# Tong Family

## What is MTF?

Well there has been so much discussion about resolution and sharpness, I’m so confused, so finally spent a little time with Imatest trying to figure out what a Modulation Transfer Function actually is. Also Scott mentioned that in addition to mingthein, checking out the lensrental.com blog is important as they Imatest every lense they bring in. The Olympus OM-MD5 is pretty much state of the art with its prime lenses. Very close to the theoretic maximum for their sensor.
So what is an MTF (according to Imatest and Bob Atkins), basically the idea is pretty simple, if you show a pattern of black and white as the distance between these bars shrinks (technically speaking the frequency of black and white rises), then eventually, you don’t see black and white, but it just looks like grey. Technically speaking you are seeing contrast (the difference between black and white) fall as the lens blurs the black and the white and smears it into grey.
How do you measure frequency of black and white stripes, with film it was line pairs per millimeter (lp/mm), that is for every millimeter of film, how many black and white pairs fit in it (1 lp/mm means that there is a 0.5mm of black and a 0.5 mm of white as an example). Because digital sensors don’t actually have something you print out, instead you typically use line widths/picture height or cycles/pixels. The former means, how many black and white lines fit into the height of the sensor (if a sensor has say 2,000 pixels in height and each line is say 1,000 pixels, the you would 2 line widths/picture height).
So when you have really big line widths, then the MTF=100% which means that you are showing perfect contrast. But when you shrink the line widths, when the contract reaches 50% of the maximu, that is called the MTF-50%. If you an equation guy, then you can define it as:

MTF = (difference in maximum and minimum intensity)/(max plus the min)
Traditionally, resolution charts from the 50s (?!) asked for a set of black and white bars, where an you not tell that the bars are black or white at all. It’s very subjective as in fact, it is a gradual function, but general this corresponds to an MTF of 10 or 20% (that is contrast is only 10-20% of pure black and white).
How is all this measures, well it is complicated, but it turns out that if you look at slanted black line.

• Perhaps the most interesting thing is that the MTF of a lense varies depending on the test pattern that you are using and also the light you are using to illuminate the target.
• One big problem is that in camera, there are all kinds of algorithms that affect sharpness because the camera boost contrast (technically increases high frequency boost) near fine images and reduces contrast to reduce noise near low contrast (eg solid colors).
• Lens have different MTF in different areas, so you can’t just take the MTF of the center and know much about the lense.
• Lens can have astigmatism where their MTF for radial lines from the center are different form lines that are tangents to the center
• The MTF doesn’t tell you much about how it matters for the actual image since it doesn’t take into account how we see things (which is why SQF for subjective quality factor was invented)

As an aside, the best metric is MTF50P which is 50% of the peak MTF. In cameras with lots of in camera sharpening, the MTF can be great than 100%, that is black and white has more contrast as the sharpener boost the dark and lower the light sections (the defintiion of sharpening(.
As an aside one of the cool thinks about MTF is that a system MTF is the product of all the elements which makes it easy to calculate for complex systems.
Since we are doing a tutorial, there are two reasons for lens blur. First is aberrations in the lenses and that is what is the problem for specific lenses and then there is diffration which means that at small apertures (large f-numbers), light bending. F-numbers is simple the focal length divided by the aperture diameter. So a F/1 means that the aperture is as wide as the focal length. And each F/stop is half the light of before since this is an area measure, the strange sequence is 1, 1.4, 2, 2.8, 4, 5.6, 11, 16, 22. Every lense is going to have an optimum aperture where it is sharpest. usually this is 2-3 stops below the maximum. And the best band is +/-2 stops from there.

### I’m Rich & Co.

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