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1. What are MTF curves?

These curves show how much of a sinusoidal wave contrast is retained by a
lens in a given image point, e.g. 0.9 means that in the image 90% of the
wave original contrast has been retained. 

You may imagine the sagittal wave as follows - Staying on a bridge
throw a stone into the water. When seeing concentric waves just aim your
camera in such a way that the image center is pointed at the place where
the stone felt in. What you see in the viewfinder is very close to what
could be used for measuring sagittal MTF curves of lens. 

Radial MTF curves are based on sinusoidal waves that go
perpendicularly to the sagittal ones, just imagine them in a very small
portion of the image in which sections of circles of sagittal waves are
almost straight lines. 

Differences between 'stone waves' and saggittal MTF waves:

 - MTF waves are not deacaying with distance.
 - Tops of MTF waves are the brightest, bottoms are the darkest, the brightness
   difference is the wave contrast I was talking above.
 - MTF waves are much denser, the most widely used pattern is 20 line pairs 
   per milimeter (500 line pairs per inch) on the lens image plane (=negative), 
   i.e. they are 20 wave tops and bottoms in each mm, 20 lp/mm.

2. Why sinusoidal waves are so widely used by engineers?

Simply, if you have a system that process some signal (image, sound), and
the system is linear and time/space invariant, then in reaction to a
sinusoidal wave the system is producing a sinusoidal wave, too. So, if you
are comparing system input and output, you are comparing apples to apples
and oranges to oranges. 

Space invariance for lenses means that MTF curve for them are
'sufficiently smooth'. In practice, for 20 lp/mm even the most wildely
changing MTF curves are 'sufficiently smooth'. 

3. MTF and a human.

Reaction of a human to MTF waves is somewhat surprising - it is a clear
peak of human susceptibility for some frequencies. My private guess is
that this has something to do with human AF system. They are cool pictures
revealing this peak, some people don't believe in explanation and think
that this is just a printing trick. 

The peak is for frequencies somewhat below 2 lp/mm seen on an image kept
at comfortable viewing distance, i.e. approximately 40 cm (16 inches) from
eyes. If you are looking at an 8x10 photo (20x25 cm), it translates into
less than 16 lp/mm on the 35 mm format negative, 8 lp/mm on the 6x7
negative and so on. The same negative line pair densities are obtained for
greater enlargements - simply, unless you want to analyze the quality of
print developing, the comfortable viewing distance for a 16x20 photo is 80
cm (32 inches), for 24x30 it is 120 cm and so on. 

At the peak of MTF performance and for the best viewing conditions a human
recognizes changes in MTF waves contrast as small as 2%. This is the case
when you compare two prints of 'peak' MTF waves laying side by side. With
growing (and decreasing) wave frequency the ability to differentiate
between print contrast diminish. In the very good article on this topic in
Color Photo from December 1996 (in German, unfortunately) a rule of thumb
is provided which says that minimum discernible differences are: 2.5% for
5 lp/mm, 5% for 10 lp/mm, 10% for 20 lp/mm, and 20% for 40 lp/mm. The data
seem to be prepared for small 4x5 prints and 35 mm format, which means
that for 8x10 print and e.g. 20 lp/mm the difference is 5%, while for 5
lp/mm it is greater than 2.5%. I have a question to people who see the
difference between professional 80-200/2.8 zooms and prime lenses,
especially 85/1.8, do you see this difference for aperture 8, too? If yes,
then the human eye is even better than that. For bad viewing conditions
the smallest discernible contrast differences could be 2-4 times greater. 

My private guess is that what is understood as 'image contrast' is a human
perception of MTF for frequencies below the human peak MTF
frequency, while 'image sharpness' coincides with perception of
frequencies above the peak. At least, everybody agrees that
contrast is depicted by low frequency MTF curves, while sharpness by
high-frequency ones, with 10 lp/mm being the border for 35 mm format. 

The maximum MTF wave frequency recognizable by a human is below 10 lp/mm
in an image seen from the comfortable viewing distance. I have played with
such images, you can only discriminate between 'possibly sharp - possibly
unsharp', at least it has been true for me. It seems then that unless you
are doing such crazy things as wall enlargements from 5x5 mm (0.2x0.2
inch) portions of negatives, the maximum usefull MTF lens data are for
around 80 lp/mm, some croping for 35 mm format and much more for larger
ones included. Don't forget, however, about the 'violin effect' - although
a human do not hear frequencies above 20 kHz, he/she can recognize lack of
sound harmonics even in the 50-60 kHz range. Maybe something similar is
true for optics? 

4. MTF and lens.

Some of you are probably familiar with the audio equipment frequency
characteristics, for optics the situation is much worse, you need a
separate characteristic for each image point! Fortunately, for a given
distance from the image center lens characteristics for all image points
are roughly the same. Additionally, you can correctly guess the lens
properties basing only on MTF values for few frequencies, e.g. 5, 10, 20
and 40 lp/mm. In fact, even a pair of radial/sagittal MTF curves for 20
lp/mm only may be sufficient for this purpose. The plots are scaled in
milimeters counted from image center (0 mm) to image corner (21 mm for 35
mm format, 40 mm for 6x6 format, and so on). 

For ideal diffraction-limited lens the MTF characteristic is an almost
straight tilted down line going from 1.0 for 0 lp/mm. I used to remember
only one number - for 20 lp/mm, lens aperture 8, and 550 nm light ray
(yellow-green) the ideal MTF is approximately 89%. 550 nm is the light
wavelength for which a human is susceptible the most, additionally, 550 nm
is close to the center of visible light wavelength range, hence, MTF for
it appropriately depicts average MTF for white light. 89 equals 100-11,
then, for aperure 11, the MTF is 84%=100%-16%, for aperure 16 it is
78%=100%-22%, for aperture 5.6 it is 92%=100%-8%, just
'100-one_aperture_higher', simple isn't it? Similarly simple is to
recalculate the MTF for other frequencies:  for 40 lp/mm (2x20 lp/mm) you
have 78%=100%-2x11%, where 100%-11% is for 20 lp/mm, for 10 lp/mm it is
94.5%=100%-0.5x11%, and so on. Finally, for deep-red light ca. 770=1.4x550
nm the MTF for aperture 8 and 20 lp/mm is 84%=100%-1.4x11%, and for
deep-blue one around 385=0.7x550 nm it is 92%=100%-0.7x11%. 

What about real lens? It seems that for low frequencies characteristics of
lens are nearly linear, too, so, if the MTF value in an image point for 20
lp/mm is 80%, then it is probably 90% for 10 lp/mm. That is why some
sources provide curves for one frequency only, usually 20 lp/mm, e.g. 
Swedish 'FOTO' magazine. For this frequency the best MTF figures are
obtained usually for aperture 8, at least for high-quality lenses, and
indeed, there are very few lenses for which curves for 20 lp/mm at any
aperture go above 85% (89% is the theoretical limit for aperture 8). 
Nevertheless, as it has been stated above, curves for 20 lp/mm show the
lens sharpness, for depicting lens contrast curves for 5-10 lp/mm are
better suited. And MTF curves for 10 lp/mm not always lay just in midway
between curves for 20 lp/mm and 1.0 (100%). 

When comparing lens avoid comparisons between focal length that do not lay
very close, and different camera formats. In particular, for SLR cameras
wide-angle lens should have compromise retrofocal construction, hence,
they are not so good performers as normal and short telephoto lens. That
is also the reason why non-retrofocal wide-angle lens of Mamiya 7 or Leica
M are so good. 

What are pitfalls of MTF tests?

1. Lens variability!!! Add to it MTF measuring error. So, if you see
   that lens A got 83.2 points, hence, it is a better buy than lens B 
   which got 82.3 points, just ignore this. In the 'FOTO' magazine two 
   samples of the same lens, Planar 50/1.7 T*, received one 5.0 points, 
   and the other 4.5 points, while nearly all tested normal 35 mm format 
   lenses received notes in the range 4.5-5.0. :-)

   It does not mean that MTF tests are useless, MTF curves should simply 
   go high and flat, on or above 80% for 20 lp/mm and aperture 8 and not
   much below for wider apertures.

2. MTF is usually measured for lens set to infinity. In this way lens 
   optimized for infinity seem to be the best. This need not be what is
   really needed (e.g. macro!). Additionally, expensive lens with 
   complicated movements of elements giving high performance for both far 
   and near images need not have the best MTF curves.  

3. Image planarity. MTF is measured in the lens focal plane, of course.
   And even for the best very wide-angle lens the image lays on something
   like a section of a sphere. It is a lens ability to reproduce objects 
   sharp that determinates our opinion about the lens performance, what 
   are sharply reproduced objects relative distances to the camera does 
   not count too much. Notice that MTF curves for a lens being sharp in 
   the (non-planar) image surface and for a nowhere sharp one (except for 
   the center) may look alike.

4. Some lens quirks weakly or not affecting MTF, but important for users. 
   These are bad flare resistance, vigneting, distortion etc.

5. Some lens quirks lowering MTF, but not important for at least some 
   users. The 'FOTO' magazine tests show a bad behaviour of Tokina 
   28-70/2.8 zoom MTF curves, as well as its newer version 28-70/2.6-2.8, 
   for focal length 70 mm. It is explained that this is caused by focus
   shift when stopping lens down. This means that the MTF curve for 
   aperture 8 is measured slightly off focus! BTW, the lens has a very 
   good reputation. 

[Ed. note: Mr. Erwin Puts is a noted Leica user and lens testing expert...]
From Leica Mailing List:
Date: Mon, 20 Mar 2000
From: Erwin Puts imxputs@knoware.nl
Subject: [Leica] technique again

There are some remarkably stubborn misconceptions aired on this list recently.

First: an MTF graph is not a single merit figure or a meaningless reduction of the optical quality of a lens to one single parameter. The MTF graph is the best condensed information you can have about the total aberration content of a lens. It is the measure of image degradation to be expected from any lens. And you can, like it or not, extrapolate from an MTF graph to the empirical results attainable with a lens in the field. Some posters seem to be unwilling to do so and that is their right. But if some person does not want to do something does that imply it is a worthless or meaningless approach?

Second: there seems to be an approach to dichotomize any topic: you can either be a tester of lenses or you can be a real world photographer, but not both, you are either a scientist or an empiricist, but not both, you test with supposedly meaningless test charts or you test with real life objects, but not both.

There is also a tendency on this list that quantity of experience is worth more than quality of investigation. Some persons note that they have shot thousands rolls of film or have been spending ten thousands of hours in the darkroom. Well that is fine, but as Seven of Nine would say; that information is irrelevant.

To give an example: I have been driving motorcycles for 25 years and clocked up half a million kilometers in all kinds of weather and road conditions. Does that make me an experienced driver? Does that give me any advantage when discussing motorcycle driving technique with some else. Nonsense of course. People have believed for thousands of years that the earth is flat and thousands of seamen have told the world that they with years and years of experience of sailing the high sees have seen no evidence that the earth should be curved.

Experience is nice, but it is no substitute for scientific investigation. If one wishes to put experience above any other type of fact finding, so be it. To deny the validity of the scientific approach in matters photographic, or to deny that theory and practice can successfully enhance each other illustrates an obsolete attitude. And to imply that 10.000 hours of darkroom work should be counted as more valuable or information-rich than 100 hours of controlled testing is just a pipe dream.

I now have a hundred rolls of Kodachrome on my desk, and I will vanish from this list for a longer period and continue with my personal photography of stray cats in small villages in France. A personal assignment I am conducting for the last 25 years.

Erwin

Date: Fri, 26 Mar 1999
From: "Dirk J. Bakker" dbakker@mindspring.com
Newsgroups: rec.photo.equipment.misc,rec.photo.misc,rec.photo.technique.misc
Subject: Re: Lenses and resolution

Hi Enio,

Enio wrote:

> What is the definition of Lens's RESOLUTION ???
>
> As a computer user, I can only imagine resolution
> as number of lines and columns display DIGITALLY on the screen.
> What does it have to do with 100% ANALOG, "real-world" lenses and light?

Using the digital model you relate to above, lens resolution: the ability to RESOLVE (in optics: to make visible ) the parts of an image, the greater it is, the more detail, the more distinguishable "lines and columns" per unit of measurement. However, the final (on-film/CCD) resolution is affected by the combined effect of the lens' as well as the recording medium's own resolution, image contrast AND chosen aperture.

> (I know that light has its "resolution", releated to its wavelength,
> but it's important only in sophisticated microsopes at very large
> enlargements!).

Yes and no. The very nature of light itself, influences image quality in more ordinary conditions (regular photography) in the form of aberrations and diffraction.

Check this page for an excellent discussion on the subject:

http://members.aol.com/daveswager/resolut.htm

HTH,

Dirk