An Imagined Diffraction Grating

[desertshaman]

TL;DR

An amateur has dreamed of an innovation, and wants to debrief

Dear Physicists
I have imagined a kind of diffraction grating that I can’t find in the books or on the market, so I want to debrief and see what others think of it.
My Imaginary Grating (IG) is made of a set of perfectly white lands separated by deep, non-reflective cuts at a spacing determined by a simple trigonometric function. The result is that every adjacent land is separated from the next by a distance differential of 1 wavelength of light, with respect to the observer.

The 1-Dimensional IG

A 1-dimensional IG is attached as image 1. The observer sees the same wavelength of light reflected towards them from the entire length of the grating.
It is noted that a grating which similarly uniformly reflects light for a wavelength λ=600nm is simply scaled lengthwise, with similar scaling applied to the observer viewpoint.
The 2-dimensional IG
The 2-dimensional IG, attached as image 2, is made up of lands spaced according to the same formula as above, with parallel lands extending much wider than the grating is long. An expected effect of this arrangement is depicted in the plan view below.
Along a line through space, at a uniform distance from the grating and at a uniform height above the plane of the grating, the entire length of the grating uniformly reflects single wavelength light towards an observer.

One has naively imagined that the great resolution of such a diffracting surface might be useful in spectroscopy.
Thanks for your attention!

 

[sophiecentaur]

TL;DR: An amateur has dreamed of an innovation, and wants to debrief

I have imagined a kind of diffraction grating

There are many designs of diffraction grating and the maths is well known. From what you write, I see you are describing one possible layout of a reflective grating. I assume you have done a fairly wide search of the field so you could tell me/us what is essentially different about your proposed model.

If you Google "Choice of diffraction grating design" there is a pretty comprehensive intro into the topic. You may find your question is answered there. The page describes many of the factors which affect the design.

 

[desertshaman]

My model is different to other models I have seen in that it provides a higher resolution of wavelength. Resolution is greater because there are more samples - a sample is provided for every reflector of the grating in the proposed model, but in gratings with evenly spaced reflectors only a few reflectors contribute to the signal received by the observer at any given wavelength.
As for the uniqueness of my dreamed model I cannot be sure.

 

[Baluncore]

TL;DR: An amateur has dreamed of an innovation, and wants to debrief

One has naively imagined that the great resolution of such a diffracting surface might be useful in spectroscopy.

I don't think you have discovered anything new. I believe that your assumptions have not been specified, and that different assumptions yield different results.

The Nyquist–Shannon sampling theorem requires twice as many samples as the number of (spatial or temporal) frequencies being analysed. If you think you can do better than that, then you are probably counting negative frequencies independently to the positive frequencies, by ignoring the symmetry.

 

[desertshaman]

I can do better than you expect not because I don't know about sampling. The DF does better than you expect because "it does know" about sampling - a sample is provided by every reflector on the grating... tens of thousands of samples.

 

[sophiecentaur]

The Nyquist–Shannon sampling theorem requires twice as many samples

A minimum of. - that's important because the Nyquist criterion assumes perfect pre-filtering. I have a feeling that a system that claims to have finer resolution would have alias angle components sitting in amongst the wanted lines. (And no way to identify them)

, but in gratings with evenly spaced reflectors only a few reflectors contribute to the signal received by the observer at any given wavelength.

What do you mean by that? The outputs of all slits from a DG will be parallel and then focussed onto a single line. Follow the full theory and you will appreciate what I'm saying. Can you really think that DGs have been used for well over a century without an optimum design having been arrived at?

 

[tech99]

I think what is being described is a zone plate.

 

[sophiecentaur]

I think what is being described is a zone plate.

That sort of thing, probably. The point is that a regular, practical DG is part of an spectrometer system and isn't used on its own. A zone plate approach could well achieve what the OP is after but other optics can achieve high efficiency and have the advantages of being linear and easy to calibrate and easy to design and produce.

10/10 for the OP, though, because he's clearly 'thinking' about the subject.