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# Meridional and sagittal MTF - a tutorial

Started Mar 17, 2005 | Discussions thread
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Meridional and sagittal MTF - a tutorial
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The MTF curves for lenses generally have two curves for each combination of aperture and spatial frequency, one for the "meridional" MTF and one for the "sagittal" MTF.

The concept behind this distinction, and the terminology that is involved, can be confusing. I thought it might be useful to explain it in what I hope is a useful way.

The lens aberration called "astigmatism" results in the rays from a single off-axis object point, traveling through the lens in different planes, not all converging at the same distance behind the lens. As a result, there is no place where we can place the film (or digital sensor) such that it will receive a point image for each off-axis point of the object, as is needed for "perfect" imaging.

In fact, the result of this inconsistent convergence is that, at the focal plane, the rays from an off-axis point form not a point image, nor even a "blur circle", but instead a "blur figure" which is shaped something like an ellipse. (This effect generally increases for greater distances of the point off-axis.)

In any situation, it is the width of the blur figure that causes the response of the lens - the MTF - to be less than 1.0 - increasingly so for increasing spatial frequency (finer detail). Because in this case the width of the blur figure is not the same in both directions, the MTF will be different for any spatial frequency if we consider response to detail along one path in once direction across the image versus along another path at right angles to the first one.

The response as we travel along along a "radial" path at the point of interest (along a line extending from the center of the image) is called the "meridional" (sometimes, "tangential") MTF. The response to detail along a "circumferential" path (along a line perpendicular to the first line - a small part of a circle centered on the center of the image) is called the "sagittal" MTF.

We test in the laboratory (or by simulation) for MTF by observing the response of the system as we traverse a pattern of parallel "lines" (they actually have luminance that follows a "sine wave" pattern). The lines must be perpendicular to the "path" along which we wish to note the response.

Thus, sagittal MTF is tested with such a pattern where the lines are oriented "radially" - that is, parallel to a line through the center of the image. Meridional MTF is tested with such a pattern where the lines are aligned "circumferentially" - perpendicular to a line through the center of the image.

Note that other lens aberrations than astigmatism (notably coma) also play a role in this picture. Discussion of this is beyond the scope of this note.

Best regards,

Doug

Doug Kerr's gear list:Doug Kerr's gear list
Leica V-Lux 4
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