Sagittal vs Meridional Resolution Differences in Lenses

Lenses usually behave very differently in resolving details that are in the sagittal versus meridional direction. Why is this?

A target designed to separate sagittal and meridional measurements

The sagittal direction is like the spokes of a wheel, pointing at the lens center (optical axis). Meridional direction is tangent to circles around the lens center. Test charts for checking resolution are available from the same site that provides the MTFMapper program, written by Frans van den Bergh. The test charts have been designed to separate out the sagittal and meridional measurements. Many of the charts also include the round ‘fiducials’ shown above, which help the program identify things like rotational errors for chart alignment issues.

The name ‘sagittal’ comes from Latin, and it means “as the arrow flies”, and is meant to indicate an arrow shot from the optical axis toward a subject. That’s also why the zodiac sign of Sagittarius is the archer...

The name ‘meridional’ is the same as ‘tangential’, referring to the meridional plane.

MTF50 plot separating out sagittal and meridional measurements

The pair of plots above show the measurements from a resolution target separated into meridional and sagittal. It’s obvious that the sagittal measurements are better than the meridional measurements throughout the photo.

Typical MTF50 resolution measurements (lp/mm)

In the image above, MTF50 resolution measurements are overlaid on the resolution target. The black trapezoid edges that are nearly vertical above are in the meridional direction, while the near-horizontal edges are sagittal (pointing toward the center of focus).

Notice how all of the meridional measurements shown are much lower than the sagittal measurements. The lens optics are fairly weak in the meridional direction. This is very typical of camera lenses; very few lenses are equally adept at resolution in both directions.

So, why are lenses sensitive to the direction of edges (light rays)? One of the main culprits in lenses is called ‘oblique astigmatism’, which causes the sagittal and meridional rays to focus at slightly different distances when off-axis from the lens center.

Decentering or tilting of lens elements during assembly can exaggerate sagittal/meridional differences. Even a very tiny slop in manufacturing tolerances can yield assembly variation causing astigmatism, and the problem worsens the further you get from the lens axis.

Designers favor making lenses that have better sagittal than meridional resolution, since they usually have to choose. Visually, lenses appear sharper with good sagittal resolution compared to equivalent meridional resolution.

Light rays in the meridional direction cross many more lens element boundaries at steep angles, compared to sagittal light rays.

Lenses with coma also affect meridional light rays more than sagittal.

Meridional light rays are refracted more steeply, and this causes the image to get focused closer to the lens. Sagittal light rays pass through the lens at a flatter angle, and therefore focus further from the lens. Designers try to account for this effect, but the inevitable slight astigmatism in lenses usually causes the meridional rays to focus less well than the sagittal rays.

All of these effects are just generalizations, and there are cases where lens designs actually cause meridional rays to focus better than sagittal rays. Designers are constantly faced with a very complicated balancing act.

What to do? Not unsurprisingly, the resolution in both directions will get improved by stopping down the lens, and usually the meridional direction will improve slightly faster than the sagittal direction.

Web sites that evaluate lens resolution almost never mention the differences between the meridional and sagittal resolution, or even discuss that such a thing exists. The best they will do is show the MTF ‘contrast’ plots, which are usually just a theoretical line plot of sagittal and meridional contrast. I think it’s important that the measurements are segregated from each other to better understand how a lens really performs. A single “edge resolution” measurement, for instance, is almost meaningless.