<p>When a star is occulted by a &quot;sharp edge&quot; such as the limb of the Moon or by an asteroid, then diffraction effects are seen.</p>
<p>The star doesn't suddenly disappear (or appear); there are a series of maxima and minima associated with the Fresnel diffraction pattern formed by the edge. This in turn is the convolution of the diffraction pattern formed by an infinitely distant point source and the finite angular diameter of a star. The result is a diffraction pattern formed where the &quot;edge&quot; of the shadow of the star would be. A fixed detector on Earth will scan across the diffraction pattern and see the brightness oscillate as a star is occulted, rather than a &quot;step function&quot; (an example is shown below).</p>
<p>If we are using the Moon as an example, a typical fringe spacing would be about 15m. But of course, the fringes track rapidly across the Earth's surface as the Moon moves in its orbit in front of the source (in much the same way that a solar eclipse tracks rapidly across the surface of the Earth). Thus to observe the phenomenon you need to use a narrow bandwidth filter (different wavelengths have different fringe spacing) and a very fast frame rate camera (<span class="math-container">$\sim 100+$</span> Hz). These restrictions mean you also need a bright star to be occulted (rare), or a big telescope.</p>
<p>In principle such measurements, if done carefully enough, reveal the angular structure of the stellar source, including angular diameters and angular separations of binary components or exploring limb darkening. Some random older examples where this has been observed and done include <a href="https://ui.adsabs.harvard.edu/abs/1980AJ.....85.1496R/abstract" rel="noreferrer">Ridgway et al. 1980</a>; <a href="https://ui.adsabs.harvard.edu/abs/1980AJ.....85..490F/abstract" rel="noreferrer">Fekel et al. 1980</a> (nice example of a binary). The technique is still being used and improved upon in the present day - the image below is the light curve caused by the tracking of the diffraction pattern across a detector during the lunar occultation of <span class="math-container">$\mu$</span> Psc (from <a href="https://iopscience.iop.org/article/10.3847/1538-3881/ab3979" rel="noreferrer">Zampieri et al. 2019</a>. The upper curve shows the data points modelled with a point source. The lower curve is the same points modelled with a disk source - a better fit, giving an angular diameter of <span class="math-container">$3.14 \pm 0.05$</span> milli-arcsec.</p>
<p><a href="https://i.sstatic.net/VHVsS.jpg" rel="noreferrer"><img src="https://i.sstatic.net/VHVsS.jpg" alt="Occultation light curve of" /></a></p>

CC BY-SA 4.0
2021-12-05T11:45:44.503Z
[Cornu (Euler) spiral!](https://en.wikipedia.org/wiki/Euler_spiral)
uhoh
CC BY-SA 4.0
2021-12-06T22:54:09.427Z
Hmm... a big telescope looking at an occultation by the Moon's dark limb of a bright but small angular diameter source, with a photodiode (and filter) at the focal plane, an amplifier and DC-blocking filter should be able to make a circa 100 Hz *audible* if everything works in one's favor, but that's probably more of a gedankenexperiment for an armchair amateur like me [also](https://astronomy.stackexchange.com/q/34348/7982) than something I'm likely to succeed with the first time, and the frequency may be too low to recognize beyond a faint, noisy "pop".  Thanks, this is *really interesting!*
uhoh
CC BY-SA 4.0
2021-12-05T10:01:48.447Z
2021-12-05T10:01:48.447Z
ProfRob
<h3>Not asking about:</h3>
<p>Interferometry can be done with multiple instruments who's light paths or signals are combined interferometrically, or even between different parts of a single aperture, e.g.</p>
<ul>
<li><a href="https://astronomy.stackexchange.com/q/36363/7982">What equipment and techniques were used to study Betelgeuse&#39;s diameter in 1920?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/39420/7982">How did Michelson measure the diameters of jupiter&#39;s moons using optical interferometry?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/39490/7982">Why does the Simbad page &quot;A.A. Michelson&#39;s Jovian Galilean-satellite interferometer&quot; show data for Betelgeuse?</a></li>
</ul>
<h3>Asking about:</h3>
<p>For example comment under <a href="https://astronomy.stackexchange.com/q/26193/7982">Is Diffraction of light observed in gravitational lensing/microlensing?</a> links to <a href="https://arxiv.org/abs/1207.4034" rel="nofollow noreferrer">Studying wave optics in the light curves of exoplanet microlensing</a> At the longer wavelengths observed via radio telescopes, the authors propose that interference fringes (in time) between a lensed and un-lensed path for light from a given object can be observed at Earth, thereby increasing the amount of detailed information that can be modeled in order to better characterize the lensing event.</p>
<p>That's an example what I would consider as &quot;interference effects (in space)... observed by a single instrument, as opposed to interferometry&quot;.</p>
<p><strong>Question:</strong> Have any such effects been observed?</p>

CC BY-SA 4.0
2021-10-30T19:39:17.747Z
Could you provide an example in principle of what you're asking for? It doesn't really make sense for interference fringes to exist in, e.g., a cloud of dust. Are you asking if it occurs in spectra...?
Daddy Kropotkin
CC BY-SA 4.0
2021-10-30T22:49:33.857Z
@DaddyKropotkin I've already provided an example and linked to a paper describing the concept in further detail. Check again.
uhoh
CC BY-SA 4.0
2021-10-31T17:53:05.463Z
You said, "That's an example what I would consider as "interference effects (in space)... observed by a single instrument, as opposed to interferometry"." But these effects are not in space, they are in the telescope, no? That's why I asked for clarification: you ask for a telescopic effect that occurs out in space...?
Daddy Kropotkin
CC BY-SA 4.0
2021-10-31T21:20:32.510Z
@DaddyKropotkin I don't know what to say here except to again refer to the words that I have already written: "**..the authors propose that interference fringes (in time) between a lensed and un-lensed path for light from a given object can be observed at Earth...**" and "**That's an example what I would consider as 'interference effects (in space)... observed by a single instrument, as opposed to interferometry'**" In my example, those paths have different path length and therefore can interfere.
uhoh
<observational-astronomy><interferometry>
Have interference effects (in space) ever been observed by a single instrument, as opposed to interferometry?
uhoh
# Have interference effects (in space) ever been observed by a single instrument, as opposed to interferometry?

(Asked by: username_0 on 2021-10-29)

### Not asking about:

Interferometry can be done with multiple instruments who's light paths or signals are combined interferometrically, or even between different parts of a single aperture, e.g.

* [What equipment and techniques were used to study Betelgeuse's diameter in 1920?](https://astronomy.stackexchange.com/q/36363/7982)
* [How did Michelson measure the diameters of jupiter's moons using optical interferometry?](https://astronomy.stackexchange.com/q/39420/7982)
* [Why does the Simbad page "A.A. Michelson's Jovian Galilean-satellite interferometer" show data for Betelgeuse?](https://astronomy.stackexchange.com/q/39490/7982)

### Asking about:

For example comment under [Is Diffraction of light observed in gravitational lensing/microlensing?](https://astronomy.stackexchange.com/q/26193/7982) links to [Studying wave optics in the light curves of exoplanet microlensing](https://arxiv.org/abs/1207.4034) At the longer wavelengths observed via radio telescopes, the authors propose that interference fringes (in time) between a lensed and un-lensed path for light from a given object can be observed at Earth, thereby increasing the amount of detailed information that can be modeled in order to better characterize the lensing event.

That's an example what I would consider as "interference effects (in space)... observed by a single instrument, as opposed to interferometry".

**Question:** Have any such effects been observed?

**Tags:** observational-astronomy, interferometry

> **Comments:**
> **username_1**: Could you provide an example in principle of what you're asking for? It doesn't really make sense for interference fringes to exist in, e.g., a cloud of dust. Are you asking if it occurs in spectra...?  
> **username_0**: @username_1 I've already provided an example and linked to a paper describing the concept in further detail. Check again.  
> **username_1**: You said, "That's an example what I would consider as "interference effects (in space)... observed by a single instrument, as opposed to interferometry"." But these effects are not in space, they are in the telescope, no? That's why I asked for clarification: you ask for a telescopic effect that occurs out in space...?  
> **username_0**: @username_1 I don't know what to say here except to again refer to the words that I have already written: "**..the authors propose that interference fringes (in time) between a lensed and un-lensed path for light from a given object can be observed at Earth...**" and "**That's an example what I would consider as 'interference effects (in space)... observed by a single instrument, as opposed to interferometry'**" In my example, those paths have different path length and therefore can interfere.  

---

## 1 answers

### Answer by username_2 on 2021-12-05. Score: 6 | Accepted answer

When a star is occulted by a "sharp edge" such as the limb of the Moon or by an asteroid, then diffraction effects are seen.

The star doesn't suddenly disappear (or appear); there are a series of maxima and minima associated with the Fresnel diffraction pattern formed by the edge. This in turn is the convolution of the diffraction pattern formed by an infinitely distant point source and the finite angular diameter of a star. The result is a diffraction pattern formed where the "edge" of the shadow of the star would be. A fixed detector on Earth will scan across the diffraction pattern and see the brightness oscillate as a star is occulted, rather than a "step function" (an example is shown below).

If we are using the Moon as an example, a typical fringe spacing would be about 15m. But of course, the fringes track rapidly across the Earth's surface as the Moon moves in its orbit in front of the source (in much the same way that a solar eclipse tracks rapidly across the surface of the Earth). Thus to observe the phenomenon you need to use a narrow bandwidth filter (different wavelengths have different fringe spacing) and a very fast frame rate camera ($\sim 100+$ Hz). These restrictions mean you also need a bright star to be occulted (rare), or a big telescope.

In principle such measurements, if done carefully enough, reveal the angular structure of the stellar source, including angular diameters and angular separations of binary components or exploring limb darkening. Some random older examples where this has been observed and done include [Ridgway et al. 1980](https://ui.adsabs.harvard.edu/abs/1980AJ.....85.1496R/abstract); [Fekel et al. 1980](https://ui.adsabs.harvard.edu/abs/1980AJ.....85..490F/abstract) (nice example of a binary). The technique is still being used and improved upon in the present day - the image below is the light curve caused by the tracking of the diffraction pattern across a detector during the lunar occultation of $\mu$ Psc (from [Zampieri et al. 2019](https://iopscience.iop.org/article/10.3847/1538-3881/ab3979). The upper curve shows the data points modelled with a point source. The lower curve is the same points modelled with a disk source - a better fit, giving an angular diameter of $3.14 \pm 0.05$ milli-arcsec.

[![Occultation light curve of](https://i.sstatic.net/VHVsS.jpg)](https://i.sstatic.net/VHVsS.jpg)

> **Comments:**
> **username_0**: [Cornu (Euler) spiral!](https://en.wikipedia.org/wiki/Euler_spiral)  
> **username_0**: Hmm... a big telescope looking at an occultation by the Moon's dark limb of a bright but small angular diameter source, with a photodiode (and filter) at the focal plane, an amplifier and DC-blocking filter should be able to make a circa 100 Hz *audible* if everything works in one's favor, but that's probably more of a gedankenexperiment for an armchair amateur like me [also](https://astronomy.stackexchange.com/q/34348/7982) than something I'm likely to succeed with the first time, and the frequency may be too low to recognize beyond a faint, noisy "pop".  Thanks, this is *really interesting!*  

---

