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 named because it is usually the lens that is closest to the eye when someone looks through an optical device to observe an object or sample. The objective lens or mirror collects light from an object or sample and brings it to focus creating an image of the object. The eyepiece is placed near the focal point of the objective to magnify this image to the eyes. 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.
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. 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 triplets. When lenses are cemented together in pairs or triples, the combined elements are called groups.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 produced by the combination of a particular eyepiece and objective can be calculated with the following formula:
where:
- is the focal length of the objective,
- is the focal length of the eyepiece.
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
where
- is the distance of closest distinct vision.
- is the distance between the back focal plane of the objective and the back focal plane of the eyepiece, typically 160 mm for a modern instrument.
- is the objective focal length and is the eyepiece focal length.
thus from the expression given earlier for the angular magnification of a compound microscope
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 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 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, 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 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.
;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. 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:
where:
- is the true field of view, calculated in whichever unit of angular measurement that is provided in;
- is the apparent field of view ;
- is the magnification.
Since where:
- is the focal length of the telescope;
- is the focal length of the eyepiece, expressed in the same units of measurement as
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 from a star to converge onto a single point.
If the apparent field of view is unknown, the actual field of view can be approximately found using:
where:
- is the actual field of view, calculated in degrees.
- is the diameter of the eyepiece field stop in mm.
- is the focal length of the telescope, in mm.
The above formulas are approximations. The ISO 14132-1:2002 standard gives the exact calculation for apparent field of view, from the true field of view, as:
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
An occasionally used approximation is
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°.