Testing Lenses: Best Individual Focus MTF Curves

OK, in the last post we did something useful, but rather boring: we looked at how MTF changes when lenses are stopped down. Today we’re going to use a more powerful optical bench tool, the MTF vs. Field vs. Focus. Unless you work in a metrology lab (and probably not even then, very few are performing this test) you aren’t familiar with what this is, so I’m going to take a minute to show you.

Standard MTF

When we (or anyone else) does a standard MTF it works like this:

  1. The machine very accurately focuses on the center point of the lens.
  2. It then measures the MTF from the center to one edge at that best center focus.

When that is done, you get the MTF graph you are used to seeing.

Olaf Optical Testing, 2017

The standard MTF says “if you focus at the center of the lens, the graph shows you how sharp the image will be from one edge to the other.” The graph above shows the image for the standard MTF for the Zeiss CP.2 35mm T2.1 and shows us it stays pretty sharp from one edge to the other. A lot of lenses don’t stay sharp from one side to the other, though.

MTF vs. Field vs. Focus

We can do things a different way, though, and measure the MTF vs Field vs Focus. We program the MTF bench to do this:

  1. The machine very accurately focuses on the center point of the lens.
  2. The machine then backs the focus away 300 microns from that focus.
  3. The machine then measures the MTF, moves forward a few microns, and measures it again.  Basically, at every point it measures the MTF 20 times, changing focus a bit each time.
  4. The machine repeats this step at 40 points from one side of the lens to the other.

So what we end up with is a huge bunch of data. At each of 21 points across the lens, there are 800 measurements saved compared to 20 measurements per point (sagittal and tangential, each at five frequencies) on a standard MTF. That’s a lot of data; a bit over 16,800 data points per tested lens.

We usually graph it something like this.

Olaf Optical Testing, 2017

That’s good information. It shows you how the field of focus curves if you’re focused on the center point. For the lens above, it also shows you that away from the center, the image will be sharpest at a different focusing distance than it is at the center. The “0” in the middle of the Y axis is the best center focus, the top and bottom of the charts are +/- 0.3mm of focusing distance.

In other words, if you focus at the center, your image will be sharper closer or further away as you look from one side to the other; what we call field curvature.

But back to MTF. Let’s take a close up of the sagittal field on the right. I’m also going to draw a black line across the graph to show the focusing distance chosen as “best focus distance for the center of the image.” That black line shows you where the focus was for the standard MTF, and the MTF values along that line are what the standard MTF showed.

Olaf Optical Testing, 2017

The graph below is that standard MTF, and it shows the lens is quite soft 12 to 16mm away from the center (the outer 1/3 of the image). But if you look at the field curvature above, you know that softness is because the best center focus isn’t the best focus for most other points across the field. The lens could be a lot sharper from 10m to 16mm if we had focused there, instead of at the center.

Olaf Optical Testing, 2017

Why is this practical? When I make an image with the subject in the outer 1/3 of the image, well, I’ll focus in the outer 1/3 of the image. When a lens has strong field curvature, as this one does, the standard MTF curve doesn’t tell me a thing about how sharp the image might be if I focus there instead of the center.

We’ve been busy writing programs that let us get more information from the MTF v Field v Focus test. The one I’m going to show you today is ‘individually focused MTF,’ which will answer the question ‘how sharp is it when I focus there?’ In other words, if I focused the lens at the point 10mm off center instead of at the center, how good would the MTF at 10mm be?

Best Individual Focus MTF  (BIF-MTF)

We could search through those 16,000 data points in the MTF v Field v Focus graph from center to edge, plotting ‘what is the best possible MTF at each individual point if we focused there.’ If I plot this ‘best individual focus MTF,’ it looks entirely different than the standard MTF above.

Olaf Optical Testing, 2017

To make it simpler, I’ll put thumbnails side by side: standard MTF on the left, ‘best individual focus MTF’ on the right. (Please ignore the different layout of the graphs, I’m working with two different versions of our software.)

Olaf Optical Testing, 2017

They look like two different lenses, don’t they? In reality, depending on how you use them, they are. If you focus at the center point, you get the standard MTF graph on the left. The standard MTF suggests that the lens is really sharp for about 5mm to either side of center (the middle 1/4 of the image) then falls off.

If you focus at a specific point away from center, though, the ‘best individual focus MTF’ graph shows you can get a sharp subject all the way out to nearly 16mm from center, which is all but the very edge of the image.

Remember, though; the graph isn’t reality. If you did focus at, say 16mm away from the center, the rest of the image wouldn’t be as sharp as the graph says. The center would be quite soft if you focused at the point 16mm away from the center, just like the 16mm point is soft when you focused at the center.

The best individual focus MTF graph tells you is how sharp the image could be at each single point; it says nothing about how the rest of the lens would look if you focused there. To demonstrate, here’s what the Zeiss 50mm T1.5 MTF looks like if I set the focus to be best at 14mm away from the center.

Olaf Optical Testing, 2017


Still, this is good information to have. If you’re framing a scene with an off-center subject, knowing how far from center you can get a sharp image is useful. And it’s different for each lens; there’s no general rule for how far away from center you can stay sharp. This is an extreme example; most lenses don’t change this much if we compare standard MTF and best individual focus MTF. But most lenses do change to some degree.

As an aside, this is a nice illustration showing that when people argue about whether the Zeiss 50mm Super Speed (as an example) is soft or sharp away from center, well, they’re both right. It depends on how they’re using the lens. A landscape or architectural photographer focusing in the center would say the lens is very soft in the outer half. A portrait photographer would counter that the eyelashes of his subject are very sharp even though they are posed in the outer 1/3 of the image.

I’m going to put up the best focus MTF charts for all of the Cinema primes we tested in the last article. On the left is the MTF taken at T4 in the standard way, on the right the ‘best individual focus MTF’. The graphs are slightly different sizes because the best focus MTFs are from a beta version of our new software.

If enough people think this is something they will find useful, we’ll start publishing them for all of the lenses we test.

85mm Lenses

All of the 85mm lenses show some improvement at best focus and perform well far away from the center. And then there’s the Sigma 85mm. I don’t have the words, other than I been telling you all that lens is amazing.

Canon CN-E 85mm T1.3

The Canon 85 can get ‘near center’ sharp out nearly half-way to the edge. Further than that there is some loss of fine detail (higher frequency lines) but it’s not severe at T4. I really wouldn’t hesitate to use this lens all the way to the edge of the field.

Olaf Optical Testing, 2017


Sigma Cine 85mm T1.5

I am unworthy. There is moderately mind-boggling goodness all the way to the edge.

Olaf Optical Testing, 2017


Rokinon Xeen 85mm T1.5 

The Xeen 85mm really didn’t drop its MTF until halfway to the edge when we used center focus. There is some improvement in the outer 1/2 with best individual focus, but performance does fall off a bit beginning 2/3 of the way to the edge.

Olaf Optical Testing, 2017


Zeiss CP.2 85mm Super Speed T1.5

The Zeiss Super Speed does improve to some degree with best individual focus, and there’s no sudden drop off.

Olaf Optical Testing, 2017


Zeiss CP.2 85mm T2.1 

The two Zeiss 85mm, if I remember correctly, are identical optically and differ only in the mechanical size of the aperture. It’s not surprising that they behave similarly at T4.

Olaf Optical Testing, 2017

50mm Lenses

As the field gets wider, we expect to see more weakness near the edge of the field, even with best possible focus, since there are often more aberrations.

Canon CN-E 50mm T1.3 

Well, it is a very old design and the only T1.3 lens at 50mm. It struggles a bit away from the center at higher frequencies (fine detail) no matter where you focus. But it is better off axis than the standard MTF curve leads us to expect.

Olaf Optical Testing, 2017


Sigma Cine 50mm T1.5 

OK, it’s not quite as spectacular as the Sigma 85mm, but it’s absolutely excellent to 2/3 of the way to the edge and pretty good even further away.

Olaf Optical Testing, 2017


Rokinon Xeen 50mm T1.5 

Like the 85mm, the Xeen 50mm doesn’t have a lot of field curvature, but there is some. It stays quite sharp till just under the halfway-to-the-edge point, but you lose sharpness and keep astigmatism in the outer half of images, even at best focus. It’s performs pretty well stopped down but doesn’t improve quite as much as the others at best focus away from center.

Olaf Optical Testing, 2017


Zeiss CP.2 50mm Super Speed T1.5 

This was the lens we used in the introduction because the difference is so amazing. It’s exceedingly sharp out to 3/4 of the way to the edge if you’re focusing out there. It’s really close to the Sigma in quality until you get very near the edge.

Olaf Optical Testing, 2017


35mm Lenses

We generally think of wider-angle lenses as having more field curvature, so we’d expect they should look entirely different with best individual focus. They do, but a bit less so than I expected. Probably aberrations are causing more issues than field curvature away from the center at this focal length.

Canon CN-E 35mm T1.5 

Again, things look a better away from the center than the standard MTF seems to indicate. It’s not quite as sharp as the longer focal length lenses, but then, it’s not the longer focal length lenses.

Olaf Optical Testing, 2017


Sigma Cine 35mm T1.5 

Like I said for the Canon, although perhaps a little better. Remember, the Sigma Cine lenses are much newer designs than the others we’re testing here.

Olaf Optical Testing, 2017


Rokinon Xeen 35mm T1.5 

The Rokinons seemed to improve the least at the longer focal lengths, but may improve the most here at 35mm. That’s a dramatic difference.

Olaf Optical Testing, 2017


Zeiss CP.2 35mm T2.1 

While we do get some improvement with the Zeiss 35 T2.1, it’s not dramatic.

Olaf Optical Testing, 2017

Wider Lenses

I was less certain what to expect with the wider lenses; they do have field curvature, but also tend to have more aberrations away from center that don’t improve with specific focus.

Canon CN-E 24mm T1.5

The Canon 24mm shows it’s capable of better performance off-axis than the standard MTF curve suggests. It has near-center sharpness to 8mm away from center, and decent performance to about 12mm before falling off.

Olaf Optical Testing, 2014


Sigma Cine 24mm FF T1.5 

The Sigma 24mm standard MTF curve looks a bit like the Zeiss 50mm SS, and I was hoping for dramatic improvement at best focus. It does improve, no question, but in the outer 1/3 there is still significant fall off. It does perform better in the middle 1/3 of the image than the standard MTF curve suggests.

Olaf Optical Testing, 2014


Rokinon Xeen 24mm T1.5

Similar to the 35mm, the Rokinon 24mm’s best individual focus stays good a bit further out than most 24mm lenses.

Olaf Optical Testing, 2017


Zeiss CP.2 28mm T2.1

The Zeiss 28mm is another lens that shows decent performance 3/4 of the way to the edge with best individual focus MTF, much better than the standard MTF suggests.

Olaf Optical Testing, 2017


Zeiss CP.2 21mm T2.9

The legendary 21mm Zeiss does improve a little bit with best individual point focus. The ‘most sharp’ area ends about 6mm away from center with both standard and best focus MTF, though.

Olaf Optical Testing, 2017


So What Should We Do About This?

With the last post, it was obvious that we should add MTF tests at apertures other than wide open. The Best Individual Focus MTF (BIF-MTF) is a different thing. For one, it’s strange. You’ve never seen it before because no one’s ever done it before.

For the major piece of data it presents, ‘How far from the center can you focus and get near-center sharpness at that point’, I could give as a number without showing the graph. For example, it would be 6mm (about 1/3 the way to the edge) for the Zeiss 21mm above; or 15mm (3/4 the way to the edge) for the Zeiss CP.2 50mm Super Speed. The graphs, though, do present a better picture of whether the drop off is gradual, or sudden. So I’m open to discussion as to whether the graphs are worth showing in our reports.

To some degree, you can get that information from the Field Curvature graphs, which we are going to show with all lenses going forward, but the field curvature compresses the data a lot. You can’t tell if a red area in the Field Curvature graph is .80 or .89 and that can be a big difference.

There’s another neat trick we can do with the MTF v Field v Focus data that may be more useful for some types of images, but this post is already plenty long so we’ll save that for Part III.

Addendum: As Ilya pointed out in the comments, the beta software BIF-MTF graphs have a soft gray T number in the upper left corner. Please ignore them, it’s an artifact caused by a combination of not-quite-finished software being used by my very tired brain. 


Roger Cicala, Aaron Closz, Brandon Dube, Max Bruggerman, and Markus Rothacker

November, 2017

Author: Roger Cicala

I’m Roger and I am the founder of Hailed as one of the optic nerds here, I enjoy shooting collimated light through 30X microscope objectives in my spare time. When I do take real pictures I like using something different: a Medium format, or Pentax K1, or a Sony RX1R.

Posted in Equipment
  • It sold one to me 🙂 Those guys are generally killing it lately.

    We’re on the same page for MTF reviews, but I think MTF wide open, f/2.8 (for the zoom-prime comparisons) and either f/4 or f/5.6 (haven’t decided yet).

  • Thank you, Ilya. That is my fault: the Beta software I used for the new graphs isn’t ready for public use yet — you may have noticed I had to make graph titles by hand. I neglected to pull off the T# on some, which, as Brandon mentioned, the new software puts a default # if the data is looking for isn’t there. I should have cleared that off when I retitled the graphs but I usually end up doing this stuff late at night and the combination of late night and my brain doesn’t work as well as it did 20 years ago.


  • Ilya Zakharevich

    This “we” in the last sentence is the company behind Olaf? Is it a trade secret, or is it (or is it going to be eventually) published? I do not remember seeing investigations of scalar correlates of useful objective or subjective measures…

    And: is this antipathy to “inverse measures” somehow related to putting curves for so many “intermediate” frequencies on your graphs? My (naive) expectations would be that the curves for 10, 40 and 100 lp/mm would contain all the relevant info in these graphs (and some more…).

  • grubernd

    You are onto something here. Practical MTF numbers for real world photographers and not for brickwallers or siemenssterners. Best Focus MTF + the focus heatmap describes the possibilities a lens has when taking images. It feels like you printed that combination of charts directly from my brain.

  • DrJon

    I think the best APOs are really good, for example here’s the performance of mine:
    However note several of the lines are non-visible.

  • Samuel H

    You’re nailing it. I don’t know what’s in store for part 3, but the three pieces of information your are checking and nobody else ever worried about should be enough for most users to get an extremely accurate idea of how sharp the lens will be for their kind of use.

    If I could ask for stuff, I’d love to see your MTF reviews including a three-graphs row for each lens.
    * standard graph, wide open, with copy-to-copy variation, which is awesome to get a general idea about the lens
    * f/4 MTF from a good copy, which tells me stuff I care about when shooting a landscape
    * best-individual-focus, wide open, which tells me stuff I care about when shooting portraits

    Oh, and move the T/x to the lower left corner 🙂

    PS: Sigma couldn’t possibly ask for better marketing than what you’re giving them for free. That graph for the 85mm is going to sell a lot of lenses.

  • Søren Stærke

    In optical simulation software OpticStudio (formerly known as Zemax) it was called MTF through focus.
    Here’s a sample lens, with the MTF vs field plot on top as we all know and have seen before, followed by 2 MTF through focus plots. MTF10 and MTF30 are plotted, and though this is non-optimized lens design of my own, it shows the displacement of best focus.

  • bokesan

    If you haven’t already done something like this: you can visualize the field curvature quite easily by photographing a flat subject at an angle. It’s a very far cry from what Roger and Brandon are doing here, but will give you a general idea. I hesitate to link a testament to my own sloppiness in this temple of exactitude, but I recently posted some examples:

  • Guido

    «If enough people think this is something they will find useful, we’ll start publishing them for all of the lenses we test.»

    Of course it’s useful and we want it 😉

    And by the way: If people want to understand lens technology to a certain degree, then the Lensrentals log is by far the best website on the entire internet. There is no other website, that explains topics like this so good. And there is no other website, that tests usually 10 or more pieces of each lens, which means the other lens tests are some kind of a lottery and less reliable.

  • Brandon Dube

    Olaf is a company and a machine.

    The company will never use MTF-50, or any other metric that inverts MTF, so long as I am involved. They are not correlated to perceptual image quality, are completely unrelated to how an optical designer would evaluate or focus the lens in design software, are not related to the camera’s autofocus algorithms, and are not shown to be an accurate method to reduce an MTF vs freq curve to a single value without loss of detail in the data.

    There are (and we have already) implemented better algorithms.

  • Ilya Zakharevich

    Anyway: I realized that I did not write down how much I appreciate what you are doing in general, and, especially, these particular “closed-down” data points. A lot of thanks!

  • Ilya Zakharevich

    Olaf does not need to. I’m pretty sure it is not Olaf what produces the MTF graphs, right? They are just results of post-processing Olaf’s data.

    Likewise, this number is also a result of post-processing the transfer functions. And I’m pretty sure that the results (“the focal planes of maximal resolution”) are going to be very similar for MTF=70%, MTF=50%, and MTF=30%…

  • Brandon Dube

    “Beta software.” The companies that make our machines are not very good at metadata in their software, which we are forced to pull from.

  • Brandon Dube

    I’ll have to quit before Olaf deals in MTF-50 😉

  • Mike Earussi

    Excellent info and very useful, and you’re right, totally different than any one else’s tests. The next question then is how do we adjust the AF to take advantage of this information?

  • Ilya Zakharevich

    Second, your spoilers for the part III led me to spell out how would *I* do the next part! 😉

    Start with a nice number which summarizes the MTF curves in a meaningful way: the total MTF=0.5 resolution. (I already described it once here?—?and it is not rocket science.) It is very easy to calculate: interpolate/extrapolate curves to find the tangential and saggital resolution for MTF=0.5 at a particular point. The product of these numbers gives the numbers of the “matching point-spread ellipses” per mm² at this point. Taking the total over the whole sensor area gives “the total MTF=0.5 resolution” (up to a multiplicative constant which does not matter for what follows).

    Now: for every displacement of teh focal plane one gets this number. Choose the base displacement not to maximize resolution at center, but the total resolution.

    Suggested Part III: Plot MTF curves for this displacement.

  • Ilya Zakharevich

    First: your BIF-MTF are marked with something like T/NUMBER at the upper left corner. I think the meaning of this number changed somewhere in the middle of data collection. At least sometimes it is the same as the open T-number, and sometimes it is the same as as-tested T-number.

    Moreover, for 50mm T1.5, it is T/2, which is neither of two. Given that the as-tested T-number is not shown in the header either, this makes it pretty confusing…

  • Philip

    ‘whether the graphs are worth showing in our reports.’
    Indeed they are, and if it is easy to implement and you are happy to do so, pls include them. If one is setting up a near-far using a subject you wish to highlight, knowing the lens’s performance cut-off gradient is very valuable (as shown so eloquently in the 50/1.5). There are indications makers are much more aware of full frame image quality (even at the expense of center IQ), whereas for simpler designs in the low res era it was a lower priority. Modern cameras will increasingly enable far off-center focusing and the trend to ‘bokeh shooting’ (esp fast wide angles) both point to the value of this information. I imagine video shooters would also benefit greatly. Finally, it would reduce trial and error. cheers.

  • IKR??? Sometimes things are bigger so they can be better.

  • L G

    Very useful. It takes looking at a lot of real world photos to get the level of understanding of lens performance that these new graphs show. At least regarding sharpness. Thank you taking the time to study and present this.

  • Yes, that is true. What I meant is that because of the 24PC-E’s relatively large field curvature, I have to carefully choose which part of the frame I want to focus on. I can’t rely on picking the center point, and having other things in the same plane be in focus.

  • Brandon Dube

    “BIF-MTF” is something you can never achieve in a real image. Each field pt has its own unique focus position. Unless you make a final image by mosaicing a bunch focused at different distances, you can’t replicate an image that corresponds to that MTF curve.

  • That Sigma 85…

  • Matt

    First off, I disagree with “OK, in the last post we did something useful, but rather boring: we looked at how MTF changes when lenses are stopped down.” I found that article to be quite interesting, but perhaps I’m easily amused.

    Second, thanks for this article. I’ve often wondered how worthwhile obsessing about center sharpness is when so many photographs frame the most important elements (at least insofar as needing sharpness) away from center. This affirms that notion and reveals that the Sigma 85 is somehow an even better portrait lens than we previously thought.

    As far as what to do, at the start of the article I was expecting it to be interesting but something that once we saw the charts we could make mental note about how this affects lenses and going forward we’d maybe only need to see the charts for some specialty lenses. After seeing them and the variation that occurs, I’m greedy and I want to see it for everything.

  • I would love to see the BIF-MTF chart included with the standard MTF chart for future posts! As someone who loves and uses the Nikon 24/3.5 PC-E for landscapes, BIFing it is kind of necessary.

  • You’re getting it. There’s more to it than, but yes.

    If the lens has a high BIF and a lower standard MTF at, say, 14mm off axis, you’ll get a much sharper image focusing there than you would with focus recompose. If standard and BIF are about the same, you’ll be fine with focus recompose.

  • l_d_allan

    So does your article suggest that “focus and recompose” is more flawed than we already suspected?

    With my Canon 6d with antiquated AF sub-system but very good center AF point, I have tended to focus with the center AF and then recompose. My bad?

    It also perhaps suggest that using native lenses on our Sony a7x cameras has that much more advantage over using adapters … I have more of the AF points to use with native lenses like the FE55 f/1.8 than when adapting a Canon EF lens.

    Or am I yet again … “unclear on the comcept”?

  • Puska, I don’t think you’ve oversimplified at all. And I think you’re going to LOVE the third post in this series. And yes, I’m shamelessly plugging the next post, but these first two are basically the path heading to the cozy warm cabin of the third post. 🙂

  • Puska

    In astrophotography, choosing the optimal focus point off center is nothing new. The optical requirements in astrophotography are more stringent than terrestrial photography because stars are point sources of light and will show optical defects right to the corners of the frame. Even highly corrected apochromatic refractors will have slightly different focal planes for different wavelengths of light, as well as varying degrees of field curvature. To mitigate these issues, it is common practice to choose a focus star that is somewhere between 1/3 and 1/2 the distance toward the frame edge. Moreover, that star may be rendered ever so slightly out of focus to split the difference between the focal planes of differing wavelengths, thus reducing the amount of chromatic aberration. In other words, you sacrifice the absolute best center focus for consistency throughout the frame.

    I’m grateful that you posted this thought provoking article, because for some reason it has never occurred to me to use the same technique for terrestrial photography. Instead, I’ve blindly depended on stopping down to mitigate field curvature and CA. Indeed, it seems the process could easily be automated by determining whether the field curvature of a given lens benefits from front or back focus and applying that setting in the camera menu. That way auto focus can continue on its merry way in the central portion of the frame and yet optimal focus for full frame consistency would be achieved. Of course, if auto focus chooses a point off center, then all bets are off. If I’m over simplifying this, someone please let me know.

    Thanks, Roger, for your continued informative (and often funny) articles.

  • Thomas Geist

    Very interesting as I have come across field curvature frequently and it may bite you in the rear if you don’t anticipate it.

    I know you are super busy and surely not waiting for us to ask you which lenses to test 😉
    But the one lens that really took me by surprise by seeming to have some extreme field curvature where I don’t need it is the Olympus 7-14 mm f/2.8 Pro.

    It is extremely wide for sure but for architecture or landscapes, even stopped down to f/5.6 it goes REALLY soft towards the edges.

    I would love to see this confirmed. Or is mine just a bad apple?

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