Dertmining MTF with a slant edge target - New technical article

The modulation transfer function (MTF) of a lens tells us how effectively the lens transfers, from the scene to the focal plane, the variations in luminance that convey detail, in particular how the "modulation transfer ratio" varies with spatial frequency (which we can think of as indicating the "fineness of the detail").

We often read today about the MTF being determined by what is called a "slant edge target test". At first it might seem that this refers to determining the MTF in a direction that is not aligned with the pixel grid of the camera. In fact, the technique does have that property, as a side effect, but that is not its purpose.

Rather, its purpose is to allow the entire MTF (over the entire range of spatial frequency of interest) to be determined, at any given place in the image, with a "one shot" test - not requiring separate determinations to be made with a repertoire of test patterns with recurrent luminance variation at different spatial frequencies.

The entire technique is very ingenious, and relies on a few pivotal mathematical concepts (whose practical execution, however, depends on the computational power we today have at our disposal).

I have just released to my technical information site, The Pumpkin, a new technical article, "Determining MTF with a Slant Edge Target", available here:

http://doug.kerr.home.att.net/pumpkin/index.htm#MTF_Slant_Edge

The article begins with a review of the concept of the MTF, followed by a discussion of the concept of a mathematical function. Then the slant edge target technique is described.

The discussion of the concept of the MTF is fairly concise, hopefully sufficient to establish the context. A more detailed article on that topic itself is under preparation, and should hopefully be published within the week.

Fascinating, Doug.

Does this require the removal of sensor the camera's anti-aliasing filter, or does the correction discussed at the end of the article accommodate that too?

Hi, Winston,

Winston Mitchell said:

Fascinating, Doug.

Does this require the removal of sensor the camera's anti-aliasing filter . . .

Click to expand...

No.

or does the correction discussed at the end of the article accommodate that too?

Click to expand...

Yes, exactly. It's a very accommodating technique. And in fact the analysis software itself figures out what needs to be done in that regard by analysis of the sensor outputs.

We will sometimes see that the MTF of a nice lens, tested on some stated camera body, will still have a substantial value (perhaps even being above the at the "50%" criterion) at a spatial frequency above the Nyquist limit for the sensor pitch of the testbed camera. People often wonder how we can know that, given that the MTF is measured with the lens in situ. But, as we have seen, the technique averts that limit.

Although I didn't use this metaphor in the article (I may add it in the next issue), we essentially use the sensels, actually in a two-dimensional array with a certain pitch, to effectively form a one-dimensional array (a "line sensor") with a much smaller pitch. (We have in effect asked them to all stand close together along the MTF axis for this shot.) Thus neither Harry Nyquist nor Claude Shanon need turn over in their graves.

An aside: Just the mere need to write those two names here overcomes me with a wave of awe for what we owe to these two wizards.

Shannon, best known for important other work, gets short shrift with regard to the sampling theorem often attributed solely to Nyquist. They were both heroic figures in their own rights, but their "triangulation" on this matter (it wasn't really collaboration") was a synergy to which we owe so much.

Best regards,

Doug

Thanks for the answer. I suspected as much.

We had a similar problem in the disk drive industry. How do you guaranty error rate in a very large disk drive? Certainly not with error-rate testing. By the time you're done, the drive is worn out and out-of-date.