 |
| |
Introduction
Chromatic aberration (CA) is one of several aberrations that degrade
lens performance. (Others include coma, astigmatism, 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.
Minimizing chromatic aberration is one of the 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.
Lateral and Longitudinal CA; Tangential and radial lines
Measurement tip— Lateral chromatic aberration is best measured using a tangential edge near the side or corner of the image, for example, B on the left. It is not visible on radial edges such as A.
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. |
|
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. A
software
technique for reducing with is described in Eliminating
chromatic aberration.
Lateral chromatic aberration is
best measured
on a tangential edge near the sides or corners of an image. It's
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 Imatest SFR
requires
edges to have an angle in the range of 3 to 7 degrees with respect to
vertical
and horizontal, only a limited number of locations in the ISO 12233 chart (on the right) are appropriate for
measuring lateral CA. One is rectangle B,
above. SFR/SVG 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.
|
ROI for CA measurement |
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 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.
CA (area) = ∫ [ Smax(x) - Smin(x) ] dx
|
Since x has dimensions of distance in pixels and S 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)
= 1.92 pixels).
The distance between the crossings (the centers of the transitions) is also shown. It is less visually significant.
While area in pixels is a good measure of CA, it has some shortcomings.
- It penalizes cameras with high pixel counts.
- The result depends on the measurement location. The chromatic aberration in most lenses is roughly proportional to the distance from the image center.
|
Chromatic Aberration figure (relatively high CA)
(shown reversed: levels always increase from left to right) |
To deal with these issues Chromatic aberration is also measured in percentage of the distance from the image center to the corner (percentage of sensor diagonal/2) , corrected for the angle of the ROI with respect to the center. In the above example, CA (area) = 0.115% of the distance from the image center. 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.
| 10-90% rise distance (original; uncorrected) in pixels and rises per picture height (PH). |
| CA (area): Chromatic aberration area in pixels. An indicator of the visibility of CA. The area between the channels with the highest and lowest levels. In units of pixels because the x-axis is in pixels and the y-axis is normalized to 1. Explained in the page on Chromatic aberration. Measured in along the axis indicated by Profile on the upper-left. Meaning (now obsolete): Under 0.5; insignificant. 0.5-1: minor; 1-1.5: moderate; 1.5 and over: serious. |
| CA (area) as a percentage of the distance to image center. A better indicator than pixels (above). Equal to 100 * (area between the channels with the highest and lowest levels) / (distance from center in pixels), corrected for the angle of the ROI. This number is relatively independent of the ROI because CA tends to be proportional to the distance from the image center. Explained in the page on Chromatic aberration. Measured along the radial line from the image center to the edge. Meaning: Under 0.04; insignificant. 0.04-0.08: minor; 0.08-0.15: moderate; over 0.15: serious. |
| CA (crossing). Chromatic aberration based on the most widely separated edge centers (positions where the edges cross 0.5). Tends to be less indicative of CA visibility than CA (area). Measured two ways: (A) in pixels along the axis indicated by Profile in the upper left, and (B) in percentage of the distance from the image center to corner along the line from the image center. |
| R-G, B-G Red−Green and Blue −Green crossing shift expressed as percentage of the distance from the image center to corner, measured along the radial line from the image center. R-G is r(R)-r(G), where r is radius in percentage of difference to the corner.. |
| R-G, B-G Red−Green and Blue −Green crossing shift expressed in pixels, measured along the axis indicated by Profile in the upper left. R-G is x(R)-x(G) for horizontal profiles or y(R)-y(G) for vertical profiles, where x and y are distances along the horizontal and vertical axes, respectively. The sign may be different from the sign in the percentage measurement, depending on the measurement quadrant. |
| Average pixel levels in the dark and light areas. Clipping can occur if they are too close to 0 or 255. |
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.
Severity
of chromatic aberration
Chromatic
Aberration
in percentage of
distance from
the image center |
Severity |
| 0-0.04 |
Insignificant |
| 0.04-0.08 |
Low. Hard to see
unless
you look for it. |
| 0.08-0.15 |
Moderate.
Somewhat visible
at high print magnifications. |
| over 0.15 |
Strong. Highly
visible at
high print magnifications. |
Severity
of chromatic aberration (old table)
Chromatic
Aberration
in pixels |
Severity |
| 0-0.5 |
Insignificant |
| 0.5-1 |
Low. Not visible
unless
you look for it. |
| 1-1.5 |
Moderate.
Somewhat visible
at high print magnifications. |
| over 1.5 |
Severe. Highly
visible at
high print magnifications. |
| Purple fringing
is not chromatic aberration, though it is often mistaken
for it. It's a saturation phenomenon in the sensor, also known as "bloom," caused by the
overflow
of electrons from highly saturated pixel sites to nearby unsaturated
sites.
It tends to be worst in cameras with tiny pixels (e.g., 8+ megapixel
compact
digital cameras). It has everything to do with the sensor and nothing
to
do with the lens. |
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 above example. Lateral CA cannot be reliably corrected after demosaicing, but it can be corrected to near-perfection prior to demosaicing. Correction coefficients can be calculated with Imatest Pro, 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-20D, 17-85mm IS lens, 53mm, f/11.
Chromatic aberration before demosaicing: easy to correct using a different
magnification for each color ( (1-0.00023)x for red;
1.000622x for blue; 1 for green).
Chromatic aberration after demosaicing: difficult to correct.
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 mesurement is relatively independent of the location of the measurement.
 Corrected chromatic aberration measurements
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,
- x = x1 + x2 is the measured chromatic aberration, along a horizontal row of pixels.
- C = the true chromatic aberration, along the radial line (angle = Θ ).
- Φ is the angle of the edge relative to vertical.
x1 = C cos Θ ; y = C sin Θ ;
x2 = y tan Φ ( x2 may be negative if Φ is negative.)
x = x1 + x2 = C cos Θ + y tan Φ = C ( cos Θ + sin Θ tan Φ )
C = x / ( cos Θ + sin Θ tan Φ )
|
| |
