What exactly is MTF?

[Joofa]

I'm sorry, while I can mistakes any time, I tend to think that I didn't make one here.

It is not just a mistake, it is lack of knowledge. ... but you lack the background for that.

Ha, you have very little idea about my background. Just your assumptions.

You seem to have a tendency to argue.

It takes two to argue.

No just look around your history on this forum. Multiple people have issues with you.

Show me authors who talk about self-adjoint operators and LSI systems.

Ha, you taunt others and have done little literature reading. Please have a look at O'Neill's book on Optics for e.g.

BTW I just gave the above reference because of a connection with Optics. Otherwise electrical engineering system theory is full of differential equations and differential operators that describe them. Hard to believe that you don't know that.

you made an implicit choice: L^2. Then you have a problem, those complex exponentials do not belong there.

Here is your problem stated below.

We are talking about cosinusoids after all they are so import to MTFs and Fourier Transforms. But, then as I'm sure you know that the Fourier Transform of even a cos / sin function doesn't directly exist due to integrability issues! So we are doomed from the start.

Another example is while MTF is being thrown around so frequently on this forum including this thread and myself, but the technically the system MTF of an imaging system does not even exist. The pixel response is not shift invariant, for e.g.

However, such issues are either mathematical curiosities, or there are ways of dealing around them, or can be swept under the rug without making much difference to practical results.

And, this is what you are doing here. Just nitpicking on mathematical curiosities that have little to do anything at all with MTF.

--
Dj Joofa
http://www.djjoofa.com

 

[Jack Hogan]

technoid wrote: Since you guys have a EE background, here's what I use for MTF...

OK technoid, I'll bite. Taking a capture of this with a digital camera and good technique produces a fairly accurate estimate of the system's MTF curve.

Where's the MTF you get out of you guys' process?

I get, and wanted, 7 points, not a curve. For instance, at 10,20,30,40,50,60,70 l/mm. These have the advantage of being pretty accurate because they are averaged over many horizontal lines, all the same but at the cost of not having a continuous MTF. The results from corner targets with were then used, with another process, to determine the image plane alignment accuracy.

Ok, mount a prime lens on your camera, capture your pattern and share MTF at those spatial frequencies.

Jack

 

[technoid]

technoid wrote: Since you guys have a EE background, here's what I use for MTF...

OK technoid, I'll bite. Taking a capture of this with a digital camera and good technique produces a fairly accurate estimate of the system's MTF curve.

Where's the MTF you get out of you guys' process?

I get, and wanted, 7 points, not a curve. For instance, at 10,20,30,40,50,60,70 l/mm. These have the advantage of being pretty accurate because they are averaged over many horizontal lines, all the same but at the cost of not having a continuous MTF. The results from corner targets with were then used, with another process, to determine the image plane alignment accuracy.

Ok, mount a prime lens on your camera, capture your pattern and share MTF at those spatial frequencies.

Jack

Nothing on my system now from back when I did that but more recently I used a modification of the concept to look at the impact of MLU and shutter vibration on the effective MTF. It uses the same pattern but in a circular configuration. Not as noise free because you pretty much have to use a single radial but still useful.

Loading…

www.dpreview.com

Do you have a specific question about it? Should be pretty obvious what the advantages are for determining 7, equally spaced responses accurately. It does require a decently profiled printer and calibration. There is some residual error in the printer as they are not perfectly linear. It shows up as small variations in the amplitude of the 7 spectral peaks and low level harmonic components beyond Nyquist. These are specific to each target.

 

[Jack Hogan]

technoid wrote: Since you guys have a EE background, here's what I use for MTF...

OK technoid, I'll bite. Taking a capture of this with a digital camera and good technique produces a fairly accurate estimate of the system's MTF curve.

Where's the MTF you get out of you guys' process?

I get, and wanted, 7 points, not a curve. For instance, at 10,20,30,40,50,60,70 l/mm. These have the advantage of being pretty accurate because they are averaged over many horizontal lines, all the same but at the cost of not having a continuous MTF. The results from corner targets with were then used, with another process, to determine the image plane alignment accuracy.

Ok, mount a prime lens on your camera, capture your pattern and share MTF at those spatial frequencies.

Jack

Nothing on my system now from back when I did that but more recently I used a modification of the concept to look at the impact of MLU and shutter vibration on the effective MTF. It uses the same pattern but in a circular configuration. Not as noise free because you pretty much have to use a single radial but still useful.

https://www.dpreview.com/forums/post/56681755

Do you have a specific question about it? Should be pretty obvious what the advantages are for determining 7, equally spaced responses accurately. It does require a decently profiled printer and calibration. There is some residual error in the printer as they are not perfectly linear. It shows up as small variations in the amplitude of the 7 spectral peaks and low level harmonic components beyond Nyquist. These are specific to each target.

No questions for now, I am just curious whether in practice it has any merit. For that we need to see MTF values.

Jack

 

[AiryDiscus]

Some recent threads and messages have explored the notion of MTF. It appears to me that there exists a confusion in many people minds regarding what exactly is an MTF - the celebrated Modulation Transfer Function. For e.g., see the threads below that have many misleading statements, IMHO:

https://www.dpreview.com/forums/post/59557798

https://www.dpreview.com/forums/post/59563398

https://www.dpreview.com/forums/post/59563735

https://www.dpreview.com/forums/post/59619529

Before proceeding, I must say that the optics community is responsible for part of the confusion.

You're an ass.

By instituting terms such as MTF, which depends upon a certain notion of contrast , sometimes confusingly called modulation contrast (more on it below), and the use of another function called CTF, Contrast Transfer Function, (more on it below also), which is different from MTF. Though they share the words 'modulation' and 'contrast' respectively, and also use the same definition of measuring contrast!

What I write below comes from my memory as an undergrad in electrical engineering a long time ago, so please pardon me for some small technical mistakes or being not very rigorous due to a fact that I don't recall many details now as I haven't dealt with these things regularly for a long time. However, the following shall provide a right template or outline for understanding MTF.

Electrical System Theory:

These is no need to pretense Linear system theory as Electrical system theory.

• A linear shift invariant system (lets call it LSI) has an output that is related to input via a convolution. That is a very important theorem in linear systems.
• That convolution kernel is called impulse response. An LSI system is completely described by its impulse response.
• The collection of the ratio of the Fourier response of the output of an LSI system at each discrete frequency to the corresponding input frequency is called The Transfer Function.
• This transfer function can be shown to be the Fourier transform of the impulse response.
• Complex Exponential Signals are eigenfunctions of an LSI system. When they pass through a LSI the output is still a complex exponential signal but modified by an eigenvalue, which in general is a complex number. This collection of eigenvalues provides a certain transfer function.
• This transfer function can be shown to be the same as the Fourier transfer function mentioned above.
• For a very important class of LSI systems that have a real impulse response, the co-sinusoidal functions are also eigenfunctions.
• With this special LSI system a cosinusodial input yields a cosinusoidal output, possibly shifted in phase and attenuated. This system transforms a real-valued input to a real-valued output.
• The above is also related to the desire to having a linear operator involving the system as hermitian (or self adjoint) - though lets not get into the details of when hermitian and self adjoint are not the same things. That is only for mathematical curiosity. Also fans of Quantum Mechanics would get a kick out of this as such operators yield real eigenvalues that are observable. But lets not invite that delusional bunch here.
• The Fourier transfer function for LSI systems describes all of this.

You've introduced a new term without defining it.

Optics:

• In Optics a transfer function is commonly used that relates the input and output via their modulation contrast.
• This transfer function, which is called the MTF, is real, as contrast by that definition is real, and so it is a ratio of reals.
• With the application of this transfer function a cosinusodial input yields a cosinusoidal output, possibly attenuated.
• It can be shown that this MTF is the magnitude part of the Fourier transfer function that we found in system theory above.

You forgot to normalize.

• The impulse response is now called Point Spread Function, PSF.

The impulse response is still the impulse response - it describes the response of an optical system to an impulse electrical field. What is observed is typically intensity, power, or brightness -- all terms for the same thing -- which is the product of the optical field and its complex conjugate. For an LSI system, this is also equal to abs()^2 of the field.

• In optics, typically not all impulse responses are called PSFs. Only those that produce observable outputs, and relates physical or real inputs and outputs.

I do not believe any of this is correct.

• Hence, the importance of transfer functions that are hermitian and / or the importance of self adjoint operators.

Takeaway:

• MTF is the response of the system to a cosinusoidal input.

You must normalize.

• And, is the magnitude of the transfer function, which is the Fourier transform of the impulse response.
• Or equivalently, MTF is the ratio of output and input modulation contrast of a cosinusoid.

MTF and CTF:

• A contrast transfer function or CTF is the response of the system to a square wave input, but otherwise measured with the same definition of contrast as the MTF.
• CTF yields values that are different from MTF, as can been seen easily by decomposing a square wave into Fourier components and applying MTF to each individually and adding up.
• There exists a relationship between MTF and CTF.

--
Dj Joofa
http://www.djjoofa.com

 

[AiryDiscus]

Thanks Joofa, that's a nice summary.

There is a question that's been nagging at me for while: in the past knowledgeable folks (perhaps you) corrected my assumption that in digital imaging a one-dimensional MTF curve (say obtained through the slanted edge method from the FT of an LSF) be symmetrical about the origin. But why would it not be - given the fact that the input (LSF) is real, so its Fourier Transform should be conjugate symmetric about the origin, hence its spectrum as well?

Jack

What origin? MTF/OTF is always symmetric about the origin in frequency space. In object/image space, it will be for a truly rotationally symmetric system, which you will rarely observe for a real, assembled system.

 

[Joofa]

You're an ass.

No problem.

As far as the technical content of the rest of your post, I can only say what optics expert doesn't even know their MTFs properly?

 

[AiryDiscus]

You're an ass.

Listen, I just tried to google search you and it appears that you are undergrad at some univ. I don't know if you are doing an undergrad later in life or are really young and juvenile, but you have a habit of insulting people without reason, instead of responding to content.

Just recently you insulted Prof. Hank Dietz, who is a senior Prof., here:

https://www.dpreview.com/forums/post/59554891

I would assume you just don't have enough practical experience in industry. I must tell you this is a very small world, these flippant comments that you make come to bite you professionally. I hope that you take that as an advice.

As far as the technical content of the rest of your post, I can only say what optics expert doesn't even know their MTFs properly?

I am well aware that you are a maths professor, and that Prof Hank D. is a professor (ECE? I do not know of what exactly, but not of optics).

Being a professor is not a carte-blanche "I am right" card. Several "optical" elements of your post are incorrect or critically omitted - see my post - and several "mathematical" elements are incorrect or omitted - see someone else's post - no amount of speaking down on the optics industry, or me personally will change that.

If you want to read my resume, you are free to do so here: http://www.retrorefractions.com/public/documents/bdube-resume-spring17-02.pdf

Since it was last updated, I have accepted an offer to work on the EECams that will fly on the 2020 rover @ JPL, and received the inaugural Kevin P. Thompson prize.

I have also released an open source matlab module that allows the computation of the PSF (and MTF) from arbitrary aberrations and arbitrary system parameters (efl, fno, wavelength, etc) - https://github.com/brandondube/AberrationSwissArmyKnife

I invite you, and anyone else reading these comments to judge each of us at our merits and not our titles. You frequently belittle the entire optics industry, do not be surprised if members of it respond in kind.

 

[J A C S]

It is not just a mistake, it is lack of knowledge. ... but you lack the background for that.

Ha, you have very little idea about my background. Just your assumptions.

My idea comes from your posts.

You seem to have a tendency to argue.

It takes two to argue.

No just look around your history on this forum. Multiple people have issues with you.

Show me authors who talk about self-adjoint operators and LSI systems.

Ha, you taunt others and have done little literature reading. Please have a look at O'Neill's book on Optics for e.g.

BTW I just gave the above reference because of a connection with Optics. Otherwise electrical engineering system theory is full of differential equations and differential operators that describe them. Hard to believe that you don't know that.

So, no reference? A whole book is a dishonest attempt to pretend that you did provide one.

you made an implicit choice: L^2. Then you have a problem, those complex exponentials do not belong there.

Here is your problem stated below.

We are talking about cosinusoids after all they are so import to MTFs and Fourier Transforms. But, then as I'm sure you know that the Fourier Transform of even a cos / sin function doesn't directly exist due to integrability issues! So we are doomed from the start.

We are not doomed because there is a well developed theory. You are dodging the question though - eigenvectors/eigenfunctions must belong to your space, and they do not. As I said earlier, there is a term for them but you refuse to listen.

Another example is while MTF is being thrown around so frequently on this forum including this thread and myself, but the technically the system MTF of an imaging system does not even exist. The pixel response is not shift invariant, for e.g.

We have discussed that a lot, and if I remember well, you resisted what I told you then. I am happy to se however that you learned something even though you pretend that you knew it all that time and I did not.

However, such issues are either mathematical curiosities, or there are ways of dealing around them, or can be swept under the rug without making much difference to practical results.

Another way to say that you have no clear idea what is going one but if it "works", you do not care.

And, this is what you are doing here. Just nitpicking on mathematical curiosities that have little to do anything at all with MTF.

Here is how this discussion could have went in an alternative universe:

Me: the complex exponentials are not eigenfunctions because they do not belong to L^2.

You: I can see your point but we still call them eigenfunctions in optics.

Is it that hard?

 

[Joofa]

You're an ass.

I am well aware that you are a maths professor,

I'm just a poor engineer. More software these days than hardware.

and that Prof Hank D. is a professor (ECE? I do not know of what exactly, but not of optics).

How about a Google search???

I invite you, and anyone else reading these comments to judge each of us at our merits and not our titles.

Right, that is why you started off with that comment above?

You frequently belittle the entire optics industry, do not be surprised if members of it respond in kind.

Which optics person have I personally insulted? Making technical comments on a group regarding their work as a whole is a different matter. And, even in that case when I have "frequently" belittled the optics industry?

--
Dj Joofa
http://www.djjoofa.com

 

[J A C S]

I am well aware that you are a maths professor, [...]

He is not.

 

[AiryDiscus]

I am well aware that you are a maths professor, [...]

He is not.

Are you the maths prof? I know it's one of the Js. My apologies if I have confused you.

 

[Joofa]

It is not just a mistake, it is lack of knowledge. ... but you lack the background for that.

Ha, you have very little idea about my background. Just your assumptions.

My idea comes from your posts.

No, you still have little idea.

You seem to have a tendency to argue.

It takes two to argue.

No just look around your history on this forum. Multiple people have issues with you.

Show me authors who talk about self-adjoint operators and LSI systems.

Ha, you taunt others and have done little literature reading. Please have a look at O'Neill's book on Optics for e.g.

BTW I just gave the above reference because of a connection with Optics. Otherwise electrical engineering system theory is full of differential equations and differential operators that describe them. Hard to believe that you don't know that.

So, no reference? A whole book is a dishonest attempt to pretend that you did provide one.

Ha, I really don't know how to respond to you here? Goal posts keep on moving. Now a book is not a reference. What next?

you made an implicit choice: L^2. Then you have a problem, those complex exponentials do not belong there.

Here is your problem stated below.

We are talking about cosinusoids after all they are so import to MTFs and Fourier Transforms. But, then as I'm sure you know that the Fourier Transform of even a cos / sin function doesn't directly exist due to integrability issues! So we are doomed from the start.

We are not doomed because there is a well developed theory. You are dodging the question though - eigenvectors/eigenfunctions must belong to your space, and they do not. As I said earlier, there is a term for them but you refuse to listen.

Man, what are you talking about? I just mentioned that the basic building blocks of a Fourier transform (viz. sin / cos functions) have certain issues in L2. Do sin / cos belong to L2 (R)? And, you just say that there is a theory to tackle that. That is what I'm saying many of these mathematical curiosities that you are interested in, and some of the difficulties they present, may be dealt with in one way or the other.

And, just for your reference, L2 space is almost universally used in electrical engineering, whether stated or not. Only when other spaces are explicitly involved they are stated so. So with this in mind that L2 is always lurking behind in electrical engineering, it is still claimed that exponentials are eigenfunctions of an LSI system.

Another example is while MTF is being thrown around so frequently on this forum including this thread and myself, but the technically the system MTF of an imaging system does not even exist. The pixel response is not shift invariant, for e.g.

We have discussed that a lot, and if I remember well, you resisted what I told you then.

I am happy to se however that you learned something even though you pretend that you knew it all that time and I did not.

Ha, I don't remember that. You have a lot of impressions of your grandeur.

However, such issues are either mathematical curiosities, or there are ways of dealing around them, or can be swept under the rug without making much difference to practical results.

Another way to say that you have no clear idea what is going one but if it "works", you do not care.

Isn't that what Dirac did with his delta function. . In any case, you can continue to believe that. I don't need any certificate from you.

--
Dj Joofa
http://www.djjoofa.com

 

[J A C S]

I am well aware that you are a maths professor, [...]

He is not.

Are you the maths prof?

Yes.

 

[J A C S]

It is not just a mistake, it is lack of knowledge. ... but you lack the background for that.

Ha, you have very little idea about my background. Just your assumptions.

My idea comes from your posts.

No, you still have little idea.

I do (know what you do not know).

You seem to have a tendency to argue.

It takes two to argue.

No just look around your history on this forum. Multiple people have issues with you.

Show me authors who talk about self-adjoint operators and LSI systems.

Ha, you taunt others and have done little literature reading. Please have a look at O'Neill's book on Optics for e.g.

BTW I just gave the above reference because of a connection with Optics. Otherwise electrical engineering system theory is full of differential equations and differential operators that describe them. Hard to believe that you don't know that.

So, no reference? A whole book is a dishonest attempt to pretend that you did provide one.

Ha, I really don't know how to respond to you here? Goal posts keep on moving. Now a book is not a reference. What next?

you made an implicit choice: L^2. Then you have a problem, those complex exponentials do not belong there.

Here is your problem stated below.

We are talking about cosinusoids after all they are so import to MTFs and Fourier Transforms. But, then as I'm sure you know that the Fourier Transform of even a cos / sin function doesn't directly exist due to integrability issues! So we are doomed from the start.

We are not doomed because there is a well developed theory. You are dodging the question though - eigenvectors/eigenfunctions must belong to your space, and they do not. As I said earlier, there is a term for them but you refuse to listen.

Man, what are you talking about? I just mentioned that the basic building blocks of a Fourier transform (viz. sin / cos functions) have certain issues in L2. Do sin / cos belong to L2 (R)? And, you just say that there is a theory to tackle that. That is what I'm saying many of these mathematical curiosities that you are interested in, and some of the difficulties they present, may be dealt with in one way or the other.

So now you are the one who says that they do not belong to L^2? This is funny. Do you even remember what you are arguing about? I am not talking about difficulties, I am saying that there are not eigenfunctions.

And, just for your reference, L2 space is almost universally used in electrical engineering, whether stated or not. Only when other spaces are explicitly involved they are stated so. So with this in mind that L2 is always lurking behind in electrical engineering, it is still claimed that exponentials are eigenfunctions of an LSI system.

Too bad, because they are not. And I have to take your word for that (that L^2 is always there), which has not been so reliable so far.

Another example is while MTF is being thrown around so frequently on this forum including this thread and myself, but the technically the system MTF of an imaging system does not even exist. The pixel response is not shift invariant, for e.g.

We have discussed that a lot, and if I remember well, you resisted what I told you then.

I am happy to se however that you learned something even though you pretend that you knew it all that time and I did not.

Ha, I don't remember that.

I do.

Look, it is pretty simple. What I said was right, and you know it. I was not trying to refute your post, it was a small remark. You were too stubborn to accept it and keep arguing something that you do not even know what it is.

 

[Joofa]

It is not just a mistake, it is lack of knowledge. ... but you lack the background for that.

Ha, you have very little idea about my background. Just your assumptions.

My idea comes from your posts.

No, you still have little idea.

I do (know what you do not know).

I guess you are the Oracle then.

You seem to have a tendency to argue.

It takes two to argue.

No just look around your history on this forum. Multiple people have issues with you.

Show me authors who talk about self-adjoint operators and LSI systems.

Ha, you taunt others and have done little literature reading. Please have a look at O'Neill's book on Optics for e.g.

BTW I just gave the above reference because of a connection with Optics. Otherwise electrical engineering system theory is full of differential equations and differential operators that describe them. Hard to believe that you don't know that.

So, no reference? A whole book is a dishonest attempt to pretend that you did provide one.

Ha, I really don't know how to respond to you here? Goal posts keep on moving. Now a book is not a reference. What next?

you made an implicit choice: L^2. Then you have a problem, those complex exponentials do not belong there.

Here is your problem stated below.

We are talking about cosinusoids after all they are so import to MTFs and Fourier Transforms. But, then as I'm sure you know that the Fourier Transform of even a cos / sin function doesn't directly exist due to integrability issues! So we are doomed from the start.

We are not doomed because there is a well developed theory. You are dodging the question though - eigenvectors/eigenfunctions must belong to your space, and they do not. As I said earlier, there is a term for them but you refuse to listen.

Man, what are you talking about? I just mentioned that the basic building blocks of a Fourier transform (viz. sin / cos functions) have certain issues in L2. Do sin / cos belong to L2 (R)? And, you just say that there is a theory to tackle that. That is what I'm saying many of these mathematical curiosities that you are interested in, and some of the difficulties they present, may be dealt with in one way or the other.

So now you are the one who says that they do not belong to L^2? This is funny. Do you even remember what you are arguing about?

Yes, it is just your habit to keep on arguing. I have maintained all along that these are issues, or rather mathematical curiosities, have certain work arounds. In fact, these issues are settled ages go. Only, perhaps you seem to have found them recently and find them magical. Possibly so. May be that explains your excitement and energy you are putting in these possible non-issues the way I see them.

I am not talking about difficulties, I am saying that there are not eigenfunctions.

And, just for your reference, L2 space is almost universally used in electrical engineering, whether stated or not. Only when other spaces are explicitly involved they are stated so. So with this in mind that L2 is always lurking behind in electrical engineering, it is still claimed that exponentials are eigenfunctions of an LSI system.

Too bad, because they are not.

As I said before, why don't you take issues with countless number of EE references (do a Google search) that say so. Don't repeat the mantra about L2 not being explicitly stated. Those people who wrote those know that they are typically working in L2, but still state that complex exponentials are eigenfunctions of an LSI system.

Why don't you write an article in a math or EE journal that the whole EE community is wrong and you are right?

Another example is while MTF is being thrown around so frequently on this forum including this thread and myself, but the technically the system MTF of an imaging system does not even exist. The pixel response is not shift invariant, for e.g.

We have discussed that a lot, and if I remember well, you resisted what I told you then.

I am happy to se however that you learned something even though you pretend that you knew it all that time and I did not.

Ha, I don't remember that.

I do.

Kindly provide a link or reference? I don't recall that.

See, I don't mind learning from you or any body. I'm always open. But, certainly I don't recall you and I talking about pixel response and shift invariance before in the sense that you mentioned.

I do remember and recall that I have known issues regarding shift invariance and pixel responses long before I even joined DPR. So it couldn't be that I learned this fact from you.

Look, it is pretty simple. What I said was right, and you know it.

HaHa. Everybody is right in their own mind.

I was not trying to refute your post, it was a small remark. You were too stubborn to accept it and keep arguing something that you do not even know what it is.

Man, you seriously have issues regarding your self-importance and grandeur. You need help. And, I don't mean just academic.

--
Dj Joofa
http://www.djjoofa.com

 

[J A C S]

Yes, it is just your habit to keep on arguing. I have maintained all along that these are issues, or rather mathematical curiosities, have certain work arounds. In fact, these issues are settled ages go.

Actually, they are not issues. The issue is to call those complex exponentials eigenfunctions in the context of L^2, which you did. You could have just accepted the fact but you really want to keep arguing. Well, I find it fun, so I will keep playing.

Only, perhaps you seem to have found them recently and find them magical. Possibly so. May be that explains your excitement and energy you are putting in these possible non-issues the way I see them.

I am not talking about difficulties, I am saying that there are not eigenfunctions.

And, just for your reference, L2 space is almost universally used in electrical engineering, whether stated or not. Only when other spaces are explicitly involved they are stated so. So with this in mind that L2 is always lurking behind in electrical engineering, it is still claimed that exponentials are eigenfunctions of an LSI system.

Too bad, because they are not.

As I said before, why don't you take issues with countless number of EE references (do a Google search) that say so. Don't repeat the mantra about L2 not being explicitly stated.

I will. It is not a mantra. Eigenfunctions must belong to a space chosen in advance.

Those people who wrote those know that they are typically working in L2, but still state that complex exponentials are eigenfunctions of an LSI system.

Do you agree that (1) eigenfunctions must be in your space and (2) the complex exponentials are not? Yes or No?

Why don't you write an article in a math or EE journal that the whole EE community is wrong and you are right?

If I have to write an article about every wrong thing in the engineering literature, ... And again, they are not necessarily wrong, you are.

Another example is while MTF is being thrown around so frequently on this forum including this thread and myself, but the technically the system MTF of an imaging system does not even exist. The pixel response is not shift invariant, for e.g.

We have discussed that a lot, and if I remember well, you resisted what I told you then.

I am happy to se however that you learned something even though you pretend that you knew it all that time and I did not.

Ha, I don't remember that.

I do.

Kindly provide a link or reference? I don't recall that.

It was a long thread about what the slanted edge really measured, and how the pixels play a role, etc. I also remember saying that blur is not a convolution (with the end result discretized to pixels) because convolution must be from one space to itself. I was attacked by people like you, but it is nice to hear it from your mouth now. I have also said that MTF is defined on continuous systems, and does not even make sense on pixel level, etc. Each time I said that, there was resistance. Anyway, I do not claim authorship, what is important is to be in agreement.

See, I don't mind learning from you or any body. I'm always open. But, certainly I don't recall you and I talking about pixel response and shift invariance before in the sense that you mentioned.

I do remember and recall that I have known issues regarding shift invariance and pixel responses long before I even joined DPR. So it couldn't be that I learned this fact from you.

Look, it is pretty simple. What I said was right, and you know it.

HaHa. Everybody is right in their own mind.

You never even tried to dispute it. You just played the tune: "everybody is doing it".

I was not trying to refute your post, it was a small remark. You were too stubborn to accept it and keep arguing something that you do not even know what it is.

Man, you seriously have issues regarding your self-importance and grandeur. You need help. And, I don't mean just academic.

Typical Joofa. Ignorant and aggressive.

 

[Joofa]

Yes, it is just your habit to keep on arguing. I have maintained all along that these are issues, or rather mathematical curiosities, have certain work arounds. In fact, these issues are settled ages go.

Actually, they are not issues. The issue is to call those complex exponentials eigenfunctions in the context of L^2, which you did. You could have just accepted the fact but you really want to keep arguing. Well, I find it fun, so I will keep playing.

Ok, I just picked up Papoulis' famous book, "The Fourier Integral and its Applications" and on page 84 he says: "Exponentials as in 5-13 are eigenfunctions of linear time invariant operators" after deriving it in the usual, well-known way. Are you gong to take issue with Papoulis also. Too bad he is deceased now. But, he was a great mathematician that understood EE systems theory very well and contributed a lot to it.

Another example is while MTF is being thrown around so frequently on this forum including this thread and myself, but the technically the system MTF of an imaging system does not even exist. The pixel response is not shift invariant, for e.g.

We have discussed that a lot, and if I remember well, you resisted what I told you then.

I am happy to se however that you learned something even though you pretend that you knew it all that time and I did not.

Ha, I don't remember that.

I do.

Kindly provide a link or reference? I don't recall that.

It was a long thread about what the slanted edge really measured, and how the pixels play a role, etc. I also remember saying that blur is not a convolution (with the end result discretized to pixels) because convolution must be from one space to itself. I was attacked by people like you, but it is nice to hear it from your mouth now. I have also said that MTF is defined on continuous systems, and does not even make sense on pixel level, etc. Each time I said that, there was resistance. Anyway, I do not claim authorship, what is important is to be in agreement.

Ha, borrowing your terminology, no reference then. Just your word of mouth. Okay then. I know how reliable that info is.

I was not trying to refute your post, it was a small remark. You were too stubborn to accept it and keep arguing something that you do not even know what it is.

Man, you seriously have issues regarding your self-importance and grandeur. You need help. And, I don't mean just academic.

Typical Joofa. Ignorant and aggressive.

There you go. Who is being aggressive here - the one who keeps labelling other people about they don't know anything. Haha.

 

[J A C S]

Yes, it is just your habit to keep on arguing. I have maintained all along that these are issues, or rather mathematical curiosities, have certain work arounds. In fact, these issues are settled ages go.

Actually, they are not issues. The issue is to call those complex exponentials eigenfunctions in the context of L^2, which you did. You could have just accepted the fact but you really want to keep arguing. Well, I find it fun, so I will keep playing.

Ok, I just picked up Papoulis' famous book, "The Fourier Integral and its Applications" and on page 84 he says: "Exponentials as in 5-13 are eigenfunctions of linear time invariant operators" after deriving it in the usual, well-known way. Are you gong to take issue with Papoulis also. Too bad he is deceased now. But, he was a great mathematician that understood EE systems theory very well and contributed a lot to it.

Where is the L^2 space? Try again.

I can play that stupid game as well. I have the Functional Analysis book by Peter Lax on my bookshelf. He clearly states there that the eigenvector has to be in the space. Do you know who Peter Lax is? Are you going to argue with Lax? He won the highest prize in math, equivalent to Nobel...

What is the answer to my question? Does an eigenfunction have to be in the underlying space or not? How long are you going to dance around that?

Another example is while MTF is being thrown around so frequently on this forum including this thread and myself, but the technically the system MTF of an imaging system does not even exist. The pixel response is not shift invariant, for e.g.

We have discussed that a lot, and if I remember well, you resisted what I told you then.

I am happy to se however that you learned something even though you pretend that you knew it all that time and I did not.

Ha, I don't remember that.

I do.

Kindly provide a link or reference? I don't recall that.

It was a long thread about what the slanted edge really measured, and how the pixels play a role, etc. I also remember saying that blur is not a convolution (with the end result discretized to pixels) because convolution must be from one space to itself. I was attacked by people like you, but it is nice to hear it from your mouth now. I have also said that MTF is defined on continuous systems, and does not even make sense on pixel level, etc. Each time I said that, there was resistance. Anyway, I do not claim authorship, what is important is to be in agreement.

Ha, borrowing your terminology, no reference then. Just your word of mouth. Okay then. I know how reliable that info is.

OK, here is one:

https://www.dpreview.com/forums/thread/3991306

See the second post there. Here is a quote:

First, MTF-XX does not even make sense on a discrete image. It is defined on a continuous one, and then somehow assumed to make sense on an image consisting of pixels.

Then read your nonsense in that thread, it is entertaining.

I was not trying to refute your post, it was a small remark. You were too stubborn to accept it and keep arguing something that you do not even know what it is.

Man, you seriously have issues regarding your self-importance and grandeur. You need help. And, I don't mean just academic.

Typical Joofa. Ignorant and aggressive.

There you go. Who is being aggressive here - the one who keeps labelling other people about they don't know anything. Haha.

I am imitating you.

 

[Joofa]

Yes, it is just your habit to keep on arguing. I have maintained all along that these are issues, or rather mathematical curiosities, have certain work arounds. In fact, these issues are settled ages go.

Actually, they are not issues. The issue is to call those complex exponentials eigenfunctions in the context of L^2, which you did. You could have just accepted the fact but you really want to keep arguing. Well, I find it fun, so I will keep playing.

Ok, I just picked up Papoulis' famous book, "The Fourier Integral and its Applications" and on page 84 he says: "Exponentials as in 5-13 are eigenfunctions of linear time invariant operators" after deriving it in the usual, well-known way. Are you gong to take issue with Papoulis also. Too bad he is deceased now. But, he was a great mathematician that understood EE systems theory very well and contributed a lot to it.

Where is the L^2 space? Try again.

Haha. So you don't even like that reference. Just like you ignored my previous one. Popoulis is among few mathematicians who understood EE systems very well, and as a mathematician was very well versed with what L2 spaces are, of course. So if he agreed with you regarding this simple point (which you are making a big deal about) that it must be represented in the way you want it to be, then he must have stated that in the passing, at least. But, no, he did not waste any time with the non-issue that you are after.

I just looked R. N. Bracewell famous book on Fourier Analysis also. Same thing he said as Papoulis - in slightly different words but same meaning. His book is old and considered important. No big deal in that book regarding L2 as you are making it out to be.

I can play that stupid game as well. I have the Functional Analysis book by Peter Lax on my bookshelf. He clearly states there that the eigenvector has to be in the space.

Mathematicians are strict about existence of stuff such integrals, convergence. So no surprises here. But, we are not after a functional analyst on strict sense basis. When I was a student ages ago I took many courses in functional analysis in math dept, some from world's best experts. I have forgotten a lot of it. And, only retained that is useful and practical. So I have a feeling when something is just a mathematical curiosity, and when a simple fact has any practical significance or not. In any case, in this particular point on which you are struck is not just my personal viewpoint. The status of complex exponentials in L2 have not stopped any EE from treating them as eigenfunctions in system theory, even when they know they are mostly working in L2. How many times do I have to repeat that? All along I'm stating a standard practise in EE, which even mathematicians such as Popoulis have not considered a big deal to even comment about it.

But you seem to be stuck on this point. As on a prowl. As I said before, what I stated is not my personal viewpoint. That viewpoint is consistent across EE. If you have an issue with all of these people then write journal articles not argue on a hobbyist forum like this.

Do you know who Peter Lax is?

Yes.

Are you going to argue with Lax? He won the highest prize in math, equivalent to Nobel...

So. He must have done good in early years to get that prize. There are highest prizes in all fields. And, math is not the most difficult subject in any case. There are tons of problems that have no math-like analytical answers, but are very difficult to solve even computationally.

I can give you examples from my Python programming that possibly you can't solve. Does that mean you are not talented enough?

What is the answer to my question? Does an eigenfunction have to be in the underlying space or not? How long are you going to dance around that?

Well, I already said that in that in strict sense even sin / cos are not in L2 (R). But, there is still a working Fourier Transform theory. So just goes to show that you are making a mountain out of a molehill. All the references that I provided, all the courses that I took as a student and to the extent I remember, nobody made that particular thing a big deal. Only you.

Another example is while MTF is being thrown around so frequently on this forum including this thread and myself, but the technically the system MTF of an imaging system does not even exist. The pixel response is not shift invariant, for e.g.

We have discussed that a lot, and if I remember well, you resisted what I told you then.

I am happy to se however that you learned something even though you pretend that you knew it all that time and I did not.

Ha, I don't remember that.

I do.

Kindly provide a link or reference? I don't recall that.

It was a long thread about what the slanted edge really measured, and how the pixels play a role, etc. I also remember saying that blur is not a convolution (with the end result discretized to pixels) because convolution must be from one space to itself. I was attacked by people like you, but it is nice to hear it from your mouth now. I have also said that MTF is defined on continuous systems, and does not even make sense on pixel level, etc. Each time I said that, there was resistance. Anyway, I do not claim authorship, what is important is to be in agreement.

Ha, borrowing your terminology, no reference then. Just your word of mouth. Okay then. I know how reliable that info is.

OK, here is one:

https://www.dpreview.com/forums/thread/3991306

See the second post there. Here is a quote:

First, MTF-XX does not even make sense on a discrete image. It is defined on a continuous one, and then somehow assumed to make sense on an image consisting of pixels.

You must be dreaming. You were replying to a certain Great Bustard. Not me. Please try to read properly.

Then read your nonsense in that thread, it is entertaining.

Haha, you don't even know what you were talking about there. As this post shows you had little idea:

https://www.dpreview.com/forums/post/57616106

As, I said you just have impressions of grandeur and self importance.

I was not trying to refute your post, it was a small remark. You were too stubborn to accept it and keep arguing something that you do not even know what it is.

Man, you seriously have issues regarding your self-importance and grandeur. You need help. And, I don't mean just academic.

Typical Joofa. Ignorant and aggressive.

There you go. Who is being aggressive here - the one who keeps labelling other people about they don't know anything. Haha.

I am imitating you.

Wrong. You attacked personally first. You can see above and in the chain of messages.

--
Dj Joofa
http://www.djjoofa.com