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
  • boeck hannes

    now we should find a way to render space according to our lens field curvature and nothing will ever be out of focus again!

    but i have to admit i shoot lots of flat surfaces actually. paintings. and i take good care that i am absolutely paralell to them. if possible i even do it with my 85mm. i stop it down to f8 to even things out. havent yet seen a difference in sharpness no matter where i focus in the frame at f8 if the camera is properly aligned. maybe i could get a sharper result at f4 and the way you describe, but it seems unpractical in the field for me.

    but i think i´ll keep shooting at f8 because if i´m not perfectly aligned it still gives me deep enough focus to get away with it. at f4 the area of acceptable sharpness gets pretty thin at 85mm.

    anyway, interesting material again!

  • Jim A.

    Seems like another application for focus stacking? Maybe instead of multiple exposures for more dynamic range, we have multiple exposures for highest MTF. If your frame rate and focusing mechanics were fast and accurate enough, you might make field curvature less of an issue and make sharper photos too…we just need the camera electronics to handle the image stacking calculations and output the final file. Obviously not gonna work for race car photos, but maybe still life and other slow things, wide, sweeping landscapes that look like they were shot on medium format. Hmmm?

  • Claudia, you did indeed!!! We can only test at infinity, but the focus and field curvature in general should not change. Absolute MTF curves and sharpness can, but only at really close distances with any modern lens. There might be a difference if we could test at 12 feet versus infinity, but it should be small, and well, we can’t anyway. 🙂

  • Claudia Muster

    Hey, but this is EXACTLY what I had asked you some time ago in a comment! Thank you very much for these interesting measurements. Yes, I think they are useful.

    That one plot of a “normal” MTF with the focus point set to 14mm is very useful, too. I didn’t think of this before, and it’s a strong warning that one should be well aware of the side effects.

    And while I’m at it: Yet another thing that would be interesting is MTF curves at various focus distances. As I understand, your MTF curves (and published MTF curves in general) are measured with the focus set to infinity. But this is only of limited interest for e.g. a portrait photographer. I suspect that different lenses are optimized for different focus distances.

  • Not THAT Ross Cameron

    No worries, hint taken. Will hold my horses until the next article 🙂
    Many thanks for the response, and thanks for these articles – they are greatly appreciated, even if I don’t fully understand the tedious time taken to get the data in the first place. Enjoy your weekend.

  • Philip Service

    First, many thanks for sharing all that data. And, yes, i’d very much like to see BIF-MTF data in future lens tests. My take-away from your results is that focus stacking could be useful even for flat (2-dimensional) subjects, if one wanted maximum resolution across the entire frame. That is, combine several images made with different focus points.

  • I’ve got one of those too, and love it.

  • Thank you! The goal of all this stuff is to show that lab tests DO have let us use the tool that is our lens better, and choose the tool better. It’s more complicated than this one is 78 and this other one is 81, but it’s way more useful.

  • You can (and we sometimes do) average MTF. But it’s kind of a slipper slope. A lens with an MTF of xx at a certain point because sag is xx+10 and tan is xx-10 looks really different than a lens with MTF xx because both sag and tan are xx. Still, it can be useful to average like that.

  • Well, we’re going to the next level in the next article. But it depends on your definition of optimal. Most lenses are at their sharpest right in the center and that’s where you AF fine tune. BUT that might not be the best way to focus a subject that’s off-center, with many lenses you should focus at that point, with some it doesn’t matter much. There’s also a point xx from center where no matter where you focus you can’t get it razor sharp. That can be as close as only 1/3 of the way from center, or as far as 3/4 of the way to the edge.

  • Samuel H

    As someone who owns 15 prime lenses and not one single zoom*, I completely understand that feeling. But somehow, over the last few years, my mind went from “how you dare, you uneducated monkey” to “use whatever you want, if you insist on a bad choice, well, my stuff will look better in comparison”. Goes for camera brands as well.

    * OK, my RX100 IV comes with a zoom, but I can’t change that. Though I wish I could buy two versions of this camera, with f/1.4 primes, one wide-angle and one for portraits.

  • picbod

    The burning question I have is more to do with what happens on the other side of the lens – that is, in front of the camera with the focus-field curvature.
    Translating the MTF vs Field vs Focus graphs into a real-world understanding of the lens’s characteristics should be on every photographer’s radar.
    For example, my antique Canon 16-35 2.8 focuses concavely at the wide end, making it ideal for interiors (the corners of the image are focused closer than the centre). At the 35mm end of the zoom range, the focus field flips to converse, with the edges focusing further back than the centre, making it suitable for 3 dimensional solids, like the exterior of a house.
    While it is well past due for replacement, I continue to use it because I know and take advantage of these characteristics, and as a result get more predictably sharp and focused images from it.
    And before you lens-nerds start berating me for using such an awful (yes it is) lens – I am a photojournalist not a landscape photographer so ultimate sharpness has never been at the top of my wish list. As I shoot fast and frequently, I need to trust that my photographs will be focused at the place and moment they need to be, and that makes for a much better result than a sharply detailed photo of yet another dull subject.
    Needless to say, the 16-35 2.8 mkIII is on my to-buy list but may get pipped by the delightful-to-use Sigma 24-35 f2.

  • Not THAT Ross Cameron

    The optics & maths are more than my feeble caffeine-free brain can cope with this early in the morning, so dumb Q – for those using AF fine tune to get best AF from ILC system (or even best focus assist for MF lens), does this imply / state that for a given lens the optimal focus point may be off-centre, and be able to determine that point (using a representative lens). Noting it depend’s upon one’s definition of ‘optimal’, I.e. Central area only or corner to corner average.

  • Lars Kvinge

    I found the in focus mtf to be very useful, more useful than common mtf curves. Especially when shooting wide open/large apertures, I always focus at the point that I want in focus, often off center. In such cases in focus mtf is what matters. Thank tou for another great article. I hope you continue publishing in focus mtf curves.

  • Andrew Milne

    Thanks! Is there a general way of combining the two to get a “overall” mtf, or is it just sum/average? Does that have some correspondence to a physical/visual phenomenon?

  • Both sagittal (dotted lines) and tangential (solid lines). You can see the point where you can’t get both the same when the lines separate widely (that can also be lateral color; MTF looks the same whether its astigmatism or lateral color).

  • Andrew Milne

    I have a question, I think just as clarification, but maybe more than that.

    If I understand what has been done, you measure the MTFs at many spots across the frame at many distances. The standard MTF graph picks the distance with the best MTF at the center, then tells you the MTFs off center. Your new BIF-MTF chooses the best MTF for that spot instead.

    My question is: which MTF? Looking at the graphs, I’m guessing sagittal?

    My follow-up questions revolve around this choice. I’m not smart enough to look at a photo and tell what blurring is sagittal and what tangential. The blurring I detect is some combination of both, I am assuming. At the center, normally we can ignore this, because that is usually where both are best. But on some of these lenses, they are quite different. So look at the Sigma 24, where the best focus tangential drops off much more steeply. Or, to put it another way, if we made a best focus tangential graph, the sagittal would probably drop off much more steeply. Is there a reason to pick one over the other?

    So: what is the joint effect of the two MTFs? Also, isn’t that often the biggest issue for many lenses – because the shape of the focus plane is different for both, you may not be able to find a good compromise – you could focus for one, and not the other, and end up fuzzy anyway. The lens works best when the focal planes overlap, right? So a good lens (off center) needs both to resolve sharply across the frame and also at the same distance (for both MTFs) across the frame.

    Am I missing something?

  • Brandon Dube

    Unfortunately, that is not possible.

  • I was wondering if it’s possible to extract the individual spectral components from the white light measurements, so you wouldn’t need to filter the light for the measurement.

  • Brandon Dube

    Could we do it – yes. Do we need to do it through focus and take the measurement time from 5 minutes to 5 hours – no.

    Will we do it – no; we don’t have a motorized filter wheel, so we can’t automate (i.e. economize) testing at different color configurations.

  • This is probably more of a question for Brandon, but I remember from past discussions that your optical bench uses multiple frequencies of light? If so, could the field curvature map be separated out for individual frequencies (eg. R, G, B), and be used to plot a LoCA graph? Sort of like what Jim Kasson does with his motorized rail, but over the entire frame instead of a central patch?

  • More like I get nauseous every time someone says this zoom is just as good as a prime because the zoom at f/2.8 is as good as the prime at f/1.4 (and actually even that is rarely true).

  • Samuel H

    So, you’re feeling generous!! Nice. ^_______^

    (I’d be happy to do my zoom-prime comparisons at f/4)

  • Miroslaw, someday when I make my grand trek across Europe, I will take you up on that!

  • Brandon Dube

    What on earth is that a plot of?

  • Brandon Dube

    Please email if you want to discuss more.

  • Brandon Dube

    Sure, MTF Thru-Focus is certainly nothing new. Code V and OSLO both do that, too.

  • Miros?aw St?pi?ski

    Just a note to my stupid self: use the other focus points instead of using just the central one and recomposing, you fool!

    Thank you Roger and the whole team for getting that far and for introducing these interesting concepts that stimulate my nerdy brain. I caught myself on checking this space for new posts a few times a day, it is some kind of addiction. I just can’t wait for part III.

    I owe you all, Gentlemen, a bottle or two, or even more. Due to the simple fact of my non-US residence I cannot be your customer and support your research this way, but our national tradition forces me to take some necessary steps.

  • For me it literally is a list of “mm off axis maintaining sharpness” for each lens. I chose about 90% of center sharpness at 30 lp/mm arbitrarily OR the point where sag-tan separation becomes significant. So I’ll shoot the 28mm Zeiss 10mm off center (half way to the edge), the 50mm Zeiss T1.5 to 3/4 the way to the edge, etc.

  • Ilya, we’re heading to the same place, although we’re trying to get there a different way. I’ll be interested in whether our method holds up mathematically when you see it. I don’t quite have Brandon’s complete antipathy to inverse measurements, probably because at my age I just don’t have much antipathy left, period. I try to stay away from MTF50 type measurements mostly because so many people think MTF50 and MTF at 50 lp/mm are the same thing.

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