Chromatic aberrations

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When different colors of light propagate at different speeds in a medium, the refractive index is wavelength dependent. This phenomenon is known as dispersion. A well-known example is the glass prism that disperses an incident beam of white light into a rainbow of colors [1]. Photographic lenses comprise various dispersive, dielectric glasses. These glasses do not refract all constituent colors of incident light at equal angles, and great efforts may be required to design an overall well-corrected lens that brings all colors together in the same focus. Chromatic aberrations are those departures from perfect imaging that are due to dispersion. Whereas the Seidel aberrations are monochromatic, i.e. they occur also with light of a single color, chromatic aberrations are only noticed with polychromatic light.


Longitudinal and transverse chromatic aberration

One discriminates between two types of chromatic aberration. Longitudinal chromatic aberration, also known as axial color, is the inability of a lens to focus different colors in the same focal plane. For a subject point on the optical axis the foci of the various colors are also on the optical axis, but displaced in the longitudinal direction (i.e. along the axis). This behavior is elucidated in Fig. 1 for a distant light source. In this sketch, only the green light is in sharp focus on the sensor. The blue and red light have a so-called circle of confusion in the sensor plane and are not sharply imaged.

Longitudinal Chromatic Aberration

Figure 1. Origin of longitudinal chromatic aberration. The focal planes of the various colors do not coincide.

Obliquely incident light leads to the transverse chromatic aberration, also known as lateral color. It refers to sideward displaced foci. In the absence of axial color, all colors are in focus in the same plane, but the image magnification depends on the wavelength. This behavior is illustrated in Fig. 2. The occurrence of lateral color implies that the focal length depends on the wavelength, whereas the occurrence of axial color in a complex lens does not strictly require a variable focal length. This seems counterintuitive, but in a lens corrected for longitudinal chromatic aberration the principal planes do not need to coincide for all colors. Since the focal length is determined by the distance from the rear principal plane to the image plane, the focal length may depend on the wavelength even when all images are in the same plane.

Transverse Chromatic Aberration

Figure 2. Origin of transverse chromatic aberration. The size of the image varies from one color to the next.

Figures 1 and 2 distinguish two simplified cases because in practice the longitudinal and lateral components are coexistent. A polychromatic subject fills a volume in the image space, which is comprised of a continuum of monochromatic images of various sizes and positions. Lateral color is particularly manifest in telephoto and reversed telephoto (retrofocus) lenses. Chromatic aberrations often limit the performance of otherwise well-corrected telephoto designs. Lateral color, and not astigmatism, is the chief cause of the separation betwee the sagittal and tangential curves in their modulation transfer functions. The archetypal manifestation of chromatic aberrations is color fringing along boundaries that separate dark and bright parts of the image. This said, descriptions of the perceptible effects of chromatic aberrations do vary in literature. It is read that lateral color is a more serious aberration than axial color, because the former gives rise to colored fringes while the latter merely reduces the sharpness [2]. Oberkochen holds a different view and points to axial color as the most conspicuous color aberration [3]. Hecht describes the cumulative effect of chromatic aberrations as a whitish blur or hazed overlay [4]. The residual color errors of an optical system with achromatic (under)correction for axial color lead to a magenta halo or blur around each image point [5,6].


Examples

A cross was made from two black matchsticks and mounted on a cork. It was photographed with the Canon EF 85/1.2 L USM at a routine portrait distance of one meter. The cross was placed in the very image center, against a bright white background. The high contrast and the large working aperture of f/1.2 are responsible for the longitudinal chromatic aberration observed in Fig. 3. When autofocus is used to focus on the cross, there are purple fringes all around it. After slightly defocusing the lens manually, the color of the fringes turns green. This green fringing is perhaps less distressing than the purple fringing, but it is still clearly visible. As the human eye and autofocus systems are particularly sensitive to green light, both manual focus and autofocus tend to bring the green image in sharp focus. The other colors of the spectrum are left defocused and add up to a magenta fringe. For this reason purple fringing is more common than green fringing.

Canon EF 85/1.2 L USM Same lens slightly defocused

Figure 3. Examples of axial color (longitudinal chromatic aberration) with the Canon EF 85/1.2 L USM. A: autofocus on the cross. B: after slight manual defocus. The lens is used at full aperture on a Canon 5D.

The same cross was photographed with three retrofocus wideangle lenses (Fig. 4). It was placed close to the top-left image corner and tilted so as to point the long bar in the radial direction. This orientation places the crossbar in the tangential direction. For both Cosina lenses the crossbar evidences color fringes while the radial bar is unaffected. The joint presence of purple and green fringes at opposite sides of a tangential detail (lens A) are very characteristic of the transverse chromatic aberration. The bluish and yellowish fringes noticed with lens B are less common. Lens C is remarkably well corrected for a short-focus lens of the retrofocus type. There is only the slightest hint of purple and green.

Cosina 3.5-4.5/19-35 Cosina 3.8/20 Carl Zeiss Distagon 2.8/21

Figure 4. Examples of lateral color (transverse chromatic aberration). A: Cosina 3.5-4.5/19-35 @ 20 mm. B: Cosina 3.8/20. C: Carl Zeiss Distagon 2.8/21. All lenses are used at f/11 on a Canon 5D.

Longitudinal and lateral chromatic aberration can both give rise to colored edges, but properties are different. Axial color causes fringes all around objects, whereas lateral color only affects tangential details. Axial color can occur at any position in the image, whereas lateral color is absent in the image center and progressively worsens toward the image corners. Axial color is cured by stopping down the lens, whereas lateral color is present at all apertures. Chromatic aberration can manifest itself as a mixture of axial and later color, in which case it is partly cured by the use of a small aperture. Axial color yields fringes of a single color for an "in-focus" object (Fig. 3), whereas lateral color delivers two differently colored fringes at either side of the tangential structure (Fig. 4). Strictly speaking color artifacts in out-of-focus parts of the image should not be called chromatic aberration, since the aberration is only defined for the plane of focus. However, the cause is the same (dispersion) and 'out-of-focus color' or 'defocus color fringing,' or whatever the best name is for the phenomenon, is an aberration in the sense of anomalous behavior. Fringes due to axial color are particularly clear in parts of the scenery that are (just) out of focus, e.g. purple in front of the subject in sharp focus and green behind it, or vice versa. Although color fringing is only observed in places with a high contrast, both the longitudinal and transverse chromatic aberration degrade the overall resolution of a lens. Longitudinal chromatic aberration often operates in tandem with spherical aberration to shape the bokeh of a large-aperture lens. The combined effect of longitudinal chromatic aberration and spherical aberration is also known as spherochromatism [7,8].


Secondary spectrum

Transverse chromatic aberration leads to difficulties mostly in retrofocus and telephoto lens designs, which are markedly asymmetrical, and longitudinal chromatic aberration in large-aperture lenses. An uncorrected design is called chromatic. The human eye is most sensitive to green light, and when a chromatic lens is focused for the green part of the visible spectrum, the blue and red ends are out of focus (see Fig. 5). The incorporation of simple achromatic doublets is quite effective against chromatic aberration. A famous example of such a doublet is the combination of a convex crown glass element with a concave flint glass element [9]. The achromatic correction of a photographic lens applies to two wavelengths toward the blue and red ends of the spectrum. Figure 5 shows a typical achromatic correction scheme. The zero crossings occur for the two matched wavelengths, the residual focus shift of the other colors is known as the secondary spectrum.

Achromatic color correction

Figure 5. Principles of color correction. The colored faces are known as the secondary spectrum.

Apochromatism also implies correction for spherical aberration, and more, depending on the definition [10].

The advent of exotic glasses featuring low or anomalous dispersion enabled great progress in chromatic correction of photographic lenses. A design that brings three visible colors together is called apochromatic. A superachromatic lens corrects for four or more wavelengths and virtually eliminates color errors [11,12]. Strictly speaking it is not the number of zero crossings that determines the image quality, but the departures of the in-between wavelengths (the secondary spectrum). The designation APO is nowadays used by many a manufacturer to indicate such a reduced secondary spectrum, but true apochromatism is of rare occurrence in photographic lens designs. The typical correction curves shown in figure 5 are usually found with a 'focus shift' along the ordinate [2, 9,13] but sometimes with the 'focal length'. This may appear unimportant, but it makes a difference as the former case implies correction for axial color and the latter for lateral color. Likewise, the term secondary spectrum is most often encountered in relation to the longitudinal chromatic aberration. Nonetheless some authors use the term also to describe the transverse chromatic aberration [3,14] or explicitly plot correction curves with 'focal length' along the ordinate [7].

Achromatic lenses

The achromatic design (Fig. 5) is the most common correction level in a photographic lens and accounts for the purple and green fringes observed in Fig. 3. When the green light is in proper focus on the sensor, red and blue are similarly defocused and add up to magenta. Conversely, when blue light is in proper focus the red light is also in focus, leaving only green defocused. Upon replacing "focus shift" by "focal length" along the ordinate in Fig. 5, the achromatic scheme also accounts for the fringes observed in Fig. 4 (case A) with purple toward the image center and green toward the image corner. For the case of transverse chromatic aberration a longer focal length corresponds to a larger image magnification. This implies that for the achromatic diagram in Fig 5, the blue and red images of a nonaxial detail are displaced slightly more outward from the image center than the green image. Figure 6 shows a cross, where the blue and red images are displaced upward relative to the green image. The addition of the three monochromatic images results in the aberrated cross at the right. Blue, green and red add up to white, blue and red add up to purple. To be sure, figure 6 is a simplified scheme of pure transverse chromatic aberration, with only three colors, and merely serves as an illustration. As it appears, the fringes are both inside and outside the original cross. The crossbar is broadened, but at the same time part of its interior is eaten away by the aberration.

Color fringing

Figure 6. Origin of color fringing due to lateral color. The addition of the constituent colors leads to fringes in the right image.


Purple fringing: lens or sensor?

Chromatic aberration, and purple fringing in particular, have received considerable attention with the advent of digital cameras. Indeed, although chromatic aberrations can be noticed on film (Fig. 7), they do look more intense on CCD or CMOS images. On the one hand the digital photographer is only a few mouse clicks away from a full screen display, and few lenses stand image inspection at high magnification. On the other hand it is possible that digital imaging somehow renders the color fringes due to chromatic aberration more distinct. One of the proposed mechanisms is an enhanced spectral sensitivity in the (ultra)violet and (infra)red regimes, where lenses tend to be poorly corrected for chromatic aberration. Purple fringing is often blamed on sensor bloom, which is odd as blooming is a quite different phenomenon [15, 16]. In fact, there are as many arguments against sensor bloom as there are in favor of chromatic aberration to account for purple fringing. The examples shown on the present page are all demonstrably due to the lens and not to the sensor. Sensor bloom has no known color preference, and if it had, it would not change its colors upon defocusing a lens (as in Fig. 3) or upon swapping lenses (as in Fig. 4). The list of arguments is long [17].


Lateral chromatic aberration recorded on film Purple fringing recorded on film Green fringing recorded on film

Figure 7. Chromatic aberrations recorded on film. The church cross is photographed off a slide projection screen; the vane, taken at the "best" focus and after slight defocusing, is a 2900 dpi scan obtained with a slide scanner. Notice the similarities with Figs. 3 and 4.

© Paul van Walree 2001–2014



References


[1]   Isaac Newton, "A new theory about light and colours," Phil. Trans. 6, 3075-3087 (1672).
[2]   SPSE handbook of photographic science and engineering, edited by Woodlief Thomas Jr., John Whiley & sons.
[3]   Carl Zeiss, Camera Lens News 12 (2000).
[4]   Eugene Hecht, Optics, 3rd ed., Addison Wesley (1998).
[5]   Warren J. Smith, Modern optical engineering, 3rd ed., McGraw-Hill (2000).
[6]   Bruce H. Walker, "Understanding secondary color," Optical Spectra 12, 44-46 (1978).
[7]   Sidney F. Ray, Applied photographic optics, 3rd ed., Focal Press (2002).
[8]   Applied optics and optical engineering, Vol. III, edited by Rudolf Kingslake, Academic Press (1965).
[9]   Arthur Cox, Optics: the technique of definition, 6th ed., Focal Press (1946).
[10]   Thomas Back, "Defining apochromatism".
[11]   Max Herzberger and Nancy R. McClure, "The design of superachromatic lenses," Applied Optics 2, 553-560 (1963).
[12]   Hans Sauer, "Zeiss Sonnar F/5.6 250mm superachromat," The British Journal of Photography 123, 166-169 (1976).
[13]   Handbuch der Fototechnik, 9th ed., edited by Gerhard Teicher, VEB Fotokinoverlag Leipzig (1986).
[14]   Francis A. Jenkins and Harvey E. White, Fundamentals of optics, 4th ed., McGraw-Hill (1976).
[15]   http://micro.magnet.fsu.edu/primer/digitalimaging/concepts/ccdsatandblooming.html
[16]   http://www.ccd.com/ccd102.html
[17]   Ronald Parr, http://www.cs.duke.edu/~parr/photography/faq.html#purplefringe