advantages; Especially with the moon and planets, observation with both eyes enables more details to be recognized. The relaxed observation also prevents symptoms of fatigue. However, the increased weight makes the instrument vibrate more easily, and each eyepiece that is to be used for observation has to be purchased twice. The built-in Barlow lens reduces the back focus , but cannot completely compensate for it, so that a B. is not suitable for every telescope or every eyepiece. The additional optical elements also reduce both image brightness and image quality.