MTF, Lens & Sensor Resolution

MTF, Lens & Sensor Resolution

I’ve been ‘banging on’ about resolution lens performance and MTF over the last few posts so I’d like to start bringing all these various bits of information together with at least a modicum of simplicity.

If this is your first visit to my blog I strongly recommend you peruse HERE and HERE before going any further!

You might well ask the question “Do I really need to know this stuff – you’re a pro Andy and I’m not, so I don’t think I need to…”

My answer is “Yes you bloody well do need to know, so stop whinging – it’ll save you time and perhaps stop you wasting money…”

Words used like ‘resolution’ do tend to get used out of context sometimes, and when you guys ‘n gals are learning this stuff then things can get a mite confusing – and nowhere does terminology get more confusing than when we are talking ‘glass’.

But before we get into the idea of bringing lenses and sensors together I want to introduce you to something you’ve all heard of before – CONTRAST – and how it effects our ability to see detail, our lens’s ability to transfer detail, and our camera sensors ability to record detail.

Contrast & How It Effects the Resolving of Detail

In an earlier post HERE I briefly mentioned that the human eye can resolve 5 line pairs per millimeter, and the illustration I used to illustrate those line pairs looked rather like this:

5 line pairs per millimeter with a contrast ratio of 100% or 1.0

5 line pairs per millimeter with a contrast ratio of 100% or 1.0

Now don’t forget, these line pairs are highly magnified – in reality each pair should be 0.2mm wide.  These lines are easily differentiated because of the excessive contrast ratio between each line in a pair.

How far can contrast between the lines fall before we can’t tell the difference any more and all the lines blend together into a solid monotone?

Enter John William Strutt, the 3rd Baron Rayleigh…………

5 line pairs at bottom threshold of human vision - a 9% contrast ratio.

5 line pairs at bottom threshold of human vision – a 9% contrast ratio.

The Rayleigh Criterion basically stipulates that the ‘discernability’ of each line in a pair is low end limited to a line pair contrast ratio of 9% or above, for average human vision – that is, when each line pair is 0.2mm wide and viewed from 25cms.  Obviously they are reproduced much larger here, hence you can see ’em!

Low contrast limit for Human vision (left) & camera sensor (right).

Low contrast limit for Human vision (left) & camera sensor (right).

However, it is said in some circles that dslr sensors are typically limited to a 12% to 15% minimum line pair contrast ratio when it comes to discriminating between the individual lines.

Now before you start getting in a panic and misinterpreting this revelation you must realise that you are missing one crucial factor; but let’s just recap what we’ve got so far.

  1. A ‘line’ is a detail.
  2. but we can’t see one line (detail) without another line (detail) next to it that has a different tonal value ( our line pair).
  3. There is a limit to the contrast ratio between our two lines, below which our lines/details begin to merge together and become less distinct.

So, what is this crucial factor that we are missing; well, it’s dead simple – the line pair per millimeter (lp/mm) resolution of a camera sensor.

Now there’s something you won’t find in your cameras ‘tech specs’ that’s for sure!

Sensor Line Pair Resolution

The smallest “line” that can be recorded on a sensor is 1 photosite in width – now that makes sense doesn’t it.

But in order to see that line we must have another line next to it, and that line must have a higher or lower tonal value to a degree where the contrast ratio between the two lines is at or above the low contrast limit of the sensor.

So now we know that the smallest line pair our sensor can record is 2 photosites/pixels in width – the physical width is governed by the sensor pixel pitch; in other words the photosite diameter.

In a nutshell, the lp/mm resolution of a sensor is 0.5x the pixel row count per millimeter – referred to as the Nyquist Rate, simply because we have to define (sample) 2 lines in order to see/resolve 1 line.

The maximum resolution of an image projected by the lens that can be captured at the sensor plane – in other words, the limit of what can be USEFULLY sampled – is the Nyquist Limit.

Let’s do some practical calculations:

Canon 1DX 18.1Mp

Imaging Area = 36mm x 24mm / 5202 x 3533 pixels/photosites OR LINES.

I actually do this calculation based on the imaging area diagonal

So sensor resolution in lp/mm = (pixel diagonal/physical diagonal) x 0.5 = 72.01 lp/mm

Nikon D4 16.2Mp = 68.62 lp/mm

Nikon D800 36.3Mp = 102.33 lp/mm

PhaseOne P40 40Mp medium format = 83.15 lp/mm

PhaseOne IQ180 80Mp medium format = 96.12 lp/mm

Nikon D7000 16.2mp APS-C (DX) 4928×3264 pixels; 23.6×15.6mm dimensions  = 104.62 lp/mm

Canon 1D IV 16.1mp APS-H 4896×3264 pixels; 27.9×18.6mm dimensions  = 87.74 lp/mm

Taking the crackpot D800 as an example, that 102.33 lp/mm figure means that the sensor is capable of resolving 204.66 lines, or points of detail, per millimeter.

I say crackpot because:

  1. The Optical Low Pass “fights” against this high degree of resolving power
  2. This resolving power comes at the expense of S/N ratio
  3. This resolving power comes at the expense of diffraction
  4. The D800E is a far better proposition because it negates 1. above but it still leaves 2. & 3.
  5. Both sensors would purport to be “better” than even an IQ180 – newsflash – they ain’t; and not by a bloody country mile!  But the D800E is an exceptional sensor as far as 35mm format (36×24) sensors go.

A switch to a 40Mp medium format is BY FAR the better idea.

Before we go any further, we need a reality check:

In the scene we are shooting, and with the lens magnification we are using, can we actually “SEE” detail as small as 1/204th of a millimeter?

We know that detail finer than that exists all around us – that’s why we do macro/micro photography – but shooting a landscape with a 20mm wide angle where the nearest detail is 1.5 meters away ??

And let’s not forget the diffraction limit of the sensor and the incumbent reduction in depth of field that comes with 36Mp+ crammed into a 36mm x 24mm sensor area.

The D800 gives you something with one hand and takes it away with the other – I wouldn’t give the damn thing house-room!  Rant over………

Anyway, getting back to the matter at hand, we can now see that the MTF lp/mm values quoted by the likes of Nikon and Canon et al of 10 and 30 lp/mm bare little or no connectivity with the resolving power of their sensors – as I said in my previous post HERE – they are meaningless.

The information we are chasing after is all about the lens:

  1. How well does it transfer contrast because its contrast that allows us to “see” the lines of detail?
  2. How “sharp” is the lens?
  3. What is the “spread” of 1. and 2. – does it perform equally across its FoV (field of view) or is there a monstrous fall-off of 1. and 2. between 12 and 18mm from the center on an FX sensor?
  4. Does the lens vignette?
  5. What is its CA performance?

Now we can go to data sites on the net such as DXO Mark where we can find out all sorts of more meaningful data about our potential lens purchase performance.

But even then, we have to temper what we see because they do their testing using Imatest or something of that ilk, and so the lens performance data is influenced by sensor, ASIC and basic RAW file demosaicing and normalisation – all of which can introduce inaccuracies in the data; in other words they use camera images in order to measure lens performance.

The MTF 50 Standard

Standard MTF (MTF 100) charts do give you a good idea of the lens CONTRAST transfer function, as you may already have concluded. They begin by measuring targets with the highest degree of modulation – black to white – and then illustrate how well that contrast has been transferred to the image plane, measured along a corner radius of the frame/image circle.

MTF 1.0 (100%) left, MTF 0.5 (50%) center and MTF 0.1 (10%) right.

MTF 1.0 (100%) left, MTF 0.5 (50%) center and MTF 0.1 (10%) right.

As you can see, contrast decreases with falling transfer function value until we get to MTF 0.1 (10%) – here we can guess that if the value falls any lower than 10% then we will lose ALL “perceived” contrast in the image and the lines will become a single flat monotone – in other words we’ll drop to 9% and hit the Rayleigh Criterion.

It’s somewhat debatable whether or not sensors can actually discern a 10% value – as I mentioned earlier in this post, some favour a value more like 12% to 15% (0.12 to 0.15).

Now then, here’s the thing – what dictates the “sharpness” of edge detail in our images?  That’s right – EDGE CONTRAST.  (Don’t mistake this for overall image contrast!)

Couple that with:

  1. My well-used adage of “too much contrast is thine enemy”.
  2. “Detail” lies in midtones and shadows, and we want to see that detail, and in order to see it the lens has to ‘transfer’ it to the sensor plane.
  3. The only “visual” I can give you of MTF 100 would be something like power lines silhouetted against the sun – even then you would under expose the sun, so, if you like, MTF would still be sub 100.

Please note: 3. above is something of a ‘bastardisation’ and certain so-called experts will slag me off for writing it, but it gives you guys a view of reality – which is the last place some of those aforementioned experts will ever inhabit!

Hopefully you can now see that maybe measuring lens performance with reference to MTF 50 (50%, 0.5) rather than MTF 100 (100%, 1.0) might be a better idea.

Manufacturers know this but won’t do it, and the likes of Nikon can’t do it even if they wanted to because they use a damn calculator!

Don’t be trapped into thinking that contrast equals “sharpness” though; consider the two diagrams below (they are small because at larger sizes they make your eyes go funny!).

A lens can transfer full contrast but be unsharp.

A lens can have a high contrast transfer function but be unsharp.

A lens can have low contrast transmission (transfer function) but still be sharp.

A lens can have low contrast transfer function but still be sharp.

In the first diagram the lens has RESOLVED the same level of detail (the same lp/mm) in both cases, and at pretty much the same contrast transfer value; but the detail is less “sharp” on the right.

In the lower diagram the lens has resolved the same level of detail with the same degree of  “sharpness”, but with a much reduced contrast transfer value on the right.

Contrast is an AID to PERCEIVED sharpness – nothing more.

I actually hate that word SHARPNESS; and it’s a nasty word because it’s open to all sorts of misconceptions by the uninitiated.

A far more accurate term is ACUTANCE.

How Acutance effects perceived "sharpness" and is contrast independent.

How Acutance effects perceived “sharpness”.

So now hopefully you can see that LENS RESOLUTION is NOT the same as lens ACUTANCE (perceived sharpness..grrrrrr).

Seeing as it is possible to have a lens with a higher degree resolving power, but a lower degree of acutance you need to be careful – low acutance tends to make details blur into each other even at high contrast values; which tends to negate the positive effects of the resolving power. (Read as CHEAP LENS!).

Lenses need to have high acutance – they need to be sharp!  We’ve got enough problems trying to keep the sharpness once the sensor gets hold of the image, without chucking it a soft one in the first place – and I’ll argue this point with the likes of Mr. Rockwell until the cows have come home!

Things We Already Know

We already know that stopping down the aperture increases Depth of Field; and we already know that we can only do this to a certain degree before we start to hit diffraction.

What does increasing DoF do exactly; it increases ACUTANCE is what it does – exactly!

Yes it gives us increased perceptual sharpness of parts of the subject in front and behind the plane of sharp focus – but forget that bit – we need to understand that the perceived sharpness/acutance of the plane of focus increases too, until you take things too far and go beyond the diffraction limit.

And as we already know, that diffraction limit is dictated by the size of photosites/pixels in the sensor – in other words, the sensor resolution.

So the diffraction limit has two effects on the MTF of a lens:

  1. The diffraction limit changes with sensor resolution – you might get away with f14 on one sensor, but only f9 on another.
  2. All this goes “out the window” if we talk about crop-sensor cameras because their sensor dimensions are different.

We all know about “loss of wide angles” with crop sensors – if we put a 28mm lens on an FX body and like the composition but then we switch to a 1.5x crop body we then have to stand further away from the subject in order to achieve the same composition.

That’s good from a DoF PoV because DoF for any given aperture increases with distance; but from a lens resolving power PoV it’s bad – that 50 lp/mm detail has just effectively dropped to 75 lp/mm, so it’s harder for the lens to resolve it, even if the sensors resolution is capable of doing so.

There is yet another way of quantifying MTF – just to confuse the issue for you – and that is line pairs per frame size, usually based on image height and denoted as lp/IH.

Imatest uses MTF50 but quotes the frequencies not as lp/mm, or even lp/IH; but in line widths per image height – LW/IH!

Alas, there is no single source of the empirical data we need in order to evaluate pure lens performance anymore.  And because the outcome of any particular lens’s performance in terms of acutance and resolution is now so inextricably intertwined with that of the sensor behind it, then you as lens buyers, are left with a confusing myriad of various test results all freely available on the internet.

What does Uncle Andy recommend? – well a trip to DXO Mark is not a bad starting point all things considered, but I do strongly suggest that you take on board the information I’ve given you here and then scoot over to the DXO test methodology pages HERE and read them carefully before you begin to examine the data and draw any conclusions from it.

But do NOT make decisions just on what you see there; there is no substitute for hands-on testing with your camera before you go and spend your hard-earned cash.  Proper testing and evaluation is not as simple as you might think, so it’s a good idea to perhaps find someone who knows what they are doing and is prepared to help you out.   Do NOT ask the geezer in the camera shop – he knows bugger all about bugger all!

Do Sensors Out Resolve Lenses?

Well, that’s the loaded question isn’t it – you can get very poor performance from what is ostensibly a superb lens, and to a degree vice versa.

It all depends on what you mean by the question, because in reality a sensor can only resolve what the lens chucks at it.

If you somehow chiseled the lens out of your iPhone and Sellotaped it to your shiny new 1DX then I’m sure you’d notice that the sensor did indeed out resolve the lens – but if you were a total divvy who didn’t know any better then in reality all you’d be ware of is that you had a crappy image – and you’d possibly blame the camera, not the lens – ‘cos it took way better pics on your iPhone 4!

There are so many external factors that effect the output of a lens – available light, subject brightness range, angle of subject to the lens axis to name but three.  Learning how to recognise these potential pitfalls and to work around them is what separates a good photographer from an average one – and by good I mean knowledgeable – not necessarily someone who takes pics for a living.

I remember when the 1DX specs were first ‘leaked’ and everyone was getting all hot and bothered about having to buy the new Canon glass because the 1DX was going to out resolve all Canons old glass – how crackers do you need to be nowadays to get a one way ticket to the funny farm?

If they were happy with the lens’s optical performance pre 1DX then that’s what they would get post 1DX…duh!

If you still don’t get it then try looking at it this way – if lenses out resolve your sensor then you are up “Queer Street” – what you see in the viewfinder will be far better than the image that comes off the sensor, and you will not be a happy camper.

If on the other hand, our sensors have the capability to resolve more lines per millimeter than our lenses can throw at them, and we are more than satisfied with our lenses resolution and acutance, then we would be in a happy place, because we’d be wringing the very best performance from our glass – always assuming we know how to ‘drive the juggernaut’  in the first place!

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Lens Performance

I have a friend – yes, a strange concept I know, but I do have some – we’ll call him Steve.

Steve is a very talented photographer – when he’ll give himself half a chance; but impatience can sometimes get the better of him.

He’ll have a great scene in front of him but then he’ll forget things such as any focus or exposure considerations the scene demands, and the resulting image will be crap!

Quite often, a few of Steve’s character flaws begin to emerge at this juncture.

Firstly, Steve only remembers his successes; this leads to the unassailable ‘fact’ that he couldn’t possibly have ‘screwed up’.

So now we can all guess the conclusive outcome of that scenario can’t we……..that’s right; his camera gear has fallen short in the performance department.

Clairvoyance department would actually be more accurate!

So this ‘error in his camera system’ needs to be stamped on – hard and fast!

This leads to Steve embarking on a massive information-gathering exercise from various learned sources on ‘that there inter web’ – where another of Steve’s flaws shows up; that of disjointed speed reading…..

The terrifying outcome of these situations usually concludes with Steve’s confident affirmation that some piece of his equipment has let him down; not just by becoming faulty but sometimes, more worryingly by initial design.

These conclusions are always arrived at in the same manner – the various little snippets of truth and random dis-associated facts that Steve gathers, all get forcibly hammered into some hellish, bastardized ‘factual’ jigsaw in his head.

There was a time when Steve used to ask me first, but he gave up on that because my usual answer contravened the outcome of his first mentioned character flaw!

Lately one of Steve’s biggest peeves has been the performance of one or two of his various lenses.

Ostensibly you’ll perhaps think there’s nothing wrong in that – after all, the image generated by the camera is only as good as the lens used to gather the light in the scene – isn’t it?

 

But there’s a potential problem, and it  lies in what evidence you base your conclusions on……………

 

For Steve, at present, it’s manufacturers MTF charts, and comparisons thereof, coupled with his own images as they appear in Lightroom or Photoshop ACR.

Again, this might sound like a logical methodology – but it isn’t.

It’s flawed on so many levels.

 

The Image Path from Lens to Sensor

We could think of the path that light travels along in order to get to our camera sensor as a sort of Grand National horse race – a steeplechase for photons!

“They’re under starters orders ladies and gentlemen………………and they’re off!”

As light enters the lens it comes across it’s first set of hurdles – the various lens elements and element groups that it has to pass through.

Then they arrive at Becher’s Brook – the aperture, where there are many fallers.

Carefully staying clear of the inside rail and being watchful of any lose photons that have unseated their riders at Becher’s we move on over Foinavon – the rear lens elements, and we then arrive at the infamous Canal Turn – the Optical Low Pass filter; also known as the Anti-alias filter.

Crashing on past the low pass filter and on over Valentines only the bravest photons are left to tackle the the last big fence on their journey – The Chair – our camera sensor itself.

 

Okay, I’ll behave myself now, but you get the general idea – any obstacle that lies in the path of light between the front surface of our lens and the photo-voltaic surface of our sensor is a BAD thing.

Andy Astbury,Wildlife in Pixels,lens,resolution,optical path,sharpness,resolution,imaging pathway

The various obstacles to light as it passes through a camera (ASIC = Application Specific Integrated Circuit)

The problems are many, but let’s list a few:

  1. Every element reduces the level of transmitted light.
  2. Because the lens elements have curved surfaces, light is refracted or bent; the trick is to make all wavelengths of light refract to the same degree – failure results in either lateral or longitudinal chromatic aberration – or worse still, both.
  3. The aperture causes diffraction – already discussed HERE

We have already seen in that same previous post on Sensor Resolution that the number of megapixels can effect overall image quality in terms of overall perceived sharpness due to pixel-pitch, so all things considered, using photographs of any 3 dimensional scene is not always a wise method of judging lens performance.

And here is another reason why it’s not a good idea – the effect on image quality/perceived lens resolution of anti-alias, moire or optical low pass filter; and any other pre-filtering.

I’m not going to delve into the functional whys and wherefores of an AA filter, save to say that it’s deemed a necessary evil on most sensors, and that it can make your images take on a certain softness because it basically adds blur to every edge in the image projected by the lens onto your sensor.

The reasoning behind it is that it stops ‘moire patterning’ in areas of high frequency repeated detail.  This it does, but what about the areas in the image where its effect is not required – TOUGH!

 

Many photographers have paid service suppliers for AA filter removal just to squeeze the last bit of sharpness out of their sensors, and Nikon of course offer the ‘sort of AA filter-less’ D800E.

Side bar note:  I’ve always found that with Nikon cameras at least, the pro-body range seem to suffer a lot less from undesirable AA filtration softening than than their “amateur” and “semi pro” bodies – most notably the D2X compared to a D200, and the D3 compared to the D700 & D300.  Perhaps this is due to a ‘thinner’ filter, or a higher quality filter – I don’t know, and to be honest I’ve never had the desire to ‘poke Nikon with a sharp stick’ in order to find out.

 

Back in the days of film things were really simple – image resolution was governed by just two things; lens resolution and film resolution:

1/image resolution = 1/lens resolution + 1/film resolution

Film resolution was a variable depending on the Ag Halide distribution and structure,  dye coupler efficacy within the film emulsion, and the thickness of the emulsion or tri-pack itself.

But today things are far more complicated.

With digital photography we have all those extra hurdles to jump over that I mentioned earlier, so we end up with a situation whereby:

1/Image Resolution = 1/lens resolution + 1/AA filter resolution + 1/sensor resolution + 1/image processor/imaging ASIC resolution

Steve is chasing after lens resolution under the slightly misguided idea the resolution equates to sharpness, which is not strictly true; but he is basing his conception of lens sharpness based on the detail content and perceived detail ‘sharpness’ of his  images; which are ‘polluted’ if you like by the effects of the AA filter, sensor and imaging ASIC.

What it boils down to, in very simplified terms, is this:

You can have one particular lens that, in combination with one camera sensor produces a superb image, but in combination with another sensor produces a not-quite-so-superb image!

On top of the “fixed system” hurdles I’ve outlined above, we must not forget the potential for errors introduced by lens-to-body mount flange inaccuracies, and of course, the big elephant-in-the-room – operator error – ehh Steve.

So attempting to quantify the pure ‘optical performance’ of a lens using your ‘taken images’ is something of a pointless exercise; you cannot see the pure lens sharpness or resolution unless you put the lens on a fully equipped optical test bench – and how many of us have got access to one of those?

The truth of the matter is that the average photographer has to trust the manufacturers to supply accurately put together equipment, and he or she has to assume that all is well inside the box they’ve just purchased from their photographic supplier.

But how can we judge a lens against an assumed standard of perfection before we part with our cash?

A lot of folk, including Steve – look at MTF charts.

 

The MTF Chart

Firstly, MTF stands for Modulation Transfer Function – modu-what I hear your ask!

OK – let’s deal with the modulation bit.  Forget colour for a minute and consider yourself living in a black & white world.  Dark objects in a scene reflect few photons of light – ’tis why the appear dark!  Conversely, bright objects reflect loads of the little buggers, hence these objects appear bright.

Imagine now that we are in a sealed room totally impervious to the ingress of any light from outside, and that the room is painted matte white from floor to ceiling – what is the perceived colour of the room? Black is the answer you are looking for!

Now turn on that 2 million candle-power 6500k searchlight in the corner.  The split second before your retinas melted, what was the perceived colour of the room?

Note the use of the word ‘perceived’ – the actual colour never changed!

The luminosity value of every surface in the room changed from black to white/dark to bright – the luminosity values MODULATED.

Now back in reality we can say that a set of alternating black and white lines of equal width and crisp clean edges represent a high degree of contrast, and therefore tonal modulation; and the finer the lines the higher is the modulation frequency – which we measure in lines per millimeter (lpmm).

A lens takes in a scene of these alternating black and white lines and, just like it does with any other scene, projects it into an image circle; in other words it takes what it sees in front of it and ‘transfers’ the scene to the image circle behind it.

With a bit of luck and a fair wind this image circle is being projected sharply into the focal plane of the lens, and hopefully the focal plane matches up perfectly with the plane of the sensor – what used to be refereed to as the film plane.

The efficacy with which the lens carries out this ‘transfer’ in terms of maintaining both the contrast ratio of the modulated tones and the spatial separation of the lines is its transfer function.

So now you know what MTF stands for and what it means – good this isn’t it!

 

Let’s look at an MTF chart:

Nikon 500mm f4 MTF chart

Nikon 500mm f4 MTF chart

Now what does all this mean?

 

Firstly, the vertical axis – this can be regarded as that ‘efficacy’ I mentioned above – the accuracy of tonal contrast and separation reproduction in the projected image; 1.0 would be perfect, and 0 would be crappier than the crappiest version of a crap thing!

The horizontal axis – this requires a bit of brain power! It is scaled in increments of 5 millimeters from the lens axis AT THE FOCAL PLANE.

The terminus value at the right hand end of the axis is unmarked, but equates to 21.63mm – half the opposing corner-to-corner dimension of a 35mm frame.

Now consider the diagram below:

Andy Astbury,image circle,photography,frame,full frame,dimensions,radial,

The radial dimensions of the 35mm format.

These are the radial dimensions, in millimeters, of a 35mm format frame (solid black rectangle).

The lens axis passes through the center axis of the sensor, so the radii of the green, yellow and dashed circles correspond to values along the horizontal axis of an MTF chart.

Let’s simplify what we’ve learned about MTF axes:

Andy Astbury,image circle,photography,frame,full frame,dimensions,radial,

MTF axes hopefully made simpler!

Now we come to the information data plots; firstly the meaning of Sagittal & Meridional.   From our perspective in this instance I find it easier for folk to think of them as ‘parallel to’ and ‘at right angles to’ the axis of measurement, though strictly speaking Meridional is circular and Sagittal is radial.

This axis of measurement is from the lens/film plane/sensor center to the corner of a 35mm frame – in other words, along that 21.63mm radius.

Andy Astbury,image circle,photography,frame,full frame,dimensions,radial,

The axis of MTF measurement and the relative axial orientation of Sagittal & Meridional lines. NOTE: the target lines are ONLY for illustration.

Separate measurements are taken for each modulation frequency along the entire measurement axis:

Andy Astbury,image circle,photography,frame,full frame,dimensions,radial,

Thin Meridional MTF measurement. (They should be concentric circles but I can’t draw concentric circles!).

Let’s look at that MTF curve for the 500m f4 Nikon together with a legend of ‘sharpness’ – the 300 f2.8:

MTF chart,Andy Astbury,lens resolution

Nikon MTF comparison between the 500mm f4 & 300mm f2.8

Nikon say on their website that they measure MTF at maximum aperture, that is, wide open; so the 300mm chart is for an aperture of f2.8 (though they don’t say so) and the 500mm is for an f4 aperture – which they do specify on the chart – don’t ask me why ‘cos I’ve no idea.

As we can see, the best transfer values for the two lenses (and all other lenses) is 10 lines per millimeter, and generally speaking sagittal orientation usually performs slightly better than meridional, but not always.

10 lpmm is always going to give a good transfer value because its very coarse and represents a lower frequency of detail than 30 lpmm.

Funny thing, 10 lines per millimeter is 5 line pairs per millimeter – and where have we heard that before? HERE – it’s the resolution of the human eye at 25 centimeters.

 

Another interesting thing to bare in mind is that, as the charts clearly show, better transfer values occur closer to the lens axis/sensor center, and that performance falls as you get closer to the frame corners.

This is simply down to the fact that your are getting closer to the inner edge of the image circle (the dotted line in the diagrams above).  If manufacturers made lenses that threw a larger image circle then corner MTF performance would increase – it can be done – that’s the basis upon which PCE/TS lenses work.

One way to take advantage of center MTF performance is to use a cropped sensor – I still use my trusty D2Xs for a lot of macro work; not only do I get the benefit of center MTF performance across the majority of the frame but I also have the ability to increase the lens to subject distance and get the composition I want, so my depth of field increases slightly for any given aperture.

Back to the matter at hand, here’s my first problem with the likes of Nikon, Canon etc:  they don’t specify the lens-to-target distance. A lens that gives a transfer value of 9o% plus on a target of 10 lpmm sagittal at 2 meters distance is one thing; one that did the same but at 25 meters would be something else again.

You might look at the MTF chart above and think that the 300mm f2.8 lens is poor on a target resolution of  30 lines per millimeter compared to the 500mm, but we need to temper that conclusion with a few facts:

  1. A 300mm lens is a lot wider in Field of View (FoV) than a 500mm so there is a lot more ‘scene width’ being pushed through the lens – detail is ‘less magnified’.
  2. How much ‘less magnified’ –  40% less than at 500mm, and yet the 30 lpmm transfer value is within 6% to 7% that of the 500mm – overall a seemingly much better lens in MTF terms.
  3. The lens is f2.8 – great for letting light in but rubbish for everything else!

Most conventional lenses have one thing in common – their best working aperture for overall image quality is around f8.

But we have to counter balance the above with the lack of aforementioned target distance information.  The minimum focus distances for the two comparison lenses are 2.3 meters and 4.0 meters respectively so obviously we know that the targets are imaged and measured at vastly different distances – but without factual knowledge of the testing distances we cannot really say that one lens is better than the other.

 

My next problem with most manufacturers MTF charts is that the values are supplied ‘a la white light’.

I mentioned earlier – much earlier! – that lens elements refracted light, and the importance of all wavelengths being refracted to the same degree, otherwise we end up with either lateral or longitudinal chromatic aberration – or worse still – both!

Longitudinal CA will give us different focal planes for different colours contained within white light – NOT GOOD!

Lateral CA gives us the same plane of focus but this time we get lateral shifts in the red, green and blue components of the image, as if the 3 colour channels have come out of register – again NOT GOOD!

Both CA types are most commonly seen along defined edges of colour and/or tone, and as such they both effect transferred edge definition and detail.

So why do manufacturers NOT publish this information – there is to my knowledge only one that does – Schneider (read ‘proper lens’).

They produce some very meaningful MTF data for their lenses with modulation frequencies in excess of 90 to 150 lpmm; separate R,G & B curves; spectral weighting variations for different colour temperatures of light and all sorts of other ‘geeky goodies’ – I just love it all!

 

SHAME ON YOU NIKON – and that goes for Canon and Sigma just as much.

 

So you might now be asking WHY they don’t publish the data – they must have it – are they treating us like fools that wouldn’t be able to understand it; OR – are they trying to hide something?

You guys think what you will – I’m not accusing anyone of anything here.

But if they are trying to hide something then that ‘something’ might not be what you guys are thinking.

What would you think if I told you that if you were a lens designer you could produce an MTF plot with a calculator – ‘cos you can, and they do!

So, in a nutshell, most manufacturers MTF charts as published for us to see are worse than useless.  We can’t effectively use them to compare one lens against another because of missing data; we can’t get an idea of CA performance because of missing red, green and blue MTF curves; and finally we can’t even trust that the bit of data they do impart is even bloody genuine.

Please don’t get taken in by them next time you fancy spending money on glass – take your time and ask around – better still try one; and try it on more than 1 camera body!

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Pixel Resolution

What do we mean by Pixel Resolution?

Digital images have two sets of dimensions – physical size or linear dimension (inches, centimeters etc) and pixel dimensions (long edge & short edge).

The physical dimensions are simple enough to understand – the image is so many inches long by so many inches wide.

Pixel dimension is straightforward too – ‘x’ pixels long by ‘y’ pixels wide.

If we divide the physical dimensions by the pixel dimensions we arrive at the PIXEL RESOLUTION.

Let’s say, for example, we have an image with pixel dimensions of 3000 x 2400 pixels, and a physical, linear dimension of 10 x 8 inches.

Therefore:

3000 pixels/10 inches = 300 pixels per inch, or 300PPI

and obviously:

2400 pixels/8 inches = 300 pixels per inch, or 300PPI

So our image has a pixel resolution of 300PPI.

 

How Does Pixel Resolution Influence Image Quality?

In order to answer that question let’s look at the following illustration:

Andy Astbury,pixels,resolution,dpi,ppi,wildlife in pixels

The number of pixels contained in an image of a particular physical size has a massive effect on image quality. CLICK to view full size.

All 7 square images are 0.5 x 0.5 inches square.  The image on the left has 128 pixels per 0.5 inch of physical dimension, therefore its PIXEL RESOLUTION is 2 x 128 PPI (pixels per inch), or 256PPI.

As we move from left to right we halve the number of pixels contained in the image whilst maintaining the physical size of the image – 0.5″ x 0.5″ – so the pixels in effect become larger, and the pixel resolution becomes lower.

The fewer the pixels we have then the less detail we can see – all the way down to the image on the right where the pixel resolution is just 4PPI (2 pixels per 0.5 inch of edge dimension).

The thing to remember about a pixel is this – a single pixel can only contain 1 overall value for hue, saturation and brightness, and from a visual point of view it’s as flat as a pancake in terms of colour and tonality.

So, the more pixels we can have between point A and point B in our image the more variation of colour and tonality we can create.

Greater colour and tonal variation means we preserve MORE DETAIL and we have a greater potential for IMAGE SHARPNESS.

REALITY

So we have our 3 variables; image linear dimension, image pixel dimension and pixel resolution.

In our typical digital work flow the pixel dimension is derived from the the photosite dimension of our camera sensor – so this value is fixed.

All RAW file handlers like Lightroom, ACR etc;  all default to a native pixel resolution of 300PPI. * (this 300ppi myth annoys the hell out of me and I’ll explain all in another post).

So basically the pixel dimension and default resolution SET the image linear dimension.

If our image is destined for PRINT then this fact has some serious ramifications; but if our image is destined for digital display then the implications are very different.

 

Pixel Resolution and Web JPEGS.

Consider the two jpegs below, both derived from the same RAW file:

Andy Astbury,pixels,resolution,dpi,ppi,Wildlife in Pixels

European Adder – 900 x 599 pixels with a pixel resolution of 300PPI

European Adder - 900 x 599 pixels with a pixel resolution of 72PPI

European Adder – 900 x 599 pixels with a pixel resolution of 72PPI

In order to illustrate the three values of linear dimension, pixel dimension and pixel resolution of the two images let’s look at them side by side in Photoshop:

Andy Astbury,photoshop,resolution,pixels,ppi,dpi,wildlife in pixels,image size,image resolution

The two images opened in Photoshop – note the image size dialogue contents – CLICK to view full size.

The two images differ in one respect – their pixel resolutions.  The top Adder is 300PPI, the lower one has a resolution of 72PPI.

The simple fact that these two images appear to be exactly the same size on this page means that, for DIGITAL display the pixel resolution is meaningless when it comes to ‘how big the image is’ on the screen – what makes them appear the same size is their identical pixel dimensions of 900 x 599 pixels.

Digital display devices such as monitors, ipads, laptop monitors etc; are all PIXEL DIMENSION dependent.  The do not understand inches or centimeters, and they display images AT THEIR OWN resolution.

Typical displays and their pixel resolutions:

  • 24″ monitor = typically 75 to 95 PPI
  • 27″ iMac display = 109 PPI
  • iPad 3 or 4 = 264 PPI
  • 15″ Retina Display = 220 PPI
  • Nikon D4 LCD = 494 PPI

Just so that you are sure to understand the implication of what I’ve just said – you CAN NOT see your images at their NATIVE 300 PPI resolution when you are working on them.  Typically you’ll work on your images whilst viewing them at about 1/3rd native pixel resolution.

Yes, you can see 2/3rds native on a 15″ MacBook Pro Retina – but who the hell wants to do this – the display area is minuscule and its display gamut is pathetically small. 😉

Getting back to the two Adder images, you’ll notice that the one thing that does change with pixel resolution is the linear dimensions.

Whilst the 300 PPI version is a tiny 3″ x 2″ image, the 72 PPI version is a whopping 12″ x 8″ by comparison – now you can perhaps understand why I said earlier that the implications of pixel resolution for print are fundamental.

Just FYI – when I decide I’m going to create a small jpeg to post on my website, blog, a forum, Flickr or whatever – I NEVER ‘down sample’ to the usual 72 PPI that get’s touted around by idiots and no-nothing fools as “the essential thing to do”.

What a waste of time and effort!

Exporting a small jpeg at ‘full pixel resolution’ misses out the unnecessary step of down sampling and has an added bonus – anyone trying to send the image direct from browser to a printer ends up with a print the size of a matchbox, not a full sheet of A4.

It won’t stop image theft – but it does confuse ’em!

I’ve got a lot more to say on the topic of resolution and I’ll continue in a later post, but there is one thing related to PPI that is my biggest ‘pet peeve’:

 

PPI and DPI – They Are NOT The Same Thing

Nothing makes my blood boil more than the persistent ‘mix up’ between pixels per inch and dots per inch.

Pixels per inch is EXACTLY what we’ve looked at here – PIXEL RESOLUTION; and it has got absolutely NOTHING to do with dots per inch, which is a measure of printer OUTPUT resolution.

Take a look inside your printer driver; here we are inside the driver for an Epson 3000 printer:

Andy Astbury,printer,dots per inch,dpi,pixels per inch,ppi,photoshop,lightroom,pixel resolution,output resoloution

The Printer Driver for the Epson 3000 printer. Inside the print settings we can see the output resolutions in DPI – Dots Per Inch.

Images would be really tiny if those resolutions were anything to do with pixel density.

It surprises a lot of people when they come to the realisation that pixels are huge in comparison to printer dots – yes, it can take nearly 400 printer dots (20 dots square) to print 1 square pixel in an image at 300 PPI native.

See you in my next post!

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