Optical Definitions & Comments

1/4 Wave: a meaningless term unless the form of the measurement, and the wavelength of the light used for the units of measurement, are specified. In general, 1/4 wave refers to 1/4 wave deviation in the highest and lowest points of a given wavefront in the d-line, and is referred to as the "peak-to-valley" wavefront error. But this measure is not useful, because it does not indicate whether this deviation is across a large area of the wavefront or a small area. For example, if half of the wavefront is 1/4 wave advanced that of the other half, the images provided are likely to be quite horrible. However if only a percent or two of the wavefront is advanced by 1/4 wave, and the rest of the wavefront is perfect, the image will be nearly indistinguishable from perfect. Because wavefront errors like this are not weighted as to their areal severity, the usefulness of the measurement is almost zero. In general, a 1/4 wave telescope is mediocre at best. See also RMS Wavefront, Diffraction Limited, and Strehl Ratio.

Abbe, Ernst: born in 23 January 1840. Received his doctorate in 1861 with a dissertation on thermodynamics. Appointed to the University of Jena in 1870 and was director of its astronomical and meteorological observatories from 1878. He was made Research Director of  Carl-Zeiss Optical Works from 1866. He invented the apochromatic microscope in 1868. Abbe also originated the oil immersion lens, the condenser lens (for evenly illuminating microscopic fields) and provided a theoretical explanation of the limits of magnification. He also discovered what is now called the Abbe sine condition, which provides a way to make lenses that form a sharp, distortion-free image without the defects of coma and spherical aberration (see orthoscopic). From this work he eventually designed the Abbe orthoscopic in 1880, originally intended for use in microscopes as a measuring lens. This was the first clear and useful treatment of aberration, diffraction, and coma in optical design, and Carl Zeiss made Abbe a partner in the business in 1876 as a reward for these advances. In 1888, Abbe became the sole owner of Carl Zeiss Optical Works. He reorganized the firm, creating a pension fund and offering severance pay to discharged workers, and also implemented the 8 hour workday, holiday pay, and sick pay, all well ahead of their time; and is therefore of some note as a social or labor reformer. He also set up and endowed the Carl Zeiss Foundation for research in science and social improvement. He is the inventor of the Abbe refractometer. Died 14 January 1905.

Abbe number: a number indicating the dispersion of an optical substance. The d-line Abbe number ranges from about 20 to about 90 for modern optical glasses. The Abbe number is large when the glass is low dispersion.

Abbe orthoscopic: an eyepiece, in a 3-element field group and one-element eye group configuration, designed by Ernst Abbe. Aka aplanar eyepiee. It is orthoscopic in the optical sense (see Orthoscopic, below). In addition, this design is resistant to internal reflections (regardless of coatings) because of the curves on the interior facing elements. The design exhibits almost no astigmatism out to about 40 apparent degrees of field; at any given distance from the center, astigmatism in a Plossl is 1.5x and in a "five-element Plossl" 1.2x (with some variation due to different lens recipes) that of the Abbe orthoscopic. The Abbe orthoscopic has about as much eye relief as focal length (i.e., a 10mm Abbe orthscopic will have about 10mm of eye relief), or a little more. Originally, Abbe orthoscopics were made with crown and flint elements. In modern times, the recipe has been slightly modified to often include a rare earth element, as with Zeiss or University Abbe orthoscopics.

Achromat: a two-element lens which brings two colors to a common focus. Typically refers to a crown and flint cemented together, but achromats may be made of more exotic glasses. A simple achromat may be made by selecting a positive lens of half the absolute focal length of a negative lens with twice the dispersion of the positive lens, and mounting them very close together. In order to control spherical aberration, the negative lens will usually have a higher refractive index than the positive lens. A classical recipe is a positive crown of index 1.5 and an Abbe number of 60, and a negative flint with an index of about 1.6 and an Abbe number of about 35. Astigmatism and curvature of field cannot be completely corrected in a normal achromat.

Achromatic: literally, "no color." In optical work, refers to a lens system that brings two wavelengths of light to a common focus.

Afocal: refers to an optical system that does not form an image. A telescope with an eyepiece is afocal, because it does not form an image of its own (the optics of the eye must be used as a "re-imager").

Air: an optical element surrounding the earth, the index of refraction of which is 1.00029, but which, in glass catalogs, is often assumed to be 1. Chief cause of bad seeing and cloudy skies.

Anastigmatic: a term used to refer to an optical system that exhibits no astigmatism.

Angular Magnification Distortion: magnification of an object for rays parallel to the axis that varies with the distance of the ray bundle from the axis. This aberration affects the shape of the object and the apparent separation between two objects, but not the sharpness of the image. An easier way to think of this is to consider that the magnification of the eyepiece (or the scale of the camera lens, etc) varies across its field of view.

Aplanatic: a lens that minimizes spherical aberration and eliminates coma. This can be done with a single lens if the front and back surface power are in the ratio of F₁ = 6F₂. It can be done with two or more lenses with more flexibility.

Apochromatic: formally, a lens design that brings three wavelengths to a common focus. For various reasons, the formal definition is not very useful by itself. If color correction is plotted by wavelength against distance from focus, the lines will cross three times for an apochromat; but it is at least as important to keep the lines from diverging very much where they do not cross. Apochromatic refractors have three elements in their objectives, sometimes air spaced and sometimes oil spaced (e.g., Astro-Physics Starfires use oil-spaced objectives). Several optical designers have suggested that the best definition of "apochromatic" is driven by what is actually seen at the focal plane, and I agree this is more useful than the formal definition. See also semi-apo.

Astigmatism: canonically, astigmatism exists when there is a difference between the optical power of the optical system in the tangential plane and that in the sagittal plane. This can be better envisioned by two planes passing at right angles through the lens or mirror. The first of these passes through the object being viewed and the optical axis of the lens, and is called the tangential plane (or the meridional plane). The second is at right angles to this plane. Rays traveling along one of these planes are focused to a specific point in the focal plane. Rays along the other plane, however, are focused at a slightly different point. This produces two focal surfaces. These two focal surfaces touch each other on the optical axis, i.e., there is no astigmatism on axis and astigmatism is therefore an off-axis aberration (unless cylinder is ground into the lens or mirror). The two focal surfaces (the tangential focal surface and the sagittal focal surface) may be convex or concave, depending on the design of the system, so there are four possible configurations for these surfaces. It is impossible to produce a sharply-focused image in the presence of astigmatism; on one side of focus the star will appear as a line; on the other side of focus it will appear as a line rotated 90 degrees from the first line, and in between the star will appear boxy. Well out of focus the star may appear oval. The diameter of the astigmatic star image at the point midway between the two focal surfaces bears an inverse relationship to the focal ratio, so that at f/5 the diameter is three times that at f/15. In almost all cases, the astigmatism of the eyepiece dominates astigmatism of the objective, which plays only a small part in perceived astigmatism in the field. Eyepiece astigmatism strongly dominates coma in a Newtonian.

Astro-Physics: A telescope making company that produces telescopes to the 1/50th wave RMS wavefront criterion, which corresponds to a Strehl ratio of 98.4%. This claim has held up in independent testing. See also Christen, Roland.

Barlow lens: a concave achromatic lens with negative focal length, used to increase the magnification of a telescope-ocular system. In pure terms, the "Barlow" lens is this design, invented by Peter Barlow and first made by George Dolland. A side effect of the Barlow is to vary the eye relief of eyepieces (e.g., Al Nagler reports that a 2x Barlow increases the eye relief of a 35mm Panoptic by 10 mm). This happens because the Barlow bends off-axis beams outward, and when this light enters the eyepiece at an angle it was not designed for, the exit pupil is moved back. Another, beneficial, side effect of Barlow lenses is to frequently cause eyepieces to perform better off-axis than they would without the Barlow; this is because in most telescopes the focal surface is inward-curving, and the Barlow flattens (or nearly flattens) it, and because the greater effective focal ratio of the system reduces the effects of astigmatism present in the eyepiece. Barlows can be designed so that their inherent astigmatism corrects the astigmatism in a given eyepiece; this was done for Brandon oculars. For best results, Barlows should also be designed specifically to match the telescope they will be used in. In general terms, in modern amateur astronomy circles, "barlow lens" refers to any telenegative lens designed to increase magnification, and is applied, more or less loosely and improperly, to the Celestron Ultima barlow (which is three elements), the Klee barlow (three elements, and designed to correct for astigmatism), the Tele Vue Powermate (four elements in a very clever configuration), and so forth.

Barlow, Peter: a mathematician born at Norwitch around October, 1776. He began his optical work around 1827, and first occupied himself with the color correction of refractors through the use of smaller lenses positioned a considerable distance from the objective. The famous barlow lens was the result of a collaboration between Peter Barlow and George Dolland. Barlow designed a concave achromatic lens; Dolland made it in 1833 and attached it to a telescope. Its first user was Dawes, who employed it while measuring close double stars. The invention was published in Phil. Trans., 124 pp. 199-207, 1834, by Dolland. Peter Barlow died in 1 March 1862 at the age of 86 years.

BK7: a borosilicate crown glass made by Schott Optical Glass, with an Abbe number of 64.2 and a refractive index of 1.517.

Brandon: an eyepiece, consisting of two groups of two elements, designed by Chester Brandon and for a long time exclusively distributed by Vernonscope. The design differs from a Plossl at least in its use of different glass on each element, and probably in the separation of the groups, and possibly in the curves put on the lenses. Brandons offer about 0.7x their focal length of eye relief.

Cassegrain: a telescope comprising a concave primary mirror and a convex secondary mirror. Cassegrains can be made to satisfy any three of four conditions: short tube length, small secondary mirror, flat focal surface, focal surface behind the primary. There are many variants. The Classical Cassegrain produces images almost identical to that of a Newtonian of the same focal ratio, except that the Classical Cassegrain has a more strongly curved field. The Dall-Kirkham and Pressman-Carmichel exhibit strong coma off-axis and are best for narrow-angle viewing, e.g., of the planets. The Ritchey-Chretien exhibits round star images a good distance off the axis, but has strong field curvature and exhibits off-axis astigmatism. For a given focal ratio, a low amplification secondary mirror will provide better off axis correction than a high amplification mirror.

Celestron Ultima: a version of the five-element Plossl. See therefore Five-Element Plossl.

Christen, Roland: leading maker of refractors in the latter part of the 20th and early part of the 21st century. Noted for designing and manufacturing (under the Astro-Physics name) a line of extremely well corrected apochromatic refractors which enjoy wide popularity among planetary observers, wide-field deep sky specialists, astrophotographers, and small-scope enthusiasts. Christen essentially originated a rebirth of the popularity of refractors and more or less single-handedly drove the development of apochromatic refractors, starting in the 1980's. His reputation is similar to that of Alvan G. Clark's in the latter 19th century.

Chromatic Aberration: the focusing of light of different wavelengths at different positions relative to the objective. In a simple lens, shorter wavelengths (blue) focus closer to the lens than longer wavelengths (red). The result at the eyepiece varies depending on the objective lens design. In a visually corrected achromatic refractor, typically a haze of purple will be seen around bright objects. In a photographically corrected achromatic refractor, the haze will be more red or ruddy. In an apochromatic refractor, the experience of chromatic aberration can be nil, or an extremely thin fringe of color around the most highly contrasting edges of the brightest objects (typically greenish, but varying depending on the lens).

Coating, antireflection: a thin dielectric or metallic film applied to lenses that reduces reflections and increases the effective transmission of the lens. For minimal reflection of a single wavelength of light normally incident to the surface, the coating can consist of a single layer, must have a refractive index equal to the square root of the product of the materials on either side of it (typically, the product of the refractive index of the glass to which it is applied and the refractive index of air), and the thickness must be 1/4 the wavelength in question. Multilayer coatings, which can correct for a wider range of wavelengths or can be made to include or exclude specific bands, are deposited in layers having alternating high and low refractive index. It was noticed in the early 1900's that refractor telescopes transmitted more light 20 or 30 years after they were built than when they were new. The cause was variously explained by a thin layer of pollution, or a thin layer of chemically altered glass, which developed as the objective was exposed to the environment. Experiments were done to simulate the aging of glass to gain the higher transmission immediately and in a controlled manner, but in 1935 both Carl Zeiss and Bausch & Lomb developed the antireflection coating nearly simultaneously. By 1939, Carl Zeiss was "multi-coating" their optics with a double layer of coatings, and in 1942 were using a triple layer coating. It was not until the 1960's that multicoatings became common or popular. The advantage of coatings is increased net transmission. An uncoated air-glass surface loses about 1.5%; a multicoated surface loses between 0.2 and 0.5 %, but some excellent coatings can lose as little as 0.12%. The benefits of multicoating are therefore most dramatic on complex multielement systems, such as binoculars or zoom camera lenses, or systems where high efficiency is required, such as telescope optics. The most common single layer coating substance is magnesium fluoride (MgF₂). Other substances used include lithium fluoride, TiO₂, SiO₂, and others. Modern multicoatings can have as many as 120 layers for specialty optics, but more typical applications use between three and seven layer coatings. One of the effects of antireflection coatings is to increase light scatter in a narrow angle; if present this will be seen as a tight haze surrounding a bright object. Sometimes this haze is green or purple in tint. Some multicoatings are soft and will not stand up well to cleaning; others are quite hard and robust (ask the manufacturer for cleaning instructions). So called "cold" coatings, often applied to internal surfaces in an eyepiece, are frequently more easily damaged than "hot" coatings applied to the outside-facing surfaces (the terms refer to the deposition temperatures) - beware if you take your eyepieces apart for cleaning yourself. In general, the quality of the optical design and execution is more important than the coating applied to it; coatings are an important accessory but good coatings cannot salvage a bad eyepiece. Most coatings encountered in amateur astronomy optics can be removed with a cotton swab and lemon juice, though I'm not sure why you would want to do this.

Crowns: glasses with an Abbe number higher than about 55 are generally called crown glass.

Coma: an aberration which results in a point object being turned into a pear-shape or comet shape at the focal plane, most commonly off-axis. It is caused by unequal magnification in different zones of a lens for obliquely incident rays from an off-axis object. An easier way of putting this may be to say that coma is caused when light enters a lens or mirror from the side, and rays from different parts of the lens intersect the axis of those rays at different distances. In a Newtonian with a paraboloidal primary mirror, coma is an inherent property. A Newtonian with a spherical mirror can be made with no coma if an aperture is placed at the radius of curvature of the mirror, creating a symmetrical system. A common commercial Schmidt-Cassegrain telescope will exhibit as much coma as a Newtonian of half the focal ratio (i.e., an f/10 SCT has as much coma as an f/5 Newtonian) at the same distance from the axis. However, this means that at a given angular distance from the center of the field, coma is quite a bit more than in the Newtonian. Coma may be corrected with a Ross coma corrector, but to eliminate spherical aberration at the focal plane a hyperbolodal mirror in the Newtonian should be used. See also Paracorr.

Curvature of Field: curvature of field is present when the sharpest focus is formed along a curved surface rather than a flat plane. Unless deliberate steps are taken to eliminate it, it will be present in any optical system, including the Newtonian, refractor, Cassegrain, Schmidt-Cassegrain, Maksutov, and others. Refractors, Newtonians, and Cassegrain telescopes exhibit inwardly-curved (concave to the sky) field curvature. The focal surface in the Schmidt-Cassegrain is quite strongly curved. In the case of the achromatic refractor, the field curvature's radius is around 0.32 times the focal length, and the curvature is concave to the sky.

Dawes Limit: better called "Dawes' Empirical Criterion," a description of the smallest separation of equally-bright stars that can be achieved with a given telescope. A close modeling of the Dawes limit is given by 116/aperture_in_millimeters, or by 4.56/aperture_in_inches; the answer is in arcseconds. Not the final word in resolving closely-spaced point sources, but a very good guide none the less. It is not correct that Dawes arrived at his Criterion using a six inch telescope (he used telescopes of various sizes). (See the quote from Dawes himself about this.) It is not true that the criterion is valid only for sixth-magnitude stars (it is valid for any equal-brightness pair).

Degree of Freedom: refers to the options or choices available to an optical designer. For example, choosing the type of glass to use is one degree of freedom. Choosing the curvature of the glass is another. In general terms, an optical designer requires as many or more degrees of freedom as there are aberrations to correct.

Delta-z: the difference in surface height between a paraboloidal mirror and a spherical mirror of the same focal length. At the Steward Observatory Mirror Laboratory, they joke that some of their mirrors have a "delta-z big enough to trip over," i.e., one measured in millimeters due to the extremely fast focal ratios of the mirrors they make.

Dielectric: an electrical insulator. (Formally, a substance in which an electrical field may be maintained with zero or near-zero power dissipation.) Dielectric coatings are not magical, but considerable marketing hype has surrounded the term in recent years.

Diffraction Limited: a claim made by almost all telescope manufacturers, but probably lived up to by only a few makers. In its purest definition, "diffraction limited" refers to a telescope that is so perfect that only the wave nature of light, and not aberrations in the optical system, provide the limit to resolution of fine details and close separations in that instrument. In other words, the telescope itself is perfect in every way, and only the limitations of light itself impose these limits; therefore a diffraction limited telescope is a theoretical construction. In practice, this pure definition is rarely if ever used. Other definitions of "diffraction limited" have been proposed. These include the 1/14 wave RMS Marechal Criterion, which states that a 1/14 wave wavefront RMS telescope satisfying certain other conditions passes as diffraction limited. In practice, a telescope built to this tolerance will have easily observable aberrations. Another definition proposed is the 1/4 wave p-v wavefront criterion, sometimes erroneously attributed to Lord Rayleigh. In pracice, a telescope built to this tolerance is quite poor; Lord Rayleigh's own statement of this criterion was that such a poor telescope was "decidedly prejudicial" to the image quality. In another definition, diffraction limited refers to a telescope that meets the 1/50th wave RMS wavefront criterion, which corresponds to a Strehl ratio of 98.4%. This is likely the only definition that is both useful, and provides a high quality telescope when the criterion is met.

Distortion: see rectilinear distortion and angular magnification distortion.

d-Line: 587.56nm, the color produced by an emission line of helium. All measures given in waves on this web page, unless otherwise specified, are given in units of the d-line.

Doublet: a two-element group.

ED: short for "extra low dispersion," a reference to glass types that do not disperse light into its component colors so easily as regular glasses. ED glasses therefore exhibit less chromatic aberration by themselves than a typical crown or flint. Not magical.

Element: in the context of optical systems such as eyepieces, "element" refers to an individual lens. For example, an Abbe orthoscopic is a four-element design; this means there are four lenses in the eyepiece.

Erfle: a class of eyepiece designs originated by Heinrich Valentin Erfle. It utilizes two doublets and a singlet in 2-1-2 configuration (see also Five-Element Plossl). A variation that he also originated utilizes three doublets. Originally intended to provide apparent fields of up to 55 degrees, some modern designs offer fields up to 70 degrees or more. These eyepieces are commonly used in binoculars, spotting scopes, military gunsights, etc. Erfles exhibit flat fields, low distortion (except sometimes at the edges of Erfles with larger than average fields), but substantial off-axis astigmatism.

Erfle, Heinrich Valentin: an optical designer, born 11 April 1884 in Duerkheim, Germany. He worked for the firm of Steinheil & Soehne until 1909, at which time he moved to Jena and worked for the telescope department at Carl Zeiss Inc. He became head of the department in 1918. He is credited with several advances in optical design and fabrication, affecting mostly military optics, and is the inventor of the well known Erfle eyepiece. He died on 8 April 1923.

Eye Relief: the distance from the vertex of the eye lens to the location of the exit pupil. This quantity can be made to vary for a given eyepiece by, e.g., the introduction of a barlow lens, but this will be more pronounced with long focal length eyepieces, and in general is difficult to detect casually.

Exit Pupil Lower Limit: commonly quoted as 1mm, or 0.5mm, or some other arbitrary value, it is said that somehow the small exit pupil projects too small an image onto the retina or that the retina does not have resolution at such a small exit pupil. This is a complete load of horse manure (actually, it is an urban myth that has propagated over the internet for a couple years now). The lower limit to useful exit pupil is determined by seeing and by the presence or absence of floaters in the eye. On the planets, exit pupils of as low as .3mm or lower have sometimes been used to advantage; on close doubles, even smaller values have been used to make large, aesthetically pleasing Airy disks.

Exit Pupil Upper Limit: commonly quoted as 7mm, any larger exit pupil "wasting light." This is totally incorrect. For a refractor, there is no upper limit to exit pupil. With an obstructed system, the exit pupil limit is reached only when the secondary shadow becomes obtrusive in the image. You can work out the math yourself - a given telescope operating at an exit pupil of 10mm will give the brightest possible view of any object at that magnification. It is only "wasted light" if you bought the telescope knowing you would always use it at 10mm exit pupil.

Eye Lens: in an eyepiece, the element or group which is closest to the users eye.

Field Curvature: a lens aberration that causes a flat surface to be imaged onto a curved surface rather than a plane. The focal plane of the system is not a plane, but a curved surface, in this case. Common commercial Schmidt-Cassegrain telescopes exhibit field curvature on a radius about equal to that of a basketball.

Field Lens: in an eyepiece, the element or group which is farthest from the user's eye.

Five-Element Plossl: an eyepiece with a two-element field group, a two-element eye group, and a single element in between (sometimes an achromatic doublet in between). In the true "five element Plossl," the field and eye groups are symmetrical. Heinrich Erfle originated this design's predecessor around 1920, at Carl Zeiss. This type of eyepiece is not a Plossl at all. This design evolved from the Erfle, not from the Plossl, but has somehow taken up the Plossl name - perhaps because Plossls are easier to market. (In some cases, five-element Plossls are, in fact, Erfles of the original design.) Many popular brand names are of this design, changing only glass recipes or coatings; many others are minor derivatives of this design. The main superficial difference between a traditional Erfle and the "five-element Plossl" derivative is that in the traditional Erfle, the eye group is smaller in diameter than the field group.

Flints: glasses with Abbe numbers below 50 are generally called "flints."

Fluorite: a type of "ED" crown glass, discovered by Ernst Abbe, which has low refractive index and low dispersion, as well as an abnormal partial dispersion. Chemically CaF2. Historically, natural fluorspar crystals were used, and applications were limited to microscopes. Development of artificial crystals was necessary to produce elements large enough for use in telescope objectives. Fluorite is about 1/4 as hard as typical glass, and it is consequently delicate and very sensitive to temperature changes. It is considered rather difficult to polish. Fluorite will be degraded by long term contact with water, acids, and other atmospheric contaminants, but in telescope objectives the coatings should protect the surface. Like lanthanum, fluorite has had a good deal of attention by marketing hypesters, and like lanthanum, it is not a magical substance, but provides optical designers with important latitude in improving optical systems. Not magical.

Fraunhofer doublet: an achromatic telescope objective in the positive crown element forward configuration. The interior radii are unequal, and the air-spaced objective is separated by only a small amount.

Group: a set of lenses, typically cemented together, in an optical system. A group of two elements is usually an achromatic doublet, but not always. A single-element group is simply one lens standing on its own in a larger optical system. For example, an Abbe orthoscopic is a two-group eyepiece, comprising a three-element group field lens, and a single-element eye lens.

Integrated Barlow: a reference to a design method that allows an eyepiece of short focal length to be made by using a longer focal length eyepiece with a permanent barlow built into the eyepiece below the field stop, to bring the effective focal length back down. This is usually done to allow the manufacture of short focal length eyepieces with good eye relief. In almost all cases, the term is incorrect, since true Barlows are not used for this purpose. Instead, it behooves the designer to optimize both the negative elements and the rest of the eyepiece, creating a system in which neither the "barlow" nor the rest of the ocular will work properly on their own. Not magical.

Kellner: an eyepiece with a single field lens and a doublet eye group invented in 1849. This eyepiece is orthoscopic in its traditional configuration. Has about 0.5x its focal length in eye relief.

Kellner, Carl: founder of the optics firm Optical Institute (Wetzlar, Germany) in 1849, which later became E. Leitz, Inc. Kellner was born March 26, 1826 in Wetzlar. Worked for Repsold prior to founding his own firm. Kellner designed the Kellner eyepiece for telescopic use, and published the design in a paper "Das orthoskopische Ocular" in 1849. The eyepiece was later included on microscopes sold by his company. Kellner died of tuberculosis at age 29, in 1855.

King Rate: (Not really an optical term.) The King Rate, a telescope drive rate, corresponds to 1,436.47 minutes per revolution. It is a "best compromise" rate for a photographic telescope, which takes into account the likely circumstances of a photograph and the effects of atmospheric refraction.

Kidney bean: a blacking out of parts of the field of view, caused by spherical aberration of the exit pupil. Rays with large exit angles intersect the optical axis nearer to the eye lens than those rays with small or moderate exit angle. This results in the kidney bean effect when the circle of least confusion of the exit pupil of the eyepiece exceeds the size of the observer's eye pupil - in other words, when the observer's eye gets too close to the eye lens. The effect is therefore more pronounced with a smaller pupil; i.e., kidney bean is more evident in daytime than during night. True kidney beaning is not sensitive to what telescope is in use; it is the same for a given eyepiece no matter what scope is used.

Konig: denotes one of a class of eyepieces by a prolific designer, or eyepieces adapted from those designs. The 112, 121, 211, and 123 configurations are most common. Some people think the 211 type is properly called a Bertele. One of the original Konig designs is a simplification of the Erfle and has a two element field group and a single element eye lens; the field group is quite thick in this design and this eyepiece is not the same as the superficially similar RKE. Most of the popular Konigs are of the 121 configuration; these include "vanilla" Konigs by University Optics, and Konigs by Unitron.

Konig, Albert: optical designer, born 16th August 1871 in Plettenberg. His doctoral thesis in 1894 was on Fresnel diffraction spectra, and was supervised by Ernst Abbe. The same year he began work at Carl Zeiss Inc., working on telescopes, distance measuring equipment, and various other instruments. He died 30 April 1946 in Jena.

Lanthanum: a type of exotic glass, developed using lanthanum, a silvery metallic element which is one of the rare-earth metals. Lanthanum oxide added to glass gives it a higher refractive index and Abbe value than crown or flint. This difference can be exploited by a good designer to reduce aberrations in lens systems. The term lanthanum derives from a Greek word meaning roughly "to lie hidden." Not magical.

Lateral Color: caused by the off-axis imaging characteristics of a lens being wavelength dependent, i.e., lateral color is off-axis chromatic aberration. It results in a star imaged at the edge of the field being smeared out into a rainbow or showing color fringing.

Longitudinal Chromatic Aberration: the dioptric separation between the shortest and longest measured wavelengths along the axis of the lens. It occurs when the focal length of a lens is wavelength dependent. In other words, this is on-axis chromatic aberration.

Maksutov-Newtonian: a telescope comprising a meniscus corrector, concave primary, and flat secondary, assembled into a Newtonian configuration. Exhibits coma, though not as much as a Schmidt-Newtonian.

Meade Super-Plossl: formerly, a version of the five-element Plossl. See therefore Five-Element Plossl. Currently, a regular Plossl; see therefore Plossl.

Monocentric: a term referring to a lens set which has their radii of curvatures at the same location, or at nearly the same location. There is an eyepiece design composed wholly of a monocentric group which is occasionally heard of.

Monochromatic Aberrations: spherical aberration, coma, astigmatism, curvature of field, and distortion are the monochromatic aberrations. They were analyzed by Seidel in the 1850's.

Multi-coated: the air to glass surfaces of the lenses are antireflection coated with more than one layer of coatings. In the past, this term was distinguished from "fully multi-coated," where "fully" meant every air-glass surface was so coated, while multi-coated could mean that some surfaces were left uncoated. This difference is no longer maintained; e.g., both Tele Vue and University Optics used "multi-coated" to describe "fully multi-coated" eyepieces. Additionally, for some applications singly-coated optics are preferred. In general, a meaningless term, somewhat perpetuated by out of date information, occasional marketing hype, and sometimes misplaced brand loyalty.

Nagler, Albert: foremost telescope ocular designer of the latter half of the 20th century, and beginning of the 21st century. He is best known for designs which offer large fields of view with good correction of off-axis astigmatism and chromatic aberration, in some cases out to 90 degrees of apparent field. Nagler's designs do not use any aspheric surfaces, which reduces manufacturing costs. While many opticians have designed many such oculars, most of them remain inventions on paper only; Al Nagler's company, Tele Vue, manufactures many of Nagler's designs. Al is also a fan of classical music, which taste endears him to the author of this page.

Nagler, Type I: a wide-field eyepiece with an apparent field of view of 82 degrees, and eye relief about 1.2 times the focal length.

Nagler Type I, 25mm: a non-existent eyepiece. According to Rutten & van Venrooij, this eyepiece, if built, would weigh 10 pounds and be 4.5" across!

Negative focal length: a lens or mirror which diverges light is said to have a negative focal length. If a collimated beam of light is passed through such an optic, it will diverge; if the angle of divergence is traced back through the optic to that angle's intersection, the negative of the distance between that point and the optic is its focal length.Common optical systems which have negative focal lengths include the Barlow lens and the secondary mirror on Cassegrain systems.

Newtonian: the first practical reflecting optical telescope, invented by Isaac Newton, consisting of a concave primary mirror and a flat secondary mirror that diverts light out the side of the tube. For best correction on-axis, the Newtonian is made with a paraboloidal primary mirror. Small Newtonians of around f/14 or slower can give acceptable performance with a spherical mirror. Spherical Newtonians with an aperture stop at the radius of curvature can be made coma-free. See also coma.

Not Magical: intended to be a flag for and a reality check against excessively and irrationally or ignorantly hyped substances or products; "magical" is a reference to supernatural properties. For example, lanthanum elements in eyepieces are not magical, and despite the widespread belief that such substances result in an inherently better product, they do not do so (only the skill of the designer can make that so). Similarly fluorite refractors are not magical; they can easily be made poorly. In general, non-magical substances do have their merits, substantially in providing designers with an additional degree of freedom in their designs. It may therefore be surmised that products containing non-magical substances might be well designed and executed, but the mere presence of the substance does not by itself guarantee it. It may also be the case that in some applications, there are inherent advantages to certain substances, e.g., BK7 prisms in binoculars, and so this is a genuine selling point - but still does not take precedence over quality of design and build.

Off-axis: used most frequently among amateur astronomers to denote something that is not at the center of the field of view. In optics, the "axis" is the axis of (symmetrical) rotation of an optical surface, and therefore "off-axis" refers to something not along this line.

Orthoscopic: a lens that is free of spherical aberration, and magnifies an image uniformly throughout the field (i.e., the lens satisfies the tangent condition in which the ratio of the tangent of a' to the tangent of a is a constant for every ray on the lens). For a description of the "orthoscopic" eyepiece, see Abbe orthoscopic.

Orion Ultrascopic: A version of the five-element Plossl. See therefore Five-Element Plossl.

Paracorr: a coma-correcting lens by Tele Vue. It is not the same as a Ross coma corrector. It comprises two doublets, and is designed for good axial and lateral color correction and coma correction, with reasonable control of spherical aberration. Tele Vue's website has some technical specs for the Paracorr the last time I checked. See also coma.

Park's Gold Plossl: A version of the five-element Plossl. See therefore Five-Element Plossl.

Park's Premium Plossl: A version of the five-element Plossl. See therefore Five-Element Plossl.

Parfocal: two eyepieces, the focal planes of which are the same distance from the barrel top, are said to be parfocal. This is demonstrable by the design of the eyepiece, but many people note that, for example, a 12mm and an 8mm eyepiece in a supposedly "parfocal" line focus at slightly different positions for them. The reason is that the eye's lens exhibits spherical and other aberrations. As a result, pupil size affects the position of best focus for the eye. When reducing the pupil size by going to the shorter eyepiece, less aberration is encountered, and the focus point shifts accordingly. In addition, there is greater focus accommodation with longer focal length eyepieces, further obscuring an eyepiece set's true parfocality.

Plano: a lens surface the radius of which is infinite (i.e., the plano surface is flat).

Plossl: an eyepiece design consisting of two groups of two elements each. As far as I can determine the original Plossl eyepiece was symmetrical in design. The most traditional design seems to be one in which all air-glass surfaces are convex and the crown elements face one another, which minimizes aberrations at the exit pupil and minimizes distortion. The design is easy to make, as the spacing between the groups is not critical. As the spacing of the groups increases, focal plane curvature decreases and astigmatism increases. It is therefore possible to make an orthoscopic Plossl, but only at the expense of pronounced off-axis aberrations. There are also designs in which the external flint surfaces are plano. The asymmetrical Plossl designs, assumed to be variants on the traditional symmetrical design, may be better corrected than the symmetrical, depending on the design and execution, but there is no inherent advantage to an asymmetrical Plossl. Manufacturers or marketers of Plossls after an early design, as far as I can tell, include Clave and Showa. Tele Vue Plossls, according to the patent, are symmetrical, and comprise two achromatic doublets the external flint surfaces of which are concave. This Tele Vue design reduces astigmatism at the edge of the field and provides some correction for coma, at the expense of slight distortion in the field and exit pupil aberrations. Plossls, including variants, offer eye relief about 0.7x their focal length. The traditional Plossl is an easy and inexpensive eyepiece to make, and can easily be built by ATMs and amateur opticians with no specialized equipment. I am currently researching the history of the Plossl eyepiece, and if you wish to bring any sources to my attention, please contact me.

Plossl, George Simon: born September 19, 1794 near Vienna. In May 1812 he began work at the Voigtlaender optical firm. Supported by J.F. Jacquin and J.J. Littrow he studied mathematics and optics, founding his own firm in 1823 in his parent's house in Vienna. He encountered severe capital problems starting his firm but moved to much larger shops in 1831 and again in 1835. He made telescopes of the dialytic type, selling a 10.5" in 1850 and several other instruments of 6" to 8" aperture. He died as the result of an injury incurred dropping a sheet of glass, which severed an artery in his hand, causing blood loss and gangrene. He died January 30 1868 in the same house where he was born. His business was carried on as Fa. Plossl & Co. by M. Wagner until the last shop was closed in 1905. In 1875 there was an unrelated shop named Plossl in Vienna. George Plossl is best known today as the designer of the Plossl eyepiece.I am currently researching the history of the Plossl eyepiece and its designer, and if you wish to bring any sources to my attention, please contact me.

Powermate: a telenegative lens by Tele Vue. They bear some similarity to Galilean telescopes. The Powermate eliminates (or nearly eliminates) the effect that a traditional Barlow lens has on eye relief (see Barlow lens). The distance between the element and the ocular does not increase image scale in the same way as with traditional Barlows (according to an answer at Ask Al, adding an 80mm extension tube makes the 5x Powermate a 7.2x,  a 4x Powermate becomes a 4.5x, and the 2.5x Powermate reduces to 2.25x; a 115mm extension to the Powermate brings it to 8x).

Prism Diagonal: a diagonal assembly where the light is diverted 90 degrees by the use of a prism, rather than a mirror. The feat is achieved by taking advantage of the critical angle to induce total internal reflection. Some prism types can transmit as much light as a good mirror diagonal, but all introduce some chromatic aberration and other aberrations depending on the focal ratio of the telescope. These effects are more pronounced in fast optical systems. In addition, in fast systems, the critical angle may not be met for positions on the prism that are inside the observable field of view. A tilt error in a prism diagonal (i.e., miscollimation of the diagonal) will result in a ray deviation of twice the tilt, as is expected.

Radian: a Tele Vue eyepiece. Exhibits inherently less kidney bean than earlier Nagler designs.

Rectilinear distortion: a condition in which straight objects appear to be curved in the eyepiece. For zero rectilinear distortion the eyepiece must satisfy the y=f*tan(b) relationship, in which y is the off-axis distance in the focal plane, b is the image angle from the optical axis, and f is the focal length of the eyepiece. Not as important in astronomical observation as angular magnification distortion.

Refractive Index: the ratio of the velocity of propagation of an electromagnetic wave in a vacuum, to its velocity in a medium. Simply put, it is a measure of how much a particular substance bends light.

RKE: an eyepiece that is derived from the Kellner design, with the difference that the field group is of two elements instead of the eye lens, and by the addition of low dispersion glasses. Exhibits a moderately curved field and moderate distortion, and less off axis astigmatism than the traditional Kellner. The eyepiece was designed by David Rank, and the name RKE is variously explained as being "Rank-Kellner Eyepiece," "Revised Kellner Eyepiece," etc.

RMS Wavefront: a reference to the root-mean-square of the wavefront error of an optical system. Since measuring protocols for the RMS wavefront weight the severity of the wavefront error areally, this measurement is much more useful than a peak-to-valley wavefront error.

Ross Corrector: a coma correcting lens system for Newtonian telescopes. It was invented by Frank Ross in 1935 at Mt. Wilson Observatory. The Ross corrector comprises three lenses placed close to the focal plane. It has no optical power; i.e. it does not change the focal length of the telescope. It makes the coma-free field of view about a half degree in diameter at f/5.

Schmidt-Cassegrain telescope: a telescope design comprising a spherical primary mirror, a full-aperture corrector plate, and a negative secondary in a Cassegrain configuration. The common commercial design is one of several possible configurations. SCT's exhibit curved focal planes, and this can become evident in very wide-angle eyepieces; when the eyepiece is focused for the center, the extreme edges of the field may show small defocus donuts. Most commercial SCT's use mirror movement for focusing; this accomodates terrestrial use and allows the indiscriminate addition of accessories onto the back of the telescope. For object distances of less than about 60 feet, moving the mirror is preferable to moving the eyepiece to focus, but the side effects of moving the mirror include a change in the focal length of the system and a change in its correction.

Semi-apo: a refractor that approaches apochromatic performance. Typically a semi-apo refractor has a doublet objective comprising at least one exotic glass, often fluorite. The performance will at least be considerably better than that of an achromat and in longer focal ratios can approach the correction of a faster apochromat, assuming both are good designs, well-executed.

Seventy-point-seven zone: a point on a lens or mirror which is distant from the center an amount equal to 70.7% of the radius of the aperture. An important zone, because the area outside this zone is equal to the area inside the zone. Color correction curves for refractors are often referenced to this zone.

Singlet: slang for "single-element," in other words, a single lens, as opposed to a multi-element group.

Snell's Law: sin(e)/sin(e') = n'/n. In this equation, n' and n are the indices of refraction of the two media involved. e is the angle of the normally incident ray, and e' the angle of the refracted ray.

Spherical Aberration: the inability to focus axial and paraxial ray bundles that are parallel to the axis at a single point in the image plane. Peripheral rays focus closer than more central rays. This creates a fuzzy image that never snaps into a sharp, clean focus.

Spherical Aberration of the Exit Pupil: it is worth noting that this problem does not affect the sharpness of the image, but may lead to the kidney-bean effect.

Sphero-Chromatism: a chromatic variation of spherical aberration; spherical aberration which varies in degree, quality, or severity depending on the wavelength at issue.

Spot Diagram: a two-dimensional representation of where a collection of rays focused by the objective cross the plane of best focus. The spot diagram is the "head on view" given by raytracing (rather than the side view, which shows a cross-section of the instrument). Spot diagrams ignore the effects of diffraction and usually seek only to provide a graphical representation of monochromatic aberrations at the focus.

Steinheil doublet: an achromatic telescope objective in which the negative element comes first. Stronger curves than the Fraunhofer doublet are needed to make such an objective.

Strehl Ratio: According to Suiter, "the Strehl ratio is defined as the intensity of the image spot at its central brightest point divided by the same image intensity without abberration." (Star Testing Astronomical Telescopes, pg. 9). Put more simply, it is the fractional degredation of the peak of the theoretical diffraction intensity. Put even more simply, it is a measurement of the amount of light put into the peak of the image spot in an actual telescope, compared to that put in the spot of a perfect telescope. Therefore a Strehl ratio of 100% would constitute a perfect telescope; 98.5% or so constitutes an extremely good telescope, perhaps as perfect as can be made; 94% begins to be a mundane telescope. The measurement is more meaningful for very high quality telescopes than for mediocre ones. Contrary to some statements, the Strehl ratio is not only useful for infrared astronomy, but it is also useful for visible-light astronomy and provides probably the best measurement of perceived optical quality for any visible-band telescope. The rumor that Strehl ratio is useful only for infrared instruments is based on a misinterpretation of several papers which state, correctly, that Strehl ratio is not used very frequently by professional visible-band optical astronomers but is used heavily by infrared astronomers. The reason that Strehl ratio is not used by visible band optical astronomers very frequently is that r₀() (the coherence diameter of the atmosphere) is preferred, since this measurement is far more meaningful for large telescopes absent adaptive optics than the Strehl ratio; on the other hand, Strehl ratio at IR wavelengths, where seeing is less troublesome and adaptive optics may correct seeing anyway, provides a better indication of the coherence of starlight at the focus. In these contexts, these measurements relate to the total performance and error budget of the telescope, atmosphere, and object, and not directly to the optical quality of the instrument.

Super Plossl: generically, a version of the five-element Plossl. See therefore Five-Element Plossl.

Surface Accuracy: a reference to how true to its design an optical surface is. When light is reflected, the amplitude of surface inaccuracies is doubled. For refracting surfaces, the error is proportional to its index such that more highly refracting materials have smaller surface tolerances. In general, the tolerances for refracting surfaces are more forgiving, often far more so, than that for reflecting surfaces. The more optical elements present, the tighter the surface accuracy tolerances must be to provide acceptable performance.

Surface Reflection: in lenses, refers to how much light is reflected from an air-glass surface. The higher the index, the higher the reflection (the table below is for normal incidence):

Refractive Index:	% reflection:
1.4	2.8
1.5	4.0
1.6	5.3
1.7	6.7
1.8	8.2
1.9	9.6

Reflection increases rapidly as the angle of incidence approaches and exceeds 35 or so. 

Symmetrical: an eyepiece exhibiting symmetry in its element configuration. The most common symmetrical are Plossl eyepieces, which comprise two identical achromats facing one another.

Takahashi LE: in some focal lengths, a version of the five-element Plossl. See therefore Five-Element Plossl.

Tele Vue: not Televue, Tele-vue, Tele-Vue, or other common variants. See Nagler, Albert.

Transverse Chromatic Aberration: the separation between the shortest and longest measured wavelengths at the focal plane of the lens.

Tuthill Premium Plossl: A version of the five-element Plossl. See therefore Five-Element Plossl.

Zemax: way cool optical design software, if you can learn enough to know how to operate it. Not magical; relies heavily on the skill of the operator.

Sources & Bibliography:

All of these definitions and comments come out of my notes. All of the following sources are cited in my notes:

Web:

For biographical information, Chris Plicht's site was referenced and is not to be missed.
For information on certain telescope makers and telescopes, Peter Abrahams' site was used.
For some information on Tele Vue products, the Ask Al site was used.
For modern patent information, the USPTO site was used.

Books:

Rutten, Van Venrooij; Telescope Optics, Willmann-Bell 1988
Smith, Warren; Modern Optical Engineering, McGraw-Hill, 1990

Jeff Medkeff's home page.
Jeff's astronomy pages.
Copyright © Jeff Medkeff, 2002, All Rights Reserved.