Generating Interference Fringes

[Ethan Every]

I’ve been wondering about the significance of generating interference fringes of 3d representations of “fresnel zones”. Would the parameters used in generating high res fresnel zones be useful in describing wave functions in the same way an actual zone plate would be? It's hard to imagine the math in the code wouldn’t be in some way related to the actual physical phenomena if the result is visually identical, but perhaps I’m mistaken. I’ve been exploring a 3d object and stumbled upon some emergent interference fringes (the fringes are not programmed intentionally) and I’m wondering if that means the object could be useful for modeling waves, wave interactions etc. Here’s some examples of what I mean, I’d be grateful for any feedback. Thanks

[swansont]

We already have the math for describing wave functions in 3D. You can solve the Schrödinger equation for hydrogen-like atoms.

 

[Ethan Every]

So would it make sense to presume some version of the schrodinger equation is present in this structure or can we make these fringes a bunch of ways?

[swansont]

41 minutes ago, Ethan Every said:

So would it make sense to presume some version of the schrodinger equation is present in this structure or can we make these fringes a bunch of ways?

Interference is the result of wave addition.The solution to the Schrödinger equation for a central potential gives one specific answer. The solution for hydrogen only looks like your zone plate interference pattern for the l=0, m_l = 0 solutions for various values of n. Get away from that and they don't look similar at all.

https://en.wikipedia.org/wiki/Atomic_orbital#/media/File:Hydrogen_Density_Plots.png

Light and deBroglie wave interference is typically of sine waves, because of Huygens principle - every point on a wavefront is itself the source of spherical waves. So you get a spherical wave when you go through an aperture, and that's the origin of the interference.

 

 

[Ethan Every]

Yea its certainly not displaying any orbitals associated with massive particle. I guess I thought maybe it was related to massless objects like photons/light or other physical waves. Seems like maybe the similarity is from the juxtaposition of a flat axis surrounded by a curved surface in the 3d object, im guessing that just mimics the way a curved lense interacts with light rays or other waves. Still I suppose its interesting to create interference like that with a single mathematical object rather than multiple interacting elements. Maybe i'll find some useful application for it. Thanks for the feedback

[Orion1]

On 11/17/2020 at 9:36 PM, Ethan Every said:

Would the parameters used in generating high res fresnel zones be useful in describing wave functions in the same way an actual zone plate would be?

The parameters are identical for modelling any real physical object. (ref. 1)

Note that all the interference patterns that you have pictured are formally called Fresnel zone plates, and informally just called zone plates.

Quote

the math in the code wouldn’t be in some way related to the actual physical phenomena if the result is visually identical

The results are identical, with the exception that the original object may be physical and the other object may be a virtual hologram.

The mathematics in (ref. 1) are capable of modelling any Fresnel zone plate, including point source holograms (ref. 2).

Can a physical Fresnel lens project a virtual hologram?....Affirmative. (ref. 3)

Reference:
Wikipedia - Fresnel Zone Plate: (ref. 1)
https://en.wikipedia.org/wiki/Zone_plate

Wikipedia - Hologram - point sources: (ref. 2)
https://en.wikipedia.org/wiki/Holography#Point_sources

Physical Fresnel Lens Hologram Test: (ref. 3)
https://www.youtube.com/watch?v=f8wSabvv1xs

 

Edited November 19, 2020 by Orion1
citation added...

[Ethan Every]

14 hours ago, Orion1 said:

The parameters are identical for modelling any real physical object. (ref. 1)

Note that all the interference patterns that you have pictured are formally called Fresnel zone plates, and informally just called zone plates.

The results are identical, with the exception that the original object may be physical and the other object may be a virtual hologram.

The mathematics in (ref. 1) are capable of modelling any Fresnel zone plate, including point source holograms (ref. 2).

Can a physical Fresnel lens project a virtual hologram?....Affirmative. (ref. 3)

Reference:
Wikipedia - Fresnel Zone Plate: (ref. 1)
https://en.wikipedia.org/wiki/Zone_plate

Wikipedia - Hologram - point sources: (ref. 2)
https://en.wikipedia.org/wiki/Holography#Point_sources

Physical Fresnel Lens Hologram Test: (ref. 3)
https://www.youtube.com/watch?v=f8wSabvv1xs

 

Thanks for the clarification! Although they look incredibly similar I wasn’t sure if it was appropriate to label the similar properties of this 3d object as fresnel zones because I am not deriving them the traditional way. Additionally as the field of vision gets broader than the first example I posted the object reveals some new characteristics that I’ve been apprehensive to label without verification (Ex. A).  I’ve been attempting to define the geometry here so I can properly measure it but it’s difficult as it warps and lenses depending on how it is observed (Ex. B).

 

Edited November 20, 2020 by Ethan Every

[Orion1]

3 hours ago, Ethan Every said:

I’ve been attempting to define the geometry here so I can properly measure it but it’s difficult as it warps and lenses depending on how it is observed

Those appear to be Moiré patterns. (ref. 1)

The interference effect can be produced when two or more zone plates overlap and are rotated, or when an opaque ruled pattern with transparent gaps is overlaid on another similar pattern and are rotated. 

Reference:
Wikipedia - Moiré pattern - rotated patterns: (ref. 1)
https://en.wikipedia.org/wiki/Moiré_pattern#Rotated_patterns
https://upload.wikimedia.org/wikipedia/commons/9/97/Moire_Lines.svg

Edited November 20, 2020 by Orion1
text edit...

[Ethan Every]

6 hours ago, Orion1 said:

Those appear to be Moiré patterns. (ref. 1)

The interference effect can be produced when two or more zone plates overlap and are rotated, or when an opaque ruled pattern with transparent gaps is overlaid on another similar pattern and are rotated. 

Reference:
Wikipedia - Moiré pattern - rotated patterns: (ref. 1)
https://en.wikipedia.org/wiki/Moiré_pattern#Rotated_patterns
https://upload.wikimedia.org/wikipedia/commons/9/97/Moire_Lines.svg

There are certainly significant similarities. The images I posted have an edge filter on to highlight the axis as they are difficult to identify with lower resolution photos. In a high resolution render (Ex. C) you can see the particulars of this model as it transitions from a traditional 2d representation of a fresnel zone out to the larger 3 dimensional space. The footage phases from frame to frame and produces some interesting overtones as the space becomes more defined. While the image changes depending on what percentage of your screen is used to display it there appear to be specific low interference axis that underlay the image at any scale, I'm trying to use these to define the geometry that produces the interference.

 

Example C : https://mega.nz/file/5Ux0hDJa#HoppqGXb8m7dm1EQyj1jTmo-QYwmei7XwevLPpBhL_g

[Ethan Every]

I’ve isolated the orbitals of the object as a whole (Ex D). The closest thing I’ve found to this structure is also interference based, in this case the object sort of resembles these Quasiparticle interference of TaAs surface states (Ex E, Ref A). The fresnel zone images emerge in a particular area of the interior of the object rather than on the surface which is why I’m having a difficult time defining the geometry of that particular space, but ultimately it emerges from the structure pictured here (ex D) . Looks like maybe sphere folding Ex E might give me something close to Ex D but I can only express that as code, I've no idea how that would be done in calculus at this point (Sphere or ball folding Ex F). Obviously my goal would be to translate the geometry of the object into something practically useful. 

Ref A : https://science.sciencemag.org/content/351/6278/1184?rss=1

 

 

Edited November 21, 2020 by Ethan Every

[Orion1]

Those images appear to be Kaleidoscopic (having complex patterns of colors; multicolored, made up of a complex mix of elements; multifaceted.) (ref. 1)

A kaleidoscope is an optical instrument with two or more reflecting surfaces tilted to each other in an angle, so that one or more (parts of) objects on one end of the mirrors are seen as a regular symmetrical pattern when viewed from the other end, due to repeated reflection. The reflectors (or mirrors) are usually enclosed in a tube, often containing on one end a cell with loose, colored pieces of glass or other transparent (and/or opaque) materials to be reflected into the viewed pattern. Rotation of the cell causes motion of the materials, resulting in an ever-changing view being presented.

Reference:
Wikipedia - Kaleidoscope: (ref. 1)
https://en.wikipedia.org/wiki/Kaleidoscope