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.

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.

Chromatic aberration

Lateral or transverse 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 point but along the same axis 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 to where parallel rays of light converge 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 identify each eyepiece by the magnification produced.

For a telescope, the approximate angular magnification ${\displaystyle M_{\mathsf{A}}}$ produced by the combination of a particular eyepiece and objective can be calculated with the following formula:

${\displaystyle M_{\mathsf{A}}\approx \frac{f_{\mathsf{O}}}{f_{\mathsf{E}}}}$

where:

• ${\displaystyle f_{\mathsf{O}}}$ is the focal length of the objective,
• ${\displaystyle f_{\mathsf{E}}}$ is the focal length of the eyepiece.

Magnification increases, therefore, when the focal length of the eyepiece is shorter or the focal length of the objective 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.

Amateur astronomers tend to refer to telescope eyepieces by their focal length in millimeters. These typically range from about 3 mm to 50 mm. Some astronomers, however, prefer to specify the resulting magnification power rather than the focal length. 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.

For a compound microscope the corresponding formula is

${\displaystyle M_{\mathsf{A}}=\frac{D\cdot D_{\mathsf{E}\mathsf{O}}}{f_{\mathsf{E}}\cdot f_{\mathsf{O}}}=\frac{D}{f_{\mathsf{E}}}\cdot \frac{D_{\mathsf{E}\mathsf{O}}}{f_{\mathsf{O}}}}$

where

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

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

${\displaystyle P_{\mathsf{E}}=\frac{D}{f_{\mathsf{E}}},P_{\mathsf{O}}=\frac{D_{\mathsf{E}\mathsf{O}}}{f_{\mathsf{O}}}}$

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

${\displaystyle M_{\mathsf{A}}=P_{\mathsf{E}}\times P_{\mathsf{O}}}$

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

This definition of lens 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 differently, 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 thus subsequently abandoned.

The generally accepted visual distance of closest focus ${\displaystyle D}$ is 250 mm, and eyepiece power is normally specified assuming this value. Common eyepiece powers are 8×, 10×, 15×, and 20×. The focal length of the eyepiece (in mm) can thus be determined if required by dividing 250 mm by the eyepiece power.

Modern instruments often use objectives optically corrected for an infinite tube length rather than 160 mm, and these require an auxiliary correction lens in the tube.

Location of focal plane

In some eyepiece types, such as Ramsden eyepieces (described in more detail below), the eyepiece behaves as a magnifier, and its focal plane is located outside of the eyepiece in front of the field lens. This plane 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

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:

True or Telescope's field of view

For a telescope or binocular, the actual angular size of the span of sky that can be seen through a particular eyepiece, used with a particular telescope, producing a specific magnification. It ranges typically between 0.1–2 degrees. For a microscope, the actual width of the visible sample on the slide or sample tray, usually given in millimeters, but sometimes given as angular measure, like a telescope. For binoculars it is expressed as the actual field width in feet or in meters at some standard distance (typically either 100 feet or 30 meters, which are very nearly the same: 30 m is only a 2% smaller than 100 feet).

Apparent or Eye's field of view

For telescopes, microscopes, or binoculars, the apparent field of view is a measure of the angular size of the image seen by the eye, through the eyepiece. In other words, it is how large the image appears (as distinct from the magnification). Unless there is vignetting by the telescope's or microscope's body tube, this is constant for any given eyepiece with a fixed focal length, and may be used to calculate what the true field of view will be when the eyepiece is used with a given telescope or microscope. For modern eyepieces, the measurement ranges from 30–110 degrees, with all current good eyepieces being at least 50°, except for a few special-purpose eyepieces, such as some equipped with reticles.

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:

${\displaystyle T_{\mathsf{F}\mathsf{O}\mathsf{V}}\approx \frac{A_{\mathsf{F}\mathsf{O}\mathsf{V}}}{M}}$

where:

• ${\displaystyle T_{\mathsf{F}\mathsf{O}\mathsf{V}}}$ is the true field of view (on the sky), calculated in whichever unit of angular measurement that ${\displaystyle A_{\mathsf{F}\mathsf{O}\mathsf{V}}}$ is provided in;
• ${\displaystyle A_{\mathsf{F}\mathsf{O}\mathsf{V}}}$ is the apparent field of view (in the eye);
• ${\displaystyle M}$ is the magnification.

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

Since ${\displaystyle M=\frac{f_{\mathsf{T}}}{f_{\mathsf{E}}},}$ where:

• ${\displaystyle f_{\mathsf{T}}}$ is the focal length of the telescope;
• ${\displaystyle f_{\mathsf{E}}}$ is the focal length of the eyepiece, expressed in the same units of measurement as ${\displaystyle f_{\mathsf{T}};}$

The true field of view even without knowing the apparent field of view, given by:

${\displaystyle T_{\mathsf{F}\mathsf{O}\mathsf{V}}\approx \frac{A_{\mathsf{F}\mathsf{O}\mathsf{V}}}{\left[\frac{f_{\mathsf{T}}}{f_{\mathsf{E}}}\right]}=A_{\mathsf{F}\mathsf{O}\mathsf{V}}\times \frac{f_{\mathsf{E}}}{f_{\mathsf{T}}}.}$

The focal length of the telescope objective, ${\displaystyle f_{\mathsf{T}},}$ is the diameter of the objective times the focal ratio. It represents the distance at which the mirror or objective lens will cause light from a star to converge onto a single point (aberrations excepted).

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

${\displaystyle T_{\mathsf{F}\mathsf{O}\mathsf{V}}\approx \frac{57.3d}{f_{\mathsf{T}}}}$

where:

• ${\displaystyle T_{\mathsf{F}\mathsf{O}\mathsf{V}}}$ is the actual field of view, calculated in degrees.
• ${\displaystyle d}$ is the diameter of the eyepiece field stop in mm.
• ${\displaystyle f_{\mathsf{T}}}$ 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 designs.

The above formulas are approximations. The ISO 14132-1:2002 standard gives the exact calculation for apparent field of view, ${\displaystyle A_{\mathsf{F}\mathsf{O}\mathsf{V}},}$ from the true field of view, ${\displaystyle T_{\mathsf{F}\mathsf{O}\mathsf{V}},}$ as:

${\displaystyle \tan \left(\frac{A_{\mathsf{F}\mathsf{O}\mathsf{V}}}{2}\right)=M\times \tan \left(\frac{T_{\mathsf{F}\mathsf{O}\mathsf{V}}}{2}\right).}$

If a diagonal or Barlow lens is used before the eyepiece, the eyepiece's field of view may be slightly restricted. This occurs when the preceding lens has a narrower field stop than the eyepiece's, causing the obstruction in the front to act as a smaller field stop in front of the eyepiece. The exact relationship is given by

${\displaystyle A_{\mathsf{F}\mathsf{O}\mathsf{V}}=2\times \arctan \left(\frac{d}{2\times f_{\mathsf{E}}}\right).}$

An occasionally used approximation is

${\displaystyle A_{\mathsf{F}\mathsf{O}\mathsf{V}}\approx {57.3}^{\circ }\times \frac{d}{f_{\mathsf{E}}}.}$

This formula also indicates that, for an eyepiece design with a given apparent field of view, the barrel diameter will determine the maximum focal length possible for that eyepiece, as no field stop can be larger than the barrel itself. For example, a Plössl with 45° apparent field of view in a 1.25 inch barrel would yield a maximum focal length of 35 mm. Anything longer requires larger barrel or the view is restricted by the edge, effectively making the field of view less than 45°.

Barrel diameter

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

Telescope eyepieces

There are six standard barrel diameters for telescopes. The barrel sizes (usually expressed in inches) are:

• 0.965 inch (24.5 mm) – This is the smallest standard barrel diameter and is usually found in retail toy store and shopping mall telescopes. Many of these eyepieces that come with such telescopes are plastic, and some even have plastic lenses. High-end telescope eyepieces with this barrel size are no longer manufactured, but you can still purchase Kellner types.
• 1.25 inch (31.75 mm) – This is the most popular telescope eyepiece barrel diameter. The practical upper limit on focal lengths for eyepieces with 1.25″ barrels is about 32 mm. With longer focal lengths, the edges of the eyepiece barrel 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 for 30 mm filters.
• 2 inch (50.8 mm) – The larger barrel size in 2″ eyepieces helps alleviate the limit on focal lengths; it is the largest size commonly available. The upper limit of focal length with 2″ eyepieces is about 55 mm. The trade-off is that these eyepieces are usually more expensive, will not fit in some telescopes, and may be heavy enough to tip the telescope. These barrel sizes are threaded for 48 mm filters (or rarely 49 mm).
• 2.7 inch (68.58 mm) – 2.7″ eyepieces are only made by a few manufacturers. They allow for slightly larger fields of view. Many high-end focusers now accept these eyepieces.
• 3 inch (76.2 mm) – The even larger barrel size in 3″ eyepieces allows for extreme focal lengths and over 120° field of view eyepieces. The disadvantages are that these eyepieces are somewhat rare, extremely expensive, up to 5 lbs in weight, and that only a few telescopes have focusers large enough to accept them. Their huge weight causes balancing issues in Schmidt-Cassegrains under 10 inches, refractors under 5 inches, and reflectors under 16 inches. Also, due to their large field stops, without large-diameter secondary mirrors, most reflectors and Schmidt-Cassegrains will have severe vignetting with these eyepieces.
• 4 inch (102 mm) – Eyepieces this size are rare, and only commonly used for long refracting telescopes in older observatories. Very few manufacturers make them, and with the current popularity of short focal length / smaller focal ratio telescopes among amateurs, the demand for this size is low. They are sometimes improvised from re‑adapted lenses scavenged out of old cinema projectors.

Microscope eyepieces

Eyepieces for microscopes have a variety of barrel diameters, usually given in millimeters, such as 23.2 mm and 30 mm.

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 farther 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 exit pupil, 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.