Timeline for What defines "minimal coherence" as a condition for the emergence of stationary interference in a chaotic wave field?
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| Mar 17, 2023 at 16:45 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 16, 2023 at 7:47 | answer | added | Jagerber48 | timeline score: 0 | |
| Mar 15, 2023 at 11:45 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 14, 2023 at 9:36 | answer | added | Doriano Brogioli | timeline score: 1 | |
| Mar 13, 2023 at 2:34 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 13, 2023 at 2:26 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 13, 2023 at 1:26 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 13, 2023 at 1:02 | comment | added | srhslvmn | ... The former is the squared modulus of the latter and therefore real and positive definite, while the latter in general complex allowing for negative values. A superposition of intensities is therefore purely additive, not allowing for destructive interference. Meaning: We always have to consider the underlying (complex) fields in order to predict intensity distributions! I just realized this thanks to your comment. | |
| Mar 13, 2023 at 1:01 | comment | added | srhslvmn | PS.: While I'm lacking a clear mathematical derivation (hence, the question), my hunch regarding your objection is that you're considering auto-correlations (each emitter producing a static fringe pattern) while neglecting the cross-correlations between the emitters. Because taken together, the global field correlations are strongly fluctuating as evident from the snapshots. Secondly, I'm not sure we can treat intensity distributions the same way as field distributions (see also field vs. intensity autocorrelation). | |
| Mar 13, 2023 at 0:41 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 13, 2023 at 0:32 | comment | added | srhslvmn | ...plots/code in the near future with these missing features added. | |
| Mar 13, 2023 at 0:32 | comment | added | srhslvmn | @DorianoBrogioli New simulations added! 2 sources, 2 frequencies, 2 phases...a large single slit and a proper double slit. Please have a look. In the case of the double slit interference, it appears as if the fringes on a hypothetical screen would oscillate left and right by "$\pi/2$" (i.e. half a fringe width) such that maxima and minima are averaged out. Unfortunately, this simulation tool has two serious shortcomings: It doesn't allow 1.) saving configurations for sharing and 2.) plotting intensities instead of amplitudes. I'm working on an FDTD code and might provide some updated ... | |
| Mar 12, 2023 at 23:37 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 12, 2023 at 23:30 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 12, 2023 at 23:08 | comment | added | srhslvmn | @DorianoBrogioli And concerning statement 2: Just search for interference experiments using everyday light sources - there is literally centuries of material available online. :) PS.: To clear out your concerns, I'll add a few more snapshots shortly | |
| Mar 12, 2023 at 23:07 | comment | added | srhslvmn | @DorianoBrogioli Hi, you can easily verify this for yourself with the linked wave simulator. Just place two point sources (right click inside the simulation box) and set different frequencies. You'll see interference patterns, but they're rapidly propagating through space - it's basically a simpler scenario of cases III & IV in above simulations, only using 2 instead of 5 emitters. And the more sources you add, the more chaotic the resulting wave field becomes. | |
| Mar 12, 2023 at 20:50 | comment | added | Doriano Brogioli | Statement (1) is wrong for sure. Consider the superposition of two frequencies. The stationary diffraction pattern of the superposition is just the sum of the intensities of the diffraction patterns of the single frequencies. There is no reason why this sum should not show any interference pattern. E.g. if the two frequencies are very close, you get the sum of two similar patterns. What follows (1) is thus incomprehensible. | |
| Mar 11, 2023 at 7:19 | comment | added | srhslvmn | I've been looking both into the Wiener–Khinchin and van Cittert-Zernike theorem, but haven't found a satisfactory explanation yet. To my understanding, they're somewhat equivalent in that they relate the spectral and spatial distribution (i.e. spectral "size" and angular size, respectively) of a source to statistical correlations (i.e. coherence) in the resulting fields. I've been, however, more focused on the Wiener-Khinchin theorem as, experimentally, increasing the spatial coherence is usually the easier/trivial part (simply decreasing the spot size of and/or distance to the source). | |
| Mar 11, 2023 at 4:42 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 11, 2023 at 4:08 | comment | added | srhslvmn | @knzhou I'm asking about the mathematical "boundary" between coherent and incoherent fields/sources, i.e. the exact minimal conditions both necessary and sufficient for stationary intensity distributions. The question is motivated by the contradiction or "constructivist gap" between 1.) my assumption that a superposition of even a "large" number of Fourier components does not produce visible interference and 2.) the observation that an overwhelmingly large class of everyday sources (e.g. candles, sunlight) does produce visible interference. | |
| Mar 11, 2023 at 3:30 | comment | added | knzhou | I'm not sure what the specific question is, but I think you're reaching towards describing the van Cittert–Zernike theorem. | |
| Mar 11, 2023 at 3:21 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 10, 2023 at 23:09 | history | edited | srhslvmn | CC BY-SA 4.0 |
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| Mar 10, 2023 at 23:01 | history | asked | srhslvmn | CC BY-SA 4.0 |