Camera lenses

Sidney Ray

All images © Sidney Ray unless indicated.

LENS ABERRATIONS

Introduction

An understanding of residual aberrations (errors) is useful in describing the types, merits and imaging limitations of camera lenses. An ‘ideal’ lens forms geometrically accurate images but actual lenses, especially simple ones, do not since the refractive index of glass varies with wavelength, lens surfaces are usually spherical in shape and because of the wave nature of light (see Chapter 2). These cause respectively chromatic aberrations, spherical aberrations and diffraction effects. The degrading effects usually increase with both aperture and angle of field.

There are seven primary chromatic and spherical aberrations. Two direct errors or axial aberrations affect all parts of the image field as well as the central zone, known as axial chromatic aberration and spherical aberration. The other five errors affect only rays passing obliquely through the lens and do not affect the central zone. The effects of these oblique errors, or off-axis aberrations, increase with the distance of an image point from the lens axis. They are called transverse (or lateral) chromatic aberration (often called ‘lateral colour’), coma, curvature of field, astigmatism and (curvilinear) distortion (see also Chapter 6). Their degrading effects appear in that order as the angular field of view increases.

Axial and lateral chromatic aberrations are chromatic effects; spherical aberration, coma, curvature of field, astigmatism and distortion are spherical effects. The latter are also called Seidel aberrations after L. Seidel, who in 1856 gave a mathematical treatment of their effects. They are also known as third-order aberrations, from their mathematical formulation. Modern highly corrected lenses have only residual traces of these primary aberrations.

Axial chromatic aberration

For transparent media, shorter wavelengths are refracted more than longer wavelengths, causing spectral dispersion and dispersive power. Focal length varies with the colour of light (see Figure 10.1); the focus for blue light is closer to the lens than the focus for red, giving axial chromatic aberration.

Using two elements of different optical glass, the chromatic aberrations in one can be made to effectively cancel out those in the other. Typically, a combination of positive ‘crown’ glass and negative ‘flint’ glass elements was used. The two elements may be separated or cemented together. A cemented achromatic doublet lens made in this way is shown in Figure 10.2. Other errors may be simultaneously corrected giving satisfactory results over a narrow field at a small aperture.

Figure 10.1   The dispersive effects of chromatic aberration in a simple lens.

Figure 10.2   The principle of an achromatic doublet lens combination.

The chromatic performance of a lens is usually shown by a graph of wavelength against focal length, as shown previously in Figure 6.3. The variation of focus with wavelength for an uncorrected lens is an approximately straight line; that of an achromatic lens is approximately a parabola. The latter curve indicates the presence of a residual uncorrected secondary spectrum. The two wavelengths chosen to have the same focus positions are usually in the red and blue regions of the spectrum, for example the C and F Fraunhöfer lines. A lens corrected to bring three colour foci into coincidence is said to be apochromatic. This term is also used for those lenses that are corrected fully for two wavelengths, but use special low-dispersion glasses to give a much-reduced secondary spectrum. It is also possible to bring four wavelengths to a common focus, giving a superachromat. The wavelengths chosen are in the blue, green, red and infrared regions, so that no focus correction is needed between 400 and 1000 nm. Using materials such as silica and fluorite, an achromatic lens may be made for UV recording, needing no focus correction after visual focusing.

Other optical materials require chromatic correction. Plastics (polymers) are used in photographic lenses either as individual elements or as hybrid glasseplastic aspheric combinations. It is possible to design an achromatic combination using plastics alone.

The use of reflecting surfaces that do not disperse light, in the form of ‘mirror lenses’, offers another solution, but most mirror designs are for long-focus lenses only. Most of these, too, are catadioptric lenses with some refracting elements and these still require some colour correction.

Lateral chromatic aberration

Lateral or transverse chromatic aberration, also called either lateral colour or chromatic difference of magnification, appears in the form of dispersed colour fringes at the edges of the image (see Figure 6.4). It is an off-axis aberration, i.e. it is zero at the centre of the focal plane but increases as the angle of field increases. Whereas axial chromatic aberration concerns the focused distance from the lens at which the image is formed, lateral chromatic aberration concerns the size of the image. It is not easy to correct: its effects worsen with an increase in focal length, and are not reduced by closing down the lens aperture. It can be minimized by a symmetrical lens configuration and at least three types of optical glass. Almost full correction is achieved by use of special optical materials (Figure 10.3). These include optical glass of anomalous or extra-low dispersion (ED), which may be used in long lenses, at increased cost. Another material with very low dispersion characteristics is fluorite (calcium fluoride), grown as large crystals for photographic use. Unfortunately, fluorite is attacked by the atmosphere, so it must be protected by outer elements in the lens construction. Also, the focal length of fluorite lenses varies with temperature so infinity focus may vary. The cost of lenses using fluorite elements is significantly higher than that of equivalent conventional designs.

Figure 10.3   Refraction and dispersion by optical materials. The refractive power of a material is shown by the deviation angle D of incident light I. Dispersion by refraction is indicated by the length of spectrum RGB. Relative partial dispersion is indicated by the ratio of lengths RG and GB. (a) Conventional optical glass: dispersion is greater at short wavelengths. (b) High index glass: deviation increases but so does dispersion, D₁ > D. (c) ED glass: anomalous low dispersion at short wavelengths. (d) Fluorite: low deviation and anomalous dispersion, D₂ < D.

Spherical aberration

The amount of refraction depends on the angles of incidence made with the lens surfaces and the refractive index of the elements. Surfaces are usually spherical, being easy to manufacture. However, a single lens element with one or two spherical surfaces does not bring all paraxial (near axial) rays to a common focus. The exact point of focus depends on the annular region or zone of the lens surface under consideration. Rays from outer (‘marginal’) zones come to a focus nearer to the lens than those through the central zone (Figure 10.4). Consequently, a subject point source does not produce a true image point. The resultant unsharpness is called spherical aberration (SA). In a simple lens, SA is reduced by using a small aperture. As aperture is reduced the plane of best focus may shift, a phenomenon characteristic of this aberration. Spherical aberration in a simple lens is usually minimized by a suitable choice of radii of curvature of the two surfaces of the lens, termed ‘lens bending’.

Figure 10.4   Spherical aberration in a simple lens.

Correction of SA is by choice of a suitable pair of positive and negative elements whose spherical aberrations are equal and opposite. This correction is combined with that for CA and coma (see below) to give an aplanatic lens. Full correction is difficult and limits the maximum useful aperture of some designs, for example to f/5.6 for symmetrical lenses. The double-Gauss configuration, with five or more elements, allows apertures of f/2 and greater.

An aspheric surface can give a larger useful aperture, or alternatively allow fewer elements necessary for a given aperture. Optical production technology now provides aspheric surfaces at reasonable cost and they find a variety of uses. Another alternative is to use optical glasses of very high refractive index, which then need lower curvatures for a given refractive power, with a consequent reduction in spherical aberration.

Spherical aberration varies with focused distance. A lens computed to give full correction when focused on infinity might perform less well when focused close up. One solution uses a group of elements moving axially for correction purposes as the lens is focused and coupled to the focusing control, termed a floating element. Most ‘macro’ lenses for close-up photography incorporate such a system.

Leaving a controllable amount of residual uncorrected SA gives a noticeable ‘soft-focus’ effect, particularly useful for portraiture. The Rodenstock Imagon lens was a well-known example. The degree of softness is controlled either by specially shaped and perforated aperture stops to select particular zones of the lens, or by progressive separation of two of the elements of the lens.

Coma

In an uncorrected simple lens, oblique (off-axis) rays passing through different annular zones of the lens intersect the film at different distances from the axis, instead of being superimposed. The central zone forms a point image that is in the correct geometrical position. The next zone forms an image that is not a point but a small circle that is displaced radially outwards from the geometric image. Successive zones form larger circles that are further displaced, the whole array adding together to give a V-shaped blur known as a coma patch, from its resemblance to a comet. Coma is significantly reduced by stopping down the lens and can be reduced in a simple lens by placing the aperture stop so that it restricts the area of the lens over which oblique rays are incident. In compound lenses coma is reduced by balancing the error in one element by an equal and opposite error in another. In particular, symmetrical construction is beneficial. Coma is particularly troublesome in wide-aperture lenses.

Curvature of field

From the basic lens conjugate equation, the locus of sharp focus for a planar object is the so-called Gaussian plane. In a simple lens, however, this focal surface is in practice not flat but spherical, called the Petzval surface, centred approximately at the rear nodal point of the lens (Chapter 6). It is impossible to obtain a sharp image all over the field: when the centre is sharp the corners are blurred, and vice versa. Some large-aperture camera lenses are designed with sufficient residual curvature of field to match the image surface or ‘shell’ of sharp focus to the natural curvature of the film in the gate; a number of slide-projector lenses have been designed in this way. Double-Gauss-derived lenses give a particularly flat image surface, e.g. the Zeiss Planar series of lenses. Given the planar nature of focal plane arrays of imaging elements, it is essential that a lens for digital cameras has a near-flat image surface.

Astigmatism

The image surface is the locus of true point images only in the absence of the aberration called astigmatism. This gives two additional curved astigmatic surfaces close to the focal or Petzval surface. The term ‘astigmatic’ comes from a Greek expression meaning ‘not a point’, and the two surfaces are the loci of images of points in the object plane that appear in one case as short lines radial from the optical axis, and in the other as short lines tangential to circles drawn round the optical axis. Figure 10.5a shows the geometry of the system, and the occurrence of astigmatism. When light from an off-axis point passes through a lens obliquely, the tangential and radial (sagittal) components are brought to different foci, forming two image ‘shells’ (see Figure 10.5b). On one surface all images of off-axis points appear as short lines radial from the optical axis, and on the other as tangential lines. The surface which approximately bisects the space between the two astigmatic surfaces contains images which are minimum discs of confusion and may represent the best focus compromise. Astigmatism mainly affects the margins of the field, and is therefore a more serious problem with lenses that have a large angle of view.

Both astigmatism and curvature of field are reduced by stopping down. Although curvature of field can be completely corrected by the choice and distribution of the powers of individual elements, astigmatism cannot, and it remained a problem in camera lenses until the 1880s, when new types of glass were made available from Schott based on work by Abbe, in which low refractive index was combined with high dispersion and vice versa, so as to reduce astigmatism without affecting other corrections. Such lenses were called anastigmats. Early anastigmat lenses were usually based on symmetrical designs, which gave a substantially flat field with limited distortion.

Curvilinear distortion

The aperture stop should be located so that it transmits the bundle of rays that surround the primary ray (i.e. the ray that passes through the centre of the lens undeviated). Image distortion occurs when a stop is used to control aberrations such as coma. If positioned in front of the lens or behind it, the bundle of rays selected does not pass through the centre of the lens, but through a more peripheral region, where it is deviated either inwards, for a stop on the object side of the lens (‘barrel distortion’), or outwards, for a stop on the image side of the lens (‘pincushion distortion’) (see Figure 10.6). These names represent the shapes into which the images of rectangles centred on the optical axis are distorted. Because the aberration produces curved images of straight lines it is correctly called curvilinear distortion, to distinguish it from other distortions such as geometrical distortion and the perceptual distortion consequent on viewing photographs taken with a wide-angle lens from an inappropriate distance.

As distortion results from stop position, it cannot be reduced by stopping down. It can be minimized by making the lens symmetrical in configuration, or nearly symmetrical (‘quasi-symmetrical’). An early symmetrical lens, the ‘Rapid Rectilinear’, took its name from the fact that it produced distortion-free images and was of reasonable aperture (‘rapidity’). A truly distortion-free lens is termed orthoscopic. The geometrical accuracy of the image given by a lens is sometimes referred to as its ‘drawing’.

Figure 10.5   Astigmatism and its effects. (a) Geometry of an astigmatic image-forming system such as a simple lens. (b) Astigmatic surfaces for radial and tangential foci. (c) Appearance of images of point objects on the astigmatic surfaces: (i) object plane; (ii) sagittal focal surface; (iii) surface containing discs of least confusion; (iv) tangential focal surface.

Lenses of highly asymmetrical configuration, such as telephoto and retrofocus lenses, are prone to residual distortions; telephoto lenses may show pincushion distortion and retrofocus lenses barrel distortion. The effect is more serious in the latter case, as these are used for wide-angle work, where distortion is more noticeable. Zoom lenses tend to show pincushion distortion at long-focus settings and barrel distortion at short-focus settings, but individual performance must be determined by the user. General-purpose lenses usually have about 1% distortion measured as a displacement error, acceptable in practice. Wide-angle lenses for architectural work must have less than this. The use of aspheric lens surfaces may help reduce distortion.

Figure 10.6   The effects of curvilinear distortion. (a) The selection of a geometrically incorrect ray bundle by asymmetric location of the aperture stop. (b) Image shape changes caused by barrel and pincushion distortion.

Lens aperture and performance

As the aperture is progressively closed down, residual aberrations (except for lateral chromatic aberration and distortion) are reduced, but the effects of diffraction (see Chapters 2 and 6) are increased. At large apertures the effects of diffraction are small, but uncorrected higher aberrations reduce the theoretical performance. The balance between the decreasing aberrations and the increasing diffraction effects on stopping down (see Chapter 2) the lens means that such aberration-limited lenses have an optimum aperture for best results, often about three stops closed down from maximum aperture. Most lenses, especially those of large aperture, do not stop down very far, f/16 or f/22 being the usual minimum values, and diffraction effects may not be noticed; the only practical effect observed may be the increase in depth of field. With wide-angle lenses in particular, a variation in performance at different apertures is to be expected, owing to the effect of residual oblique aberrations. Here it may be an advantage to use a small stop (similarly for zoom lenses). For close-up photography, photomacrography and enlarging, the value of N′ = v/d (Chapter 6) is much greater than the f-number of the lens, and the effects of diffraction are correspondingly greater than when the same lens is used for distant subjects. In these circumstances the lens should therefore be used at the largest aperture that will give an overall sharp image.

PHOTOGRAPHIC LENSES

Photography uses a variety of general-purpose and specialist lenses whose primary function is to form an image of sufficient image illumination, resolution and accuracy suited to the camera format and application. Selection of a suitable lens is facilitated by knowledge of imaging requirements and lens limitations related to catalogued properties.

Many lenses are adaptable for a variety of uses; some have restraints on their operating conditions and others are application specific. Photographic lenses are multi-element types and this optical unit is usually in a focusing mount or uses internal focusing, often integrated with an autofocus system. An automated iris diaphragm is incorporated and often a leaf shutter too. A checklist of relevant properties includes the following:

•  Focal length. The (effective) focal length (EFL) (f) of the lens determines the image size from a given viewpoint and also the physical size of the lens. The EFL may be fixed as in a prime lens, or variable as in a zoom or varifocal lens (including internal focusing types). The marked EFL is nominal and exact values are determined by calibration.

•  Aperture. Light transmission by a lens depends upon the aperture stop and is calibrated either as an f-number (N) or a T-number (T-no) or perhaps as numerical aperture (NA). For a lens with entrance pupil diameter E_N and transmittance T, we have:

   Maximum aperture is of some importance, but values better than f/2 or f/2.8 depending on EFL are achieved at considerable cost and even then may be a compromise as imagery degrades, being aberration limited rather than theoretical diffraction limited. Zoom lenses have modest maximum apertures.
Minimum aperture may be important for considerations such as depth of field (DOF). Aperture range is used to control exposure and is usually more limited than shutter speed range. Choice of optimum aperture is a compromise between optical performance and DOF obtained.

•  Angular field of view (FOV). The film gate or active sensor dimensions in a camera act as the field stop and together with EFL or image conjugate (v) determine the FOV obtained, which provides an unambiguous method of classifying the lens for this format into a type such as wide-angle, standard or long-focus. Taking a format dimension K (horizontal, vertical or diagonal distance) and semi-field angle θ:

For marketing purposes, the diagonal FOV is quoted, being the largest value, but the horizontal FOV is of more practical use. Note that a lens of EFL 50 mm related to format and FOV may be either a wide-angle or standard or even long-focus category. A standard lens has EFL z K (diagonal) or z 2K for cine and video.

•  Covering power. Irrespective of aperture stop shape, a lens gives an image circle containing detail. The diameter of this circle or covering power is determined by lens design and any vignetting from optical and mechanical causes. Normally the diameter must circumscribe or be greater than the format diagonal, otherwise vignetting occurs. For use of camera movements, extra covering power is needed. Covering power is minimum at infinity focus and maximum aperture, but increases at reduced aperture and close focus.

•  Focusing range. The focusing range of mounted lenses is usually from infinity to a subject distance (u) giving a magnification of 0.1–0.2. Optical performance usually deteriorates with decrease in u, unless it is a macro type with suitable correction. Fixed focus lenses are used for simplicity with focus set on the hyperfocal distance.

•  Spectral transmission. Most lenses have broad-band transmission in the visible and IR regions and little in the UV, depending on the optical materials and lens coatings used. Families of lenses have matched transmissions to give a constant colour rendering irrespective of lens configuration. Colour filters may be used either to ‘fine-tune’ results or isolate transmission bands or improve resolving power (RP, Chapter 24). Lenses for use in the UV or IR use materials such as silica and fluorite or germanium respectively.

•  Chromatic correction. Lenses may have residual amounts of lateral and transverse chromatic aberration depending upon the type and level of chromatic correction. Residual lateral chromatic aberration or secondary spectrum is illustrated by a graph of focus shift against wavelength (see Chapter 6). Achromatizing a lens is for two chosen wavelengths and depends on application. Visual and photographic corrections use the C and F spectral lines. A reduced tertiary spectrum is given by use of ED glasses and fluorite elements in apochromatic lenses or by high-index glasses in ultra-achromatic lenses. Special lenses to give high RP are best used with monochromatic light.

•  Residual curvilinear distortion. Two varieties, termed barrel and pincushion, are detectable as shape changes in images otherwise highly corrected to be sharp, stigmatic and planar. Stopping down the lens to its optimum aperture has no effect. Distortion worsens off-axis and with focused distance. The prime cause is the position of the aperture stop and a symmetrical lens configuration greatly reduces distortion. A fish-eye lens is exceptional in that it deliberately retains excessive barrel distortion to improve peripheral illumination (Chapter 6).

•  Image contrast. Apart from the inherent value of image contrast that varies with spatial frequency as a consequence of lens design, residual aberrations and diffraction, a lens may suffer reduced contrast due to its construction, the presence of flare and inefficiency of anti-reflection coatings as well as environmental factors.

•  Lens type. Lenses may be classified by their type of configuration as well as FOV and EFL. Alternative configurations of the additional elements used downstream from the first one for aberration correction also give useful properties such as compactness, a long back focal distance (BFD) or freedom from distortion.

PHOTOGRAPHIC LENS TYPES

Simple lenses

A simple lens, i.e. a one-element type with spherical surfaces, has all of the primary aberrations. Chromatic aberrations, spherical aberration, coma, astigmatism and curvature of field all combine to give poor image quality, while distortion leads to misshapen images. Image quality is decidedly poor. But aberrations can be partially reduced by choice of suitable curvatures for the two surfaces and by location of an aperture stop. If, in addition, the subject field covered is restricted, it is possible to obtain image quality that is acceptable for some purposes, especially for simple cameras and single-use cameras.

A simple, positive, biconvex lens is shown in Figure 10.7. Performance is improved by modification to give derivatives by alteration of curvatures, the use of other glasses and adding corrective elements. This compounding and splitting distributes the power and correction among more elements.

Compound lenses

The performance of a single-element lens is limited by the available number of optical variables or degrees of freedom. In particular, there are only two surfaces. Using two elements to give a doublet lens provides three or four surfaces instead of two over which to spread the total refraction. Different types of glass can be used for the elements, their spacing can be varied or they can be cemented in contact. More elements increase the possibilities. A triplet lens of three airspaced elements can satisfactorily be corrected for the seven primary aberrations for a modest aperture and field of view. Five to eight elements give highly corrected, large-aperture lenses. Zoom lenses require more elements to give a suitable performance, and up to a dozen or more may be used.

Figure 10.7   Derivatives from a simple biconvex lens to give improved performance. (a) Aspheric front surface. (b) Changing to meniscus shape and positioning a stop in front. (c) ‘Compounding’ with another element of a different glass into an achromatic doublet. (d) ‘Splitting’ to give a doublet symmetrical lens.

Such compound lenses, i.e. multi-element, were progressively developed to give better image quality, larger apertures and greater covering power than those of simple lenses. The general principle is to balance aberrations from one element with equal but opposite values in another element ‘downstream’ in the configuration. Full correction is not usually feasible, just reduction to acceptable levels. Compromises have to be made with a lens intended for general-purpose use. If, however, maximum correction is desired in a lens designed with one particular use in mind, and which will therefore be employed only under a fixed set of conditions (say, always at full aperture, or at one magnification, or with monochromatic light), then improved performance is possible under these conditions at the expense of performance under other conditions for which the lens is not intended.

Photographic lenses use a few basic types of configuration or arrangements of individual elements, as shown in Figure 10.8. Only the simplest form of each is shown. Practical designs usually have many more elements for the control of aberrations.

Development of the photographic lens

Lenses are categorized related to nineteenth-century lens design. By the beginning of the twentieth century, lenses were available (albeit of modest aperture and field angle) which were virtually fully corrected for all the primary lens aberrations. The configurations of some early lenses are shown in Figure 10.9. By convention in such diagrams, light enters from the left. Recent progress has largely been dependent on the availability of improved optical materials, lens-coating techniques, computer-assisted calculations, advances in lens production technology, and more appropriate means of lens testing and evaluation.

Simple lenses and achromats

The year 1839 marked the beginning of practical photography. The use of lenses prior to this date was for for spectacles, telescopes, microscopes and the camera obscura. The landscape lens as used in the camera obscura was adapted for use in early cameras in meniscus form with a front stop. Wollaston had shown in 1812 that a flatter field plus reduced coma and astigmatism were given by this arrangement. Such lenses were used in box cameras and now in single-use cameras. In 1757 Dollond produced an achromatic doublet telescope lens and this was later adopted for landscape lenses for photography. Because of uncorrected off-axis aberrations, such lenses could only be used at small apertures and fields. Maximum apertures seldom exceeded f/14.

The Petzval lens

Simple lenses were inconveniently slow for portraiture with the insensitive plates of the period, and active efforts were made to design a lens of large aperture; the principles were already well understood, but lack of suitable optical glasses was a problem. In 1840 J. Petzval designed a lens of aperture f/3.7 using two separated, dissimilar achromatic doublets. This was the first lens to be computed specifically for photography. It had about 15 times the transmission of other contemporary designs. Some residual uncorrected aberrations, particularly astigmatism, caused poor peripheral definition, but this was found particularly pleasing for portraiture, giving a characteristic softness and vignetting. The restricted field of good sharpness needed a longer focal length than normal to cover a given format. The consequent need for a more distant viewpoint helped improve perspective in portraiture. This design is still the basis of many long-focus, large-aperture systems, especially projection lenses.

Symmetrical doublets

Landscape lenses did not improve until the 1860s, when lenses of good definition, flat field and moderate aperture became available as in the Steinheil Periskop lens of 1865, which used two meniscus components placed symmetrically about a central stop. The significance of symmetrical or near-symmetrical construction is that it permits almost complete correction of coma, lateral chromatic aberration and distortion. This non-achromatic lens was soon superseded in 1866 by the introduction of two independent designs: the Rapid Rectilinear by Dallmeyer and the Aplanat of Steinheil, in which the meniscus lenses were replaced by achromatic combinations. Maximum aperture was around f/8, but astigmatism was still uncorrected.

Figure 10.8   The basic achromatic doublet lens may be further split and compounded in various ways to provide the basic types of photographic lenses.

Anastigmats

Originally, astigmatism and field curvature could not be corrected together with other aberrations, as the dispersion of available glasses increased more or less proportionally with refractive index. However, pioneer work by Abbe and Schott in the 1880s produced new types of optical glass. Use of these resulted in the first anastigmatic lenses. Symmetrical construction was used, with components using a multiple cemented combination of old and new glass types, with maximum aperture up to about f/6.8.

Figure 10.9   Configurations of early lenses. (a) Landscape lens of Wollaston. (b) Achromatic landscape lens of Chevalier. (c) Grubb’s landscape lens. (d) Petzval portrait lens. (e) Steinheil’s Periskop lens. (f) Rapid Rectilinear lens. (g) Zeiss Double Protar lens. (h) Goerz Dagor lens. (i) Cooke triplet lens. (j) Zeiss Tessar lens.

Triplets

The complexity of early anastigmat lenses meant high manufacturing costs. In 1893 the Cooke Triplet lens was introduced. This used only three single separated elements having simplicity of construction, while giving sufficient variables for full correction. Then by splitting and/or compounding the three elements, various triplet derivatives were produced. The Zeiss Tessar lens of 1902, and in production ever since, is one of the best known of these.

Double-Gauss lenses

A major disadvantage of symmetrical construction is the inability to correct additional aberrations, particularly higher-order spherical aberration; this limits maximum apertures to about f/5.6. Triplet construction has a limit of about f/2.8. To obtain useful maximum apertures of f/2 or better, a derivative of a symmetrical design was adopted based on an achromatic telescope doublet due to Gauss. This doublet was air-spaced with deeply curved surfaces concave to the subject. Two such doublets, both concave to a central stop, give the double-Gauss form of lens. Derivatives with up to seven elements have useful apertures up to f/1.2.

MODERN CAMERA LENSES

Camera lenses of fixed focal length (‘prime’ lenses) are based on triplet designs for the lower priced, moderate aperture varieties and double-Gauss designs for larger apertures. Symmetrical design is used for lenses for large-format cameras, for copying lenses and for some types of wide-angle lens. Complex and highly asymmetric designs are used for zoom, telephoto, retrofocus and ‘fish-eye’ lenses. A selection of typical configurations is shown in Figure 10.10. Different in concept, and used only for long-focus lenses, the ‘mirror lens’ employs reflecting surfaces both as the primary means of image formation and to fold the light path for compactness.

The standard lens for a camera is one whose (fixed) focal length approximates to the length of the diagonal of the image format or photoplane. Such lenses are highly developed, with large usable apertures and excellent performance over their field. However, they cannot meet all needs, particularly for large angular fields in cramped surroundings, or long-distance shots of inaccessible subjects. Then the use of wide-angle or long-focus lenses respectively is necessary. Also, where there is a need for a big close-up of a subject, a ‘macro’ lens is preferable. These alternative lenses also have a number of distinct design types, the results of intensive development work, aided by a number of interrelated advances in optical production technology such as aspheric and floating elements and anti-reflection coatings. Groups of moving elements were first used in zoom lenses to change focal length, and now ‘floating elements’ that move axially can correct for spherical aberration and retain performance at close object distances. This feature is particularly useful in macro lenses and wide-angle lenses of large aperture. The technique is commonly used for ‘internal focusing’ in a range of lenses from autofocus (AF) types to super-telephotos, giving a means of rapid focus change with little mechanical movement and allowing the lens barrel to be sealed against the environment.

Figure 10.10   Configurations of representative lenses. (a) 8 mm fish-eye. (b) 24 mm retrofocus wide-angle. (c) 50 mm f/1.4 double-Gauss derivative. (d) 105 mm f/1.8 double-Gauss derivative. (e) 200 mm f/4 telephoto. (f) 400 mm f/2.8 super-telephoto with ED glass element (hatched).

An example of improvements in just one class of lens is given by the wide-angle lens. The old problems of poor covering power, low marginal resolution, small usable apertures and flare have been overcome. Typically, for the 24 × 36 mm film or sensor format, 15 mm f/3.5, 24 mm f/2, 24 mm f/3.5 perspective-control and 35 mm f/1.4 lenses are commonly available, all in retrofocus configurations. The 60 × 60 mm film format has available lenses of 30–50 mm focal length and aperture f/4 to f/2.8. Large formats also have wide-angle lenses with usable apertures of f/5.6 to f/4 and sufficient covering power to permit limited use of camera movements.

By far the most popular type of lens, the zoom lens, has been much improved with many interesting design variants. Short-range zoom lenses have largely replaced the ‘standard’ lens for general-purpose cameras.

The macro lens, which is specifically designed and corrected for close-up work, now has an excellent all-round performance and a maximum aperture of f/2, its versatility making it a contender to the traditional standard lens.

WIDE-ANGLE LENSES

Wide-angle lenses, i.e. lenses where the focal length is less than the diagonal of the 35 mm film format, originate from early symmetrical film types. These were limited in practice by severely restricted covering power, owing to the cos⁴θ law, fall-off in marginal resolution, and small useful apertures (typically about f/22). Today, with digital sensor sizes often smaller than the 35 mm film frame, they come with even shorter focal lengths than wide angle lenses built for SLR 35 mm cameras.

Symmetrical-derivative lenses

Forms of quasi-symmetrical or near-symmetrical configuration give improved evenness of illumination and better image quality, as well as larger apertures up to about f/2.8. The symmetry means that correction for curvilinear distortion is particularly good. These symmetrical derivatives use very large negative meniscus lenses either side of the small central positive groups, giving the lens a characteristic ‘wasp-waisted’ appearance and increasing its bulk.

Such lenses, used on technical cameras, allow full use of camera movements, depending on focal length and covering power. The ability to use the rising-front movement is particularly valued. Unfortunately, just like the simpler symmetrical form, such lenses have a very short back focal distance (BFD) with the rear element very close to the film plane, so any form of reflex viewing and focusing is impossible; when this is necessary, lenses of retrofocus configuration must be used instead. Note that for compact cameras, a ‘telephoto wide-angle configuration’ is used to give as short a BFD as possible.

Retrofocus lenses

Departing from the symmetrical form of construction by using a front divergent (negative) group with a rear convergent (positive) group of elements results in a lens that has a short focal length in relation to its BFD, caused by a shift in the positions of the nodal planes (Figure 10.11). As this arrangement is the opposite of the telephoto construction, it is often described as a reverse or inverted telephoto configuration.

The asymmetry of this design can cause some barrel distortion. The long BFD allows devices such as reflex mirrors, shutters and beamsplitters to be located between the lens and film plane. The disadvantages are increased complexity of construction and the associated extra cost, bulk and weight.

Figure 10.11   Retrofocus construction. (a) A retrofocus combination of front negative lens and rear positive lens resulting in back focal distance B being much greater than focal length f. (b) An equivalent short-focus lens where B and f are similar.

Fish-eye lenses

The geometry of image formation and image photometry limit the field of view of a distortion-free lens to about 120°. However, if barrel distortion is permissible, a lens covering angles of view of 180° and even more is possible. Retrofocus configuration allows use of such lens systems in single-lens reflex cameras. These lenses are called fish-eye lenses, and are available in two versions. The quasi-fish-eye lens has a circle of illumination that circumscribes the film format and gives a 180° angle of view across the diagonal. The true fish-eye lens has its circular image wholly within the film frame, thus recording more of the scene. The diameter of the image circle depends on the focal length of the lens.

A different form of image projection is used for image formation. A conventional photographic lens of focal length f and semi-field angle θ forms images by central projection, where the distance (y) of an image point from the optical axis of the lens is given by the relationship y = ftan θ. Most fish-eye lenses use equidistant projection, where y = fθ when θ is measured in radians. Such lenses have many technical applications.

LONG-FOCUS LENSES

Long-focus designs

A long-focus lens is a lens whose focal length is greater than the diagonal of the format in use. As image size is proportional to focal length, an increase in focal length gives a bigger image. Lens configurations of achromat, Petzval, symmetrical and double-Gauss have all been used, depending on the maximum aperture and focal length required. Very-long-focus lenses of small aperture can be of simple construction, possibly just achromatic doublets. There are practical problems associated with long-focus lenses. Conventional refracting (dioptric) lens design is limited by the diameter of available glass blanks (some 150 mm) and by the degrading effects of lateral chromatic aberration as focal length increases. Also, the length and weight of such lens systems pose problems in design and handling. Internal reflections from the long lens barrel may cause flare. The use of telephoto construction and mirror optics reduces some of the problems of excessive length and lateral chromatic aberration. Refracting elements made from fluorite or special extra-low-dispersion glass can greatly improve colour correction.

Telephoto lenses

By placing a negative lens group behind a positive one, the transmitted light is made less convergent, as though it had been formed by a lens of much greater focal length; the nodal planes are now in front of the lens (Figure 10.12). The length of the lens barrel can be much less than is needed for a conventional lens of similar long focal length.

Figure 10.12   Telephoto construction. (a) A long-focus lens where the back focal distance B is similar to the focal length f as measured from the rear nodal point N₂ to film plane F. (b) An equivalent design using a front positive lens and a rear negative lens in a telephoto combination so that B is much less than f. (c) Another equivalent design using two optical reflecting surfaces to give a mirror lens, where B is very much less than f.

Using this idea, early telephoto attachments, the precursors of the modern teleconverter, were placed behind normal lenses to give a variety of increased focal lengths with relatively short camera extensions. The resultant combinations had small apertures, and performance was poor. Such systems were replaced by telephoto lenses, which are fully corrected and can have large apertures. Any residual pincushion distortion is due to the asymmetric construction.

Cameras using telephoto lenses are easier to handle, and less prone to camera shake, than those equipped with a long-focus lens of conventional design, as the camera is better balanced and lighter. The use of optical materials such as extra-low-dispersion (ED) glass and fluorite give a class of lens called super-telephoto. These have focal lengths of 200–1200 mm with the exceptionally large apertures of f/2 to f/2.8 in the shorter focal lengths and f/4 to f/5.6 in the longer focal lengths. Such lenses are state-of-the-art designs using multi-coatings, internal focusing and anti-flare construction. They are costly but are exceptionally easy to use hand held, with applications in sport, natural history and surveillance work. Apart from the ease of focusing and the capability of using slower films/ISO setting or short exposure times, an advantage of the large aperture is that the use of suitably matched teleconverters gives very-long-focus lenses that still have a usefully large aperture. For example, a 300 mm f/2.8 camera lens can be converted into a 450 mm f/4 or a 600 mm f/5.6 lens by the use of ×1.5 and ×2 teleconverters respectively.

Catadioptric lenses (‘mirror lenses’)

The advantage of real image formation using a concave mirror rather than a convex lens is that there is no chromatic dispersion. The Cassegrainian double-mirror system is preferred that uses a secondary mirror to reflect the image out through a hole in the primary mirror. For photographic purposes a paraboloid mirror is not suitable due to cost and small field angles. A spherical mirror gives a larger field but the image suffers from both SA and curvature of field.

Residual SA is corrected using different optical modifications (Figure 10.13). An aspheric Schmidt corrector plate at the centre of curvature of the spherical mirror is used for large-aperture, wide-field astronomical cameras, but is very expensive to manufacture. Cheaper alternatives for photography are to use either a Mangin mirror, which has the reflecting surface coated on to the rear surface of a thin refracting correcting element, or alternatively to use large, thick refracting elements that are concentric with the spherical prime mirror. This latter approach was pioneered independently by Bouwers in Holland and Maksutov in Russia during World War II. The introduction of refracting elements constitutes a catadioptric design. A dioptric system is a system consisting of transmitting and refracting elements, i.e. lenses, whereas a catoptric system consists only of reflective elements, i.e. optical mirrors. The refracting elements need to be achromatized and their power chosen so as to give a flat field. They are positioned to seal the barrel and provide a support for the secondary mirror. Flare is a serious problem, so baffling and other anti-flare measures are essential.

Because of the central obstruction caused by the secondary mirror, the transmission of the lens cannot be controlled by an iris diaphragm. Mirror lenses are available with focal lengths in the range of 300 mm to more than 2000 mm and with apertures from f/5.6 to f/11. The compact design with its short length and large diameter compares favourably with equivalent long-focus or telephoto constructions. A useful feature of mirror lenses is their ability to focus close. Typically, an axial movement of a few millimetres of the secondary mirror will focus a 500 mm lens from infinity to a magnification of some 0.25. A characteristic feature of a mirror lens is the ‘ring doughnut’ shape of out-of-focus highlights due to the annular shape of the entrance pupil.

Figure 10.13   Mirror lens designs. (a) Simple spherical mirror with spherical aberration at the focus. (b) Cassegrainian construction with secondary reflector. (c) Bouwers–Maksutov design. (d) Mangin mirror design.

ZOOM AND VARIFOCAL LENSES

Zoom lenses

A zoom lens is one whose focal length can be varied continuously between fixed limits while the image stays in acceptably sharp focus. The visual effect in the viewfinder is that of a smaller or a larger image as the focal length is decreased or increased respectively. The zoom ratio is the ratio of the longest to the shortest focal length – for example, a 70–210 mm zoom lens has a zoom ratio of 3:1. For 35 mm still photography, zoom ratios of about 2:1 up to 10:1 are available. For digital photography, where formats are much smaller, zoom ratios of 10:1 or 20:1 are common, further increased by digital methods to perhaps 100:1 with concomitant loss of image quality (see Chapter 14).

The EFL of a multi-element lens depends on the focal lengths of individual elements and their axial separations. An axial movement of one element will therefore change the focal length of the combination. This gives a primitive zoom lens or strictly a varifocal lens, as is used for a slide projector. The simplest possible arrangement is a front negative lens plus rear positive lens; reducing their separation increases the equivalent focal length.

A simple zoom lens has an aberrated image and does not retain sharp focus while being ‘zoomed’. Both problems require additional lens elements and in practice any number between four and 20 may be needed. A sharply focused image is retained while zooming by a process of compensation, provided, for example, by another element moving in conjunction with the zoom element. Two types of compensation are used: optical, where the moving elements or groups are coupled and move together; and mechanical, where the groups move independently at different rates, sometimes in different directions (Figure 10.14). Optical compensation was used originally but mechanical compensation is preferred as higher levels of correction are possible. The moving groups can follow non-linear paths, so that as the zoom control is operated the elements may advance and recede at different rates. Some zoom lenses use three to five moving groups, with a mixture of both optical and mechanical compensation.

The classic design of zoom lens used an arrangement of four groups of elements. Two linked movable zoom groups are located between a movable front group (used to focus the lens) and a fixed rear group that also contains the iris diaphragm. This rear group is positive and acts as a relay lens to produce an image in the film plane from the zoom groups, which behave as an afocal telescope of variable power. This system also keeps the f-number constant as focal length is altered, by controlling the size and location of the exit pupil of the system. This ‘fixed-group’ feature means that a separate mechanical control to adjust the iris according to focal length is not required. Close focusing (i.e. nearer than 1–2 metres) is also possible. For example, a separate macro-zoom control uses and rearranges the zoom groups so that for a particular focal length one group is moved to give a form of internal focusing over a limited close-up range with the prime focus control set at infinity focus. (In practice, there may be a gap between normal close focus and the far point of the close-up range so an achromatic close-up lens is required.) An advantage of this system is that the f-number stays almost constant over the close-up range, which is not the case with a conventional macro lens.

Figure 10.14   Configuration of a wide-angle zoom lens design (17–35 mm f/2.8–4) with mechanical compensation using three moving groups. Two aspherical elements and internal focusing are incorporated.

Not all ‘macro’ zoom lenses offer a genuine 1:1 image scale; the term ‘macro’ has become devalued and is often just used to mean a close-focus capability. A tele-zoom lens may now be no larger than an equivalent fixed-focal-length lens of the longest focal length it replaces. The use of ED glass elements and aspheric surfaces provides even more correction and compactness.

Zoom lenses include wide-angle-to-standard lenses for SLR cameras with 35 mm film or sensor format, such as 20–35, 24–70 and 28–85 mm, and their equivalents for digital cameras with smaller sensors. Continuous close focusing is possible with a single focus control, by movement of all or part of the lens groups, making separate macro modes obsolescent. The internal focusing may be under the control of an in-camera autofocus system, and the lens contains suitable electronics to relay data back into the central processing unit of the camera.

A penalty of mechanical compensation is that the f-number changes with focal length, typically giving a loss of one-half to one full stop from minimum to maximum focal length. This may be acceptable in order to keep the size of a zoom lens to within reasonable limits. Some lenses do have additional mechanical control of the iris to keep the f-number approximately constant while zooming. Today all cameras now have through-the-lens (TTL) metering, which will correct for changes in effective f-number. The modern zoom lens is very much a view-finder-oriented lens in that it carries little information on its controls as to focus setting, focal length and depth of field. The distortion correction of zoom lenses is now also much improved, and image quality may approach that of a fixed-focal-length lens.

The trend is to use a zoom lens as a replacement for a set of fixed-focal-length (prime) lenses. Cameras with zoom lenses but no reflex viewing system use a complex coupled direct viewfinder system which is also a miniature zoom lens corrected for visual use. Only an approximate indication of the subject area is given with total reliance upon an autofocus system. Digital cameras can use similar systems but also may provide useful direct viewing of focus and field of view by means of an LCD viewing screen.

For general-purpose photography, the zoom lens is a very useful tool. One lens, say of 28–105 mm and f/2.8–4 specifications with close-focus capability to an image magnification of 0.25, can perform adequately for most purposes, especially if medium apertures can be used. Zoom lenses are still of modest maximum aperture, some f/2.8 at most, and the double-Gauss type of lens with aperture f/2 to f/1.4 is still useful for some low-light photographic tasks, as is the super-telephoto lens. A selection of zoom lens configurations is shown in Figure 10.15.

In a varifocal lens there is no attempt to hold the focus constant when the focal length is changed. This makes for a simpler and cheaper design, especially where a constant focal plane has little or no advantage, as in slide and movie projectors. To offset the slight inconvenience of having to refocus the lens when the focal length (i.e. the projected image size) is changed, it is possible to produce very good correction with comparatively few glass elements. This type is especially useful in autofocus cameras, where the focus is monitored and adjusted as necessary.

Figure 10.15   Typical zoom lens configurations. The various groups of elements alter their relative positions in various ways to change focal length. (a) All the elements in three groups move between the extremes shown to give 21–35 mm. The iris also shifts. (b) All the elements move in two groups with the iris to give 35–70 mm. (c) Two groups move to give 70–150 mm, the iris remaining static. In focusing, the whole lens is moved axially.

Zoom lenses for compact and digital cameras

Compact cameras use both the 135 and APS formats, while digital cameras use focal plane arrays of much smaller formats, typically from 2/3 to 1/4 inch diagonal. Apart from small formats, most of these cameras do not use reflex viewfinders but rely instead on separate optical viewfinders or LCD screens. Both factors influence lens design in that the rear element can be very close to the focal plane, and that a useful zoom range is possible with only a few elements, especially if the maximum aperture is modest, perhaps f/4 at the most. The lens must also telescope down into the camera body for storage, to help keep the size of the camera small. For the 135 format, long-range zoom lenses of 38–200 mm are used, although the aperture reduces to some f/11 at the long-focus setting. The lenses are non-interchangeable and the collapsible telescoping barrel may cause some optical misalignment.

The basis of such compact designs was the Zeiss Biogon wide-angle lens, which has a very short back focal distance (BFD). From this was derived a ‘telephoto wide-angle’ lens (see Figure 10.16a), a short-focus lens using both telephoto configuration to reduce its physical length and internal focusing to keep its external size constant. This led to compact zoom lenses by using a moving element or group to alter focal length (Figure 10.16b) and moving the lens to give unit focusing under autofocus control. By use of technology such as plastic elements and aspheric lens surfaces, as few as four elements could be used for a satisfactory zoom or varifocal lens with a 2:1 zoom ratio. The lenses may suffer from noticeable curvilinear distortion at both ends of the zoom range and possibly some vignetting. The modest apertures available limit the useful range of an integral flash and low-light-level use may cause camera shake due to the slow shutter speeds needed, unless a fast film of 400–800 ISO is habitually used. The lenses usually lack a filter thread to take accessories such as lens hoods, filters and converters.

Figure 10.16   Zoom lens design for compact cameras. (a) Wide-angle telephoto configuration (35 mm f/2.8) as precursor to a zoom lens. (b) A 38–110 mm zoom design. Glass element A is aspherical.

Many digital cameras offer a ‘digital zoom’ feature. This is not an optical zoom using a lens, but uses a digital image processing routine to magnify a selected portion of the image frame stored as digital data (see Chapter 14). A bigger image is given by pixel interpolation (see Chapters 14 and 27) and too much ‘zooming’ causes unpleasant pixellation of the image.

MACRO LENSES

Design of a lens with good aberration correction requires the object conjugate distance to be specified. Most photography is of subjects at least 200 focal lengths away, so for convenience in design the object conjugate is taken as infinity. General-purpose lenses are therefore designed to give their best performance for distant subjects. The performance of such a lens will be less satisfactory when focused on a short distance, as in close-up work or photomacrography. Design features such as floating elements and aspheric surfaces may help in some cases, as can lens reversal rings, but it is preferable to use a lens optimized to produce a high-quality result when used for close-up work. Such a lens is known as a macro lens.

A macro lens has an extended focusing mount using a double helicoid arrangement. This gives enough extension to provide a magnification of 0.5, though many do give actual-size reproduction with m = 1 or more. A range from infinity to half-life-size is usually sufficient in practice, at least in the 24 × 36 mm format, and this keeps the focusing mount to a reasonable size. For the magnification range from 0.5 to 1.0, an extension tube can be added. Such a lens has full automation of the iris, and full aperture metering. Correction is optimized for a magnification of 0.1 (not infinity as discussed above) and the corrections hold well down through the close-up range to unit magnification. Thereafter, the lens is best used reversed, with possible consequent loss of the automatic features. The lens barrel may be engraved with scales of magnification and exposure correction factors: these are more useful when using manual electronic flash, as TTL metering systems automatically correct exposure at long extensions.

Macro lenses use a double-Gauss design computed to give a flat field and a distortion-free image essential for copying work. The maximum aperture can be f/2. For optimum results with distant subjects it is advisable to close down about two stops from maximum. Macro lenses often have focal lengths that are longer than normal; they are typically in the range 55–200 mm for a 24 × 36 mm format. Some are obtainable as just a lens head, an optical unit for attachment directly to an extension bellows so as to give an extended focusing range. Others have very short focal lengths of 12.5–50 mm to allow greater magnification with a modest bellows extension.

Autofocus macro lenses use complex arrangements of internal adjustments of elements to provide both focus and aberration correction. The use of ED glass, aspheric surfaces and floating elements is common, and a typical design may have 10 or more elements. A long-focus macro lens is a specialist lens but is favoured for the improved perspective it gives by virtue of its more distant viewpoint and the increased working distance from front element to subject. Internal focusing is convenient in a macro lens as there is then no need for a complex double-helical lens barrel extension system, but the effective focal length also changes continuously over a short range, so an indication of magnification to help calculate depth of field is useful. Internal focusing also means that the lens barrel does not rotate during focusing, useful with direction-sensitive devices such as polarizing filters.

OPTICAL ATTACHMENTS

A variety of optical attachments can be used in front of a camera lens. Like filters (see below), these are produced in a range of fittings and sizes, and are attached in a similar manner. Materials used range from high-quality anti-reflection coated optical glass to moulded plastics. Dependent on its function, the device may be transparent and non-selective, or it may absorb some wavelengths selectively.

Afocal converter lenses

These multiple-element optical systems are fitted in front of the lens and are generally used with non-interchangeable lenses to alter effective focal length. The term ‘afocal’ indicates that they have no focal length of their own, i.e. parallel light incident on the unit emerges parallel. Optically, they are related to the Galilean telescope, used either normally or in reverse mode in front of a camera lens. However, when such a converter is used with a camera lens, the effective focal length of the combination may be greater or less than that of the camera lens alone, depending on the orientation of the converter (Figure 10.17). The telephoto converter increases the focal length of the camera lens by factors of from ×1.5 to ×3 or even more, and the wide-angle converter decreases it by a factor of about ×0.7 (‘wide-angle’) or even ×0.5 to give a ‘fish-eye converter’. Afocal converters were originally used with twin-lens reflex cameras but are now available for any types of camera that lack interchangeable lenses, particularly digital cameras.

Figure 10.17   Afocal attachments. (a) Wide-angle attachment T. (b) Telephoto attachment T. Key: n, rear nodal plane of combination of focal length f_c; N₁ and N₂, nodal planes of prime lens of focal length f.

Unless the converters are of high optical quality the results can be disappointing. Large apertures give poor resolution and small apertures produce vignetting. No change in the marked apertures of the camera lens is necessary and no exposure compensation is needed. Screen focusing is essential. With the telephoto converter the near focusing range is lost. Within their capabilities they are useful devices to give a modest change in focal length of a prime lens and consequent change in field of view.

Close-up (supplementary) lenses

Single-element lenses added in front of a camera lens will alter its focal length, a positive supplementary lens giving a reduction in focal length and a negative lens an increase. However, the most valuable use of such supplementary lenses is for close focusing, especially with cameras having a limited focusing capability. Focusing on a subject at a given (close) distance is possible by using a positive supplementary lens of focal length equal to the subject distance, irrespective of the focal length of the camera lens. The camera lens is then focused for infinity; the path of the rays is shown in Figure 10.18. This is the basis of close-up or portrait attachments. The focusing movement of the prime camera lens then provides a useful close-up focusing range.

Supplementary lenses are specified by their power in dioptres rather than focal length. The relationship between power (K) and focal length (f) is that a focal length of 1000 mm is a power of one dioptre (1 D), so f = 1000/K (Chapter 6). The power of a convergent supplementary lens is positive and that of a divergent lens is negative. Specification of lenses by their power is convenient because in a combination the powers of the lenses are simply added to obtain the power of the combination.

Figure 10.18   The close-up lens. (a) Positive meniscus close-up lens of focal length F_S. (b) Used with a camera lens C of focal length f_C, nearest close focus is at distance F_S. (c) Using the focusing extension of the camera lens to give a close-up focusing range.

Close-up lenses are available in a range of +0.25 to +10 dioptres. The weaker powers of 0.25 and 0.5 dioptres are used chiefly with long-focus lenses to improve their close-focusing capability. They do not seriously affect the corrections of the camera lens. Supplementary lenses are usually meniscus singlets which have only a small detrimental effect, especially at medium apertures. Some supplementary lenses are coated achromatic doublets, ideally designed for use with a specific camera lens, such as long-focus and long-range zoom types to provide an essential close-focus capability in the range from 0.5 to 2 metres, where often there is a ‘focus gap’. The reduction in effective focal length and little change to the entrance pupil diameter mean that the effective aperture of the combination conveniently compensates for any necessary exposure increase for the change in magnification.

Other attachments

The use of a properly designed lens hood or sunshade with any lens will contribute significantly to image quality. The lens is shielded from light outside the subject area, and flare is reduced, especially in back-lit and side-lit conditions. The usual shape is a truncated cone or box shape, allowing maximum depth for shading without causing vignetting. The internal finish is ridged and painted matt black. Owing to the danger of vignetting (‘cut-off’) by a lens hood, especially if a filter is also in use, many wide-angle lenses are not expected to be fitted with them; many such lenses are constructed with a recessed front component so that the front rim acts as a vestigial type of lens hood. Alternatively, a hood of cut-out ‘petal’ shape is used. As focal length increases, the need for an efficient hood becomes greater. Many long-focus lenses are supplied with an integral retractable hood. In the case of zoom lenses, the hood can only be of depth sufficient to avoid vignetting at the minimum focal length setting, even though the greatest need for a lens hood is at the maximum setting. Again, a hood can be of petal or flower shape to give some protection.

Various optical attachments and devices are available for effects produced in-camera rather than by later image manipulation, although most of the optical effects can be duplicated by digital image processing beginning with a ‘straight’ image. An optical soft-focus effect is given by the spreading of the highlights of a subject into adjacent areas. Special portrait lenses are available using controllable residual spherical aberration to give this effect, but these are expensive and limited in application. A soft-focus attachment is a cheap alternative for use with any lens. Two basic types of device are available, one having a number of concentric grooves in plain glass and the other having small regular or irregular deposits of refractive material about 1 mm thick, randomly scattered over a flat glass disc. The former type gives diffusion effects that depend on the aperture in use: the larger the aperture, the greater the diffusion. The latter type operates independently of lens aperture. The softening of the image results from the effects of scattering and refraction due to the presence of the attachment. Various degrees of diffusion are available and devices can be used in tandem or combination. Other devices use black or white netting of various mesh sizes encapsulated or laminated between clear plastic plates. These types give softening of the image and controllable reduction in image contrast with no effect on colour balance. Experimentation is necessary to obtain practical familiarity with predictable effects. Also available are devices termed ‘haze effect’ and ‘fog effect’ filters, which find particular application in landscape photography. This type of ‘haze’ filter is not to be confused with the UV-absorbing variety.

Teleconverters

These optical accessories are not photographic lenses since they do not form a real optical image on their own, only a virtual one as they are negative in refractive power. However, these optical devices are in common use with interchangeable lenses. The astronomer Barlow reported in 1834 that placing a secondary negative lens behind a primary positive lens would increase effective focal length; indeed, this is the principle of the telephoto lens. These teleconverter or multiplier lenses use typically four to eight elements with a net negative effect, housed in a short extension tube fitted between the camera lens and body (Figure 10.19); linkages transmit the functions of automatic iris and focus and metering information. The effect of a teleconverter is typically to double or triple the focal length of the prime lens, forming a telephoto combination of short physical length. As the size of the entrance pupil is unaffected, this doubling or tripling means that the maximum aperture is reduced by two or three whole stops, turning, for example, a 100 mm f/2.8 lens into a 200 mm f/5.6 or a 300 mm f/8. Where these losses are unacceptable, a × 1.4 converter with only one stop loss may be preferred, especially where a long-focus lens is already in use. A highly corrected apochromatic matched multiplier may be supplied with a prime lens for this purpose.

The change to the marked apertures is usually automatically corrected for by the TTL metering system used in most cameras, but must be remembered for use with manual, automatic and non-off-the-film electronic flash. The modest cost, small size and excellent results make teleconverters useful accessories. The minimum focusing distance of the camera lens is retained, with image magnification increased. Thus, a 90 mm f/2.8 macro lens focusing unaided to give 0.5 magnification, when used with a specially designed converter, will give a combination 180 mm f/5.6 lens focusing which gives unit magnification. Some manufacturers produce highly corrected converters designed especially for a particular lens or range of focal lengths; in such cases the performance is excellent. In general, teleconverters do not perform well with wide-angle lenses, as aberration correction may be affected adversely. It is pointless to convert a 24 mm lens into a 48 mm lens of mediocre performance when a good 50 mm standard lens may be available; on the other hand it is useful to be able to convert a 200 mm lens to 400 mm to save buying a heavy and expensive lens that may seldom be needed.

Figure 10.19   The teleconverter principle. (a) Camera lens C of focal length f in body B focuses light on to film F. (b) Addition of teleconverter T of thickness d gives rear nodal plane N and combined focal length 2f.

OPTICAL FILTERS

Absorption filters

An optical filter can be either a passive absorption type or an interference type. Their role is that of frequency filtering to remove unwanted spectral bands or lines otherwise transmitted by the optical system. Colour depends on the transmitted wavelengths and for absorption types is independent of orientation and angle of incidence. Filters are characterized by their spectral transmission properties, presented in various ways (see Figure 10.20). Absorption filters tend to have broad-band characteristics, but ‘narrow-cut’ versions have reduced bandwidths. Any additional absorption in the UV or IR may be important. The designating alphanumerics of a filter often give an indication of the short-wavelength cut-off region, e.g. R64 and Y52 are red and yellow filters that transmit beyond 640 and 520 nm respectively.

For properly exposed results when using a filter, an increased camera exposure compensates for light absorption. The ratio of the filtered exposure to the unfiltered exposure is called the filter factor or exposure factor, expressed as a multiplying factor such as ×4 or as a negative EV such as −2EV. Filter factors depend on spectral absorption, spectral response of the detector and the exposure duration if film reciprocity law failure effects are significant. Cameras incorporating TTL exposure metering may compensate for certain filters such as pale coloured ones and neutral density (ND) types. Polarizing filters can also give problems for exposure metering if a beamsplitter is used in the TTL system; a circular polarizing filter is preferable (see Chapter 6).

The optical quality of a filter must be high if used in an imaging system, so as not to degrade performance, but can be of lesser quality if used in an illumination system. Optical quality is measured as flatness and parallelism of the filter surfaces. Multi-layer anti-reflection coating is desirable. Various forms of filter are available, including gelatin, cellulose acetate, polyester, solid glass, cemented types and interference types. The solid glass type offers only a restricted range of colours. Some filters, such as heat-absorbing and UV-transmitting types, are available only in glass form. Filters can be used in tandem such as for overall colour correction and local ND effects.

Figure 10.20   Methods of showing spectral absorption data for a colour filter. The four graphs show the same data for a pale green filter plotted in different ways to show the variations in curve shape given.

Gelatin filters are imbibition dyed and some 0.1 mm thick, giving almost no detectable degradation to optical systems, but are easily damaged. Polymer materials give intermediate optical quality and lightweight, unbreakable filters. A thickness of 2 mm is typical. The optical resin types are made from allyl diglycol carbonate. Filters should be anti-reflection coated where possible to reduce light losses.

Full discussions of the range and application of colour filters are given in the Bibliography below. For black-and-white photography, tonal reproduction may be altered by use of correction filters and contrast filters. The former are used to record subject colours in their true luminosities by partial absorption of spectral regions of the illuminant to suit the non-uniform spectral sensitization of panchromatic film materials. The latter control the tonal contrast in a print arising from colour contrast in the subject. An empirical rule is that a filter lightens subject colours of its own colour and darkens those of complementary colour. Haze penetration in telephotography is improved by orange or red filters, restricting photography to longer wavelengths which are scattered less.

Colour photography uses a wide range of filters to retain acceptable colour reproduction with variations of illuminant and exposure conditions. Colour materials are commonly balanced for illuminants of colour temperature (CT) 3200, 3400 or 5500 K, termed white balance in digital photography. For quasi-Plackian sources, light-balancing and colour conversion filters partially absorb specific spectral regions to match the illuminant to the photographic material. Their spectral effect is quantified by the micro-reciprocal degree (mired) scale, where the mired value (MV) of an illuminant of colour temperature T in kelvin is given by:

The mired shift value (MSV) of the filter required to convert a CT of T₁ into a value T₂ is given by:

Light-balancing filters are for small changes, while colour conversion ones are for large shifts. They are used mainly in film photography and are substituted by white balancing processes in digital cameras (Chapters 14 and 23). Another group, colour-compensating filters, have selective absorption in specific spectral regions and are used as trimming filters to offset colour imbalances such as those from optical systems, local colour effects and film reciprocity law failure behaviour.

UV and IR filters

Other filters have special or distinct functions. Some are colourless as their absorption lies outside the visible spectrum; others are visually opaque, as their transmission lies outside the visible spectrum.

The sensitivity of photographic materials to scattered UV radiation and blue light causes a loss of contrast, and a blue cast with colour materials, increasing with increasing subject distance. In addition, the spectral transmission of different lenses, especially older designs, may vary for the UV region and give different colour balances in terms of ‘warmth’ of image. Use of UV-absorbing or haze filters gives a better match between lenses. An additional use is as a ‘skylight filter’ to reduce the effect of excessive scattered light from a blue sky. Such filters are usually colourless or a very pale pink or straw colour, depending on their cut-off for short wavelengths. Often the digits in a filter code number indicate this point, e.g. 39 denotes 390 nm. The use of a good-quality UV filter for mechanical protection of the lens surface is always useful.

For some specialist applications of photography, UV radiation is used as the illuminant. However, UV sources also emit visible light. Special opaque glass filters which transmit only in the near-UV region are used to block all visible radiation. Due to uncorrected ‘chromatic’ aberration between the UV and visible regions, a lens focus correction is usually needed unless a specially computed lens made with quartz and fluorite elements is used.

As well as visible light, all thermal sources emit much of their energy in the form of IR radiation. In an enclosed optical system such as an enlarger or slide projector, the negative or transparency in the gate must be protected from this unwanted radiation. Colour-print materials are sensitive to IR radiation, and its elimination from the image-forming light is therefore essential for correct colour reproduction. Colourless glass filters (‘heat-absorbing glasses’), which transmit visible radiation but block IR radiation, are used for these purposes. They do not need to be of optical quality if they are mounted in the illumination system of an enlarger or projector. A mounting to hold the filter loosely is necessary to avoid cracking due to thermal expansion. Interference-type filters are also used. Usually such a filter transmits IR radiation and reflects visible light. Termed a cold mirror, the filter may usefully form an integral reflector of ellipsoidal shape for a tungsten–halogen light source.

Silicon, the photosensitive layer on CCD and CMOS sensors in digital cameras, has also an inherent sensitivity to IR. Digital cameras are equipped with IR blocking filters placed in front of the sensor to preserve colour rendition. Removing the IR filter is a possibility in some SLR cameras to allow IR photography. Infrared-sensitive film materials have an extended spectral response to some 950 nm as well as the usual sensitivity to visible light and UV radiation. Consequently, their use needs a special infrared filter opaque to both UV and visible radiation but transmitting in the IR region. Any filter factor must be determined empirically. These filters, which are almost opaque to visible light, are available in either gelatin or glass. Once more, due to uncorrected ‘chromatic’ aberration between the IR and visible regions, a lens focus correction is usually needed unless a suitably corrected lens is used. This may be an apochromatic or superachromatic lens. Usually, the focus shift correction is by means of a supplementary index mark on the focusing scale of the lens, and the visually focused distance is transferred to this IR index. The lens is seldom chromatically corrected for the IR and the image may be characteristically ‘soft’ and ‘hazy’ due to this. Foliage appears very light in tone due to the high reflection of IR from chlorophyll in leaves.

Neutral-density filters

Neutral-density (ND) filters absorb all visible wavelengths to a more or less equal extent. They may be scattering or non-scattering. A filter for use in front of the camera lens must be non-scattering, but for other applications such as the attenuation of a beam of light, the scattering type can be used. Optical quality ND filters are made by dispersing colloidal carbon in gelatin. The addition of dyes with the necessary spectral absorption properties, combined with the brown colour due to the carbon, give the necessary neutral characteristics. ND filters are also available in graduated form, to give continuous light control over a given range of attenuation, or to give attentuation to part of the scene only, e.g. the sky region but not the foreground.

ND filters for camera use are calibrated in terms of their optical density and filter factor, e.g. a 0.3 ND filter with filter factor ×4 (+2EV). They can be used with monochrome, colour films and digital sensors (although rarely needed in digital photography), as they have no effect on colour balance. Their uses range from a means of avoiding overexposure with a fast film in very bright conditions to a way of using large apertures for selective focus in well-lit conditions. Mirror lenses use ND filters in lieu of aperture stops to enable selection of a different shutter speed.

Graduated filters are tinted over about half their area, with a gradual transition between the grey or coloured and the clear areas to give selective filtration to parts of the subject. A graduated yellow filter may be used with black-and-white film to filter the sky in a landscape picture, leaving the foreground unfiltered, the horizon approximately coinciding with the transition zone. Pairs of differently coloured graduated filters can be used in tandem in rotated opposition to give selective filtration to different zones of the scene. In colour photography, graduated colour filters can provide either a colour accent to part of a scene or correct the colour balance likewise, or give a strong colour effect. A graduated grey ND filter will reduce exposure to a selected area of the scene to help balance excessive luminance ratio, as in a landscape with a brilliant sky area. A radially graduated ND filter or ‘spot’ filter compensates for the loss of illumination at the edges of extreme wide-angle lenses, with need for an exposure increase of +1EV or +2EV.

Polarizing filters

As discussed in Chapters 2 and 6, light can be considered as a transverse wave motion, i.e. with vibrations orthogonal to the direction of propagation. The direction of vibration is completely randomized, giving unpolarized light. If the vibrations are restricted to one particular plane called the plane of polarization, the light is then linearly polarized, or plane polarized (or simply polarized). Such light can be produced, controlled and attenuated by a polarizing filter.

A polarizing filter is a sheet of polymeric material containing a layer of transparent polymer molecules whose axes are aligned in one direction during manufacture. They are optically active, so that light waves vibrating in one plane are transmitted, but light waves vibrating at right angles to this plane are blocked. Light waves vibrating in intermediate directions are partially transmitted. Such a linearly polarizing filter can be used to select light for transmission if some of it is polarized. Light coming from different parts of a scene may be in various states of complete or incomplete polarization.

Polarizing filters have several distinct applications. The light from any point in a clear blue sky is partially polarized by scattering, the direction of polarization being at right angles to the line joining it to the sun. The polarization is strongest over the arc of the sky that is 90° from the sun, and is weakest at 0° (i.e. close to the sun itself) and 180° (opposite the sun). Clear blue sky can thus be rendered darker by use of a polarizing filter over the camera lens, the amount being controlled by rotation of the filter. A polarizing filter does not otherwise affect colour rendering, and so is used in colour photography to control the depth of colour of a blue sky.

Unwanted surface reflections may also be reduced and even eliminated. Light that is specularly reflected from the surface of a non-metal at a certain angle is almost totally polarized in a plane perpendicular to the plane in which the incident and reflected rays lie. This is called s-polarization. Note that polarization at right angles to this plane, i.e. in the plane containing the incident and reflected rays, is known as p-polarization. The light that is transmitted is partly p-polarized. Total s-polarization occurs when the angle of incidence is such that the reflected and refracted rays are orthogonal, i.e. the tangent of the angle of incidence is equal to the refractive index (Brewster’s law). For material with a refractive index of about 1.5 (i.e. most polishes, gloss paints, plastics and glass), the angle of maximum polarization (the Brewster angle) is about 56°. For water with a refractive index of 1.33 it is about 53°. Light reflected from a wide range of substances at approximately this angle is largely polarized. Polarizing filters may therefore be used for the control of reflections from non-metallic materials, for example glass, wood, paint, oil, polish, varnish, paper and any wet surface. Practical applications include removal of glare spots from painted walls, wood panelling, furniture and glass, provided a suitable viewpoint can be used. In colour photography, the presence of surface reflections reduces colour saturation, degrading the picture quality.

In copying applications, a polarizing filter over the lens offers little control of reflections, but full control is possible if the light source itself is plane polarized, the method being to place polarizing filters over both the lens and the lamps, the direction of polarization of the lens filter being orthogonal to that of the lamp filters. In this technique, the diffusely reflected light forming the image is depolarized, whereas the unwanted, directly reflected light remains polarized, and does not pass through the filter on the lens. In the same way, reflections from metal objects can be controlled by placing polarizing filters over the light sources as well as over the camera lens. Large sheets of polarizing material are needed for use over light sources, and they must not be permitted to overheat.

The ideal polarizing filter works equally well for all wavelengths and has no effect on colour. Due to the absorption of both polarized light and transmitted light by the materials of the filters, the filter factor is usually about ×3.5 (+1.6EV) rather than the theoretical ×2 (+1EV), but a TTL metering system will usually take such variations into consideration (with the qualification below). The filter factor is independent of the sensitive material and illuminant.

A practical problem arises when a linear polarizing filter is used with a camera that has an optical system with a beamsplitter device to sample the incoming light for exposure determination, or to direct part of the image to an array of photosensors in an autofocusing module set in the well of the camera. The beamsplitter divides the incident light into two beams that are orthogonally polarized. Consequently, when a plane polarizing filter is rotated over the camera lens, the beamsplitter does not divide this partially polarized beam in the correct proportions for viewing and light measurement, or transmit enough light to the autofocus module for this to operate satisfactorily. The effects depend on the orientation of the filter over the lens (see Chapter 6). If, however, a circularly polarizing filter is used instead of a linear type, the properties of the beamsplitter are unaffected so light measurement errors and inoperative autofocus systems are avoided. The filter uses in its construction an additional thin layer of optically active material behind the polarizing material. This is known as a quarter-wave plate, and its effect is to displace the relative phases of the electric and magnetic components of the propagated wave so that the plane of polarization rotates through a complete circle with every wavecrest (see Chapter 2).

BIBLIOGRAPHY

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