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Focal length Calculatortelescope

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).

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The reason it’s purple is that most sensors are most sensitive to green, so that uncorrected (raw) output has a strong greenish cast (the compliment of purple). Color-correction makes the image neutral by boosting the red and blue = purple components. Hence the overflow from saturated pixels takes on a purple cast. This effect is shown in the two crops below of the area indicated by the red rectangle of the image on the right. The image on the left is a crop of the JPEG, straight out of the camera. The image on the right is a crop of the image converted from raw without color correction. The sky is still saturated, but purple fringing is not visible.

In Imatest, edge profiles are measured along horizontal or vertical lines. The blue line (x) on the right is an example. But chromatic aberration takes place along radial lines– lines from the center of the image to the region of measurement (shown in red on the right). Unless this line is vertical or horizontal, there will be a measurement error that must be corrected. The correction is illustrated on the right for a near-vertical edge, where the profile, and hence CA, is measured horizontally. In this illustration,

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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.

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.

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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.

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Lateral chromatic aberration is best measured on a tangential (or nearly tangential) edge near the sides or corners of an image. It is not visible on radial edges. Tangential curves and radial lines (which differ by 90 degrees) are shown in burgundy and blue in the Test chart illustration, above. 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 obsolete ISO 12233:2000 chart (shown on the right) has a very limited number of appropriate edges. One is rectangle B, above. SFRplus charts, which are available in a wide variety of sizes and media, are much better for measuring CA.

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-ROI distance. This measurement is relatively independent of the location of the measurement.

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

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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.

The following Imatest modules can be used for chromatic aberration measurement. All but Dot Pattern measure Lateral Chromatic Aberration from tangential or nearly 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.

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.

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Measurement tips— Lateral chromatic aberration is best measured using (nearly) tangential edges near the sides or corners of the image, for example, edge B (above). It is not visible on radial edges such as A.

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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.

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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.

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.

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

CA cannot be measured reliably if the center of the region of interest (ROI) is less than 30% of the distance from the center to the corners. In this case, the chart will be displayed in pale colors and CA in % will be omitted.

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It’s a saturation phenomenon in the sensor, also known as “blooming,” caused by overflow of electrons from highly saturated pixel sites to nearby unsaturated sites. It tends to be worst in cameras with tiny pixels (< 2μm). It has everything to do with the sensor and little to do with the lens.

Pixel shift (not CA) is best measured on near-vertical and horizontal edges near the center of the image where CA is minimum.

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 see simple shifts.

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 corrected in the digital domain if the correction is applied before demosaicing (as long as it’s not too extreme).