Chromatic Aberrations MTF Mapped

A number of interesting insights come to light once one realizes that as far as the slanted edge method (of measuring  the Modulation Transfer Function of a Bayer CFA digital camera and lens from its raw data) is concerned it is as if it were dealing with identical full resolution images behind three color filters, each in their own separate color planes:

CFA Sensor Frequency Domain Model
Figure 1. The Modulation Transfer Function of the three color planes can be measured separately directly in the raw data by open source  MTF Mapper

Because each color filter lets through a different mix of wavelengths each sensing plane will see an image with slightly different spatial characteristics.   The differences will be evident in wavelength dependent effects like diffraction and chromatic aberrations.   We dealt with the effect of the spectral sensitivity of CFA filters on diffraction in an earlier post, we will take a closer look at lateral and longitudinal CA in this one.

Chromatic Aberrations: Shifts in xy and z

Lateral (or Transverse) CA is a result of imperfect optics which are unable to place different wavelengths exactly in the same place on the sensing plane.  The edge will be slightly shifted and amplified up or down, left or right (along the xy axes) in the images of the three color planes depending on its distance from the center, as hinted to by the different position of the gray edge in Figure 1.  If the raw color channels are used as-is to demosaic an image in a standard RGB color space they will produce the well known reddish-greenish-bluish fringes around areas of high contrast.  Most lenses are designed to keep LaCA under control but because the three color planes are captured separately in the raw data it is relatively easy to re-size and re-align them before assembling them into a rendered RGB image.  Therefore Lateral CA can often be partly compensated for during raw conversion.

Longitudinal Chromatic Aberrations (LoCA) will cause the edges in the three color planes to come to focus at slightly different distances (the z axis) from the lens principal plane , as hinted to by the blue arrows in Figure 1.  Assuming that the sensor is positioned so that the green channel is perfectly in-focus, both the red and the blue color planes will see very slightly out of focus images, reducing the overall sharpness of the final photograph.

Figure 2. Longitudinal Chromatic Aberrations cause the focal length to be wavelength dependent. Image Copyright 2006 Bob Mellish, licence

How far out of focus will depend on how well the lens has been corrected for LoCA.  Unfortunately there is no way to recover the spatial information lost to defocus so there is very little or nothing one can do to minimize the effects of Longitudinal CA during raw conversion, which makes having a well corrected lens in the first place a very desirable feature.

Measuring Chromatic Aberrations via MTF50

Frans van den Bergh has provided as part of his open source MTF Mapper a test chart that will allow one to determine best focus and Longitudinal CA from a single capture.  The approach is convenient even though the setup is a bit finicky and somewhat prone to corruption by the other aberrations inevitably present throughout the field of view.

Figure 3. From single capture of ‘Focus Fine Tune’ chart, by MTF Mapper. Image courtesy Frans van den Bergh

Jim Kasson has independently performed a marvellous series of tests documenting this effect for a number of mid-tele primes, I highly recommend the read.  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.  He used MTF Mapper to extract the MTF performance of the individual raw color planes and graciously let me have some of his data.  Here are the MTF50s of 49 such captures from a Sony a7RII coupled with an FE55mm at f/1.8:

Longitudinal CA a7RIIFE55
Figure 4. 49 captures by Jim Kasson. Manual focus was kept fixed while moving the camera 4mm towards the slanted edge target each time.

The first time I saw this graph with separate spatial resolution readings for the three raw color planes I was blown away: there’s Longitudinal CA (and so much more) in all its glory.  It looks like this lens  is well corrected for blue but less well for red.  Apparently this is typical.  The question that immediately popped into my mind was where should the camera focus for best overall sharpness, hence the journey described in the last three articles. For instance we would not want it to focus based on the peak of the red plane.

Where Should The Camera Focus?

I believe that the most accurate grayscale image we can get off a hueless slanted edge is the baseband image available in the raw data, which has linear spatial resolution performance based on that of the separate color planes as defined in the last article:

MTF50_Y = 0.25 MTF50_r + 0.5 MTF50_g + 0.25 MTF50_b

The following figure shows the measured MTF50s read off the separate r,g,b color planes in the raw data as respectively colored lines; the composite system grayscale values calculated as above as the solid black line; and the measured fully mosaiced white balanced raw data image as a dashed black line.

Measured rgb MTF50 and Computed Grayscale Composite
Figure 5. 49 raw captures by Jim Kasson with an a7RII+FE55.

It looks like for this lens the green and blue planes would be good references for finding best overall focus, which occurs around frame 29/30 as indicated by the solid black curve.

Measuring the Impact of CA on System MTF50

At frame 29/30 the green and blue planes are near their peaks but the red plane is about 300 lp/ph down  from its own.  Since red contributes 1/4 of the grayscale MTF50 value that means that red Longitudinal Chromatic Aberrations cost this imaging system about 75lp/ph in ‘sharpness’ when perfectly focused at f/1.8.  Calculating it more precisely, red LoCA costs the system 7.6% of what could have been the system peak MTF50 value in its absence.  That’s a loss that can be noticed by a careful observer.

Figure 6.  Longitudinal and Lateral Chromatic Aberrations for the a7RII with a FE55mm lens at f/1.8, Jim Kasson captures.

On the other hand the WB raw dashed line, that is the MTF50s obtained directly off the white balanced full mosaic raw image, is about 65 lp/mm below the system grayscale curve, obtained from the individual color planes.  The latter discount the effect of LaCA so we can tell that, if uncorrected, Lateral Chromatic aberrations will cost this imaging system about 65 lp/mm at f/1.8 when perfectly focused.  That’s about  6.4% of the grayscale MTF50.  However we can assume that a decent raw converter will correct or allow for the correction of at least some of this LaCA.

The remaining ‘blur’ is typically mostly due to pixel aperture and Spherical Aberrations at these wide f-numbers.  Keep in mind that this is a very good prime lens.

So how well tuned is the focusing on your camera and lenses and how well corrected are they for aberrations?

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