Bart, maybe this deserves a hard look / article. There is something counterintuitive here.Of course, moving from the spatial to the frequency domain and back is never obvious, and here we also have the fact that MTF numbers are used which again brings the shape of the MTF curve into play etc.

Hi Edmund,

In addition to Jim's example chart for a lens quality (MTF) that varies with aperture on one axis, and sampling density (sensel pitch) on the other, one can see that with better lens quality (here it's due to optimum balance between residual aberrations and diffraction) AND denser sampling, the combined result gets better.

One could replace the aperture differences on one axis by different lenses at their optimum aperture on that same axis. Then combined response would still increase with denser sampling for all lenses, with a peak at the combination of best lens and most dense sampling.

To put it in other words, at a certain level of detail with an MTF of 50% for a lens, and and MTF of 50% for a sensor, the combined system response will be 0.5 x 0.5 = 0.25 MTF response (MTF25). If at the same level of detail the lens could be improved to 100% MTF, and the sensor is still 50%, then the combined MTF is raised to 1.00 x 0.5 = 0.5 MTF (MTF50, and it will never get better than the lowest contributor which therefore sets the maximum achievable limit, unless sharpening is added).

Likewise, if at the same level of detail the lens remains at 50% MTF, and the sensor could be improved to 100%, then the combined MTF is 0.5 x 1.00 = 0.5 MTF (it will also never be better that the lowest contributor). With both components at 100%, their combined MTF would become 1.00 x 1.00 = 1.00 MTF response (MTF100).

Therefore, increasing the MTF response for either component will raise the combined response. Of course, a 100% MTF for either component is virtually impossible (except for the lowest spatial frequency or with sharpening). It may also be easier to improve the MTF of one component for a reasonable price than for the other component. We also face physical limitations that prohibit 100% MTF, like diffraction and available sampling density. So it becomes an optimization problem for both components with bounds, and the lowest contributing component keeps dictating the best achievable combined response.

Cheers,

Bart

P.S. I've added a chart as attachment to show the trade-offs between lens quality (expressed as least achievable blur), sensel pitch, and resulting resolution in (simulated) Cycles/mm at MTF50. Diffraction is not fully modeled in, so that may reduce the amplitude at narrower sensel pitches a bit.