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.

Fresnel lens

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

fresnellens中文

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.

Fresnel LensSheet

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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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.