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In lens design textbooks, a distinction is often made between longitudinal chromatic aberration and spherochromatism. (See for instance Kingslake's lens design book.) What is simple way to understand the difference? As far as I can tell, both involve the focal plane varying in distance from the lens as the wavelength of the light changes.

In particular, how do we identify the following image as primarily an example of spherochromatism and not longitudinal CA?

(From https://www.lensrentals.com/blog/2010/10/how-to-shoot-with-wide-aperture-lenses/.)

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Spherochromatism is simply the change in longitudinal chromatic by lens zone. Both aberrations are closely related. If you have a lens with longitudinal, there will be some change in color focus by lens zone (spherochromatism). The use of conventional optical glass in long lenses was not able to control either longitudinal nor the spherochromatism to a great degree. Stopping down the lens to avoid the poorly corrected marginal rays was necessary to attain an acceptable image. With the advent of low dispersion glass, both problems were nearly eliminated. I view spherochromatism as a subset of longitudinal chromatic. Fringing in the picture is from longitudinal chromatic. To say that an optic has spherochromatism, one must compare color focus of various lens zones (Paraxial, zonal and marginal). You would need 3 pictures; one for each lens zone to determine if the optic had noticeable spherochromatism.This cannot be determined in a single picture. The green fringing (mid spectrum) indicates that the chromatic is not lateral chromatic.

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Longitudinal chromatic aberration is the variation of the focal length with color. It does not vary with the aperture (or f/#) that the lens is being used at. For example, if a lens has 50 microns of longitudinal chromatic aberration at f/8, it will have that value at another f/#. 

Spherical aberration is the variation of focus with the aperture of the lens. The position where rays located close to axis focus is called the axial focus. As the lens is used at an increasingly wider aperture, the rays focus increasingly inside of the axial focus (undercorrected spherical aberration) or increasingly further from the axial focus (overcorrected spherical aberration). This variation of focus position is not linear with respect to the aperture, so it becomes more significant if the lens is used a lower f/# (lower f/# means higher angle for the converging cone forming the image, lower f/# is also called faster f/#).

Spherochromatism is the variation of the spherical aberration with color. So say if a lens has 50 microns of longitudinal spherical aberrtion, when used at f/2 in the red, and the same lens has 75 microns of longitudinal spherical aberration, when used at f/2 in the blue, then spherochromatism for the lens is blue is 25 microns greater than for the red. 

Practically, it looks like your photo is of a tilted scale. The primary aberration is likely defocus. Again, from a practical point of view, it would be hard to tease out what is longitudinal chromatic aberration and what is spherochromatism. For one thing, it would help a lot to have images taken at different f/#s. (Since the spherical aberration varies with used f/#). I'm not saying it couldn't be done, but most people would measure the MTF at different colors and use that information. All of the aberrations get wrapped into the MTF, so it is an all-encompassing measure.

Note that transverse aberrations (the size of the spot in the plane perpendicular to the optical axis) behave differently than longitudinal aberrations. A topic for a different time.

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  • $\begingroup$ Is that definition of spherical aberration correct? The focus doesn't vary with aperture, rather focus point of a ray varies with distance from the center of the lens, it seems. This leads me to believe we're seeing primarily spherochromatism. The tint of the image is shifting with distance from the focus plane (purple in front, green behind). This is a change in color intensity, which seems to come from a splaying of the focus along the optical axis characteristic of spherical aberration. LoCA alone would change magnification and leave a correctly colored image except for tinted fringing. $\endgroup$
    – Potato
    Jul 8, 2019 at 2:36

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