Lens Design & Manufacturing

In Lesson 2, we saw that a single glass element cannot form a perfect image — aberrations degrade the result in multiple ways. The history of lens design is the history of solving these problems, element by element, with increasingly clever combinations of glass. In this lesson we trace the evolution of photographic lens formulas, examine how they relate to the lenses found in TLR cameras, and explore the physical process of manufacturing a lens.

The Five Primary Aberrations

In 1857, the German mathematician Philipp Ludwig von Seidel classified the five primary monochromatic aberrations of a lens system. These are called the Seidel aberrations, and understanding them is essential to understanding lens design, because every multi-element lens formula is fundamentally an exercise in balancing these five errors:

Spherical Aberration

Rays passing through the outer zones of a spherical lens surface are bent more than paraxial theory predicts, causing them to focus at a shorter distance than rays through the center. The result is a soft, glowing quality to the image — sometimes deliberately exploited for portraiture (the famous Petzval "swirl" background is partly a spherical aberration effect). Correcting spherical aberration requires carefully balancing the curvatures of multiple surfaces.

Coma

Off-axis point sources of light are rendered as asymmetric, comet-shaped blurs rather than points. Coma is particularly objectionable in wide-angle and fast lenses and is one of the hardest aberrations to control. It manifests most visibly in the corners of the frame.

Astigmatism

For off-axis points, the lens focuses rays in the tangential plane (lines radiating from the center) and the sagittal plane (lines perpendicular to those) at different distances. This means that at any given focus position, either radial or tangential lines will be sharp, but not both simultaneously. Older lenses often show this as progressively deteriorating sharpness toward the edges of the frame.

Field Curvature (Petzval Curvature)

The natural image surface of a lens is not flat but curved. Joseph Petzval described this mathematically in 1843. Since film is flat, the center and edges of the image cannot both be perfectly focused at the same time. Flattening the field requires specific combinations of positive and negative lens elements, and it was one of the most challenging problems in early lens design.

Distortion

Straight lines in the scene are rendered as curves in the image. Barrel distortion bows lines outward from the center; pincushion distortion bows them inward. Distortion does not reduce sharpness — every point is in focus — but it misrepresents geometry. Most well-corrected normal-focal-length lenses have negligible distortion.

In addition to these five, there is the sixth major aberration we encountered in Lesson 2:

Chromatic Aberration

Because glass refracts different wavelengths by different amounts (a property called dispersion), a single lens focuses red, green, and blue light at different distances. This produces color fringing at high-contrast edges. Chromatic aberration is not monochromatic — it arises specifically from the wavelength dependence of refraction — so Seidel did not include it in his five, but it is equally important to correct.

The Great Lens Formulas

The history of photographic lens design is a story of progressive innovation, with each new formula building on the insights of its predecessors. Three designs are particularly important for understanding TLR camera lenses.

The Cooke Triplet (1893)

The Cooke Triplet was designed by Harold Dennis Taylor at the T. Cooke & Sons optical works in York, England, and patented in 1893. It was a breakthrough: the first lens design to correct all five Seidel aberrations plus chromatic aberration using only three separated elements. The design places a negative (concave) element between two positive (convex) elements, with air spaces between them. Taylor realized that by carefully choosing the powers, spacings, and glass types of three elements, he had exactly enough variables to control all the primary aberrations simultaneously.

The Cooke Triplet is remarkable for its economy. Three elements and four glass-air surfaces produce a well-corrected image suitable for general photography. Many inexpensive cameras used Triplet-derived lenses well into the mid-20th century. The design does have limitations — maximum aperture is typically restricted to about f/3.5 to f/4, and performance degrades at wider apertures — but for its simplicity, it is extraordinarily capable.

The Zeiss Tessar (1902)

Paul Rudolph at Carl Zeiss in Jena designed the Tessar in 1902. Zeiss marketed it with the slogan "das Adlerauge" — the Eagle Eye — and the name was well-deserved. The Tessar modifies the Triplet formula by replacing the rear positive element with a cemented doublet (two elements glued together). This gives the designer an additional glass surface and an additional glass type to work with, significantly improving correction of chromatic and spherical aberration without adding much complexity or cost.

The Tessar became one of the most widely produced lens designs in history. Carl Zeiss manufactured millions. The formula was licensed, copied, and adapted by manufacturers worldwide. At f/3.5, a Tessar delivers excellent central sharpness and very good performance across the frame when stopped down to f/8 or f/11. It is a four-element, three-group design (the rear cemented doublet counts as one group).

Many TLR cameras use Tessar-type lenses. The Yashica-Mat 124G's Yashinon 80mm f/3.5 is a Tessar-type design. So are the Rolleicord's Xenar (made by Schneider-Kreuznach) and the Minolta Autocord's Rokkor. These are all four-element designs that follow the same basic optical layout as Rudolph's 1902 original.

The Zeiss Planar (1896)

The Planar was also designed by Paul Rudolph, patented in 1896 — actually predating the Tessar. It uses a symmetric or near-symmetric arrangement of elements around a central stop: two groups of elements, roughly mirroring each other on either side of the aperture. The original Planar was a six-element design. Symmetry is a powerful tool in lens design because many aberrations (coma, distortion, and lateral chromatic aberration) cancel naturally in a symmetric configuration.

The Planar type was refined over the decades. The version used in the Rolleiflex 2.8F (refined during the 1950s) is a five-element design that delivers exceptional performance: superb sharpness, excellent contrast, minimal distortion, and beautiful rendering of out-of-focus areas. The Schneider Xenotar, used in some Rolleiflex models, follows a very similar design philosophy and performs comparably.

Planar-type lenses can achieve wider maximum apertures than Tessars while maintaining high image quality. The Rolleiflex 2.8 models with their f/2.8 Planar or Xenotar are prized among TLR photographers precisely because of the superior optical performance these more complex designs deliver, especially at wider apertures where the Tessar begins to struggle.

TLR Cameras and Their Lenses

Understanding these lens formulas helps explain the hierarchy of TLR camera quality. The lens is the single most important component affecting image quality, and different TLR models span the full range of optical sophistication:

• Entry-level TLRs (Lubitel, some Seagull models) — Simple three-element Triplet-type lenses. Adequate when stopped down but soft at wider apertures. These cameras can produce pleasing images, but they lack the optical refinement of higher-end models.
• Mid-range TLRs (Yashica-Mat 124G, Minolta Autocord, Rolleicord) — Four-element Tessar-type lenses. The Yashinon 80mm f/3.5, Rokkor 75mm f/3.5, and Schneider Xenar 75mm f/3.5 are all excellent performers. Sharp across the frame when stopped down to f/8, and entirely usable wide open for the Yashinon and Rokkor.
• Premium TLRs (Rolleiflex 2.8F, 2.8E, 3.5F) — Five- or six-element Planar or Xenotar lenses. The Zeiss Planar 80mm f/2.8 and Schneider Xenotar 80mm f/2.8 are among the finest medium format lenses ever made. They deliver outstanding sharpness, contrast, and microcontrast at all apertures, with particularly impressive wide-open performance.

Manufacturing a Lens

Designing a lens formula is only half the challenge. The design must then be manufactured with extraordinary precision. A photographic lens requires surface accuracy measured in fractions of a wavelength of light — tolerances far tighter than almost any other manufactured product.

Glass Selection

Optical glass is not ordinary glass. It is manufactured to precise specifications of refractive index, dispersion (how much the refractive index varies with wavelength), and internal quality (freedom from bubbles, striae, and inclusions). Otto Schott founded the Schott Glassworks in Jena, Germany, in 1884, specifically to develop new optical glasses in collaboration with Ernst Abbe and Carl Zeiss. Schott's innovations in glass chemistry directly enabled many of the great lens designs of the late 19th and early 20th centuries.

Optical glasses are broadly classified as crown glass (lower refractive index, lower dispersion) and flint glass (higher refractive index, higher dispersion). Lens designers select from a catalog of glass types — Schott's catalog has historically listed over 200 — choosing specific combinations that allow aberrations to be corrected. Rare-earth glasses, developed from the mid-20th century onward, offer unusual combinations of refractive index and dispersion that enable designs impossible with traditional glass types.

Grinding and Polishing

A lens element begins as a disk of raw optical glass called a blank. The blank is first rough-ground on an abrasive lap to approximate the desired curvature. Then progressively finer abrasives are used until the surface is smooth at a sub-microscopic level. Finally, the surface is polished with extremely fine cerium oxide or rouge on a soft pitch or polyurethane lap.

The finished surface must conform to the designed curvature to within a fraction of a wavelength of light — typically better than λ/4 (about 0.14 micrometers for green light). Quality is verified interferometrically: a reference surface is placed near the lens surface, and the interference pattern of reflected light reveals deviations from the ideal shape. Newton's rings — the colorful concentric patterns you sometimes see when two glass surfaces are placed in near-contact — are essentially an interferometric measurement of surface accuracy.

Cementing

Some lens designs include cemented elements — two or more elements bonded together with optical cement (traditionally Canada balsam, now synthetic UV-curing adhesives). Cementing eliminates two glass-air surfaces, reducing reflections and improving light transmission. The Tessar's rear cemented doublet is a key example. The cement layer must be extremely thin and uniform, with no bubbles or imperfections. Each glass-air interface reflects approximately 4% of incident light (for uncoated glass), so eliminating two such interfaces through cementing recovers about 8% of the light that would otherwise be lost.

Assembly and Centering

The finished elements must be assembled into a metal barrel with extreme precision. Each element must be perfectly centered on the optical axis and spaced at exactly the designed distance from its neighbors. Tilted or decentered elements introduce asymmetric aberrations that degrade image quality. High-quality manufacturers use precision-machined spacers and spring-loaded retaining rings to hold elements in alignment. The completed lens assembly is then tested on an optical bench, and adjustments are made if necessary.

Anti-Reflection Coatings

Uncoated glass surfaces reflect about 4% of light at each glass-air interface. A four-element Tessar has six glass-air surfaces (the cemented pair shares a surface with no air gap), which means about 22% of the light is lost to reflections — and worse, some of that reflected light bounces between surfaces and reaches the film as stray light, reducing contrast and causing flare.

In 1935, Alexander Smakula at the Zeiss factory in Jena developed the first practical anti-reflection lens coating, initially kept as a military secret by the German government. The principle is thin-film interference: a coating of precisely controlled thickness (one-quarter wavelength of light) and refractive index causes the reflections from the top and bottom of the coating to destructively interfere with each other, dramatically reducing the total reflection.

Single-layer coatings can reduce surface reflections from 4% to about 1.5%. Multi-layer coatings (multicoating), which became widespread from the 1970s onward, can reduce reflections to 0.2% or less per surface. The improvement in contrast and color saturation when comparing coated to uncoated lenses is dramatic. If you have ever compared images from an uncoated 1930s lens to a multicoated 1970s lens of similar design, the difference in contrast and "pop" is immediately visible.

MTF Charts: Measuring Lens Quality

Modern lens quality is often described using Modulation Transfer Function (MTF) charts. An MTF chart measures a lens's ability to reproduce contrast at different spatial frequencies (levels of fine detail). A perfect lens would transfer 100% of the subject contrast at all spatial frequencies; a real lens transfers less, and the percentage drops as detail gets finer.

MTF charts typically plot contrast transfer (0–100%) on the vertical axis against distance from the image center (0 to the corner) on the horizontal axis, at two or more spatial frequencies (often 10 lines/mm and 30 lines/mm for medium format). Higher curves indicate better performance. Curves that stay flat across the frame indicate even performance from center to edge.

While MTF charts do not capture everything about how a lens "renders" an image — they say nothing about bokeh quality, color rendering, or flare behavior — they are the most objective measure of resolving power and contrast available. When you see claims about the "legendary" sharpness of the Zeiss Planar, MTF data backs it up: the Planar 80mm f/2.8 maintains high contrast even at 30 lines/mm in the corners of the frame, an impressive achievement for any lens.

Looking Ahead

We now understand how lens designers balance aberrations across multiple elements, why certain lens formulas produce better images than others, and how the manufacturing process demands extraordinary precision. In the next lesson, we turn to the mechanism that controls how much light the lens lets through: the aperture. The iris diaphragm, f-numbers, and depth of field are the photographer's primary tools for controlling the lens, and they build directly on the optical principles we have covered so far.