Cart 0


This is a continuation from the previous tutorial - Cameras



Camera lenses have been discussed in a large number of books and articles. The approach in this chapter is to concentrate on modern types and to describe imaging performance in detail both in terms of digital applications and in terms of the optical transfer function.

By modern types, we mean lens forms that were found on cameras in 1992. The chapter deals almost entirely with lenses for the 35-mm (24 \(\times\) 36-mm) format. This limitation is unfortunate but not really inappropriate, given the widespread use of this format. Moreover, the different lens types that are described are used for applications ranging from 8-mm video to 6 \(\times\) 9-cm roll film.

We have not included any specific design examples of lenses for large-format cameras, but the imaging capabilities of these lenses are described in terms of digital applications. By digital applications we mean the comparison of different lens types in terms of total pixels and pixels per unit solid angle. It is hoped that this feature will make comparisons between radically different imaging systems possible and also help to classify lenses in terms of information capability. See ‘‘Further Reading’’ at the end of this tutorial for related information about photographic lenses, particularly with respect to older design types.



There are some limitations that are imposed on the design of camera lenses. The most significant ones are listed as follows.

Microprism focusing in single lens reflex cameras (SLRs) is difficult at apertures smaller than about F/4.5.Recent advances permit the use of microprisms at apertures down to F/5.6 and this is usually the smallest maximum aperture permitted in the specification of a lens for the SLR camera.

Depending on the camera type, there is a maximum rear lens opening allowable at the flange on SLR lenses. The limitation is approximately 33 to 36-mm diameter at flange to film plane distances of 40.5 to 46 mm. This affects the maximum possible aperture on normal lenses (typically to F/1.2) and also requires appropriate design of the exit pupil location on long-focal-length and high-speed retrofocus lenses in order to avoid excessive vignetting.

The minimum back focal length (BFL) allowable on SLR lenses (because of the swinging mirror) is about 38.5 mm. The BFL cannot be too short on non-SLRs because of in-focus dust or cosmetic problems on optical surfaces close to the film plane. The actual limitation depends on the minimum relative aperture that would be used but is rarely less than 4 mm and usually more than 8 mm.

Since most lens accessories such as filters and lens-shades are mounted on the front of a lens, there is a practical limitation to the allowable front diameter of most lenses. Filter sizes larger than 72 mm are not desirable, and smaller is always preferred.

The actual clear aperture at the front of a lens is considerably smaller than the filter size, depending on the angular field and the mounting details of the filter. Obviously there are lenses such as 600-mm F/4 telephotos for which the 72-mm limitation is not possible.

In these cases, the lens can be designed to use internal filters that are incorporated into the design.

Mechanical cams are still in widespread use for the practical realization of the required motions in zoom lenses. This technology requires that the motions themselves be controlled at the design stage to be reasonably monotonic and often to have certain mutual relationships. These requirements are particularly severe for the so-called ‘‘one-touch’’ zoom and focus manual control found on many SLR zoom lenses.

In general, size and weight restrictions pose the biggest problems for the designer of most camera lenses. Almost any lens can be designed if there are no physical limitations. These limitations are sometimes a consequence of ergonomic considerations but can equally be an effort to achieve a marketing advantage. Size restrictions almost always adversely affect the design, and exceptionally small lenses (for a given specification) should be regarded with suspicion.




2.1.  Normal (with Aspherics) and Variations

35-mm SLR normal lenses are invariably Double-Gauss types. Refer to Fig. 1. This lens form is characterized by symmetry about a central stop to facilitate the correction of coma, distortion, and lateral color. These lenses are relatively easy to manufacture and a user can expect good quality in a production lens. Total angular coverage of about 45\(^\circ\) is typical, and speeds as fast as F/1 are achievable. Extremely good optical performance is possible, particularly if the angular field and speed are reduced somewhat.

Image quality generally deteriorates monotonically from axis to corner and improves dramatically as the lens aperture is reduced by about two F-numbers. With the addition of a fixed rear group, conjugate stability can be achieved over a wide range. Refer to Fig. 2.


2.2.  Wide-angle

An interesting new wide-angle lens type is a four-component form found commonly on the so-called compact 35-mm cameras. This lens is characterized by a triplet construction followed by a rear element that is strongly meniscus-shaped, convex to the image plane. This lens has much less astigmatism than either conventional triplets or Tessars and can cover total fields of up to 75\(^\circ\) at speeds of around F/4. Faster speeds are possible if the angular field is reduced. Most importantly, the rear meniscus component takes the burden


Figure 2.  90-mm F / 2 . 5 macro for 35-mm SLR.


of field flattening away from the triplet front part. This results in considerably lower individual element powers and correspondingly lower sensitivities to tilts and decentrations of the elements. It is this problem that makes conventional triplets extremely difficult to manufacture. Refer to Fig. 3. 


2.3.  Inverted Telephoto (Retrofocus)

These lens types, characterized by a long back focal length, are typically used for wide-angle applications for single lens reflex cameras having a swinging viewing mirror behind the lens. Inverted telephoto implies a front negative group followed by a rear positive group, just the reverse of a telephoto construction. This type of construction tends to result in relatively large front aperture sizes, and it is not easy to design small lenses without compromising on image quality. Retrofocus designs sometimes have a zone of poorer image quality in a field area between the axis and the corner.

This zone is a by-product of the struggle to balance lower- and higher-order aberrations so that the outer parts of the field have acceptable image quality. These lenses have particularly good relative illumination both because the basic construction results in an exit pupil quite far from the image plane and also because it is possible for the size of the pupil to increase with field angle. In order to achieve conjugate stability, it is necessary to employ the use of so-called ‘‘floating elements’’ or variable airspaces that change with focusing. However, this feature does result in additional optomechanical complexity.

The newer forms of this lens type fall into four broad subcategories.

Very Compact Moderate Speed. These include six-element 35-mm F/2.8 with a front negative element and seven-element 28-mm F/2.8 with a leading positive element. Refer to Figs. 4 and 5, respectively. These relatively simple constructions are suitable for speeds of F/2.8 or slower and total angular coverages of up to 75\(^\circ\).

Highly Complex Extreme Speed. As the complexity of both the front and rear groups is increased, the inverted telephoto form can be designed to achieve speeds of F/1.4 and angular fields of 90\(^circ\). The use of aspherical surfaces is essential in order to achieve these specifications. Refer to Figs. 6, 7, 8, and 9.


2.4.  Highly Complex Extreme Wide-angle with Rectilinear Distortion Correction.

These are inverted telephoto designs covering total fields of up to 120\(^\circ\) , often with speeds as fast as F/2.8. Distortion correction is rectilinear. The chromatic variations of distortion, astigmatism, and coma are usually the limiting aberrations and are virtually impossible to correct beyond a certain point. Refer to Figs. 10 and 11.

Extreme Wide - angle with Nonrectilinear Distortion (‘‘Fish-eye Lenses’’ ). Without the requirement of rectilinear correction of distortion, inverted telephoto designs can be achieved quite readily with total angular fields exceeding 180\(^\circ\). For these lenses, the image height \(h\) and focal length f are often related by \(h=f\cdot\theta\), where \(\theta\) is the semifield angle. See, for example, USP 4,412,726.


2.5. Telephoto Lenses

The term telephoto strictly applies to lenses having a front vertex length less than the focal length (telephoto ratio less than one). The classic telephoto construction has a front positive group followed by a rear negative group. This can lead to telephoto ratios that are as short as 0.7 or less. The term telephoto is often loosely used to refer to any long-focal-length lens and one sometimes sees references made to the telephoto ratio of a wide-angle lens. 


Two significant advances characterize the newer types of telephoto lenses, particularly those used for 35-mm SLR cameras. The first is the use of small internal groups for focusing, sometimes in conjunction with the front group. This feature has also led to significant improvement in the performance of these lenses with change of conjugate.
This has been a problem with telephoto lenses, particularly with respect to attaining close focus with good optical quality. Internal focusing of a long-focal-length lens also has considerable advantages in terms of mechanical simplicity because a smaller mass is being moved over a significantly shorter distance.
The second advance is the employment of optical glasses having anomalous dispersion for the correction of chromatic aberrations. These newer glasses have anomalous dispersion characteristics similar to those of calcium fluorite, but with physical and chemical properties that make their use practical. These glasses are still expensive and more difficult to use than ordinary ones, but they do of fer significant advantages in terms of reducing the chromatic aberrations that otherwise severely limit the imaging potential of all long-focal-length refracting optics. Typical available versions of these glass types are the FK Schott, FCD Hoya, FPL Ohara, and PFC Corning series of glasses.
These design types offer outstanding optical correction together with remarkable specifications , resulting in considerable size and cost. Commercial embodiments include 300-mm F/2 and 400-mm  F/2.8 for 35-mm. They are widely used for sports and wildlife photography. Since secondary color increases as the front vertex distance is reduced, it is advisable to regard excessively short all-refractive telephotos with some caution. Refer to Figs.12 and 13.

2.6.  Zoom Lenses

Zoom lenses have evolved significantly in the past twenty years. In the early 1970s, there was basically only the classic four-group type of zoom lens. This four-group zoom has two moving groups between a front group used only for focusing and a stationary rear (‘‘master’’) group. This type is still found on consumer video cameras. Figures 14 and 15 show a variation of this form with the rear group also moving for zooming. The master group could often be changed to yield a different zoom with the same ratio over a different range.

The second basic form, originating in the mid 1970s, was the two-group wide-angle zoom, typically 24 to 48 mm and 35 to 70 mm for the 35-mm format. Both the front negative group and the rear positive group move for zooming, and the front group is also used for focusing. This lens type has an inherently long back focal length, making it eminently suitable for the SLR camera. See, for example, USP 4, 844, 599. The maximum zoom range is about 3 : 1.

In order to achieve lens types such as a 28- to 200-mm zoom for 35-mm, new ideas had to be employed. The resulting lenses have up to five independent motions, including that of the diaphragm. These degrees of freedom allow for the location of the entrance pupil to be near the front of the lens at the short-focal-length position and also for the exit pupil to be located near the rear, particularly at the long-focal-length setting. These conditions result in acceptably small size.

The extra zooming motions permit a large focal-length range to be achieved without any one motion being excessively long. There is a constant struggle in the design of these zooms to minimize the diameter of the front of the lens. This is not only to reduce size and weight, but also to permit the use of acceptably small filters. Some designs do have problems with relative illumination at the wide-angle end.

In the past, these lenses have been focused either by moving the front group or by moving the entire lens, the latter option leading to the so-called varifocal zoom. However, more recent developments in miniature electromechanical and autofocusing systems have led to the evolution of extended range zooms in which the distinction between a focusing



and a compensating group has become academic. As a result, small internal zooming groups can serve a dual function as focusing groups under the control of an autofocusing system. Refer to Figs.16, 17, and 18.
A recent new development in zooms is one for the so-called compact 35-mm camera. In its most basic form, this type can have as few as three elements and is characterized by having a front positive component and a rear negative component. This lens has an inherently short back focal length at the wide end, making it not suitable for SLR cameras with swinging mirrors.
In more complicated versions , this idea can be extended to 28 to 160 mm or further, the main limitation being a small relative aperture at the long-focal-length end.
A recent practical embodiment is a four-element 38- to 90-mm F/3.5 to 7.7 having three aspherical surfaces. See, for example, USP 4, 936, 661.
Zoom lenses are also found on most consumer video cameras. The classic fixed front-and rear-group type (with the aperture stop in the rear group) is still commonly used because the very small format sizes can permit acceptably small lenses. This lens form is also used for motion picture and television zooms. In many of these applications, it is desirable to have an exit pupil position that does not change with zooming.
Telecentricity of the exit pupil is also sometimes required. In addition, the motion picture industry still prefers zoom lenses that have conventional front-group focusing in order to easily calibrate tape-measure focus measurements.
Very long range television zooms (often 30 : 1 or more) are also of the fixed front and rear type, with a succession of cascading zooming groups in between.


A wide variety of camera lenses has been classified in Table 1 in terms of total pixel capability \(P\) and pixels per steradian \(AD\). Pixels are defined as digital resolution elements relative to a specified modulation level and are calculated as follows:

The polychromatic optical transfer function of each lens is calculated and the spatial frequencies at which the modulation falls to 0.5 and 0.2 is noted at each of five field points. The lower of the meridional and sagittal values is used.

The image field of the lens , assumed to be circular with diameter \(D\), is divided into four annular regions. The outer boundaries of each region correspond respectively to \(0.35H\), \(0.7H\), \(0.85H\), and \(1.0H\), where \(H\) is the maximum field height. The area of each region is computed.

The average of the inner and outer boundary-limiting spatial frequency values is assigned to each region. This is done for both the 0.5 and 0.2 modulation levels.

The area of each annular region, in square millimeters, is multiplied by the square of the spatial frequency values from the previous step to yield regional pixel counts for both 0.5 and 0.2 modulation levels.

The pixel counts are summed over all regions to yield the \(D\) data in Table 1.

The \(AD\) data in Table 1 are obtained by dividing the total pixel values by the solid angle of the lens in object space. The solid angle \(S\) is given by the following formula:

\[S=2\pi(1-\cos W)\]

where \(W\) is the semifield angle of the lens in degrees.

In general, for a given image diameter \(D\), a larger \(P\) implies higher image quality or greater information-gathering capability. A lens designed for a smaller \(D\) will have a lower \(P\) than a lens of similar quality designed for a larger \(D\). These same generalizations hold for \(AD\) except that, in addition, a lens designed for a smaller field angle and a given \(D\) will have a larger \(AD\) than a lens of similar image quality designed to cover a wider field for


the same \(D\). In other words, for the same image-quality level and format size, wide-angle lenses have lower \(AD\) values than do narrow angle lenses.


A wide variety of camera lenses has been selected to show typical performance characteristics. In most cases, the data have been derived from the referenced published United States patents. The authors have taken the liberty of reoptimizing most of the data to arrive at what would, in our judgment, correspond to production-level designs.

All performance data have been shown at maximum aperture. It is important to realize that photographic lenses are invariably designed so that optimum performance is achieved at F-numbers at least 2 stops slower than maximum. A general explanation of the data page follows.

The lens drawing shows the marginal axial rays together with the upper and lower meridional rays for seven-tenths and full field.

The lens prescription and all other data are in millimeters. Glass catalogs are Hoya, Ohara, and Schott. Distances to the right of a surface are positive. A positive radius means that the center of curvature is to the right of the surface. The thickness and glass data indicate the distance and medium immediately following the particular surface.

The optical transfer function (OTF) plots show the through-focus modulation transfer function (MTF) on the left and the OTF at best axial focus on the right . The data are shown for five field points, viz., the axis, \(0.35H\), \(0.70H\), \(0.85H\), and \(1.0H\), where \(H\) is the maximum field angle in object space.

The actual field angles are indicated in the upper-right-hand corner of each best-focus OTF block and are in degrees. The through-focus data are at the indicated spatial frequency in cycles per millimeter with an additional frequency on-axis (dotted curve). Both the through-focus and best-focus data indicate meridional (solid curves) and sagittal (dashed curves) MTF. The modulus scale is on the left of each block and runs from zero to one. The phase of the OTF is shown as a dotted curve in the best-focus plots. The scale for the phase is indicated on the right of each best-focus block and is in radian measure.

All the OTF data are polychromatic. The relative weights and wavelengths used appear in the lower-right-hand corner of each page. The wavelengths are in micrometers and the weights sum to one. The axial focus shift indicated beneath the best-focus plots is relative to the zero position of the through-focus plots. The best-focus plane is at the peak of the additional axial through-focus plot (dotted curve).

Vignetting for each field angle is illustrated by the relative pupil area plots on the right-hand side of each page. The distortion plots shows the percentage of radial distortion as a function of fractional field height. The MTF Astigmatism plot shows the loci of the through-focus MTF peaks as a function of fractional field height. The data can be readily determined directly from the through-focus MTF plots.

Certain acronyms are used in the System First-Order Properties:

Effective focal length (EFL)
Back focal length (BFL)
Front vertex distance (FVD)
Barrel length (BRL)
Entrance pupil distance (ENP)
Exit pupil distance (EXP)


The ENP and EXP data are measured from the front and rear vertices of the lens, respectively. A positive distance indicates that the pupil is to the right of the appropriate vertex. 



Share this post



Sold Out