Chromatic Aberration AKA Color fringing

Introduction

Chromatic aberration (CA) is one of several aberrations that degrade lens performance. (Others include coma, astigmatism, spherical aberration, and curvature of field.) It occurs because the index of refraction of glass varies with the wavelength of light, i.e., glass bends different colors by different amounts. This phenomenon is called dispersion. It appears as color fringing, most visibly on tangential edges near the boundaries of the image. It is sometimes confused with another effect, which we call pixel shift— a color channel offset that is typically uniform over the sensor and can be caused by physical misalignment of multi-chip sensors or demosaicing errors.

Minimizing chromatic aberration is one of the traditional goals of lens design. It is accomplished by combining glass elements with different dispersion properties. But it remains a problem in several lens types, most notably ultrawide lenses, long telephoto lenses, and extreme zooms. In many designs intended for digital cameras, CA is no longer a major consideration because it can be completely corrected in the digital domain if the correction is applied before demosaicing.

Lateral and Longitudinal CA; Tangential and radial lines

ROI for CA measurement

The two types of chromatic aberration are illustrated above.

• Longitudinal chromatic aberration causes different wavelengths to focus on different image planes. It cannot be measured directly by Imatest; it causes a degradation of MTF response– by differing amounts for different colors.

• Lateral chromatic aberration is the color fringing that occurs because the magnification of the image differs with wavelength. It tends to be far more visible than longitudinal CA. Imatest measures Lateral CA.

Lateral chromatic aberration is best measured on a tangential edge near the sides or corners of an image. It is not visible on radial edges. Radial lines and tangential curves (which differ by 90 degrees) are shown in burgundy and blue on the right side of the above illustration. Because typical Imatest SFR edges have angles in the range of 3 to 7 degrees with respect to vertical and horizontal, the best edges for measuring CA are near-vertical edges on the left and right of the image. The ISO 12233:2000 chart (shown on the right) has a very limited number of appropriate edges. One is rectangle B, above. SFRplus charts, which can be printed any size on high quality photographic inkjet printers, are much better for measuring CA.

The thumbnail on the right is from a 12 megapixel compact digital camera with fairly high chromatic aberration. The selected area is shown below. Red fringing, the result of lateral CA, is clearly visible. The black-to-white edge to the right side of this rectangle has equally vivid green fringing. Imatest analyzes the edge and produces a number that indicates the severity of the lateral chromatic aberration.

Imatest chromatic aberration measurement

The average transitions for the R, G, and B color channels, calculated by Imatest SFR for the above edge, are shown in the figure below. The edges have been normalized to have asymptotic limits of 0 and 1, i.e., they are dimensionless, approaching 0 and 1 at large distances from the transition center. Note that the three edges are not simply shifted, as you might expect if the focal lengths for the three colors were slightly different. They are distorted due to demosaicing (RAW conversion), as discussed below. When Bayer RAW images (undemosaiced) are analyzed, you do indeed see simple shifts.

The visibility of the chromatic aberration is proportional to the area between the edges with highest amplitude (in this case, red) and the lowest (in this case, blue). This area can be expressed by the following integral.

\(displaystyle CA (text{area}) = int left[ Edge_{max}(x) – Edge_{min}(x) right] dx\) 

Since x has dimensions of distance in pixels and Edge is dimensionless, CA(area) has units of pixels— units of distance even though it is an area. CA defined by this equation is called the area chromatic aberration. It is displayed in magenta in the figure on the right. (CA(area) = 1.88 pixels).

The distance between the crossings (the centers of the transitions) is also shown. It is proportional to the optical CA (the actual chromatic aberration of the lens, unless it has been corrected during raw conversion), but it is less visually significant.

Chromatic Aberration figure (relatively high CA)
(shown reversed: displayed levels always increase
from left to right)

Although area in pixels is a good measure of perceptual CA, it has some shortcomings.

• It penalizes cameras with high pixel counts.
• The result depends strongly on the measurement location. The chromatic aberration in most lenses is roughly proportional to the distance from the image center.

To deal with these issues Chromatic aberration is also expressed in percentage of the distance from the image center to the Region of Interest (ROI), corrected for the angle of the ROI with respect to the center. In the above example, CA (area) = 0.110% of the distance from the image center to the ROI. The correction is described in the green box, below. This measurement gives the best overall results, since it’s relatively independent of the measurement location and the number of pixels. A table below presents rough guidelines for the severity of CA. Measurements displayed on the right of the figure are summarized in the following table.

Because Chromatic Aberration cannot be measured accurately near the image center, the chart is rendered in pale colors with the Region of Interest (ROI) is less than 30% of the distance from the center to the corner.

Imatest modules

The following Imatest modules can be used for chromatic aberration measurement. All but Dot Pattern measure Lateral Chromatic Aberration from (near) tangential slanted-edges, and also measure MTF. Some also measure optical distortion. Auto-detection slanted-edge modules are compared in www.imatest.com/docs/#sharpness.

Module	Comments
SFRplus	Measures a great many image quality factors.
eSFR ISO	Measures a great many image quality factors, including noise. Limited distortion measurements.
Checkerboard	Can operate over a wide range of distances and/or Fields of View. Very accurate distortion measurements.
Dot Pattern	Also measures Optical Distortion (but not MTF). Corresponds to several standards.
SFR	Any slanted-edge, selected manually.
SFRreg	Works with ultra-wide Fields of View. Does not measure distortion.

Demosaicing

Demosaicing is the process of converting Bayer RAW images, which have one color per pixel (RGRGRG…; GBGBGB…), to standard images, which have three colors per pixel. In the process of demosaicing, missing detail for each channel is inferred from detail in other channels. This is especially significant for Red and Blue pixels, which are half as common as Green. Demosaicing algorithms can be very mathematically sophisticated, but all of them can perform poorly in the presence of lateral CA, where detail is shifted from its expected location.

Demosaicing explains the shifted edges shown in the examples on this page. Lateral CA cannot be reliably corrected after demosaicing, but it can be corrected to near-perfection prior to demosaicing, and this is frequently done on modern cameras and camera phones. Correction coefficients can be calculated with Imatest Master, which can analyze Bayer RAW files created by converting manufacturer’s Camera RAW files. Details are in the page on RAW files.

Here is an example illustrating the same region for a RAW and demosaiced file. Canon EOS-40D, 17-85mm IS lens, 50mm, f/8.

Chromatic aberration before demosaicing: easy to correct using a different magnification for each color ((1-0.00024)x for red; 1.00062x for blue; 1 for green).

Chromatic aberration after demosaicing: difficult to correct. Many recent cameras (since ~2011) have CA correction built-in.

R-G and B-G are the CA correction coefficients. They are the spacing between the Red and Green and Blue and Green crossings, respectively, expressed as percentage of the center-to-corner distance. This measurement is relatively independent of the location of the measurement.