While perusing Jim Kasson’s excellent Longitudinal Chromatic Aberration tests I was impressed by the quantity and quality of the information the resulting data provides. Longitudinal, or Axial, CA is a form of defocus and as such it cannot be effectively corrected during raw conversion, so having a lens well compensated for it will provide a real and tangible improvement in the sharpness of final images. How much of an improvement?
In this article I suggest one such metric for the Longitudinal Chromatic Aberrations (LoCA) of a photographic imaging system: the linear spatial resolution lost to LoCA at MTF50 by the camera+lens under review as setup, in the location and direction under examination, expressed as a negative percentage. For instance based on the last post on CA we could say that the MTF50 of Jim’s a7RII+FE55mm at f/1.8 near the center was about 7.7% lower than it could have been – as a result of Longitudinal Chromatic Aberrations. Clearly a smaller number is better.
Longitudinal CA = Color Plane Defocus
Taking that system as an example, this is how one of Jim’s LoCA capture sets presents itself. Recall that he takes many raw captures of a slanted edge chart in manual focus mode by moving the camera 4 mm towards the target each time without touching focus, thereby effectively walking it through back focus, perfect focus and front focus. The distance to the target is of the order of a few meters, not infinity. He uses MTF Mapper to extract the MTF50 performance of the individual raw color planes for each capture. I am grateful to Jim for generously sharing his data which in this case results in the following plot :
As the camera is moved closer to the target slanted edge each of the three color planes comes into focus in turn. If there are Longitudinal Chromatic Aberrations in the imaging system the three color planes do not come into focus at the same time, as shown by the colored curves achieving peaks in different frames. The black curve is instead the combined grayscale response calculated as discussed in a related article, representing overall system performance:
Spatial Resolution Performance Without LoCA
If this imaging system had been perfectly corrected for Longitudinal CA the three r,g,b planes would have come into best focus at the exact same time, something that can be simulated by shifting the color curves above so that their peaks align.
A combined grayscale MTF50 curve of the color plane data as shifted would then be indicative of the performance of the system in the absence of Longitudinal Chromatic Aberrations:
Loss of System MTF50 Due to Longitudinal CA
Figure 3 plots both composite grayscale curves (with and without LoCA) to show how much linear spatial resolution is lost in this system to Longitudinal CA . I aligned the curves approximately by hand but their relative position doesn’t really matter: what we are after is the magnitude difference of the two peaks, which represent perfect focus. In this case the grayscale curve with LoCA zeroed out peaks at an MTF50 of 1118 lp/ph, while the original grayscale curve with LoCA achieves only 1032 lp/ph, a loss attributable to Longitudinal Chromatic Aberrations of 7.7% of total system performance as setup, in the location and direction tested.
We could say that the LoCA score for this system at f/1.8 near the center of the field of view is -7.7%.
A difference of 7.7% in MTF50 is typically just noticeable by a pixel peeper.
Calculating the Metric
Therefore to calculate this LoCA metric all one needs to do is
- calculate the original system grayscale MTF50 curve from the individual color plane values and the first formula above as shown by the black curve in Figure 1 ;
- find the MTF50 at which this curve peaks;
- for each of the three color planes obtain its peak MTF50 value;
- combine the r,g,b peak MTF50 values by applying the coefficients of the grayscale formula to obtain the peak System MTF50 in the absence of LoCA;
- the difference between the two peak MTF50 values in 2. and 4. above expressed as a percentage of 4. is the linear spatial resolution lost to Longitudinal CA.
Clearly the smaller the number, the better corrected the system. Peeking at some of the other excellent prime lenses that Jim has tested on the a7RII we can see that LoCA scores typically, but not always, get better as the f-number gets larger. As a reference, the range for those lenses at f/2.8 near the center is between about -1 and -8%.
Since chromatic aberrations vary throughout the field of view those results are only valid for the given test conditions in the position and direction measured. Having played with a few combinations, if noise is controlled (good technique, properly illuminated edge, long enough) I think that these results should be repeatable within about +/-0.25%, all other things being equal.
Intuitively I would think that results should not change much if an AAless sensor with differently sized pixels is used aotbe, because MTF50s are multiplicative in a cascaded linear system and all else should be about the same. But I do not have the data to verify this thought, yet.
Notes and References
1. A7RII LOCA & AF VS COLOR PLANE. The Last Word, Jim Kasson.
2. The context of this post are raw captures of neutral (hueless,achromatic) slanted edges under a uniform illuminant by Bayer CFA digital cameras for the purpose of measuring by the slanted edge method the linear spatial resolution (‘sharpness’) of photographic equipment.