Advances in Camera Optical Engineering

Hello. Last time, you saw how achromats, Petzval lenses, rapid rectilinear lenses, and anastigmats relieved different constraints on color, speed, distortion, and off-axis sharpness. Their designers mainly worked with glass choice, spherical surfaces, element spacing, and stop placement.

This lesson adds four capabilities that changed the design problem itself. Anti-reflection coatings made numerous air–glass interfaces practical. Aspherical surfaces gave designers new control over how rays from different pupil zones converge. Floating groups preserved correction as subject distance changed. Zoom mechanisms made focal length variable while trying to keep the image in focus on a fixed recording plane. The common theme is that a lens must perform as a system, not merely form a sharp point in one ideal configuration.

Coatings: making complex lenses usable

Every uncoated air–glass boundary diverts some light from the intended image. At normal incidence, ignoring absorption, its Fresnel reflectance is

For air with $n_{\mathrm{a}}\approx 1$ and glass with $n_{\mathrm{g}}=1.5$, this gives $R\approx 0.04$. If ten such surfaces each transmitted 96% of the light, their combined direct-path transmission would be approximately $0.96^{10}\approx 0.66$. This deliberately simple calculation ignores absorption, angle, wavelength, and rays that reflect and later return, but it exposes the historical constraint: adding elements to correct aberrations could impose a substantial transmission penalty.

Lost direct-path light is only part of the problem. A ray reflected at one surface can reflect again at another and reach the recording plane in the wrong place. Such ghosts may resemble displaced images of bright sources or spread into broad patches. More diffuse unwanted illumination creates veiling flare, reducing contrast even where no distinct ghost is visible. These are stray-light problems, not failures to bring the intended rays to a common focus.

For the distinction between lost light, ghosts, and veiling flare, and for the single-layer coating conditions, read the selected parts of Lens Surface Reflections from ƎXCLUSIVE ARCHITECTURE. Use its optical diagrams and equations; the derivation below supplies the physical interpretation.

Consider a transparent coating of refractive index $n_{\mathrm{c}}$ and thickness $d$, between air and glass. Light reflected at the coating’s front boundary interferes with light reflected at its rear boundary. At normal incidence, choosing

makes the coating’s round-trip optical path equal to half the design vacuum wavelength ${\lambda }_0$. The two reflected electric fields can then oppose one another. For their amplitudes to cancel as well as their phases, the ideal index for this simple, lossless, single-layer case is

Reduced reflection means increased transmission by energy conservation; interference is the mechanism, with no quantum-mechanical explanation required. The cancellation is exact only under its design assumptions. Wavelength, incidence angle, polarization, available coating materials, and fabrication tolerances all matter. Multilayer coatings supply additional indices and thicknesses with which to reduce reflection over a broader useful range, rather than only at one wavelength and direction.

The effect on ghosts can be disproportionately valuable. A path involving two reflections has intensity roughly proportional to the product of the two surface reflectances, before accounting for its geometry and further losses. Reducing each of two illustrative reflectances from 4% to 0.5% reduces that product from $0.04^2$ to $0.005^2$, a factor of 64. It does not eliminate ghosts: bright sources, sensor reflections, contamination, and scattering from the lens barrel still require attention.

Watch this portion of Stephen Remillard’s Telephoto Prime Lens Design: A Patent Study for a concrete comparison of traced stray-light paths with and without coatings. It is a study of one design, not a universal estimate of coating gains.

Before effective coatings, cementing elements could remove an air–glass interface and its associated reflection, but cementing also constrained the choice of curvatures and spacings. Coatings did not correct aberrations directly. They made more elaborate aberration correction less costly in throughput and stray light.

Aspheres: controlling rays across the pupil

The previous lesson’s multi-element designs used spherical surfaces because spheres can be ground, polished, and tested comparatively readily. But a spherical surface does not generally send all zones of an axial bundle to the same focus. Correcting the resulting spherical aberration with further spherical elements consumes design freedom and often adds weight and reflecting interfaces.

An aspherical surface departs from a sphere in a controlled way. One useful description of its surface position, or sag, as a function of radial distance $r$ is

The added coefficients let a designer adjust how the surface refracts rays at different pupil radii without making the same change everywhere. In particular, a suitable departure can bring marginal rays closer to the focus of paraxial rays at a chosen design condition. This is not equivalent to merely stopping down: stopping down excludes marginal rays, whereas an asphere attempts to use them well.

Canon Imaging Plaza’s short Aspherical Lens animation provides a visual comparison. Treat its depiction of a common focal point as an idealized illustration, not a claim that an asphere is free of all aberrations.

The engineering gain is an additional shape variable. An asphere can reduce spherical aberration, and appropriately placed aspheres can help with other errors, including some off-axis aberrations and distortion. It does not, by being aspherical, eliminate dispersion or guarantee a flat, sharp field. Correction selected for one focus distance or field point may also be less effective elsewhere.

That optical freedom has a manufacturing price. The intended departure must be produced and measured accurately; surface-form errors or decentring can undo its benefit. Molding and precision machining made aspheres practical in settings where making each surface individually would have been too costly. The result could be a faster or smaller lens, or one using fewer elements—but fewer elements is a possible system-level outcome, not a defining property of an asphere.

Floating groups: correcting a lens at more than one distance

A lens optimized for a distant subject encounters a new condition when focused close. Even a thin ideal lens needs a different image distance: $1/f=1/s+1/s^{\prime }$. Moving the lens to place that image on the recording plane corrects defocus. It does not ensure that its spherical aberration, coma, astigmatism, and field curvature retain their previous balance. The ray bundles now have different object conjugates and encounter the surfaces at different heights and angles.

A floating-group design makes at least one group’s position change relative to another group during focusing. The designer can prescribe that relative movement to control aberrations as subject distance changes. For example, shifting a rear correction group relative to the main focusing group can improve close-distance performance that would deteriorate if the entire optical assembly simply moved as one rigid unit.

Return to the patent-study video for an example of relative group movement in a fixed-focal-length design.

Two distinctions matter here. Internal focusing names where the focusing movement occurs; it does not by itself promise that aberrations remain well corrected. Floating correction names the use of relative group movement to improve performance across focusing distances. The same movement can alter effective focal length somewhat, producing focus breathing—a change in image scale or framing while focus changes. Mechanical simplicity, compactness, stable framing, and close-focus quality cannot always be maximized together.

Zooms: changing focal length without moving the recording plane

A prime lens is designed around a nominal focal length. A zoom lens offers a controlled range of focal lengths, so its field of view changes at a fixed camera position and recording format. Merely changing the separation between lens groups is not sufficient: that generally changes both effective focal length and where a distant object comes into focus.

The simplest paraxial model makes the coupling explicit. For two thin groups of powers ${\Phi }_1$ and ${\Phi }_2$, separated by distance $d$ in air, the combined power is

Changing $d$ changes focal length. For parallel incoming light, however, the distance from the second group to the paraxial focus is

Thus focal length and back focal distance generally change together; they are not the same quantity. For illustration, take ${\Phi }_1=0.020{\mathrm{mm}}^{-1}$ and ${\Phi }_2=-0.010{\mathrm{mm}}^{-1}$. At $d=20\mathrm{mm}$, the model gives $f_{\mathrm{eff}}\approx 71.4\mathrm{mm}$ and $b\approx 42.9\mathrm{mm}$. At $d=30\mathrm{mm}$, it gives $f_{\mathrm{eff}}=62.5\mathrm{mm}$ but $b=25.0\mathrm{mm}$. The example is not a practical zoom prescription; it shows why a single spacing adjustment would lose focus at a fixed image plane.

A usable zoom therefore coordinates group motions. A variator changes effective focal length, while compensating motion keeps the image close to the fixed recording plane. Mechanical cams or controlled actuators can prescribe the positions. A parfocal zoom is designed to maintain focus as focal length changes; a varifocal lens requires refocusing, which may be acceptable when a camera can do it automatically. Keeping paraxial focus fixed still does not guarantee good images: aberrations, distortion, vignetting, and sometimes maximum aperture vary across the zoom range.

For a real-world description of those coupled units and changing aberrations, read the indicated passages of Canon’s Broadcast Television Lenses. This is a manufacturer’s account of its engineering approach, not independent evidence that a particular lens meets every performance claim.

This makes zoom design a broader optimization than the two-group equations suggest. A designer must distribute correction across many focal lengths, focus distances, wavelengths, pupil positions, and field angles, while allowing space for moving groups. The additional elements and mechanisms impose demands on coatings, manufacturing tolerances, size, and reliability. The four developments in this lesson therefore reinforce one another: coatings support complex air-spaced assemblies; aspheres can recover correction without always adding more elements; and coordinated moving groups make that correction useful across focus and zoom settings.

Conclusion

Anti-reflection coatings reduced Fresnel losses and stray reflections, making complex optical layouts more viable. Aspheres added control over ray convergence that spherical surfaces alone could not provide as economically. Floating groups addressed the fact that refocusing a lens does not automatically preserve its aberration correction. Zoom mechanisms made focal length adjustable, but only through coordinated group motion and correction across many configurations.

None of these features guarantees image quality by its name alone. In the next lesson, you will assess the resulting lens as a whole—using contrast transfer, vignetting, flare, distortion, and telecentricity rather than a single claim of sharpness.