# Lens MTF and resolution

#### Doug Kerr

##### Active member
We often look to the MTF curves for a lens to give us insights into various of its properties. Often we say in particular that these curves - in the form we often see them, as in lens catalogs - show us the resolution of the lens. But do they?

Well, first we would have to say what we mean by resolution. Perhaps we mean the finest test target that, when imaged by the lens, leads to an image of which some guy says, "yep - I can see that OK".

But if we want an objective measure, we might decide to call the "revolution" of the lens the spatial frequency at which the MTF drops to 50% of its value at "low" spatial frequency.

Here we see MTF plots for two lenses, in each case at the center of the frame, lets say wide open. (We will assume that these are the conditions for which we are interested in the lens resolution.) They are presented in the "scientific" form: MTF plotted vs. spatial frequency. We don't have to have separate curves for sagittal and meridional response as these are always identical at the center of the frame.

The horizontal line for MTF=50% has been darkened. We can see that:

For lens A, the MTF just drops to 50% at a spatial frequency of 60 line pairs per millimeter (lp/mm). So we would say that its resolution (wide open, at the center of the frame) was 60 lp/mm.

For lens B, the MTF just drops to 50% at a spatial frequency of 70 line pairs per millimeter (lp/mm). So we would say that its resolution (wide open, at the center of the frame) was 70 lp/mm.

Tidy enough.

But of course we probably do not have this form of the plot of the lenses' MTF's. Instead , we have what I call the "lens catalog" form. There, we plot MTF vs. distance from the center of the frame, with curves for two spatial frequencies, 10 lp/mm and 30 lp/mm.

Now, in our first figure, what part of all that information is presented in the "lens catalog" form of the MTF plot? Only the portion inside the two orange boxes - just the MTF (at the center of the frame) at spatial frequencies of 10 lp/mm and 30 lp/mm.

Now yes, it contains other information - the MTF at those two spatial frequencies for other distances from the center of the frame. But here we are only interested in the lens resolution at the center of the frame.

Let's now look at a "lens catalog form" of the MTF plot that shows all the information it can show from our other plot:

Wow! All there is are the two dots on the "center of the frame" position.

What about the MTF for other spatial frequencies, shown on the first chart? Sorry - the convention for the lens catalog form is to only show data for the spatial frequencies 10 lp/mm and 30 lp/mm.

What about the difference between the sagittal and meridional directions? The data for those is always identical at the center of the frame - so the dots really show us both.

How can we tell from this very limited MTF plot (lens catalog form) what the resolution is of the two lenses?

We can't.

Can we even guess for which it is higher? Well, the "curve" for lens A (we only see the "center of the frame," point on it) is higher than curve B. Maybe that is a hint that lens A has the greater resolution. Nope - we earlier saw that Lens B has the greater resolution.

What about from an "entire" lens catalog form MTF plot, like this (this is not for either "Lens A" or "Lens B" - sorry):

MTF curves for Canon EF 50mm f/1.8 USM lens
Courtesy of Canon , U.S.A.​

Can we tell from that? No.

What does the difference on this type of chart in how fast/far the "30 lp/mm" (thin) curve drops, for the two lenses, tell us? How fast/much the lens performance falls off as we move from the center of the frame. Is that important? Sure. Does that tell us about the resolution of the lens at the center of the frame? No. At some distance out? No.

Best regards,

Doug

#### Mike Shimwell

##### New member
Doug

Can you prepare some surface plots?

Mike

#### Doug Kerr

##### Active member
Hi, Mike,

Can you prepare some surface plots?
Do you mean MTF vs. spatial frequency and distance from the center of the frame in "3D"?

I have no sets of data from which I could do that.

Best regards,

Doug

#### Doug Kerr

##### Active member
Hi, Mike,
Can you prepare some surface plots?
The Zemax optical design package, published by Optima Research, can supposedly produce "3D" MTF plots (theoretical) for a lens design.

I have sent a wire to Optima Research, asking them if they can provide a sample such plot.

Best regards,

Doug