How to calculate MTF ? Need help with the formula

Question

I'm trying to reproduce MTF chart programmatically but I'm stuck at some point.

I'm starting with a clean bar chart like this:

I then take a picture of this pattern with a smartphone (printed on HD quality paper, no gloss, no texture, ...) and I get something like this: (there is a big of distortion)

I used the following page to understand how MTF is calculated: https://www.imatest.com/docs/sharpness/

With my script, I'm basically scanning all vertical lines one by one, I scan pixels one by one from top to bottom for each line and I get the min and max value for luminance (I get the LAB value for each picture and I take the "l" value).

For the first step (amplitude), I get the following graph for my "perfect" example:

And when I do the same with the picture I took, I get something like this:

So far, it seems to be in line with what I see on the Imatest page except that my values seem inverted and that I go above 100 while I only apply the following formula: C(f)=Vmax−Vmin/Vmax+Vmin

Now my problem is that I can't get to the MTF formula, if I apply MTF(f)=100%×C(f)C(0), I get exactly the same graph. My maths are rusty and maybe I'm missing something somewhere.

What I'm trying to achieve is to give a easy to understand score to sharpness. MTF is a good starting point but in the end, I would like to give a score like an average. I know it's not accurate because the center is sharper than the edge but at least it would allow to rank sharpness in a more or less neutral way.

Any idea on how I can build the MTF chart or how I could assign a final score?

Thanks

Update, based on Steven's comment hereunder, I have built an average MTF curve and it looks like this:

Am I right to assume that this indicates oversharpening caused by the device software starting somewhere in the middle and then gradually losing sharpness?

Answer 1

From my previous comment to your previous question:

Horizontal and vertical bars do not, strictly speaking, measure tangential and sagittal performance. Sagittal lines are like the spokes of a wheel spreading out from the center of the lens' field of view. Tangential lines are tangent to the circular surface of the wheel that rolls over the ground.

Further, matte paper is notorious for blurring sharp edges. You're starting with a poor quality chart. All that follows will suffer the consequences for that decision. There's a reason real test charts are expensive. They're held to very high standards of quality control and use more expensive printing methods to achieve them.

Answer 2

Now my problem is that I can't get to the MTF formula, if I apply MTF(f)=100%×C(f)C(0), I get exactly the same graph.

From the Imatest page (emphasis added):

"To correctly normalize MTF at low spatial frequencies, a test chart must have some low-frequency energy. This is supplied by large light and dark areas in slanted edges and by features in most patterns used by Imatest, but not satisfied by lines and grids."