# Eyepiece

For the device for looking through a camera, see viewfinder.
File:Eyepieces random selection.jpg
A collection of different types of eyepieces.

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 it to focus creating an image. The eyepiece is placed at the focal point of the objective to magnify this image. The amount of magnification depends on the focal length of the eyepiece.

An eyepiece consists of several "lens elements" in a housing, with a "barrel" on one end. The barrel is shaped to fit in a special opening of the instrument to which it is attached. The image can be focused by moving the eyepiece nearer and further from the objective. Most instruments have a focusing mechanism to allow movement of the shaft in which the eyepiece is mounted, without needing to manipulate the eyepiece directly.

The eyepieces of binoculars are usually permanently mounted in the binoculars, causing them to have a pre-determined magnification and field of view. With telescopes and microscopes, however, eyepieces are usually interchangeable. By switching the eyepiece, the user can adjust what is viewed. For instance, eyepieces will often be interchanged to increase or decrease the magnification of a telescope. Eyepieces also offer varying fields of view, and differing degrees of eye relief for the person who looks through them.

Modern research-grade telescopes do not use eyepieces. Instead, they have high-quality CCD sensors mounted at the focal point, and the images are viewed on a computer screen. Some amateur astronomers use their telescopes the same way, but direct optical viewing with eyepieces is still very common.

## Eyepiece properties

Several properties of an eyepiece are likely to be of interest to a user of an optical instrument, when comparing eyepieces and deciding which eyepiece suits their needs.

### Design distance to entrance pupil

Eyepieces are optical systems where the entrance pupil is invariably located outside of the system. They must be designed for optimal performance for a specific distance to this entrance pupil (i.e. with minimum aberrations for this distance). In a refracting astronomical telescope the entrance pupil is identical with the objective. This may be several feet distant from the eyepiece; whereas with a microscope eyepiece the entrance pupil is close to the back focal plane of the objective, mere inches from the eyepiece. Microscope eyepieces may be corrected differently from telescope eyepieces; however, most are also suitable for telescope use.

### Elements and Groups

Elements are the individual lenses, which may come as simple lenses or "singlets" and cemented doublets or (rarely) triplets. When lenses are cemented together in pairs or triples, the combined elements are called groups (of lenses).

The first eyepieces had only a single lens element, which delivered highly distorted images. Two and three-element designs were invented soon after, and quickly became standard due to the improved image quality. Today, engineers assisted by computer-aided drafting software have designed eyepieces with seven or eight elements that deliver exceptionally large, sharp views.

### Internal reflection and scatter

Internal reflections, sometimes called scatter, cause the light passing through an eyepiece to disperse and reduce the contrast of the image projected by the eyepiece. When the effect is particularly bad, "ghost images" are seen, called ghosting. For many years, simple eyepiece designs with a minimum number of internal air-to-glass surfaces were preferred to avoid this problem.

One solution to scatter is to use thin film coatings over the surface of the element. These thin coatings are only one or two wavelengths deep, and work to reduce reflections and scattering by changing the refraction of the light passing through the element. Some coatings may also absorb light that is not being passed through the lens in a process called total internal reflection where the light incident on the film is at a shallow angle.

Mikefitzman (talk) 12:12, 20 January 2008 (UTC)===Chromatic aberration === Lateral chromatic aberration is caused because the refraction at glass surfaces differs for light of different wavelengths. Blue light, seen through an eyepiece element, will not focus to the same plane as red light. The effect can create a ring of false colour around point sources of light and results in a general blurriness to the image.

One solution is to reduce the aberration by using multiple elements of different types of glass. Achromats are lens groups that bring two different wavelengths of light to the same focus and exhibit greatly reduced false colour. Low dispersion glass may also be used to reduce chromatic aberration.

Longitudinal chromatic aberration is a pronounced effect of optical telescope objectives, because the focal lengths are so long. Microscopes, whose focal lengths are generally shorter, do not tend to suffer from this effect.

### Focal length

The focal length of an eyepiece is the distance from the principal plane of the eyepiece where parallel rays of light converges to a single point. When in use, the focal length of an eyepiece, combined with the focal length of the telescope or microscope objective, to which it is attached, determines the magnification. It is usually expressed in millimetres when referring to the eyepiece alone. When interchanging a set of eyepieces on a single instrument, however, some users prefer to refer to identify each eyepiece by the magnification produced.

For telescope, the angular magnification produced by the combination of a particular eyepiece and telescope or microscope combination can be calculated with the following formula:

${\displaystyle \mathrm {MA} ={\frac {f_{O}}{f_{E}}}}$

where:

• ${\displaystyle \mathrm {MA} }$ is the calculated angular magnification.
• ${\displaystyle f_{O}}$ is the focal length of the telescope objective.
• ${\displaystyle f_{E}}$ is the focal length of the eyepiece, expressed in the same units of measurement as ${\displaystyle f_{T}}$.

For a compound microscope the corresponding formula is

${\displaystyle \mathrm {MA} ={\frac {DD_{\mathrm {EO} }}{f_{O}f_{E}}}={\frac {D}{f_{E}}}\times {\frac {D_{\mathrm {EO} }}{f_{O}}}}$

where

• ${\displaystyle D}$ is the distance of closest distinct vision (usually 250 mm)
• ${\displaystyle D_{\mathrm {EO} }}$ is the distance between the back focal plane of the objective and the back focal plane of the eyepiece (called tube length) typically 160 mm for a modern instrument.
• ${\displaystyle f_{O}}$ is the objective focal length and ${\displaystyle F_{E}}$ is the eyepiece focal length.

Magnification increases, therefore, when the focal length of the eyepiece is shorter, or when the focal length of the instrument is longer. For example, a 25 mm eyepiece in a telescope with a 1200 mm focal length would magnify objects 48 times. A 4 mm eyepiece in the same telescope would magnify 300 times.

Telescope eyepieces tend to be referred to by their focal length, by amateur astronomers. In astronomy, the focal length is usually expressed using millimetres, and typically ranges from about 3 mm to 50 mm. The actual magnification delivered at these focal lengths depends on the telescope.

Some astronomers do, however, prefer to specify the resulting magnification power, rather than the focal length, when describing the eyepiece used for observations. It is often more convenient to express magnification in observation reports, as it gives a more immediate impression of what view the observer actually saw. Due to its dependence on properties of the particular telescope in use, however, magnification power alone is meaningless for describing a telescope eyepiece.

By convention Microscope eyepieces are usually specified by power instead of focal length. Microscope eyepiece power ${\displaystyle P_{\mathrm {E} }}$ and objective power ${\displaystyle P_{\mathrm {O} }}$ are defined by

${\displaystyle P_{\mathrm {E} }={\frac {D}{f_{E}}},\qquad P_{\mathrm {O} }={\frac {D_{\mathrm {EO} }}{f_{O}}}}$

thus from the expression given earlier for the angular magnification of a compound microscope

${\displaystyle \mathrm {MA} =P_{\mathrm {E} }\times P_{\mathrm {O} }}$

This definition of power relies upon an arbitrary decision to split the angular magnification of the instrument into separate factors for the eyepiece and the objective. Historically Abbe described microscope eyepieces using a different decomposition in terms of angular magnification of the eyepiece and `initial magnification' of the objective. While convenient for the optical designer, this turned out to be less convenient from the viewpoint of practical microscopy and was abandoned.

Common eyepiece powers are 8X, 10X, 15X, and 20X. These powers assume the generally accepted visual distance of closest focus ${\displaystyle D}$ of 250 mm, so the focal length of the eyepiece can be calculated by dividing the eyepiece power into 250 mm. Although the accepted standard focal length is 250 mm, microscopes are now built with 160 mm focal lengths, to allow for them to be more compact. Modern instruments may also use objectives designed for an infinite tube length (with an auxiliary correction lens in the tube).

The total angular magnification of a microscope image is calculated by multiplying the eyepiece power by the objective power. For example, a 10X eyepiece with a 40X objective will magnify the image 400 times.

### Location of focal plane

In some eyepiece types, such as Ramsden eyepieces (described in more detail below), the focal plane is located outside of the eyepiece in front of the field lens, consequently the eyepiece will behave like a magnifier. This is therefore accessible as a location for a graticule or micrometer crosswires. In the Huygenian eyepiece the focal plane is located between the eye and field lenses inside the eyepiece and is hence not accessible.

### Field of view

Main article: Field of view

The field of view, often abbreviated FOV, describes the area of a target (measured as an angle from the location of viewing) that can be seen when looking through an eyepiece. The field of view seen through an eyepiece varies, depending on the magnification achieved when connected to a particular telescope or microscope, and also on properties of the eyepiece itself. Eyepieces are differentiated by their field stop, which is the narrowest aperture that light entering the eyepiece must pass through to reach the field lens of the eyepiece.

Due to the effects of these variables, the term "field of view" nearly always refers to one of two meanings.

• Actual field of view is the angular size of the amount of sky that can be seen through an eyepiece when used with a particular telescope, producing a specific magnification. It is typically between one tenth of a degree, and two degrees.
• Apparent field of view is a derived constant value for a given eyepiece. By itself, the apparent field of view is only an abstract value, but it can be used to calculate what the actual field of view will be when the eyepiece is combined with a telescope to produce a particular magnification. The measurement ranges from 35 to over 80 degrees. The apparent field of view of an eyepiece is often stated in eyepiece specifications, as it provides a convenient method for a user to calculate the actual field of view with their own telescope.

It is common for users of an eyepiece to want to calculate the actual field of view, because it indicates how much of the sky will be visible when the eyepiece is used with their telescope. The most convenient method of calculating the actual field of view depends on whether the apparent field of view is known.

If the apparent field of view is known, the actual field of view can be calculated from the following approximate formula:

${\displaystyle FOV_{C}={\frac {FOV_{P}}{mag}}}$
or
${\displaystyle FOV_{C}={\frac {FOV_{P}}{({\frac {f_{T}}{f_{E}}})}}}$

where:

• ${\displaystyle FOV_{C}}$ is the actual field of view, calculated in the unit of angular measurement in which ${\displaystyle FOV_{P}}$ is provided.
• ${\displaystyle FOV_{P}}$ is the apparent field of view.
• ${\displaystyle mag}$ is the magnification.
• ${\displaystyle f_{T}}$ is the focal length of the telescope.
• ${\displaystyle f_{E}}$ is the focal length of the eyepiece, expressed in the same units of measurement as ${\displaystyle f_{T}}$.

The focal length of the telescope objective is the diameter of the objective times the focal ratio. It represents the distance at which the mirror or objective lens will cause light to converge on a single point.

The formula is accurate to 4% or better up to 40° apparent field of view, and has a 10% error for 60°.

If the apparent field of view is unknown, the actual field of view can be approximately found using:

${\displaystyle FOV_{C}={\frac {57.3d}{f_{T}}}}$

where:

• ${\displaystyle FOV_{C}}$ is the actual field of view, calculated in degrees.
• ${\displaystyle d}$ is the diameter of the eyepiece field stop in mm.
• ${\displaystyle f_{T}}$ is the focal length of the telescope, in mm.

The second formula is actually more accurate, but field stop size is not usually specified by most manufacturers. The first formula will not be accurate if the field is not flat, or is higher than 60° which is common for most ultra-wide eyepiece design.

### Barrel diameter

Eyepieces for telescopes and microscopes are usually interchanged to increase or decrease the magnification and to allow the user to select a type with a certain performance characteristic. To allow this eyepieces come in standardized "Barrel diameters".

#### Telescope eyepieces

File:Eyepiece three types.jpg
Examples (from left to right) of a 2 inch (50.8 mm), a 1¼ inch (31.75 mm), and a 0.965 inch (24.5mm) eyepiece.

There are three standard barrel diameters for telescopes. The barrel sizes are usually expressed using inches.

• The smallest standard telescope barrel diameter is 0.965 inches (24.5mm), but has been largely abandoned. The only telescopes still manufactured that use this size are poor-quality telescopes usually found in toy stores and shopping malls. Many of these eyepieces that come with such telescopes are plastic, and some even have plastic lenses. High-quality telescope eyepieces with this barrel size are no longer manufactured.
• The most popular telescope eyepiece barrel diameter is 1¼ inches (31.75mm). The practical upper limit on focal lengths for eyepieces with 1¼ inch (31.75mm) barrels is about 32 mm. With longer focal lengths, the edges of the barrel itself intrude into the view limiting its size. With focal lengths longer than 32 mm, the available field of view falls below 50°, which most amateurs consider to be the minimum acceptable width. These barrel sizes are threaded to take 30 mm filters.
• Telescope eyepieces with 2 inch (50.8 mm) barrels are also available. The Larger 2 inch (50.8 mm) size helps alleviate the limit on focal lengths. The upper limit of focal length with 2 inch eyepieces is about 50 mm. The trade-off is that these eyepieces are usually more expensive, won't fit in some telescopes, and may be heavy enough to tip the telescope. These barrel sizes are threaded to take 48 mm filters (or rarely 49 mm).

#### Microscope eyepieces

Microscopes have standard barrel diameters measured in millimeters: 23.2mm and 30mm, slightly smaller than telescope barrels.

### Eye relief

Main article: Eye relief

The eye needs to be held at a certain distance behind the eye lens of an eyepiece to see images properly through it. This distance is called the eye relief. A larger eye relief means that the optimum position is further from the eyepiece, making it easier to view an image. However, if the eye relief is too large it can be uncomfortable to hold the eye in the correct position for an extended period of time, for which reason some eyepieces with long eye relief have cups behind the eye lens to aid the observer in maintaining the correct observing position. The eye pupil should coincide with the Ramsden disc, the image of the entrance pupil, which in the case of an astronomical telescope corresponds to the object glass.

Eye relief typically ranges from about 2 mm to 20 mm, depending on the construction of the eyepiece. Long focal-length eyepieces usually have ample eye relief, but short focal-length eyepieces are more problematic. Until recently, and still quite commonly, eyepieces of a short-focal length have had a short eye relief. Good design guidelines suggest a minimum of 5-6 mm to accommodate the eyelashes of the observer to avoid discomfort. Modern designs with many lens elements, however, can correct for this, and viewing at high power becomes more comfortable. This is especially the case for spectacle wearers, who may need up to 20 mm of eye relief to accommodate their glasses.

## Eyepiece designs

Technology has developed over time and there are a variety of eyepiece designs for use with optical telescopes. They vary in their internal lens configuration and different designs are sometimes more appropriate both for different types of viewing, and for different types of telescope. Eyepiece designs include Huygens, Ramsden, Kellner, Orthoscopic, Erfle, König, Plössl, RKE, and Nagler. These are described in more detail below.

### Huygens

The two element Huygens eyepiece was invented by Christiaan Huygens in the 17th century. This optical design is now considered obsolete. Their main use in optics is as an example of the simplest possible compound lens design.

Despite being deprecated, these eyepieces are inexpensive to make and so are often sold with the cheapest telescopes and microscopes. Huygens eyepieces suffer from short eye relief, high image distortion (especially on short focus telescopes), chromatic aberration and have very narrow apparent field of view.

Essentially their only good use is for projection of a solar image onto a screen. Because Huygens eyepieces do not contain cement to hold the lens elements, they are less likely to be damaged by the intense, concentrated light of sun. Lens cement can overheat and either dissolve or burn.

Huygens eyepieces consist of two plano-convex lenses with the plane sides towards the eye separated by an air gap. The lenses are called the eye lens and the field lens. It is usually designed for zero transverse chromatic aberration. The focal plane is located between the two lenses. If the lenses are made of glass of the same refractive index, to be used with a relaxed eye and a telescope with an infinitely distant objective then the separation is given by:

${\displaystyle d={\frac {1}{2}}(f_{A}+f_{B})}$

where ${\displaystyle f_{A}}$ and ${\displaystyle f_{B}}$ are the focal lengths of the component lenses.

### Ramsden

The Ramsden eyepiece, created by astronomical and scientific instrument maker Jesse Ramsden in the 18th century, comprises two plano convex lenses with the same focal length and glass, placed less than one focal length apart. The separation varies between different designs, but is typically somewhere between 7/10 and 7/8 of the focal length of the lenses, the choice being a trade off between residual transverse chromatic aberration (at low values) and at high values running the risk of the field lens touching the focal plane when used by an observer who works with a close virtual image such as a myopic observer, or a young person whose accommodation is able to cope with a close virtual image (this is a serious problem when used with a micrometer as it can result in damage to the instrument).

A separation of exactly 1 focal length is also inadvisable since it renders the dust on the field lens disturbingly in focus. The two curved surfaces face inwards. The focal plane is thus located outside of the eyepiece and is hence accessible as a location where a graticule, or micrometer crosshairs may be placed. Because a separation of exactly one focal length would be required to correct transverse chromatic aberration, it is not possible to correct the Ramsden design completely for transverse chromatic aberration. The design is slightly better than Huygens but still not up to today’s standards.

It remains highly suitable for use with instruments operating using near monochromatic light sources e.g. polarimeters.

### Kellner or "Achromat"

File:Kellner 25mm eyepiece.jpg
A 25 mm Kellner eyepiece

Carl Kellner designed this first modern achromatic eyepiece in 1850, also called an "achromatized Ramsden". Kellner eyepieces are a 3-lens design. An achromatic doublet is used in place of the eye lens in the Ramsden design to correct the residual transverse chromatic aberration. They are inexpensive and have fairly good image from low to medium power and are far superior to Huygenian or Ramsden design. The biggest problem of Kellner eyepieces was internal reflections. Today's anti-reflection coatings make these usable, economical choices for small to medium aperture telescopes with focal ratio f/6 or longer.

### Abbe or "Ortho"

The 4-element Abbe eyepiece was invented by Ernst Abbe in 1880, and is called "orthoscopic" or "orthographic" because of its low degree of distortion; usually the eyepiece is simply called an "ortho". The Abbe design uses a convex-convex triplet field lens and a convex-flat singlet eye lens. Orthos have nearly perfect image quality and good eye relief, but a little bit narrow apparent field of view — about 40°–45°.

Until the advent of multicoatings and the popularity of the Plössl, orthos were the most popular design for telescope eyepieces. Even today these eyepieces are superior to most others for planetary and lunar viewing.

### Erfle

Erfles were invented during the first world war for military purposes, described in US patent by Heinrich Erfle number 1,478,704 of Aug 1921. They are a 5-element design which is a logical extension to wider fields of the four lens military eyepiece design. In effect, they are Plössls with extra lenses.

Erfle eyepieces are designed to have wide field of view (about 60 degrees), but they are unusable at high powers because they suffer from astigmatism and ghost images. However, with lens coatings at low powers (focal lengths of 20 mm and up) they are acceptable, and at 40 mm they can be excellent. Erfles are very popular because they have large eye lenses, good eye relief and can be very comfortable to use.

### König

The König eyepiece was designed in 1915 by German optician Albert König (1871−1946). The original design is a simplified Abbe, with a leading doublet instead of a triplet. The original design allows for high magnification with remarkably high eye relief — the highest eye relief proportional to focal length of any design before the Nagler, in 1979. The field of view of about 55° makes its performance similar to the Plössl, with the advantage of requiring one less lens.

König's original 1915 form is the simplest, and is composed of two lens groups: a concave-convex positive doublet and a convex~flat positive singlet. The strongly convex surfaces of the doublet and singlet face and (nearly) touch each other. The doublet has its concave surface facing the light source and the singlet has its almost flat (slightly convex) surface facing the eye.

Modern versions of Königs can use improved glass, or add more lenses, grouped into various combinations doublets and singlets. The most typical adaptation is to add a positive, concave-convex simple lens before the doublet, with the concave face towards the light source and the convex surface facing the doublet. Modern improvements typically have fields of view of 60°−70°.

### Plössl

File:Clave 25mm eyepiece.jpg
A 25 mm Plössl eyepiece

Originally designed by Georg Simon Plössl in 1860, several versions can be found on the amateur astronomy market. By far the Plössl eyepiece is currently the most widely used design. The name Plössl eyepiece covers a range of eyepieces with at least 4 optical elements. Usually consisting of two sets of doublets, a convex and concave element sandwiched together, the lens provides a large apparent field of view along with relatively large FOV. This makes this lens ideal for a variety of observational purposes including deep sky and planetary viewing.

The chief disadvantage of the Plössl optical design is short eye relief, which is restricted to about 70-80% of focal length. The short eye relief is more critical in short focal lengths, when viewing can become uncomfortable.

This eyepiece is one of the more expensive to manufacture because of the quality of glass, and the need for well matched convex and concave lenses to prevent internal reflections. Due to this fact, the quality of different Plössl eyepieces varies. There are notable differences between cheap Plössls with simplest anti-reflection coatings and well made ones.

### RKE

An RKE eyepiece is an adaptation of a Kellner eyepiece designed by Dr. David Rank for the Edmund Scientific Corporation, who marketed it throughout the late 1960s and early 1970s. This design provides slightly wider field of view than classic Kellner design.

There is some ambiguity about what RKE stands for. According to an e-mail from Edmund, RKE stands for Rank Kellner Eyepiece. Others speculate it stands for Rank Kellner Edmund or Reversed Kellner Eyepiece; the latter because the elements within the eyepiece in effect have been reversed from the Kellner design on which it is based. This arrangement makes the design similar to a widely spaced version of the König design.

### Nagler

Invented by Albert Nagler and patented in 1979, the Nagler eyepiece is a design optimized for astronomical telescopes to give an ultra-wide field of view (82°) that has good correction for astigmatism and other aberrations. This is achieved using exotic high-index glass and up to eight optical elements in 4 or 5 groups; there are 5 similar designs called the Nagler, Nagler type 2, Nagler type 4, Nagler type 5, Nagler type 6.

The number of elements in a Nagler makes them seem complex, but the idea of the design is fairly simple: every Nagler has a negative doublet field lens, which increases magnification, followed by several positive groups. The positive groups, considered separate from the first negative group, combine to have long focal length, and form a positive lens. That allows the design to take advantage of the many good qualities of low power lenses. In effect, a Nagler is a superior version of a Barlow lens combined with a long focal length eyepiece. This design has been widely copied in other wide field or long eye relief eyepieces.

The main disadvantage to Naglers is in their weight. Long focal length versions exceeding 0.5 kg, which is enough to unbalance many telescopes. Amateurs fondly refer to Naglers as "paperweights", because of their heft, or "hand grenades", because of their size and shape. Another disadvantage is a high purchase cost, with large Naglers prices comparable to the cost of a small telescope. Hence these eyepieces are regarded by many amateur astronomers as a luxury. [1]

## References

• A. E. Conrady, Applied Optics and Optical Design, Volume I. Oxford 1929.
• R. Kingslake, Lens Design Fundamentals. Academic Press 1978.
• H. Rutten and M. van Venrooij, Telescope Optics. Willmann-Bell 1988, 1989. ISBN 0-943396-18-2.