Related Local Links:
Reading MTF Curves by Ryszard Stasinski
Pseudo-MTF Tester Project

Related Links:
MTF Interpretation (select MTF - Photozone)
MTF Lens Charts and Lens Quality .pdf (schneider Optics)
Hasselblad Products and Lenses (see sample MTF charts)
MTF and Graphical examples
Zeiss notes on MTF - MTFLB (.doc) MTF80 (.doc) and notes
MTF measurement (bar targets, java plug-in)
MTF of the eye

From: nycfoto@aol.com (NYCFoto)
[1] Re: Hasselblad Heresy!
Date: Thu Feb 19 1998

Could we please have a little lecture on how to read an MTF chart or curve, for those less initiated? Thank you very much in advance. --
Joseph White

I'm not certain of all of the science but as far as I understand an MTF curve is a means of expressing the ability to depict contrasts with a lens. The chart usually shows modulation transfer (M) as 0.0 going up to 1.0 on the vertical scale, and the distance from the off center axis of the lens is on the horizontal axis of the graph.

They usually employ Tangental and sagittal measurements ( which are the orientations of the line pairs being measured to the radius of the lens, either parallel or perpendicular). Basically the higher the M value ( closer to 1.0) the higher the ability to discern contrasts, also the flatter the graph the better the lens performance is off the center axis of the lens.

It also seems that normal to wide angle lenses measure better than longer telephoto lenses so when you are comparing lenses use a similar focal length lens for comparison.

Anyway I hope I explained it properly, I just wish that more lens compan ies would make their MTF curves public. One really good company for that is Sinar.

I have the actual charts for each Sinaron lens I own, the actual serial numbered lens itself. It shows me the optimum aperture and the qualitative fall off for each lens, and that quality fall off can be surprisingly big. Good shooting, Brian

From: nycfoto@aol.com (NYCFoto)
[1] Re: Hasselblad Heresy!
Date: Thu Feb 19

My work is routinely used for billboards, trade show display prints etc. so sharpness does matter to me. In addition the price difference between hasselblad and mamiya is not all that much so in my opinion you have to go with any difference in quality as well as features that are more applicable to your type of work. For me the hasselblad is mostly a location camera and it is far lighter than a comparable mamiya system. in my own tests, and tests done by people that I respect, the hasselblad lenses tend to be on average, superior. However that superiority is offset by the larger negative of the mamiya, so ultimately it all comes down to a personal preference. One thing that I must commend hasselblad for is the fact that they post the MTF curves for all of their lenses so you can tell which lens is a great design or not.

For more information, see Medium Format Camera List Page

Date: Thu Feb 19From: zanekurz@ix.netcom.com (Zane)
[1] Re: Hasselblad Heresy!
Date: Thu Feb 19

commend hasselblad for is the fact that they post the MTF curves for all of their lenses so you can tell which lens is a great design or not.

(snip)

I was waiting in a camera repair place the other day and looked through a nifty Hasselblad book with a set of curves for a lot of their lenses---sort of like the Canon Lens Work Book. The curves were pretty impressive and would be really helpful for picking lenses and knowing the limitations in using each lens.

But, I use a Pentax 67. Do you know if Pentax makes a similar publication?

Zane

rec.photo.equipment.35mm
From: hrfoto@aol.com (HRfoto)
[1] Re: MTF curves for lenses
Date: Mon Jul 13 11:29:34 CDT 1998

Re: MTF curves for lenses

I think just about everyone will agree that MTF curves present the most complete information about lens performance available today. However, they unfortunately don't tell the whole story. MTF curves do not specify maximum resolution, however, they do give rather complete information about the contrast properties of a lens. Lens contrast is by many considered more important than overall resolution. This has nothing to do with photographic contrast, but it refers to the ability of a lens to pick up small, similar colored or shaded detail. Imagine a test target with the customary black and white spaces. This constitutes relatively high contrast, and most any lens will therefore show relatively high resolution. Now replace the target with light gray and white spaces. Only a lens with high contrast will show optimum resolution. A lot of inexpensive lenses would show seriously degraded performance.

MTF curves are unfortunately not readily accessible, and they do not give any information about coma or astigmatism. However, there are some relatively simple tests which all of us can do. While they will not render scientific performance data, they will however, show performance differences among lenses and therefore are valid as an instrument to chose between lenses. For anyone interested, please contact me and I will pass on the information.

Heinz Richter
HRphotography

From: dickburk@ix.netcom.com (Richard Knoppow)
Newsgroups: rec.photo.equipment.large-format
Subject: Re: Interpreting MTF graphs...
Date: Fri, 17 Jul 1998

"waco" waco@ibm.net wrote:

>I have been looking at some of the MTF graphs on the Schneider web site (for
>example 
http://www.schneideroptics.com/large/super_angulon/xl72/mtf2.html )
>and I was hoping that one of you guys could explain a few things to me.
>First, I understand the basic MTF graph where Percentage modulation is shown
>a function of spatial frequency (%modulation on Y-axis, spatial freq on
>X-axis).  As I understand it, this shows the performance at a single point
>in the lens.  On their site however, they show percentage modulation as a
>function of image height (% mod on Y-axis, % max image height on X-axis) for
>a given spatial frequency, and at two different aperatures (5.6,22)
>Conceptually I understand what they are doing, but am not quite sure how to
>apply the data; thus a few questions:
>How exactly does one define "image height"?
>How does one determine resolving power with this type of graph?   
>How does one compare the resolving power of the lens vs. film using such a
>graph?  (for example a film might have a r.p. of 63l/mm @ 1.6:1 and 125l/mm
>@ 1000:1, but the graphs show spatial freq's of 5/10/20 l/mm...)
>
>Thanks,
>waco 

Schneider has a pretty good explanation of the terms used in their measurements on their site at:

http://www.schneideroptics.com/info/white_papers/quality_criteria_of_lenses.pdf

The image height they are refering to is the radial distance from the center of the image to its edge. The maximum image height is the same as the maximum radius of coverage at infinity focus.

In the case of this lens it is 113mm indicating an image circle of 226mm, which is the maximum of this lens when it is stopped down to f/22.

There is no general rule for giving a combined film and lens resolution number. It must be computed based on the curves for each since the shape of the curve varies.

MTF curves are somewhat akin to the frequency-responce curves familiar to all hi-fi lovers. They are in the spaceial domain rather than the temporal domain but otherwise the math is the same.

A lens or film can have an MTF curve which rolls off slowly and reaches a high number of lines/mm but at at a low level, or it can have a curve which stays up until it reaches middle levels and then falls off rapidly. The first lens will have better resolution but the second will look sharper and have better edge contrast. Film can do the same thing. High-acutance developers tend to produce curves which are high in the middle of the range and fall off rapidly toward the high end. These images look very sharp but actualy have rather poor resolution.

As far as human perception of sharpness (what is called "definition") acutance is more important than absolute resolution.

For a simple system the rules of thumb are that the combined resolution of film and lens is 1/T = 1/L + 1/F Where T= Total resolution, F is film resolution, and L is lens resolution.

Another rule is that the combined resolution is the square root of the sum of the squares. Neither of these is correct and neither is wrong. If you do both you will get some idea of what is actually going on.

There are a very large number of factors which affect actual resolution of a system and even more when one is considering percieved sharpness. Ultimately, the test is to shoot pictures and see what they look like.

---
Richard Knoppow
Los Angeles, Ca.
dickburk@ix.netcom.com

Date: Wed, 08 Jul 1998
From: Eric Goldstein egoldste@bu.edu
To: rollei@mejac.palo-alto.ca.us
Subject: Re: [Rollei] Rollei TLR lenses

bills wrote:

> A year ago someone posted the resolution tests on the Rollei lens'  I have
> experienced a crash and they were lost.  If that someone could post them
> again it would be wonderful and I would save them to floppy.

Here are some tests posted by John Leaman early in 1997. This was two seperate posts and the methodology could very well have been changed between tests. Also, no note was made of whether these are l/mm or lp/mm:

> 3.5 Tessar Old Standard
>         Center  Edge
> 3.5     59      21
> 5.6     59      30
> 8       59      33
> 11      66      47
> 16      66      47
> 22      66      47
>
> 3.5 Tessar Automat 1
>         Center  Edge
> 3.5     42      17
> 5.6     75      37
> 8       75      47
> 11      75      47
> 16      66      59
> 22      59      53
>
> 3.5 Xenar MX-LVS
>         Center  Edge
> 3.5     32      25
> 5.6     32      25
> 8       57      32
> 11      64      36
> 16      64      40
> 22      57      40
>
> 3.5 Tessar T
>         Center  Edge
> 3.5     66      42
> 5.6     84      42
> 8       94      42
> 11      75      59
> 16      75      59
> 22      66      59

(Next post:)

> With regard to the thread on 2.8 Tessars, while not relevant
> for the discussion on Super Icontas, here is some comparative
> resolution information (informal test with Edmond Scientific
> lens chart, Ilford Pan F+ and PMK).  In line pairs per mm:
>
> Rollei 2.8 Opton (from 1951 2.8A)
>
> Stop         Center            Edge
> 2.8             24              15
> 4               37              15
> 5.6             37              15
> 8               60              35
> 11              60              42
> 16              60              37
> 22              53              37
>
> Rollei 2.8F Planar
> 2.8             47              47
> 4               47              47
> 5.6             53              47
> 8               53              53
> 11              60              60
> 16              60              53
> 22              60              53
>
> More test data later
> --
> John Lehman  (907) 474-6275 (voice)  (907) 474-5219 (FAX)
> School of Management, University of Alaska Fairbanks
> Snailmail: PO Box 756080, Fairbanks, AK 99775-6080 USA

Date: Wed, 08 Jul 1998
From: Richard Knoppow dickburk@ix.netcom.com
To: rollei@mejac.palo-alto.ca.us
Subject: Re: [Rollei] Rollei TLR lenses

At 09:33 AM 7/8/98 -0400, you wrote:

>bills wrote:
>
>> A year ago someone posted the resolution tests on the Rollei lens'  I have
>> experienced a crash and they were lost.  If that someone could post them
>> again it would be wonderful and I would save them to floppy.
>
>Here are some tests posted by John Leaman early in 1997. This was two
>seperate posts and the methodology could very well have been changed
>between tests. Also, no note was made of whether these are l/mm or
>lp/mm:
>

Data snipped since everyone has it...

The trends are interesting, i.e. the optimum stop. I am skeptical of the actual resolution numbers. In a couple of cases the edge values are more than diffraction permits (assuming about a 25deg hjalf-angle), which suggests to me that they are the sort of false readings which can be gotten from some types of resolution charts.

The diffraction limit varies with both angle and with the direction of the lines, being less for tangential than for radial lines. As an example, for an ideal (aberration free) lens, using monochromatic light at 589.3mu (mid green) the limit at f/22 is: on axis, 61 lines/mm, at 25deg, 46 l/mm Tangential, 56 l/mm Radial. White light resolution will be less.

As a general note, anytime you can get 60 l/mm of of _film_ you are doing very well.

Another note. The resolution of a lens/film combiation is hard to calculate in any simple way. Although a couple of simple formulas are given in text books an examination of MTF data for lenses and films will show that they have different shapes.

As a result the overall transmission characteristic must be calculated for each combination. This is not a trivial problem.

As a very general rule of thumb if the lens and the film have about the same resolution when measured separately the combination will have about half this value.

I don't want to seem to denigrate the measurements, they are a valuable comparison, and very interesting. I just want to caution against taking them too literally.

----
Richard Knoppow
Los Angeles,Ca.
dickburk@ix.netcom.com

From: rschiller@worldnet.att.net (Rick Schiller)
Newsgroups: rec.photo.equipment.medium-format
Subject: Re: Lens Resolution Test Chart???
Date: 10 Sep 1998 17:40:11 GMT

Edmund Scientific had a test chart that mimics the 1951 Air Force chart and it works fine, I beleive they are in New Jersey and I suspect they have a website. I believe it was under $20.

Rick

From: "Christopher M. Perez" chrisper@vnd.tek.com
Newsgroups: rec.photo.equipment.large-format
Subject: Re: lens testing
Date: Mon, 14 Dec 1998

Sandy King wrote:

> The quality of a lens is often related to its resolving capability in lpm.
> I presume there is a standard set of parameters which exists to carry out
> such testing (target, type of film, development, etc). What are they? Are
> there specific testing materials which one can buy to do such testing?

It depends on if one desires to test a 'system' or if one is looking at reporting numbers for just a lens.

- In the first case, call up Edmond Scientific or visit http://www.edsci.com and look for one of their USAF lens resolution charts.

- I'd suggest using the finest grain film _you_ typically use. Tech Pan is reported to be limited to around 120-140 l/mm in a 6:1 contrast ratio scene (typical of the contrast found in most photographic subjects) but not many people use it as it's contrast is difficult to deal with. TMax100 and the fine grained color slide films (Velvia comes to mind) are reported to be limited to around 100-120 l/mm and may be more representative of what people use. The faster the film the lower the resolution typically reported.

- Setup lights that approximate the standard daylight spectrum and consistantly shoot under those conditions.

- If you are shooting B&W; and use the zone system, use it consistantly in testing as well. If you shoot color, then use the same lab you would normally use.

If, OTOH, you want to know just the resolution of the lens, then there is a method where a microscope is used on a test bench. This test setup is described elsewhere (ie: look on the web). From what I've heard, it's difficult to test in this fashion and, in the end, fails to report the overall performance in a way that relates directly to one's setup in practical use in the real world. For the testing that Kerry, Mike, and I have done we standardized on TMax100/D-76/20:1 distance (in many cases)/same lighting throughout/same camera/tripod/film holders when testing 4x5. If you're testing 120 format cameras, be prepared to deal with film alignment and accuracy problems on nearly all cameras. All this work tells one what their own environment will return. There may be some difficulty in talking about lenses tested by two different parties under more than one set of test conditions. In such cases all discussions need be tempered by this realization.

For the testing that Kerry, Mike, and I have done we standardized on TMax100/D-76/20:1 distance (in many cases)/same lighting throughout/same camera/tripod/film holders when testing 4x5. If you're testing 120 format cameras, be prepared to deal with film alignment and accuracy problems on nearly all cameras. All this work tells one what their own environment will return. There may be some difficulty in talking about lenses tested by two different parties under more than one set of test conditions. In such cases all discussions need be tempered by this realization.

All this work tells one what their own environment will return. There may be some difficulty in talking about lenses tested by two different parties under more than one set of test conditions. In such cases all discussions need be tempered by this realization.

But for comparative purposes, if one tests enough lenses, one can begin to see patterns. Some of the things people might be interested in is the consistancy of manufacture between or across lens lines. The other is (and perhaps more importantly) consistancy of the accuracy of one's film holders/camera focussing system/groundglass position.

As a basis to begin discussion all this can prove very useful. It's time consuming, but I think the three of us have learned some very interesting things from the process. None of it can be displaced by wishful thinking, marketing, myth, or theory...

I hope this helps.

- Chris

From: steved@united.ussinc.com (Steve Dunn)
Subject: Re: Value of photodo ratings?
Organization: United System Solutions Inc.
Date: Tue, 8 Jun 1999

"Fred Whitlock" afc@cl-sys.com writes:

>OK so what does MTF stand for?

Modulation Transfer Function.

In simple terms, it refers to how well the lens can reproduce a pattern of alternating black and white lines. A "perfect" lens would reproduce them exactly, with the black lines showing up as pure black and the white lines showing up as pure white, and with a sharp boundary between them. There would be no change in performance from the center of the lens towards the edges, and the lens would have equal ability regardless of how the lines are oriented. Oh, and performance wouldn't depend on aperture, either.

In the real world, of course, lenses aren't perfect. The center of the lens has a higher resolution than you get at the edges. A series of black and white lines will show up as black (but not necessarily 100% pure black) and white (but not necessarily 100% pure white), with shades of gray at the edge between the two. Lines running radially (from the center to the edges) tend to be represented better than lines running perpendicular to radial lines. The closer together the lines get, the less accurately they're represented. And sharpness and contrast improve as you close down the aperture a couple of stops from wide open.

As you look at the MTF graphs from left to right, you're looking at the performance of the lens from the center to the edges.

In each pair of lines, one (the solid line, in the case of photodo) represents lines running from the center of the lens outwards; the other (broken line) represents lines running at right angles to this.

And the three pairs of lines represent different densities of the test pattern; the lower ones in the graph represent higher spacial frequencies.

You'll also notice that photodo runs MTF tests at different apertures.

>          I've run some comparisons between some of the
>lenses that Photodo tested and arrived at exactly the
>opposite conclusions they have.  I have no way to measure
>MTF but I'm pretty good at judging image quality with a
>loupe after 40 years of practice.

In general, I don't believe that most things can be quantified by a single number - or even a set of numbers. One test doesn't tell the story, the whole story, and nothing but the story. Is MTF useful? I don't have any training in optics so I'm not qualified to provide anything remotely resembling a definitive answer. I _think_ it's useful to keep it in mind, but my skepticism of using only one test to evaluate something makes me believe that researching a lens should consist of more than just finding MTF results for it.

Fred has found lenses that give him good results, regardless of how they did on photodo's tests. That's the bottom line - find something that gives you the results you're looking for, whether it's a lens, film, camera body, or a brand of chewing gum.

--
Stephen M. Dunn (SD313), CNE, ACE steved@ussinc.com

From: P l Jensen paal@norvol.hi.is
Newsgroups: rec.photo.equipment.35mm
Subject: Re: Value of photodo ratings?
Date: Tue, 08 Jun 1999

"Billy R" willreed@worldnet.att.net wrote:

>MTF is the key to modern optical
> technology and it is so accurate that lens designers can rely on MTF
> calculations to optimize the lens design without needing to run prototype
> samples.

I had a Leica lens brochure from the late 80's that used three or four pages explaining why MTF test should not be used as criteria for selecting lenses. They used lot of space to explain why MTF had little correlation with a lens real life performance. They also explained why some Leica lenses did not perform well in such tests, and the design decicion behind such lens performance. Unfortunately, I don't have the brochure in front of me.

From: "Billy R" willreed@worldnet.att.net
Newsgroups: rec.photo.equipment.35mm
Subject: Re: Value of photodo ratings?
Date: Tue, 8 Jun 1999

While MTF is certainly not the only factor that gives a lens exceptional performance, it is an objective parameter by which to judge optical performance. In fact, MTF is crucial in evaluating every optical component. In scientific digital imaging for example, the MTF of the CCD must be matched to the expected resolution requirements. (You can find out more on this subject by running a web search on the Hubble Space Telescope Wide Field Planetary Camera.) Zeiss publishes MTF data for all of its lenses and states that the 3 most important factors to lens performance are MTF, distortion, and light fall-off at the corners of the image field. If Zeiss, which also owns the Schott glass company and is one of the best lens manufacturers in the world, believes in the value of MTF tests, I can't imagine why Leica would have any reasons to feel otherwise.

Date: Fri, 8 Oct 1999
From: Julio's Mail gluemax@ora.auracom.com
To: rmonagha@post.cis.smu.edu
Subject: MTF Curves, Significance

Thank you for your article on MTF which is quite informative.

Your article however seems to omit to deal with the significance of the divergence of the MTF line pairs (radial/tangential).  As one of the results of astigmatism is the inability of the lens to read radial and tangential subject matter equally well, this seems suggest that the separation of the two MTF curves is indeed indicative of astigmatism. It has been my experience using lenses whose MTF is published, (Zeiss), that those lenses whose line pairs are close together are distinctly sharper than those whose lines are widely divergent as is the case with some telephotos. 

As the divergence (astigmatism) can increase in some lenses when closed down, I also have found empirically that the lens will be sharpest at the diaphragm opening which shows tighter MTF lines. I could go on to cite several examples but in the interest of brevity, I will only add that lenses whose line pair MTFs show at least one curve maintaining fairly high contrast across its coverage are able to deliver images of high contrast even though the lens may lack in sharpness. 

In previous publications, a Zeiss writer has argued that the viewer can be fooled into believing that an image appears to have higher resolution and impact than another, by virtue of its high contrast, in spite of the fact that the lower contrast image has the higher resolution.  It seemed to me then that the writer was making a case for high contrast astigmatic lenses. Microscopic examination of slides of photographed Lens Charts, clearly showed a dramatically different appearance of the images taken with a high contrast/low resolution lens and a lower contrast /higher resolution lens. The lenses in question were Leica and Zeiss.  Because contrast can be manipulated to some degree by film selection, and by processing. (The great majority of slide films have MTFs higher than 100, some right up to fairly high spatial frequencies!).  It seems then that  small deficiencies of the lens in the contrast department can be overcome and improved upon by film selection and processing.  Not so with resolution.   On the other hand, if resolution is not there in the photographic negative or positive, to begin with, it can not be improved (perhaps other than digitally, not the issue here.) 

Some other sources pick the higher of the two lines and base their lens evaluation on it. (Photodo).  I would suggest to those interested to look carefully at the published MTFs and select lenses whose MTF lines run closest together, as long as they stay sufficiently high in the chart.  Zeiss's Super Achromat 250mm for the Hasselblad and the 100 mm Macro for the Contax are among the sharpest lenses I know.  The 100 mm Planar for the Hasselblad has also a reputation for sharpness.  All these lenses share particularly tight MTF line pairs and of course relatively high contrast at even higher spatial frequencies.  Rodenstock's Apo-Rodagon  and Apo Ronar lenses among others should be outstandingly sharp also based on their extremely tight MTF curves which show also an extremely high response in the MTF charts.

There are many lenses from other 35 mm lens manufacturers (surprisingly, not camera manufacturers) who are now turning out a few lenses,  that should be quite free of astigmatism, if the MTF charts are to be believed.  Some of these lenses also appear to have high contrast.  I realize of course there is more to optics that can be defined by MTF charts, specially when color, distortions, flare, consistency are taken into consideration.  However this issue with MTFs I feel is important and needs a great deal of clarification.  Your comments would be appreciated.

[Ed. note: Astigmatism as usually used in optics is different from the use suggested in the above mailing. Lenses that are more consistent in their radial and tangential curves may perform better as noted. Perception of contrast by the eye is very much impacted by subject matter and projection of detail that isn't there by the brain. Contrast measured scientifically can be quite different from what we perceive it to be. Contrast can indeed be shifted by changes in developing times and choice of films. Choosing a higher lpmm resolution film can also provide a huge improvement in on-film resolution, versus aerial resolution figures for lenses or MTF based tests.

From Rollei Mailing List:
Date: Wed, 27 Oct 1999
From: bigler@jsbach.univ-fcomte.fr
Subject: Re: [Rollei] [soon OT] confusing circles

About MTF and spot size.

There is another "academic" case where the correspondence between spot size (in mm) and MTF (line pairs per mm) is easy to compute and predict : it is the case of a de-focused lens. Then the image of a single point in input is the projection of the aperture blades (see discussions about "bokeh"), diffraction and other aberrations being negligible, hidden by defocusing.

If we assume for simplicity a circular shape for the lens aperture, then the output for a single point is a small circle of diffusion, conventional DOF approach. The corresponding MTF curve can actually be mathematically computed. This MTF curve drops to zero for a number of line pairs lp_max=1.22/d where d is the diameter of the circle of confusion. The 1.22 coefficient is the same as in the diameter of a diffraction spot size, but it is a mathematical coincidence since the same circular functions (Bessel's) are used in the computations. For a square diffusion spot, size a x a (truly an academic case!!!), lp_max would simply be 1/a.

The MTF curve resulting from a spot shape with sharp edges either circular or square or whatever is something which oscillates and becomes negative, something never seen in real lens MTF curves without defocusing. You can visualize these negative parts of the MTF curve of a de-focused optical system by projecting a target made of radial sectors alternatively B&W.; For example 144 B&W; pairs of sectors of 2.5 degrees each. When you defocus, you can visualize on the de-focused image the first zero of the MTF as a circle of total blur, followed if you move from the periphery (low number of line pairs) towards the center (high l/p rate) by successive images of the radial target with an inverted contrast B sectors becoming W and conversely, each inversion of contrast being separated by a circular zone of total blur.

-- Emmanuel BIGLER
bigler@lpmo.univ-fcomte.fr

[Ed. note: Mr. Bob Shell is a noted photographer, editor of Shutterbug, author of many photobooks, a noted former camera repair expert etc....]
From Contax Mailing List;
Date: Thu, 20 Apr 2000
From: "Bob Shell" bob@bobshell.com
Subject: Re: What is MTF Anyway? WAS: Re: [CONTAX] blad zoom

- ----------

>From: John Coan jcoan@alumni.duke.edu
>To: contax@photo.cis.to
>Subject: What is MTF Anyway? WAS: Re: [CONTAX] blad zoom
>Date: Wed, Apr 19, 2000, 7:19 PM
>

> that's big honker of a lens!
>
> I hate to be obtuse, but can someone explain to me what the heck a modulation
> transfer factor is?  Here's what Hassy said on the link below:

MTF is Modulation Transfer Function, that is a measurement of how accurately a lens takes the modulation it is presented with and transfers it to the film plane. Obviously the more accurat this transfer the better the image represents the subject.

An MTF measuring device presents the lens with alternating bands of black and white, which a physicist would recognize as a square wave with a given amplitude between "black" and "white". A measuring device at the film plane reads the transmitted light and outputs a wave, which is more or less converted to a sine wave.

The closer the output wave matches the input wave, the higher up on the chart the MTF line will be drawn.

Testing is typically done at three different spatial frequencies, 40, 20 and 10, which you can equate to line pairs per millimeter in old fashioned resolution testing. The solid lines on the MTF chart represent sagittal targets and dotted lines represent tangential targets. Sagittal targets have the black and white segments arrayed like pieces of a pie, that is radial in their symmetry. Tangential targets are like a series of concentric circles. The difference between the two is a measure of astigmatism. Ideally the two lines should be the same, but in realtiy they tend to diverge toward the edges of the image field (the horizontal axis on the MTF chart. The farther to the right, the farther from the center of the field.)

Testing is typically done at two lens apertures, wide open and f/5.6 (which is the best aperture for most lenses). Sometimes other apertures are tested, so when comparing MTF charts from different sources make sure you are comparing the same aperture.

Generally speaking the higher the lines on the chart the better the lens. Also the straighter the line the better, and the closer the solid and dotted lines to each other the better.

Another point: Zeiss publishes real MTF charts made by testing real lenses. Some lens companies publish theoretical MTF calculated based on the lens design but assuming perfect manufacture. This is not how things work in the real world, so I generally pay little attention to that sort of MTF.

Hope this helps. It sounds really technical, and the testing is, but reading the charts is not all that hard.

Bob

FRom Contax Mailing List:
Date: Tue, 30 May 2000
From: Paul van Walree odobenus@xs4all.nl
Subject: Re: [CONTAX] MTF considerations

Bob Shell wrote:

> An MTF machine presents a lens with a square wave and measures
> how closely the lens transmits this as a square wave. The more the
> lens converts the square wave to a sine wave, the lower the MTF.

In practice that is true, but theoretically a sine wave can still have a modulation depth of 1. I think it is for this reason that Leica considers the edge spread function, which tells them in which way the converted wave deviates from a square wave.

Walrus

Date: Sat, 09 Sep 2000
From: bc1959@my-deja.com
Newsgroups: rec.photo.technique.nature,rec.photo.digital
Subject: Re: lens, film resolution, MTF limits

The rule of of thumb among lens designers (I am one) is that a high quality 35mm objectives have an on axis MTF of about 50% at 30 cycles/mm and 30% at 50 cycles/mm at FULL APERTURE. The corners are typically poor at full aperture unless the field angle is small (long focal length), but ideally the transition from decent performance on- axis to whatever happens at the extreme corner is a smooth one. Stopping down improves things, of course. I once bought a 50mm f/1.2 Nikkor for a consulting project not because of its high aperture performance (it actually is substantially WORSE than the above rule of thumb), but because it can resolve in excess of 200 cycles/mm near the optical axis when stopped down to f/4 - which I needed for imaging onto a small high resolution CCD. I have raytraced and analysed literally tens of thousands of optical designs from the patent literature, and have found that most 35mm objectives obey the above rule of thumb pretty closely. Very few designs are substantially better, and they tend to be the fast telephoto types.

It seems to me (personal experience taking pictures, of course) that everything has to be close to perfect for a film image to be substantially better than a digital image from one of the better current digital cameras. I used to use Tech-pan and Kodachrome-25 a lot, but I like the smoothness of the 2.7 megapixel images I get from my D1 BETTER. The D1 images look a lot like 4x5 and 11x14 images I have taken in terms of image smoothness. The resolution of slow film combined with a good lens used near its optimum aperture is visually better than a 2.7MP digital image, but the visual difference to me is subtle, and not overwhelming. Something that a lot of people overlook is that traditional film photography is a two-stage optical process in which the MTF of the taking lens is cascaded (multiplied) by the MTF of the enlarging/scanning lens (film scanners are not perfect enlargers - they use lenses too!). Digital photography is a single-stage optical process, so digital cameras do not have to have the same MTF as a film image to have an identical print MTF.

I have a strong negative reaction to film grain, which is why I tend to prefer digital images now, even though the resolution is not quite as good. For low-light shots that would require ISO 400 film or faster it is a no-brainer for me: digital images are simply better.

Brian

Chris Kelly ctk4@columbia.edu wrote:

> A_M,
> There seems to be a lot of information out there.  There are some
> people out there, however, who take "actually looking themselves"
> very seriously.  Bryan over at RRS is one.  He used to have be in
> the habit of shooting from heavy tripod, with mirror locked up,
> with cable release, on Velvia, and looking at the actual results with
> a microscope.  The Nikkor 85mm 1.4, for instance, comes in at
> around 100 lpm.  Some are even sharper.  I have shot some VERY
> sharp lenses with all the correct technique on several different film,
> ProviaF, Astia, and Velvia and there is a definite difference.
> Intererestingly enough, I have shot on some lenses which do not
> have excellent MTF ratings, with proper technique, and the film
> still makes a difference.  The resolution of Velvia still effects the
> outcome.
>
> Oh, on your last statment.  Practical experience of MANY
> professionals in the field, as well as testers, show the 50lp/mm
> to be totally false.  Someone is making a mistake in the math.
> I have a feeling that your sources are in the digital community and
> have an interest in making the film look worse much worse than
> it is.
>
> Chris

....

Date: Sat, 09 Sep 2000
From: bc1959@my-deja.com
Newsgroups: rec.photo.technique.nature,rec.photo.digital
Subject: Re: lens, film resolution, MTF limits

Testing lenses with charts is a very good technique and I use it often. But aside from being able to see the lines or not is the question of how well you can see the lines when you can see them. With test charts you can only answer this question subjectively. An MTF measurement can give much more detailed information. One reason I like the test chart method is that it is easy to do and it gives an overall impression of lens quality at a glance. MTF testing is a lot more tedious and doesn't give the same visual feedback. It also requires outrageously expensive equipment. On the other hand, in designing a lens it is trivial to compute MTF curves but very difficult to predict exactly what a set of bars will look like.

Brian

....

Date: Sat, 9 Sep 2000
From: "Bob Talbot" BobTalbot@st-abbs.fsnet.co.uk
Newsgroups: rec.photo.technique.nature,rec.photo.digital
Subject: Re: lens, film resolution, MTF limits

....

Brian

I go along with all of that.

My point was simply that MTF test results are poorly understood, and thier interpretation vis-a-vis ultimate quality even more so. To most people a simple grid, resolved or not is much easier to grasp as a visual concept: and much less easy for others to discredit.

This is a nature list: unlike a general photography forum I expect there to be a much higher fraction here who are "anal" about quality. Many here do use tripods as a matter of course, not as an afterthought. Do use MLU when appropriate. Do use chromes to avoid the "two step" second generation image issue.

As to test charts etc: ultimately too the decision about whether an image is good or not is *always* subjective. Certain types of image do not need high res to work (arty type smooth transitions etc). But shots where feather detail, butterfly wings, spiders webs etc are the essence: you really don't want to be aware of the aliasing then ;o)

Bob

Samples of what I like to photograph at:
http://www.st-abbs.fsnet.co.uk/pf/
90% of the time it's all insects, birds and plants

From: "Tom Bloomer" bloomer@/"NoSpam>"/snip.net>
Newsgroups: rec.photo.equipment.medium-format
Subject: Re: Where can i find MTF for zenzanon lens
Date: Mon, 29 Oct 2001 

http://www.tamron.com/bron/etrsi_lens.htm
http://www.tamron.com/bron/sq_lens.htm
http://www.tamron.com/bron/gs1_lens.htm

Each lens has a single MTF curve on its page, the graphic is very small.
Make of it what you will.  Some folks believe the MTF information is
useless.  YMMV
--
Tom Bloomer
Hartly, DE

lorenzoquaresima@libero.it> wrote 
hallo,
as subject,
please help me, thanks
lorenzoquaresima@libero.it


From: wiltw@aol.com (Wilt W)
Newsgroups: rec.photo.equipment.medium-format
Date: 29 Oct 2001 
Subject: Re: Where can i find MTF for zenzanon lens

What is the point of getting MTF on MF lenses?...You should choose your camera
based on features needed, feel in the hand, etc. and then accept the
manufacturer's lenses...as there are no third-party alternative lenses, unlike
for 35mm format!

If there are two brands of cameras which meet your needs, and both feel equally
at home in your hands, then maybe MTF should enter your decision criteria.  

I find it funny (black humor sort of way) that portrait photographers often use
cameras like Hassy or Mamiya or Bronica, and then put diffusion filters over
the lens to degrade the quality of the lens and hide blemishes or give the
picture a 'dreamy' look.   MTF intentionally degraded!!!

--Wilt


From: "Tom Bloomer" bloomer@/"NoSpam>"/snip.net>
Newsgroups: rec.photo.equipment.medium-format
Subject: Re: Where can i find MTF for zenzanon lens
Date: Thu, 1 Nov 2001 

The 180mm is one of their newest designs.  It focuses very close and has a
very good reputation as a sharp lens.  The 200mm is one of the worst lenses
in the lineup and it does not focus very close at all.  You might notice
that the 180mm  is priced a lot higher than the 200mm.  Part of the reason
for the higher cost is because it is a better lens in terms of its sharpness
and contrast - possibly the sharpest next to their new 1:1 macro lens.  If
you are using the 180mm for portraits, you might find it a little long
compared to the 150mm.  You will be making a tight head/face only portrait
at about 5 feet and a head and shoulders from about 9 feet(~3meters).
Bronica also has a new 135mm lens that is much sharper than the 150mm.  It
also focuses down to 1meter.  You might want to consider that one as well
depending on your preference for focal length.
--
Tom Bloomer
Hartly, DE
lorenzoquaresima@libero.it> wrote...
On 29 Oct 2001 21:48:43 GMT, wiltw@aol.com (Wilt W) wrote:

>What is the point of getting MTF on MF lenses?...You should choose your
camera
>based on features needed, feel in the hand, etc. and then accept the
>manufacturer's lenses...as there are no third-party alternative lenses,
unlike
>for 35mm format!
>
>If there are two brands of cameras which meet your needs, and both feel
equally
>at home in your hands, then maybe MTF should enter your decision criteria.
>
>I find it funny (black humor sort of way) that portrait photographers often
use
>cameras like Hassy or Mamiya or Bronica, and then put diffusion filters
over
>the lens to degrade the quality of the lens and hide blemishes or give the
>picture a 'dreamy' look.   MTF intentionally degraded!!!

Hallo, thank you and everyone answered.
I ask for mtf beacause i have a zenza bronica 4,5x6 and 50, 75 and
150mm lenses. I'm very happy dor 50 and 75 because they are very harp
and i can see a lot of details in my pictures but i can't tell the
same thing for 150mm zenzanon MC. I asked mtf because i'd like to know
if 180mm and 200mm are sharper than 150mm and eventually i could buy
one of these.


From: brianc1959@aol.com (brian)
Newsgroups: rec.photo.equipment.35mm
Subject: Re: Nikon - primes that deliver creamy bokeh
Date: 7 Dec 2001 

Robert:

I didn't use MTF equipment for that particular measurement, but rather
a fairly simple projection device that uses a precision glass test
slide that you project onto a wall.  The test slide has numerous bar
targets marked in cycles/mm, so you can read the resolution directly
from the projected image.  At the time I was in charge of optical
design and testing at a U.S. based camera company.

You can do a similar test by photographing a large test target that
you can print on an ordinary inkjet printer, but in this case the
performance of the film/processing will be mixed in with the pure
optical performance of the lens.  For this reason I usually prefer
projection testing, which is standard practice at many optical
companies.  MTF testing is very useful, but it is somewhat cumbersome
and slow, and unless you spend an enormous amount of effort you can't
get an overall impression of optical performance the way you can at a
glance with projection testing.

Brian


Roberto Strappafelci roberto.strappafelci@tin.it> wrote 
> brian at
> brianc1959@aol.com wrote on 6-12-2001 23:33:
> 
> 
> > - I've done projection testing with this lens that revealed resolution
> > well in excess of 100 cycles/mm even wide open.
> > 
> 
> Brian,
> 
> just out of curiosity, did you make your own MTF or what?
> 
> Roberto


From: brianc1959@aol.com (brian)
Newsgroups: rec.photo.equipment.35mm
Subject: Re: Nikon - primes that deliver creamy bokeh
Date: 8 Dec 2001 

Hi Bob:

I used Pearl projectors, which look something like miniature WW1
tanks.  They sell a wide variety of projectors and test charts
suitable for testing lenses ranging from 1/5" digicam lenses up to
medium format.  The contact information is Pearl Optical Industry Co.,
Ltd., Tokyo, Japan  TEL: 81-3-3760-8871, FAX: 81-3-3793-2722.  The
test targets themselves are solid glass with either black on white or
white on black patterns on one side.  Their stuff isn't cheap - around
$4500 for a projector and $450 per test target, but they have been a
standard for many years and you might be able to locate a surplus used
one for a good price.  Personally, if I were putting together one for
my own use I would build something and put an interchangeable lens
mount on it.

The MTF equipment I used was designed and built by Optikos in
Cambridge, Mass., and worked on the principle of performing a Fourier
transform of a point image formed by the lens.  Good commercial
equipment is extremely expensive, but all you really need is a good
collimated light source, a precision high-NA microscope objective, and
some good mechanical parts to hold everything together.  Plus a
computer and the willingness to write the analysis software.  A more
direct approach would be to photograph sinewave targets of varying
spatial frequency.  You might want to check out
http://www.sinepatterns.com/ for more information on this.  These
targets are pretty expensive, but you can probably do a reasonable job
printing your own on a good inkjet printer (see
http://www.normankoren.com/ ).  Photographing with film might lead to
large errors because of enhanced mid-range MTF due to adjacency
effects in processing, so some type of digital image detection might
help here.  You could use a microscope objective to relay the image
formed by the lens onto a CCD to greatly enlarge the pattern so that
the limited resolution of a CCD will not effect accuracy.  Off-axis
measurements might be a challenge here, however.  Of course, you could
always simply measure the combined MTF of the lens and the film.

Brian


rmonagha@smu.edu (Robert Monaghan) wrote 
> Hi Brian,
> 
> an interesting observation and point, thanks again for sharing this tip!
> 
> I would be interested in any sources for such precision projection slides 
> (esp. surplus? ;-) and info on how to do such a setup?  I think I have 
> seen a similar X shaped chart used by Nikon, IIRC, to project slides and 
> check lenses on final assembly...
> 
> I have seen something I suspect is similar, using a kodalith film slice of 
> a series of stripes, projected thru the lens, for use with a scanner or
> other photosensor to derive a pseudo-MTF chart and response value for a 
> given cycle frequency. 
> 
> I'd also be interested in any homebrew MTF or similar contrast testing
> gizmo designs out there, esp. any that could be made to work using more 
> modern electronics (e.g. interface to a PC, use a scanner and existing 
> software?) in place of older commercial MTF testing gear...
> 
> thanks for any pointers or tips on above! bobm


From contax mailing list:
From: Paul van Walree odobenus@xs4all.nl
Subject: Re: [Contax] zoooms vrs primes.
Date: Wed, 23 Jan 2002 

"Austin Franklin" darkroom@ix.netcom.com wrote:
>> ... Anyway, I will ask
>> Zeiss.
>
>Fantastic!


Here is the reply of Dr. Hubert Nasse from Zeiss Oberkochen:
-----------------------------------------------------------

Dear Mr. van Walree,


the statement, that the second graph of our MTF-presentation (the lens
stopped down) is assumed to represent the f-stop with best overall
performance, is not strictly true. In many cases it is however correct,
because usually the second graph shows the performance stopped down by
two stops - and most lenses have reached the peak after two stops. There
are however exceptions: lenses with very high speed reach the peak
performance after 3-4 stops, some of the long focal lengths have best
performance nearly fully open.

I include a graph, which shows MTF as function of f-number for the
Planar 2.8/80 for Hasselblad:


You may be surprised about the fact, that the graph says, that at f/8
the sagittal performance at the edge is higher than in the centre. This
is simply due to the fact, that all our published MTF- measurements are
strictly made in one single image plane: the focus criterion for that
plane is the MTF maximum at 20 Lp/mm when the lens is fully open. When
the lens is stopped down, the image plane of peak MTF is usually shifted
a little bit; the amount of shift depends on the distance from the
centre. When the measurement at the edge of the frame happens to be just
in the best focus at f/8, but the centre measurement is note quite in
the best focus at f/8, then the centre performance seems to be inferior
to the edge performance. But in fact the peak MTF in the centre is
always higher than the peak MTF at the edge, they are just not in the
same plane.

In practical pictures you will however hardly see this effect. In our
words: because most photographed subjects are 3-dimensional and because
focusing with the camera always has some slight errors, including other
tolerances like film-to-screen alignment, film flatness etc. the lens
performance has actually to be described in a 3-dimensional way.

Just to keep the things simple, we publish 2-dimensional MTF-data, but
one has to aware of the fact, that these curves contain the described
simplification. The MTF-curve is not always what you see in the picture!


From contax mailing list:
From: Paul van Walree odobenus@xs4all.nl
Subject: Re: [Contax] On lens performance
Date: Wed, 23 Jan 2002 

"Alan Naylor" alan.naylor@skynet.be wrote:
>Do you know for a fact that your definition and Zeiss's are the same?

The only way to know for sure is to ask Zeiss:

>Dear Mr. Nasse,
>
>I hope you allow me two short questions.
>
>1. Is it correct that the values displayed in the Zeiss MTF charts
>correspond to the image contrast (Imax-Imin)/(Imax+Imin), where Imax is
>the maximum intensity measured in the image plane and Imin the minimum
>intensity? (I assume that the object contrast is 1.)

and while asking questions, I figured it might be a good idea to address
Oon's brain wave too:

>2. Is the MTF at 10 lp/mm a good indication of "the contrast" of a lens?
>What would an MTF curve for 1 lp/mm look like? Could it be significantly
>higher than the 10 lp/mm curve, or is the spatial frequency of 10 lp/mm
>already representative for the low end of the spectrum?

The answer of Dr. Hubert Nasse:

Dear Mr. van Walree,

short answers to your short questions:

1. Yes, your given formula is the MTF, if the assumed input contrast is
1. You have in addition to take into account, that this contrast
transfer refers to a sinusoidal intensity pattern of the object. When
the pattern is different, e.g. a square wave pattern like in most real
test plates, the contrast transfer for that pattern is different,
usually slightly higher than for sinus pattern.

MTF is usually measured for two different pattern orientations,
tangential and sagittal, according to the main symmetry axes of a lens.
Real lenses may deviate from perfect central symmetry, thus the two
measured orientations may not represent the best and worst MTF depending
on pattern orientation.

MTF depends on the spectrum of the light, and for some lenses where the
chromatic aberrations are dominating, a measurement (and as well
photography) in a more narrow spectral band results in quite different
MTF-curves. An example for that are the old Tele-Tessar lenses, which
have excellent monochromatic correction, and may be superior to a
complex Apo-lens is e.g. used in just green light.

Complete MTF has to be understood 3dimensional.


2. Yes, 10 Lp/mm corresponds somehow to the "contrast" of the image, or
in other words, to what you see from a distance. For this general
impression of an image viewed from a distance the even lower frequencies
are also important. (E.g. when you see a slide by naked eye, the
resolution limit of the eye is roughly 8 Lp/mm) The very low frequency
range is often the range where images with gentle softeners are most
different from the basic lens.

To judge the correction of a lens for low frequencies the 10 Lp/mm are
quite sufficient; you will not gain information from the lower
frequencies. And in addition the overall "contrast" is as well affected
by the false light which exists during normal picture taking. False
light influence is however not measured during MTF-measurement. This is
why MTF-measurement of much lower frequencies than 10Lp/mm makes no
sense in normal lenses.




From: "Duncan Murray" duncan.duncan@btinternet.com
Newsgroups: rec.photo.equipment.35mm
Subject: Re: Why is MF nikkor 50mm 1.8 so cheap?
Date: Sun, 14 Apr 2002


This thing about the Pentax 43mm f1.9 having a three-dimensional property is
really getting on my nerves.  As far as I know it was Pentax's all-out
effort at creating the best (sharpest, least distortion, max contrast, nice
bokeh, etc etc etc) standard lens.  However, looking at photodo's website, I
was really surprised to see it have such a low rating.  The 43mm was chosen
to mimic the exact same proportions (not perspective) of the human eye, so
would that be to do with the 3d effect?  However, I clicked on the MTF
graph, and if you look carefully, you can see why these average MTF's can be
very misleading, favouring the planar lens rather than one that has a curved
field of focus.  Looking at the graph, on the far left, you can see the
amazingly high MTF value at the centre of the frame, this is even higher
than the other lens I was comparing it with (50mm FA, 4.6(!)).  Then the
curve smoothly runs down (unlike many lens that represent a mountain-range)
to the bottom right.  Obviously Pentax were going the whole hog in mimicing
the eye, and were even giving the lens the curved focus fields that our eyes
have.  I really wander what the average MTF of this lens is when focused on
a curved screen, rather than a planar one they did the tests on.

Duncan.
....



From: handerle@klosterneuburg.net (Dr. Heinz Anderle)
Newsgroups: rec.photo.equipment.35mm
Subject: Re: Leica M lens tests URL followup was Re: Leica...Is It Worth It?
Date: Wed, 17 Apr 2002

Tony_Polson tp@nospam.com
...
>
>For the same reason, MTF test results are beloved of people such as
>yourself (and the writers on CdI, and the Photodo groupies on here).
>The MTF results appear to be objective and unquestionable.  Of course
>they aren't; they are both subjective and *highly* questionable.  In
>the absence of a standard, widely accepted method of designing a test
>regime, choosing what individual tests are appropriate and how the
>results of those tests should be interpreted, they are virtually
>worthless.
>

...
MTF tests alone are insufficient, because they don't measure
vignetting, distortion, color shift, or transmission. Also field
curvature is measured only indirectly. But in combination with all
these other data, the MTF curves give valuable information about the
optical imaging quality of a lens at infinity (of course not about
build quality and durability).


Zeiss is one of the few manufacturers providing data sheets for its
lenses. These show that also Zeiss lenses are made of ground and
polished spherical glass lenses, and that optical compromises have to
be made to design a lens useful in its entire f-stop range.

Photodo's MTF curves aren't difficult to understand - if you have
decreasing sagittal contrast with increasing distance from the center
at 40 lp/mm, you will get poor detail resolution e. g. for leaves or
twigs in landscape photographs.

MTF tests are of greater practical value than e. g. resolution tests
for film.



From minolta mailing list:
Date: Wed, 1 May 2002 
From: "Ze'ev Kantor" zeevk@bezeqint.net
Subject: Re: 28-85 higher MTF than 24-85!

The difference between the measured MTF values (84.533 - 84.050) is 0.493 ->
less than 1% !!! It is much less than the allowed production variations of same
lenses!! How can this make ANY VISIBLE affect on the image produced? With these
results - the 24-85 is clearly better lens, only because a greater zoom range.

Ze'ev Kantor
http://www.angelfire.com/art2/kantor_z

  ----- Original Message -----
  From: ca_creekin
  To: Minolta@yahoogroups.com
  Sent: Tuesday, April 30, 2002 
  Subject: [Minolta] 28-85 higher MTF than 24-85!


  According to the lens tests recently URLed here,
 http://www.par.univie.ac.at/~bob/photo/lenses/
  the 28-85/3.5-4.5 gets an average 84.533 MTF score
  versus 84.05 for the 24-85/3.5-4.5.

  The 28-85 is clearly sharper at the long end,
  while the 24-85 is a bit sharper at wide angle.

  So extrapolating, the Photodo.com score for the
  28-85 ought to be around 3.6!  The 28-70/2.8 G
  gets a 3.7 Photodo score, not much better.



[Ed. note: special thanks to Paul Van Walree and Dr. Nasse of Zeiss for sharing these resources!]
Date: Tue, 26 Mar 2002
From: Paul van Walree info@vanWalree.com
To: rmonagha@post.cis.smu.edu
Subject: Re: query: MS word optics docs by Mr. Nasse

Hi Bob,

>Greetings Paul,
>Do you still have the MSWORD optics docs by Dr. Nasse?
>Can I get a copy of them?

Yup, see the attachments and the accompanying emails from Dr. Nasse that
I included below.

....

Anyhow, I will send out mails to people who link to my old site when the new
site is prepared.

Regards,
Paul

To: odobenus odobenus@xs4all.nl
Subject: Antwort: Zeiss MTF
From: "Dr. Hubert Nasse" nasse@zeiss.de
Date: 08 Jan 2002 

Dear Mr. van Walree,

the statement, that the second graph of our MTF-presentation (the lens
stopped down) is assumed
to represent the f-stop with best overall performance, is not strictly true.
In many cases it is however correct,
because usually the second graph shows the performance stopped down by two
stops - and most lenses
have reached the peak after two stops. There are however exceptions: lenses
with very high speed reach the
peak performance after 3-4 stops, some of the long focal lengths have best
performance nearly fully open.

I include a graph, which shows MTF as function of f-number for the Planar
2.8/80 for Hasselblad:



You may be surprised about the fact, that the graph says, that at f/8 the
sagittal performance at the edge
is higher than in the centre. This is simply due to the fact, that all our
published MTF-measurements are strictly made
in one single image plane: the focus criterion for that plane is the MTF
maximum at 20 Lp/mm when the lens is fully open.
When the lens is stopped down, the image plane of peak MTF is usually
shifted a little bit; the amount of shift depends on the
distance from the centre. When the measurement at the edge of the frame
happens to be just in the best focus at f/8, but the
centre measurement is note quite in the best focus at f/8, then the centre
performance seems to be inferior to the edge performance.
But in fact the peak MTF in the centre is always higher than the peak MTF at
the edge, they are just not in the same plane.

In practical pictures you will however hardly see this effect. In our words:
because most photographed subjects are 3-dimensional
and because focusing with the camera always has some slight errors,
including other tolerances like film-to-screen alignment, film
flatness etc. the lens performance has actually to be described in a
3-dimensional way.

Just to keep the things simple, we publish 2-dimensional MTF-data, but one has to aware of the fact, that these curves contain
the described simplification. The MTF-curve is not always what you see in the picture !

[ MTF(k)P80.doc ]

To: odobenus odobenus@xs4all.nl
Subject: Antwort: Zeiss MTF
From: "Dr. Hubert Nasse" nasse@zeiss.de
Date: 22 Jan 2002 

Dear Mr. van Walree,

short answers to your short questions:

1. Yes, your given formula is the MTF, if the assumed input contrast is 1. You have in addition to take
into account, that this contrast transfer refers to a sinusoidal intensity pattern of the object. When the pattern
is different, e.g. a square wave pattern like in most real test plates, the contrast transfer for that pattern is different,
usually slightly higher than for sinus pattern.

MTF is usually measured for two different pattern orientations, tangential and sagittal, according to the main
symmetry axes of a lens. Real lenses may deviate from perfect central symmetry, thus the two measured orientians
may not represent the best and worst MTF depending on pattern orientation.

MTF depends on the spectrum of the light, and for some lenses where the chromatic aberrations are dominating,
a measurement (and as well photography) in amore narrow spectral band results in quite different MTF-curves.
An example for that are the old Tele-Tessar lenses, which have excellent monochromatic correction, and may be
superior to a complex Apo-lens is e.g. used in just green light.

Complete MTF has to be understood 3dimensional.


2. Yes, 10 Lp/mm corresponds somehow to the "contrast" of the image, or in other words, to what you see from a distance.
For this general impression of an image viewed from a distance the even lower frequencies are also important.
(E.g. when you see a slide by naked eye, the resolution limit of the eye is roughly 8 Lp/mm)
The very low frequency range is often the range where images with gentle softeners are most different from the basic lens.

To judge the correction of a lens for low frequencies the 10 Lp/mm are quite sufficient; you will not gain information from
the lower frequencies. And in addition the overall "contrast" is as well effected by the false light which exists during normal
picture taking. False light influence is however not measured during MTF-measurement. This is why MTF-measurement
of much lower frequencies than 10Lp/mm makes no sense in normal lenses.

To: odobenus odobenus@xs4all.nl
Subject: Antwort: Re: Antwort: Zeiss MTF
From: "Dr. Hubert Nasse" nasse@zeiss.de
Date: 23 Jan 2002 

Dear Mr. van Walree,

of course you may share my reply with other people who are interested in that matter.

According to common practice in the scientific world you should correctly refer to the
source of this information (quotation), if you use it in public.

By the way, please excuse the many misprints in my yesterday mail, which was
written in a hurry.

Let me complement my information by some illustrations about the meaning of MTF, referring
to the shape of the line image. You find this in the attached word-file:

[ linienbild-MTF.doc ]

With best regards

Dr. Hubert Nasse
Camera Lens Division, PH-LA
Tel. 07364/20-2846
Fax: 07364/20-3466
eMail: nasse@zeiss.de
www.zeiss.de/photo


From: Jean-David Beyer jdbeyer@exit109.com
Newsgroups: rec.photo.equipment.large-format
Subject: Re: Schneider lens
Date: Wed, 15 May 2002


Milburne Drysdale wrote:
>
> >Would a Schneider 300/9 G Claron or Rodenstock Apo Ronar 300/9 be a  good
> >sharp lens but with the German look?
>
> Verrrrry interrrrrrressssstinggg....
>
> The German look?  Vos ist das?

At one time, someone compared the modulation transfer function a
Germain lens (E.Leitz?) with a Japanese lens (Nikon?) of similar
aperture and focal length.

As I recall, the German lens had greater overall resolution, but it
started falling off sooner and slower although it went much higher.
The Japanese lens's mtf stayed quite high much longer than the German
lens did, but when it got to a certain point, it fell off very
sharply. IMO, the Japanese design was better because it got the area
under the mtf curve higher in the range where it most usually
mattered.

A professional photographer I once knew had a Nikon and a Leica with
lenses like that. She could easily tell which negative was made by
which lens just by looking at 11x14 prints, but I could not. I think
she could really tell and was not remembering which image was made on
which camera.

--
 .~.  Jean-David Beyer


From: dickburk@ix.netcom.com (Richard Knoppow)
Newsgroups: rec.photo.equipment.large-format
Subject: Re: Schneider lens
Date: Wed, 15 May 2002

... (quote above)

  I've heard the same thing. Its possible: the shape of the MTF curve
depends on the balance of higher order aberrations. A lens with high
midrange resolution may look sharper than one with greater actual
maximum resolution, an effect similar to acutance in film. The eye
tends to interpret high edge contrast as sharpness.

  Whether German and Japanese designers actually do this is another
matter. It would be interesting to know if there is any reliable data
on it.
---
Richard Knoppow
Los Angeles, CA, USA.
dickburk@ix.netcom.com


From: brianc1959@aol.com (brian)
Newsgroups: rec.photo.equipment.35mm
Subject: Re: Resolution threshold
Date: 19 May 2002 


> brian wrote:
> >
> > Also, I doubt that your Leica lens can resolve 650 line pairs in white
> > light, even on-axis.  The reason is that the lanthanum crown glass
> > commonly used in double-Gauss lenses increases the secondary spectrum.
> >  In order to approach the diffraction limit at f/2 you need
> > apochromatic performance, even in a 50mm lens.  If you go moderately
> > far off axis it is absolutely impossible.
>
> How about checking MTF(40 lpm) from photodo and then using the roll-off
> function
>
> MTF(f) = 1/(1+(f/flens)^2), where MTF(flens) = 0.5?

This equation will only be roughly correct occasionally.  For example,
it doesn't model a diffraction-limited MTF vs. frequency curve well at
all, which is much more linear.  I think it is probably better to get
a patent prescription and calculate the MTF with the appropriate
software.  This seems to work very well for most of the Japanese
lenses because the designs are well documented.  However, Leitz rarely
publishes anything worth analysing.

Brian


From: dickburk@ix.netcom.com (Richard Knoppow)
Newsgroups: rec.photo.equipment.large-format
Subject: Re: MTF and lp/mm
Date: Fri, 16 Aug 2002


"Bruce Wilson" b.e.wilson@usa.net wrote:
>Thanks, Richard, Michael, and Ralph for your insight.
>
>It seems the problem is a little too complex for meaningful simplification.
>I was hoping the errors from a simple single-figure evaluation of MTF were
>small enough to be ignored, but after studying some MTF curves I see the
>differences can be too large for estimation or simplification (for example,
>film MTF changes dramatically depending on contrast, lens MTF depends very
>much on aperture, and system MTF depends very very much on unquantifyable
>camera shake; and then there are resolution losses during enlargement or
>digital processing).
>I think maybe the best solution is, as Ralph suggested, dropping the
>sharpness tab from the applet.
>
>--
>Bruce Wilson
>http://chem.dynu.com/photo
>-
>"Richard Knoppow" dickburk@ix.netcom.com wrote
> Richard Knoppow
>> Los Angeles, CA, USA.
>> dickburk@ix.netcom.com

  Think of MTF as audio frequency curves. There is one for every bit
of equipment in the chain from pickup of the sound to reproduction.
Trying to use a single number for optical MTF is like trying to use
some high frequency limit as a single number to describe and evaluate
an audio system.

  In audio people are interested in the shape of the frequency
response curve. Two pieces of equipment or systems can have the same
high frequency cut off point (say where its 6db or 12db down) but have
widely varying behaviour below that. Something analogous happens in
optical systems. Usually, the resolution limit is given, but this is
simply where the contrast falls off to some prescribed value. Its well
known that an image with relativly low resolution but high edge
contrast will look sharper to the eye than one with considerably
higher resolution but lower contrast. The analogous situation in audio
would to compare, say two loudspeakers. One has a flat response to
perhaps 10Khz but falls like a brick above that. The other has a slow
roll off so it may be down 6db at 10 Khz but continues out to, say
25Khz before the output really drops. In fact, the first will sound
"brighter" and appear to have more treble, although it will not
reproduce transients well.

  Even trying to specify the high end cut off of an audio system
requires combining the values of the various responses.

  We also have the fact that the overall response of either a sound
system or a photographic system is going to be no better than the
worst component.

  I don't discuss audio much any more since my hearing is no longer
good enough to evaluate components. A very great frustration.

---
Richard Knoppow
Los Angeles, CA, USA.
dickburk@ix.netcom.com


From: brianc1959@aol.com (brian)
Newsgroups: rec.photo.equipment.medium-format
Subject: Re: Is Zeiss batch testing lenses?
Date: 1 Nov 2002 

...(query about batch lens testing..)

Hi Bob:
I have no idea what Zeiss does with their photographic lenses, but I
do challenge the notion that 100% testing is rare and expensive.  I
once toured a factory in China in which small scanner lenses were 100%
MTF tested using some fairly clever and economical equipment.  I think
that for this application is was critical that the lenses actually
come very close to the design performance.  It took only about 10
seconds to completely evaluate each lens.  Mind you, these lenses
undoubtedly cost less than $10!

Another tidbit;  on page 213 of "Eyes of Nikon" (a Nikon publication
from 1985), there is the following quote:
"As an additional benefit, MTF testing is incredibly fast (individual
testing takes only 6 seconds!), so every single Nikkor or Nikon Series
E lens coming off the production line can be tested."

Brian
www.caldwellphotographic.com


From: tls@panix.com (Thor Lancelot Simon)
Newsgroups: rec.photo.equipment.large-format
Subject: Re: testing a new (to me) lens leads to questions
Date: 22 Nov 2002

Hemi4268  wrote:
>Hi
>
>It really has to do with resolution which is measured in lines per millmeter
>much like the digital people use dots per inch.

That's not actually true.  What really matters is the modulation transfer
function (MTF) of the lens and the rest of the system used to reproduce
the image.  Because the negative is so much larger in a 4x5 camera, lots
of interesting detail in most subjects will fall much nearer the peak of
the lens' MTF curve and be more accurately reproduced, even when compared
to a small-format system with much higher maximum resolution.

--
 Thor Lancelot Simon 


From manual SLR Mailing list:
Date: Fri, 23 May 2003 
From: Peter Svensson petersven@yahoo.com
Subject: RE: RE: Miranda cameras


Actually, both "sharpness" and "contrast" can be expressed in terms of
the Modulation Transfer Function, or MTF, and measured by equipment.
Lens "contrast" is its ability to transfer the contrast of the subject's
larger features to film, while "sharpness" is contrast transfer of finer
details.
...



From: fcarello@tiscalinet.it (Fernando)
Newsgroups: rec.photo.equipment.medium-format
Subject: Re: only 6x8" prints from 645? Re: Are used MF...
Date: 6 Jun 2003 

rmonagha@engr.smu.edu (Bob Monaghan) wrote 
> So you are saying that a medium format 645 camera is only delivering 25.7
> lpmm on film at best? You think this has to be the film, not your scanner?

Bob, you're stretching math to your goals here. ;)

Let's talk seriously, let's talk MTF.

We all have access to a good bunch of MTF charts (photodo etc.).
So let's compare EOS 1Ds with a normal lens (Canon 50/1.4 USM), and a
Contax 645 with a normal lens (Zeiss Planar 80/2).
The 645 will shoot on Provia 100F, and its slides will be acquired by
a Nikon 8000ED.

Let's see what happens at 40 lp/mm.

MTF of the DSLR system:

Lens = 0.63
CCD = 0.90 (assumed as a worst-case figure, given that at 55 lp/mm,
the Nyquist frequency for the 1Ds, strong Moir‚ occurs if you remove
the anti-aliasing filter)

Final MTF at 40 lp/mm = 0.63*0.9 = 0.57


MTF of the 645 + scanner system:

Lens = 0.51
Film = 0.60 (from http://www.fujifilm.com/JSP/fuji/epartners/bin/Provia100f.pdf)
Scanner = 0.80 (maybe optimistic: from various published tests, scans
of targets reveal a good bunch of contrast loss even at lower target
resolutions. Let's say we carefully USM here)

Final MTF at 40lp/mm = 0.51*0.6*0.8 = 0.24

So, while it's true that for example I can go as far as 78 lp/mm with
645 gear + a good film scanner (which I cannot with a 1Ds), pratically
I get very little *actually useable* details there. Unless you like to
enlarge/print grain, that is.

While, digital shots will retain very strong details and clariness up
to the Nyquist frequency. :)

Actually, I found that in practical real-world shots, my 645 gear
(w/Provia 100F) is capable of about 14 MP of actually-useable
resolution.

Please note, that I'm very actively using 645 and 6x6 film-only gears,
and don't plan switching to DSLRs until a 20MP camera would drop under
$1000 (two-three years from now?), so I'm not a "digiuser". :)
I'm a (very happy, for instance) traditional and, I think, quite
unbiased amateur photographer.

Greetings!

Fernando


From: "Bart van der Wolf" bvdwolf@nospam.nl
Newsgroups: rec.photo.equipment.medium-format
Subject: Re: Photodo site
Date: Sun, 6 Jul 2003 

"bowser" fuged@bout.it wrote...
> Photodo, AKA Photopoo, tests a single sample at infinity under controlled
> conditions. This tell you nothing about what will actually appear on film
> when you use the lens at various focal lengths, while mounted on a camera,

Wouldn't it be wonderful having the lens tested at 3.17 meters subject
distance, if that happens to be your most used distance? The camera changing
the optical performance, how?

> under varied lighting conditions,

Yeah, studio lighting (which variety?), outdoors (what % cloud cover?)

> and after the lens has been used for a while.

Your camera bag or mine?

> It also doesn't address distortion,

Distortion is mentioned on the site you try to avoid.

> color, or other anomolies, like flare.

Propose an unambiguous test...

> And then there's build quality. Will the lens perform the same in six
> months? What about dust and environmental sealing?

Propose an unambiguous test...

> However, if you shoot photos of black bars on white backgrounds at infinity
> under controleld conditions, Photodo is the single resource you can rely on.

I see, the distinction between testing for limiting resolution and MTF got
lost somewhere in an attempt to, declare field testing holy, or what IS the
purpose of the comments?

MTF testing (amongst others) is a common way of testing and quantifying
optical elements and systems. It recognizes the importance of detail
contrast for the human perception of sharpness. It doesn't tell the whole
story, but just an important part of it. Nobody claims it is the only
criterium, nor is the importance of it the same for everybody. Photodo
happens to be one of the few resources that offers MTFs. It is up to the
reader to interpret the offered information.

Bart


From: bhilton665@aol.comedy (Bill Hilton)
Newsgroups: rec.photo.equipment.35mm
Date: 30 Aug 2003 
Subject: Re: What are MTF ratings?

>Looking at lenses and find there are MTF ratings, such as on Photodo.
>What do the numbers mean? ... Other info would be helpful.


These sites explain it

http://luminous-landscape.com/tutorials/understanding-series/understanding-mtf.shtml

http://www.normankoren.com/Tutorials/MTF1A.html

Bill



From: Kennedy McEwen rkm@nospam.demon.co.uk
Newsgroups: alt.comp.periphs.scanner,rec.photo.equipment.35mm,rec.photo.equipment.medium-format
Subject: Re: how much resolution do we need (was Re: New Nikon Coolscan 9000ED)
Date: Sat, 15 Nov 2003 

David Littlewood david@nospam.demon.co.uk writes
>
>People sometimes say "how can I possibly see the difference between 5
>lp/mm and 10 lp/mm at normal viewing difference?". Well, you just can.

This is one of the examples where the difference between limiting
resolution and MTF comes into its own. The typical human eye can
resolve no ore than 7.5cy/mm at the normal close viewing distance of 10"
(25.4cm). So the obvious conclusion of the novice is that if I have an
image with a limiting resolution of 8cy/mm then nobody will be able to
tell the difference between that and anything with more resolution. As
David notes, it's actually very easy, but it is not the limiting
resolution of the image on the retina that makes the difference, its the
contrast of the relatively well resolved information.

A typical lens diffraction limited MTF curve is similar to a triangle
plot - starting at 100% MTF at 0cy/mm and falling almost linearly to 0%
at the limiting resolution. A reasonable assumption is the final system
resolution will be similar - not identical but of the same general form.
So, whilst the human eye can't tell the difference at its limiting
resolution of 7.5cy/mm between a print with 8cy/mm and 15cy/mm limiting
resolution, there is twice as much contrast in the latter at the spatial
frequencies that the eye can resolve. For example, at 4cy/mm the lower
resolution print has 50% MTF (ie, fine detail is reproduced at 50% of
the original contrast) whilst the high resolution print has 75% MTF -
50% more contrast at the same level of resolved detail.

If you then took a print from a 4x5" film at the same size, I would
guess that the limiting resolution would be above 30cy/mm and the MTF of
the eye resolved information at 4cy/mm would be around 85% MTF. Again,
significantly better (70%) than the low resolution print but only
marginally better (13%) than the high resolution sample.

This comparison between two sources which both exceed the limiting
resolution of the eye demonstrates clearly that limiting resolution
(which is all the marketing and sales people eve talk about) is only a
very small component of the image quality equation.

--
Kennedy



From: brianc1959@aol.com (brian) 
Newsgroups: rec.photo.equipment.35mm 
Subject: Re: Older Leica lenses better? 
Date: 30 Aug 2003

Mxsmanic mxsmanic@hotmail.com wrote
> An ideal lens, in other words, will always transmit 100% of the original contrast 

An ideal lens has a Strehl ratio of 1.0, and such a lens *will not* 
have an MTF of 100% for all spatial frequencies unless it has an 
infinitely large aperture. 

> The contrast of a lens may vary 
> with the contrast of an original scene; it might be 99% of a 
> low-contrast scene, but only 20% of a high-contrast scene. 
The MTF of a lens depends on spatial frequency, not scene contrast. 

Brian 
www.caldwellphotographic.com 



From: brianc1959@aol.com (brian) 
Newsgroups: rec.photo.equipment.35mm 
Subject: Re: Leica answers 
Date: 14 Sep 2003 

Mxsmanic mxsmanic@hotmail.com wrote
> Q.G. de Bakker writes: 
> 
> > You can have high resolution, but very low contrast, 
> > and vice versa. 
> 
> No, you cannot. Contrast is never fixed at all resolutions; it drops at 
> high resolutions. It follows, then, that the higher the contrast, the 
> lower the maximum usable resolution of the lens. 
> 
> > The thing to have is a high contrast at high resolutions. 
> 
> If you don't have a high contrast at low resolution, you'll never have 
> it at high resolution. And since "resolution" is nothing more than 
> contrast to begin with, low contrast at resolution x simply means that 
> resolution x isn't there. 

You may not be aware that contrast does not always drop steadily as 
the spatial frequency increases. Sometimes it can drop to a low 
value, and then actually increase at higher frequencies, and without 
any phase reversals either. 

By the way, there are at least two ways you can achieve almost 
arbitrarily low contrast at low freqencies while maintaining extremely 
high resolution - without resorting to simple defocus which will 
result in spurious resolution (phase reversals). Can you describe 
them? 

Brian 
www.caldwell



From: Mxsmanic mxsmanic@hotmail.com
Newsgroups: rec.photo.equipment.35mm 
Subject: Re: Leica answers 
Date: Sun, 14 Sep 2003 

Q.G. de Bakker writes: 
> You can have high resolution, but very low contrast, 
> and vice versa. 

No, you cannot. Contrast is never fixed at all resolutions; it drops at 
high resolutions. It follows, then, that the higher the contrast, the 
lower the maximum usable resolution of the lens. 

> The thing to have is a high contrast at high resolutions. 

If you don't have a high contrast at low resolution, you'll never have 
it at high resolution. And since "resolution" is nothing more than 
contrast to begin with, low contrast at resolution x simply means that 
resolution x isn't there. 



From: "jriegle" jriegle@att.net 
Newsgroups: rec.photo.equipment.35mm 
Subject: Re: Leica answers 
Date: Sat, 13 Sep 2003

...
> You can have high resolution, but very low contrast, and vice versa. That's 
> not difficult, nor uncommon, at all. 
> The thing to have is a high contrast at high resolutions. 

So true. Without each being high on a given lens would mean the MTF 
(modulation transfer function) score would suffer. 
Check this out: 

http://home.att.net/~jriegle/viv19mm.htm 

This is an example of a lens with okay sharpness and terrible contrast wide 
open. Lenses like this will look soft or hazy soft depending on the subject 
and/or film. 

John 




From: "Q.G. de Bakker" qnu@tiscali.nl
Newsgroups: rec.photo.equipment.35mm 
Subject: Re: Leica answers 
Date: Sun, 14 Sep 2003 


Mxsmanic wrote: 
> > Msx, you can protest all you want, you're statement 
> > "You can't have high resolution with low contrast" 
> > is pure nonsense. 
> 
> How do you normally measure contrast and resolution in a lens? 

I don't. That's because i don't have the equipment necessary. ;-) 
Resolution and contrast produced by a lens can be (and are) plotted as a 
curve. A curve that shows how a test pattern presented to a lens (a high 
contrast line pattern) is rendered by the lens. 

And this curve generally will have a sinoidal form, the peak and troughs 
representing the black and white lines in that high contrast subject, the 
frequency representing the spatial separation of the subject (line pattern). 
(Ideally, the curve would be a block-wave, not a sinoid. But ideal lenses 
only exist in ideal worlds). 

Resolution is the ability to render a given pattern such that a distinct 
patern is visible in the image too: there must be peaks and troughs. 
Contrast is the magnitude of this sine-wave curve, of these peaks and 
troughs, the difference in brightness between what in a 100% rendition 
should be white or black. 

It is in no way impossible to have two different lenses produce curves that 
at the same frequency, same resolution, show different magnitudes, different 
contrast. And vice versa. 

Since you say you have studied that MTF thingy, you should know that.


From: Kennedy McEwen rkm@nospam.demon.co.uk
Newsgroups: alt.comp.periphs.scanner,rec.photo.equipment.35mm,rec.photo.equipment.medium-format
Subject: Re: how much resolution do we need (was Re: New Nikon Coolscan 9000ED)
Date: Sat, 15 Nov 2003 

jjs nospam@nospam.xxx writes
> David Littlewood david@nospam.demon.co.uk wrote:
>
>> Total resolution = 1/(1/resA^2 + 1/resB^2 + 1/resC^2 ... etc.)^0.5
>>
>> Just like Pythagoras' theorem for the hypotenuse of a right angled
>> triangle, only in n dimensions.
>
>Oh yeah! Now I remember. Good old Pythagoras. One hell of a photograher.
>
>Okay, seriously. That's one very trick algorithm. So a negative having 80
>lp/mm enlarged through a lens that does 80 lp/mm and with no other factors
>(my perfect Focomat :)) theoretically produces 56.57 lp/mm. Then we add in
>the enlargement factor, right? How do I plug that in?

Be careful, David's equation is very much a "rule-of-thumb" rather than
an absolute, and it certainly can't be applied over more that a couple
of steps, and sometimes not even that.

To undertake a proper estimate of resolution you need to have the MTF
curves for the camera lens, film, enlarger lens and photographic paper.
The curves should then be scaled to the same spatial frequency range,
taking account of the magnification at the enlarger, and then multiplied
point by point. It is more difficult to describe than to do.

The result is an overall system MTF, which can be used to determine how
the contrast of the original scene is reproduced on the final image and
compared to the noise, or total granular contrast. Where the MTF curve
crosses the granular contrast is the limiting resolution of the system.

If you try this you will see immediately why the above equation is only
indicative at best - it all depends on how steeply the MTF curves of the
components are falling off. Film, in particular, is often a source of
error, with MTFs which are distorted by the emulsion swelling during
development, resulting in a curve which can be very flat up to a spatial
frequency where it plummets. Similarly, practical aberrations in optics
often reduce the MTF at low spatial frequencies were it stays flat until
eventually being reduced by diffraction limits. Both of these issues
cause the approximation to depart significantly from practice.
--
Kennedy


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