Astronomical Optics

Part 5: Eyepiece Designs

Design Considerations
Field Lens & Eye Lens
Apparent Field Categories
Theory vs. Experience

Pre 19th Century Designs

19th Century Designs
Barlow/Smyth Lens

20th Century Designs
Hastings Triplet
Zeiss Astroplanokular
Takahashi LE
Pentax XW

A "Gleanings for the ATM" column in the February, 1944 Sky & Telescope began by observing that "eyepieces are commercially available, but not in any particular profusion of types or focal lengths, and not always easily procured." How times change! The amateur astronomer is likely to be staggered by the variety of eyepiece brands, designs and price points available today. While there might be three basic types of telescopes, there are dozens of generic designs, proprietary designs, and manufacturing variations of eyepieces.

Once I had acquired a basic understanding of telescope optics and eyepiece design, I was ready to make a much closer inspection of the eyepieces in my collection and intelligently evaluate the eyepieces I borrowed from others.

There are many ways to evaluate eyepieces, and many criteria, but I was limited to the evaluations I could make without an optical test or specific testing tools. Some of the tests could be objective (e.g., dimension measurement), but others (contrast, color) would be more or less subjective.

Eyepiece Virtues

If the mere reproduction of the image is accepted as a baseline performance standard, then eyepiece virtues are the ways in which an ocular can qualitatively excel in that task. The four key virtues are sharpness, brightness, contrast; certain comfort or convenience factors are important as well.

Sharpness is simply another word for veridical image reproduction: all elements of the image appear in perfect focus, without any visible distortion or aberration. As all ocular errors increase with field height (distance from the central optical axis), sharpness is typically evaluated as any degradation of the image of a star as it is moved from the field center to the edge.

Brightness is the overall throughput or transmission efficiency of the eyepiece. Ideally, 100% of the luminance of the image will be transmitted to the eye; the eyepiece will absorb or deflect no light. In practice, brightness is reduced by the number of elements and groups (air/glass or glass/glass boundaries) in an eyepiece, and by lenses that are uncoated. These all cause reflections and ghost images, which divert light.

Contrast is the luminance difference between the lightest and darkest areas of an image, and is primarily produced by high transmission oculars that do not scatter light. Light scattering is caused by destructive interference in lens coatings, lens edges or ocular mountings that are not blackened.

The comfort and convenience factors in a good eyepiece will vary with the individual, but typically include (1) comfortable eye relief, (2) eye guards or eye rests, especially in longer focal length eyepieces, (3) size and weight, (4) apparent field of view.

Eyepiece Flaws

Eyepiece flaws occur when the ocular fails the minimum task of accurately reproducing the objective image.

Scatter. Ideally, and separate from the errors of focus and projection, all light entering the eyepiece should be transmitted to the focal plane as a coherent image. When this does not happen, a variety of "stray light" artifacts appear in the image. These are reflections off interior surfaces that are combatted by painting surfaces flat black, installing baffles, etc.

Ghosting is the appearance of secondary images of either the field stop or bright objects in the image. The maximum number of potential ghost images is equal to the pairwise combination formula [N*(N–1)]/2, where N is the number of air/glass and glass/glass boundaries in the optical path that differ in refractive index by more than 0.25. These are normally controlled by antireflection coatings, which are very thin layers of materials with refractive indices that differ from each other and from air or glass by less than 0.25, and therefore provide intermediate steps in the refraction.

Spherical Aberration of the Exit Pupil. If the exit rays of light leaving the eyepiece do not converge in a single focal plane, there is no single, well defined location for the position of the observer's pupil. This typically occurs because the peripheral rays are focused at a point closer to the eyepiece than the central rays, which is a form of spherical aberration: thus, this defect is called spherical aberration of the exit pupil, or SAEP. When this occurs, it produces an off axis "blackout" or blank area in the eyepiece field of view opposite the direction of view, which has a lenticular form that is referred to as a "kidney bean". Generally, observers will not object to an SAEP of 10% or less of the exit pupil diameter.

A. Manufacturing Quality

x. Packaging

x. End caps/cap fit

x. Field stop focus - sharply defined?

x. Field fringe color - overcorrected = green or greenish blue, undercorrected = reddish, will not work well with a fast objective.

x. Field illumination - evenly bright from center to edge: if not, and/or different locations are required to see the field stop and to produce even illumination, then there is spherical aberration of the exit pupil.

x. Distortion - is the entire field stop visible without moving the eye? if not then there is either angular or rectilinear distortion.

x. Scatter - Is the dark boundary of the field stop black, or milky? milky indicates scatter.

x. Mechanical and assembly quality

x. Binoviewer fit

x. Draw tube fit

x. Under cut

x. Weight

x. Scratch/dig ratio - Although optics can be laser tested, a measure of scratch width (in millionths or 10–6 millimeters) and pit diameter (in hundredths or 10–2 millimeters); often as high as 60/40 in consumer optics but as low as 10/5 in military and certain industrial optics. Substitute glare, scatter evaluations. Edmund Optics sells inexpensive, approximate and expensive, precise tools for assessing scratch/dig in finished optics.

x. Coatings - Roland Christen evaluates eyepiece coatings by placing them in lateral daytime shade and viewing them under sky light illumination with the black end lens caps on the field end. The photo (below) shows the results using this method.

He also suggests checking the color of the coatings and glasses by viewing a white surface through the eyepieces, as shown in the next photo (below).

B. Observing Comfort

x. Eye relief - Eye relief is usually shorter in higher power eyepieces. Some astronomers remedy short eye relief in high power oculars by using lower power oculars with a barlow lens.

x. Exit pupil spherical aberration (dark adapted)

x. Critical alignment

x. Eye guard

x. Condensation

x. Focal position. The position at which the eyepiece achieves focus turns out to be an important attribute. Parfocal eyepieces share the same focal position, or nearly; this minimizes refocusing when eyepieces are changed. In commercial SCTs, it minimizes refocusing by moving the mirror, which can be locked and then adjusted only with the crayford focuser. Extreme focal positions may require a focusing tube extender, or may make focusing impossible.

The diagram (right) shows the focusing position of over 60 brand name commercial eyepieces with focal lengths of 3.2 mm to 55 mm. Most of these focus within a relatively small 2 cm interval; most of the exceptions are on the extrafocal side. Eyepiece brands are shown by color: many are parfocal series, excepting only the longest focal lengths, which usually require more focal distance.

C. Image Quality

x. Apparent field of View

x. True Field of View

x. True field accuracy/variation within the line

x. Color - Two excellent tests are (a) moon, (b) WZ Cas

x. Contrast - (a) moon, (b) jupiter, (c) deep sky (illumination level, and pupil size) - faintest visible extended area on the moon.

x. Transmission - faintest visible stars

x. Diffusion - (a) center field, (b) bar, (c) field edge

x. Glare, Scatter - (a) off field sirius, (b) center field sirius

x. Ghosting - how bright? colored? follow, mirror image, or remain in center? in focus or diffuse?

x. Barlow image

x. Spherical aberration

x. Astigmatism - worse with wider field and faster objective

x. Coma - worse with wider field and faster objective

x. Field curvature - (center to edge focus, amount of focuser turn) ...

x. Angular magnification distortion - requires rectilinear pattern

x. Rectilinear distortion - requires rectilinear pattern

x. Lateral color - in almost all eyepieces. increase near edge of field? red toward center — undercorrected, blue toward center — overcorrected.

x. Lateral color

Design Considerations

The ideal eyepiece is succinctly defined as crisp, wide, flat, bright, dark, comfortable, durable and affordable. This means the eyepiece must produce an image with minimal or no aberrations within the range of objective focal ratios it is designed to magnify; display a wide field without perceptible curvature or distortion, transmit almost all light from the image without ghosts, glare or scatter, provide enough eye relief for comfortable viewing (preferrably with an adjustable eye rest), withstand years of normal use, environmental exposure and the occasional accident without affecting any of the previous qualities, and be offered new at an affordable price.

The first five constitute the optical performance of the eyepiece, the first seven constitute the manufacturing quality of the eyepiece, and the last constitutes the market availability of the eyepiece. The market availability is affected by business and marketing costs, market demand and manufactured supply and is irrelevant to design issues. The optical performance is partly dependent on the optical design but also and importantly on the manufacturing tolerances and the quality of raw materials (optical glass) used in fabrication, and the focal length specification of the eyepiece. The optical performance of an eyepiece is a product of the optical design and of the skill and care with which the design has been made into a physical object required to magnify at a specific focal length.

The development of the modern eyepiece has been a history of progress on three fronts: the optical theory necessary to optimize the crisp, wide and flat attributes of the image; the optical materials and coatings necessary to optimize the optics with a bright and dark presentation; and the fabrication technology necessary to create the object at reasonable cost. Quite often fabrication issues or materials costs require compromise in the optical design.

Due to a variety of proprietary restrictions and marketing misnomers, the details of eyepiece optics are difficult to penetrate with assurance. In nearly all cases I was unable to find prescription data for the earliest example of an eyepiece design, and nearly all the designs have been tweaked significantly since they were invented through the use of newer optical glasses and small changes in the optical proportions. I have tried to select design schematics that use a 25 mm focal length.

The following summary is based principally on the chapter "Eyepieces" the Handbook of Optical Systems, Volume 4: Survey of Optical Instruments edited by Herbert Gross, Fritz Blechinger & Bertram Achtner; the chapter "Eyepieces for Telescopes" in Harrie Rutten & Martin van Venrooij's Telescope Optics; the chapter "Oculars" the Handbook of Optical Systems, Volume 4: Survey of Optical Instruments edited by Herbert Gross, Fritz Blechinger & Bertram Achtner; and "The Evolution of Eyepiece Design" by Christopher Lord, along with many other primary and secondary sources.

Adopting Lord's eyepiece format, each illustration gives the eyepiece name and year of design or patent, with the design apparent field of view, eye relief as a proportion of the focal length (ƒe), and the fastest objective focal ratio.

Field Lens & Eye Lens

The diagram (below) illustrates the two basic strategies of eyepiece design. In eyepieces constructed on the 19th century or standard design, the eyepiece can be divided into two components which serve two distinct functions. The field lens is weakly positive, and concentrates the peripheral (abaxial) light rays (blue lines) so that they pass through the eye lens. The eye lens is strongly positive, and defines the apparent field of the eyepiece. This type of design is not used for apparent fields greater than about 50°.

In contrast, many wide field designs can be divided into three functional units. The field lens is a negative Smyth group (effectively, a built in Barlow lens) that is actually brought in front of the telescope focal plane, sometimes followed by a negative lens after the field stop. This diverges the peripheral rays to an even higher field angle, where they are first approximately converged by the central elements of the eyepiece and then brought into the exit pupil by the eye lens at a steeper angle, thereby forming a wider apparent field (typically 70° or more).

Note that astronomical oculars are sometimes referred to as inverting eyepieces. In fact, as a species of magnifier, eyepieces produce images that are both erect and normal when used by themselves: the "inverted" (actually rotated) image is created by the objective, not the eyepiece. This usage apparently originated in the 17th century with Schryleus, as a contrast term to "erecting eyepiece" (also known as a terrestrial eyepiece or image erector).

Apparent Field Categories

Eyepieces can be classified by the width of their apparent field of view, or the eyepiece field as a virtual window. This is separate from the true field of view, which is the eyepiece field as an area of the sky. The apparent field is generally divided into three categories: (1) traditional or standard eyepieces have an apparent field of view from as little as 25° up to about 1 radian (57°); (2) wide angle eyepieces have an apparent field of view from 60° up to 80°; and (3) super wide angle or ultra wide angle eyepieces have an apparent field above 80° (the largest field achievable is around 120°).

The following table lists the apparent field widths that can be simulated by viewing a standard compact disk (12 cm in diameter) at the given distances.

diameter to
distance ratio
viewing distance

standard30°1:1.8722.4 cm
40°1:1.3716.4 cm
50°1:1.0712.8 cm
wide angle60°1:0.8710.4 cm
70°1:0.718.5 cm
super wide angle80°1:0.607.2 cm
90°1:0.506.0 cm
100°1:0.425.0 cm

The field stop is the physical edge of a specific diaphragm or lock nut that vignettes the image for the eyepiece. Ideally it will exclude all areas of the image much below 100% illumination, although this is much easier for eyepieces with short focal length that only utilize the central centimeter of the image plane than for wide field and long focal length eyepieces that may utilize an image area two or more centimeters wide.

DFS = 0.964·(AFOV·ƒe)/57.3

where AFOV is in degrees and the factor 0.964 is a correction for distortion averaged across 60 eyepieces of different design and manufacture. (As eyepiece designs vary widely and distortion increases with field height, the correction is approximate.) The same formula can be used by substituting the eyepiece true field of view for AFOV and the objective focal length for the eyepiece focal length; if TFOV is measured directly (e.g., by star drift timing) rather than calculated from AFOV, the correction factor can be omitted:

DFS = (TFOV·ƒo)/3438

where TFOV is in arcminutes. The telescope objective projects a fully illuminated or partially illuminated image area whose linear diameter depends on the telescope construction, but within a constant design (refractor, SCT, etc.) varies only with the projection magnification of the objective focal length. Objective focal lengths greater than about 4200 mm will not be able to utilize the largest (40 mm and above) eyepiece focal lengths because the image area of telescope will be smaller than the eyepiece will be vignetted by the drawtube internal diameter; the shortest eyepiece focal lengths (or equivalent focal length in combination with a barlow lens) utilize only the central millimeter or two of the objective image. 

Theory vs. Experience

We are lucky to live in an era when computers can do much of the thinking for us, in particular all of the rote and routine calculations that had to be done by hand, laboriously, in days before. Across many fields of inquiry this has liberated "theory" or the way things ought to be according to calculation, so much so that computer simulation is now one of the principal "observational" instruments in astronomy. We can run different simulations of how things should behave, and compare the outputs to events as we observe them, as a form of astronomical experiment.

In eyepiece optics theory similarly describes what are the optical performance and aberrations for any design. The difficulty is that these predictive descriptions very often do not conform to personal observational experience. In particular, field curvature, distortion, chromatic aberration, spherochromatism amd spherical aberration of the exit pupil can go entirely unnoticed, or ignored, by some observers in eyepieces where theory predicts the aberrations should be visually significant.

There is a fundamental difference between an observational attitude that examines the image as an optical test of an optical design, and the attitude that explores the image as visual testimony about the universe. Optical theory cannot predict where you will place your visual interpretation between those extremes, so it cannot predict whether or how much optical attributes will appear to intrude into your perception. Perhaps more important, your eyes are limited or aberrated in ways that are both unique to you and important in your visual experience, including your experience of telescope images. These cannot be predicted by optical theory; they are part of who you are, and there is no computer simulation to anticipate them.

One way to greet these complications is through two basic facts: nearly all commercial oculars available today are manufactured with methods and materials that make them optically among the most desirable visual tools ever made; and any ocular designs with obvious defects, such as the Huygens, Ramsden or Kellner, has dropped out of the market entirely. Eyepieces do differ among themselves in subtle ways: whether those differences matter or not is primarily due to your idiosyncratic eyes, and not the predictions of optical theory.

Pre 19th Century Designs

The earliest telescopes were empirical constructions produced without a theory of optics or an analytical approach to telescope design. Lenses were ground and put together in various combinations to find those that worked. Galileo wrote: "Spyglasses that are most exquisite and capable of showing all the observations [described in his Sidereus nuncius of 1610] are very rare, and among the sixty that I have made, at great cost and effort, I have been able to find only a very small number." The quality of optical glass and lens manufacture was poor, so lenses could be neither large nor thick; telescopes were made with focal lengths of 100 feet or more, and routinely stopped down in aperture, to minimize the negative effects of chromatic aberration and poorly figured optics. The story of pre 19th century eyepieces traces the efforts necessary to master the three basic challenges of optical theory, optical aberrations and lens manufacture.

Kepler – The biconvex lens is sometimes cited as the earliest form of magnifier. In fact, the ocular in the astronomical telescopes constructed by Gailileo Galilei from 1609 to 1621 was a plano concave lens, following the designs manufactured by the Dutch and Parisians. The biconvex ocular is first described in the Dioptrice (1611), a discussion of telescope optics by Johannes Kepler (1571-1630), which was published to affirm and also clarify the physical basis for Galileo's observations. Though he reasoned with only an approximate theory of refraction, Kepler showed that a telescope made with a biconvex objective and ocular produces a magnified image when the focal points of both lenses coincide. This has the potential for a larger apparent and actual field of view than was possible with Galileo's telescope, and by extending the radius of curvature for one side of the lens it is possible to reduce somewhat both chromatic and spherical aberration — but unlike the Dutch design it produces an inverted image. The field of view beyond 15° was badly distorted by off axis aberrations; eye relief is approximately the eye lens focal length.

Huygens – The brilliant Dutch mathematician Christiaan Huygens (1629-1695, pronounced Hoyghenz) was author of Traité de la Lumière (1690), which summarized optical theories he began developing in the 1650's and was the first optical treatise to apply the law of refraction to lenses of spherical surface and the design of telescopes. In 1662 Huygens developed the eyepiece that bears his name: it consists of two plano convex crown lenses with both curved surfaces facing the objective, mounted with a spacing between the lenses equal to half the sum of their separate focal lengths, which minimizes chromatic aberration, and with the two focal lengths in the ratio 3:1 (field:eye), which minimizes spherical aberration; however two common early designs utilized the ratios 3:2 (for high power magnification) and 4:1 (for low power). The Huygens is a negative eyepiece, meaning that it cannot be used as a simple magnifier (to examine a postage stamp or insect, for example). It places the objective image plane inside the eyepiece (between the two lenses) where it is transmitted to the eye with the uncorrected chromatic aberration of the eye lens; as a result, use of a reticule or crosshairs becomes impractical as these will be blurred and fringed with color. The huygenian eyepiece has significant spherical aberration, field curvature and some negative (pin cushion) distortion and coma; it also has slight negative astigmatism, which can be used to counteract the negative astigmatism of a high focal ratio (> ƒ/12) objective. It works best with refracting telescopes. The design originally had a 25° to 30° apparent field of view and very short eye relief — less than 8mm at ƒe = 28mm. English astronomer George Airy minimized the spherical aberration and field curvature by using a positive meniscus field lens and a biconvex eye lens; German optician Moritz Mittenzwey widened the field to 50° by using a positive meniscus field lens and a plano convex eye lens. Despite its antique origin, the huygenian eyepiece is still sometimes used in professional high focal ratio refractors, which minimize its optical flaws.

Dollond – John Dollond (1706-1761) was an English manufacturer of fine navigational and "philosophical" (scientific) instruments. After years of experimentation, he developed an achromatic doublet which he described to the Royal Society in 1758 and patented for manufacture a year later as both achromat objectives and eyepieces. It consists of a biconvex (positive) lens of lower index crown glass cemented into a plano concave (negative) lens made with higher index flint glass. The two lenses were designed so that their relative dispersions counterbalanced to eliminate chromatic aberration while their refractive indexes combined to focus the image. Used as an ocular, the doublet has a 20° field of view and eye relief of about 26mm at ƒe = 28mm.

Ramsden – Jesse Ramsden (1735-1800) was Dollond's son in law, learned from him the manufacture of optical and precision instruments, and founded his own instrument manufacturing company. His eyepiece design consists of two plano convex crown lenses of equal focal lengths, separated by about 2/3d the sum of their focal lengths and with the plane surfaces facing outward (away from each other). The Ramsden is a positive eyepiece that can be used as a simple magnifier, meaning that the focal plane is in front of the field lens. In this form the Ramsden design has a 25° apparent field of view and better correction than the Huygens for spherical and off axis aberrations, though with some residual lateral chromatic aberration. But it also has zero eye relief and all flaws of the field lens (surface scratches and dirt, enclosed bubbles) appear in focus. To mitigate these drawbacks, the spacing and focal lengths of the lenses are modified away from the optical ideal, which yields an eye relief of about 7mm (at ƒe = 28mm) but introduces significant field curvature, ghosting and lateral chromatic aberration (color correction can be improved by the choice of glasses); however the external focal plane does allow this eyepiece to be used with a reticle in long focal ratio telescopes.

19th Century Designs

At this stage the problems of chromatic and spherical aberration were well appreciated and increasingly minimized in optical instruments, and the technology of precision machine manufacture was capable of producing scientific instruments of unparalleled excellence. Microscopy and daguerrotype photography expanded the range of optical requirements and applications, and these often laid the foundation for telescope eyepiece design. Nineteenth century optical designers of eyepieces were concerned with increasing the field of view and eye relief, shortening the focal length, and reducing further the optical errors that persisted in 18th century designs. These efforts were advanced in the mid 1800's through techniques of mathematical optical design and aberration analysis developed by Joseph Petzval (1807-1891) and Philipp Ludwig von Seidel (1821-1896). Perhaps most important, after 1830 a greater variety and quality of optical glasses were available for experimentation and combination from manufactories such as Guinand (France) and Chance Bros. (England); innovation accelerated again after 1886. These gave optical designers greater control over refraction and dispersion and new avenues for innovation. German entrepreneurs founded some of the first major optical manufacturing companies (Zeiss, Leitz, Steinheil), and the profit motive — meeting end user requirements and minimizing manufacturing costs — shaped lens designs as well.

Barlow/Smyth Lens – The idea of using a negative doublet to extend the virtual focal length of an objective or flatten a curved field was introduced more than once in the 19th century. Peter Barlow (1776-1862), an English mathematician and engineer, developed the negative achromat with George Dollond, who presented it to the Royal Society in 1834. Charles Piazzi Smyth, Astronomer Royal for Scotland, conceived the idea of using a negative achromat to minimize field curvature in an otherwise aberration corrected wide field lens. After World War II, the barlow lens became a standard tool for multiplying from 1.5 to 3 times the magnification of eyepieces (for objectives with focal ratios longer than f/6); the Smyth lens was adapted to correct wide angle field curvature in 20th century lens designs — the 110° military binocular eyepiece developed by Tronnier in 1943, the 110° periscope eyepiece patented by Köhler in 1959, the Pretoria eyepiece designed by Klee & McDowell to compensate for aberrations in an f/4 parabolic reflector, the astonishingly well corrected "extreme wide field" (90°) eyepiece patented by Don Dilworth in 1988, and the several commercial designs by Al Nagler and Explore Scientific.

Kellner – Carl Kellner (1829-1855) was a German mathematician and machinist. The Kellner is basically a Ramsden modified by replacing the plano convex eye lens with an achromatic doublet, which effectively eliminates chromatic aberration. It is probably the oldest eyepiece design still used in binoculars and marketed to amateur astronomers; the various aplanatic eyepieces, which correct both spherical aberration and coma, were developed from it. It has very little longitudinal chromatic aberration and very low astigmatism, field curvature and distortion; its spherical aberration can be minimized by modern optical glasses, and its tendency to excessive ghosting can be controlled with lens coatings. It offers a very sharp, bright central field at low to medium powers, but very short eye relief at high powers (short focal lengths). Sometimes a biconvex lens is substituted for the plano convex field lens. The Kellner design typically has a 40° to 45° apparent field of view but with eye relief of 13mm (at ƒe = 28mm).

Plössl – Georg Simon Plössl (1794-1868, pronounced Plursul) was an Austrian scientific instrument maker. His design is derived from the Dialsight or symmetrical eyepiece, which consists of two identical achromatic doublets, oriented so that the biconvex crown elements face each other and spaced at roughly 20% of their focal lengths. (The kinship of this concept to a triplet magnifier appears if we imagine joining the two central crowns as a single crown biconvex lens.) However, the symmetrical is prone to ghosting, a problem Plšssl addressed by bringing the doublets almost into contact, increasing the refraction of the field lens flint element, and reducing the diameter of the field doublet; these modifications were further developed and patented by König in 1939. In these versions the negative flint elements are slightly concave on the exterior surfaces. Through alternative choice of glasses, these can be made flat, and all curved surfaces of equal radius, but with noticeable loss in performance. The design shown has modest distortion of about 8%; lateral color, spherical aberration and coma are completely corrected, and ghosts are almost entirely absent. The largest residual aberration is field curvature, which can be corrected somewhat by increasing the eyepiece astigmatism. Plšssl eyepieces typically offer a superior field of view to the orthoscopic: variants can reach a 50° apparent field of view and eye relief of about 20mm (at ƒe = 28mm).

Monocentric – Hugo Adolph Steinheil (1832-1893) was son of Carl August, inventor of the first miniature camera, and from 1855 head of the family's optics company. His monocentric design is an elaboration of spherical eyepieces, made by dropping beads of molten glass into hot water, that were used by microscopist Anthony van Leeuwenhoek and astronomer William Herschel. These led to a variety of spherical or rodlike single element lenses devised in the 18th and early 19th centuries by Wollaston, Brewster, Coddington, Stanhope, Tolles and others; all were limited by very short eye relief and usually also by spherical and/or chromatic aberration. Steinheil perfected the concept by fitting two concentric flint caps over a crown core; all surfaces are spherical around a common center. Steinheil's version is almost completely achromatic with very slight spherical aberration and a flat, very dark field free of ghosts; it has a narrow 25° to 30° apparent field of view, best at f/6 and above, and substantial eye relief of about 24mm (at ƒe = 28mm). Sidgwick describes the monocentrics as "without doubt the most nearly perfect oculars that have yet been designed".

Orthoscopic – Ernst Abbe (1840-1905, pronounced Abbay and in England sometimes incorrectly spelled "Abbé") was a brilliant German mathematician and physicist. He introduced the orthoscopic design in 1860. It consists of a triplet field lens with a single biconvex or plano convex eye lens. It shows a longitudinal spherical aberration of about 0.5 diopters, no coma, sagittal astigmatism of about 1.2 diopters and very little tangential astigmatism. It was the first eyepiece with almost completely corrected and distortion (less than 4% at a field height of 8), hence the name (Greek for "straight seeing"). It offers excellent sharpness, color correction, and contrast, and improves on the Kellner design with unusually good eye relief. This design has a 45° apparent field of view and eye relief of about 22mm (at ƒe = 28mm).

20th Century Designs

Eyepieces of the 20th century were strongly influenced by military requirements, where manufacturing cost is no consideration and a distortion free, very wide field is essential. The flood of surplus eyepieces that appeared after every major war stimulated commercial interests to imitate and innovate from them, and several defense contractors (Brandon, Scidmore, König) patented unique designs. Late in the century, computer assisted design and ray tracing programs put much more complex solutions within reach, but as a result ultra wide field eyepieces became almost absurdly large and heavy. The most recent innovations suggest that minimizing the mass of glass, the number of lenses and the number of air/glass or glass/glass boundaries necessary to produce a wide field has become a priority, at the same time that computerized lens manufacture in Europe and Asia has greatly driven down the cost of exotically figured (aspherical) surfaces.

Hastings Triplet – Patented for Zeiss in 1911, this is a modification by Paul Rudolph (1858-1935) and Charles Hastings (1848-1932) of the symmetrical and monocentric triplet devised by Steinheil in 1860. It is today one of the most common forms of the loupe or pocket magnifier, but despite that humble occupation it is close to diffraction limited and is the basic design of the TMB Monocentric.

Erfle – Heinrich Erfle (1884-1923, pronounced Airfluh) was a German physicist who worked for Steinheil & Söhne and Carl Zeiss. His design marks the transition to 20th century and the first truly "wide field" eyepiece, which was not coincidentally created for military applications (and was widely available as war surplus in the 1950's). Patented in 1923, the three erfle eyepieces consist of 5 elements in a 1-2-2 or 2-1-2 arrangement that offers long eye relief but a relatively close alignment of field lens to field stop. The distortion (for similar angular fields) is comparable to that of the orthoscopic. This design has a 60° apparent field of view and eye relief of about 20mm (at ƒe = 28mm).

Kaspereit – The modification of the Erfle design by Otto Karl Kaspereit adds a sixth lens to create a 2-2-2 design of three corrected doublets. It is currently offered by Edmund Optics as the "RKE Wide Field eyepiece", a design modified by David Rank. It expands the apparent "wide field" of view to 68° and provides eye relief of about 10mm (at ƒe = 28mm).

König – Albert König (pronounced Kurnigk) patented in 1940.

Brandon – Chester Brandon designed military optics during World War II and subsequently established his own optical manufacturing company. The Brandon eyepiece resembles a modified Plössl, but is made as two biconvex lenses of dense barium crown capped by medium and high dispersion flints. Brandons are widely esteemed by binary, planetary and lunar astronomers for their central sharpness, high contrast, color correction and lack of astigmatism and ghosting. As currently manufactured by VernonScope, the lenses are fully coated but not multicoated. The design has a 45° apparent field of view (not the advertised 50°) and eye relief of about 11mm (at ƒe = 28mm).

Zeiss Astroplanokular – No longer manufactured, the Zeiss APO is considered to be This design has a 45° to 30° apparent field of view and eye relief of about 11mm (at ƒe = 28mm).

RKE – Trademarked in 1979 as the acronym for Rank Kaspereit Erfle, "incorporating optical designs attributable to individuals bearing those three names," the RKE eyepiece was designed for Edmund Scientific Company by physicist David Rank (1907-1981). It improves on the Kellner design by offering a wider, sharper field, excellent aberration correction and longer eye relief. The current design has a 45° apparent field of view and eye relief of about 26mm (at ƒe = 28mm). It is currently proprietary to Edmund Optics.

Köhler Panoptic – This design was developed by Horst Köhler for Zeiss in 1955. It is derived from the Erfle 2-1-2 design by splitting the central positive lens into two asymmetrical lenses turned with their stronger surfaces touching. Variants of this design were also produced by Wright Scidmore and Hans Bertele, and later manufactured by both TeleVue and Takahashi under the name Panoptic. has a 25° to 30° apparent field of view and eye relief of about 11mm (at ƒe = 28mm).

Takahashi LE – The LE ("long eye relief") designs are proprietary to Takahashi, This design has a 50° apparent field of view and eye relief of about 11mm (at ƒe = 28mm.

Nagler – Al Nagler was an optical designer for Farrand and Keystone Camera who founded Tele Vue in 1977. In the 1980's he patented and popularized a variety of wide field eyepiece designs especially suitable for fast focal ratio, hand guided Dobsonian telescopes developed by John Dobson in the 1960s. Like many wide field designs of the era, the Naglers are known for their egregious weight and high cost (even in short focal lengths), as well as their excellent correction of angular magnification distortion, coma and spherical aberration. The early Naglers suffered from severe spherical aberration of the exit pupil (the so called "kidney bean" blackout), which was largely but not entirely remedied in later designs. This eyepiece has an 82° apparent field of view and eye relief of about 5mm (at ƒe = 13mm).

Pentax XW – The design here represents the 10 and 14mm focal lengths. Compared to several other wide field designs patented in the past few decades by Nagler, Koizumi, Kanai and others, the innovation is the negative meniscus placed immediately after the effective focal plane; this element is moved ahead of the smyth doublet in the shorter focal lengths, and replaces or is replaced by the smyth lens in the longest focal lengths. All eyepieces in the series have complete correction for coma, chromatic and spherical aberration, a 70° apparent field of view and a constant eye relief of 20mm. The longest focal lengths have a slightly positive field curvature, while the shortest focal lengths have a negative field curvature.

Ethos – This design .

Further Reading

Astronomical Optics, Part 1: Basic Optics - an overview of basic optics.

Astronomical Optics, Part 2: Telescope & Eyepiece Combined - the design parameters of astronomical telescopes and eyepieces, separately and combined as a system.

Astronomical Optics, Part 3: The Astronomical Image - analysis of the image produced by a telescope and the eye that receives it.

Astronomical Optics, Part 4: Optical Aberrations - an in depth review of optical aberrations in astronomical optics.

Astronomical Optics, Part 6: Evaluating Eyepieces - methods to test eyepieces, and results from my collection.

"Eyepieces" - Chapter 37 in Herbert Gross, Fritz Blechinger & Bertram Achtner (eds.), Handbook of Optical Systems, Volume 4: Survey of Optical Instruments. (Berlin: Wiley-VCH, 2008).

Optipedia - Online reference on optical topics by the SPIE, an international society advancing an interdisciplinary approach to the science and application of light.

Optical Design for Visual Systems by Bruce H. Walker.

Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics - fine history of early optical theory by Fokko Jan Dijksterhuis.

The Inverting Eyepiece and Its Evolution - a brief but useful summary of eyepiece design up to the mid 20th century, by E. Wilfred Taylor.

The Evolution of the Eyepiece - Chris Lord's detailed narrative of the steps in astronomical eyepiece development, not without factual errors (for example, "Max von Seidel" for Philipp Ludwig von Seidel).

The Amateur Astronomer's Handbook by J.B. Sidgwick.

Peter Dollond Answers Jesse Ramsden - An account of conflicting priority claims to the achromatic doublet.

Eyepieces - John Savard's overview of eyepiece design with special attention to the selection of glasses.


Last revised 11/26/13 • ©2013 Bruce MacEvoy