Started 7 months ago | Discussions thread
AiryDiscus Senior Member • Posts: 1,731
Re: BxU, JBM and CRB / FI

Joofa wrote:

AiryDiscus wrote:

Well Joofa, while I wouldn't say I'm one of the top experts in the world on imaging,

You are not. At all. Period. It would really be undermining the real experts in the imaging world if you are considered an 'expert'. Especially in theory.

That I have not come across "the matrix theory of optics" is a genuine surprise.

As I said before, not surprising for me considering your background.

I also have a fairly thorough understanding of the math (both theoretical and numerical implementation) of imaging,

Since you have a 'fairly thorough understanding of math', I shall help you out with the so called 'matrix theory of optics', and with your formidable math skills you should be able to fill out the details. See below.

Given the breadth of minutia in the biblical texts on imaging, its absence to my memory, and my inability to find it on OSA Publishing or SPIE, I am lead to believe it is very obscure or, like JIMD, an unpublished invention of yours.

Lol, no it is not an invention of mine. Some of the best known experts in optics are behind this theory.

While no one knows the depths of what they don't know, there are likely precious few 'best' experts in imaging that I have not heard of.

I can give you a photo of my bookshelf at work tomorrow if you want, but I own the following texts on optics:

These are reasonable texts. However, your list is far from extensive for somebody like yourself who thinks too highly of himself as an 'optical expert'.

I am not a "general optical expert" (whatever that means).  I am an expert in two subjects; MTF and interferometry.

I have nothing to do with optics.

Your post history makes it seem like you want oh so strongly for us to think that.

I'm not at all an expert in optics


Still, I have more books on optics than that list in my collection including a vast majority that you mentioned. So lets not show off.

I am not intending to show off.  You balk at the number of pages, but I do own several thousand pages of textbooks on optics specifically related to imaging.

Besides, you're what, twice, maybe thrice my age?  I would hope you had accumulated more reading material than my meager finances can acquire.

Ok, now to get you started on matrix methods. And, here we shall even deal with the standard formulation of image plane intensity. Not even the 'other one' that I talked about in my response to Franz. Just standard stuff.

Start with the mutual coherence function. Write down the equation for mutual coherence in the imaging plane in relation to PSF and object plane coherence. This is well-known stuff in optics, so you should be able to look this thing up in any reasonable optics book.

Indeed, it is very well covered in Born and Wolf's book or in Statistical Optics.

Now, notice that PSF can be expanded using an orthogonal set of functions (why? I leave that to your thorough math skills to figure that out).

Yes and no.  I forget the name at the moment (go ahead and get the criticism out of your system) but a Belgian (I think) research group related to the photolithography industry has a nice thesis and body of related work that has an analytical expression based on a series of bessel functions.  There is even a name for their method, but it escapes me at the moment and isn't referenced in either Goodman or Wolf.

However, I do remember that there were wavefronts they could not expand into a finite series, and perhaps this is why they do not get the attention of the 800lb gorillas of the literature.

Write that out and substitute that in the mutual coherence equation. Make a few reorderings, and voila, you have your very first matrix representation of image plane intensity.

Try it out, before we go on to more exotic stuff. If you are stuck, reach out, and I can help you out further.

I was looking more for one of the papers you claim exist than to do a derivation.

I assume now that this is another fabrication of yours intended to waste the time of the honest contributors to this forum.

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