<p>As far as <em>microlensing</em> is concerned:</p>
<h3>Not likely</h3>
<p>This is a bit of a dodge on the question, but it is hard to come up with a scenario where microlensing becomes the dominant PSF term.</p>
<p>Microlensing occurs during conjunction with a stellar or planetary object, and results in a momentary (seconds-to-days timescale) increase in the brightness of the observed star. It is an extremely rare event, <a href="https://arxiv.org/abs/astro-ph/0002510" rel="nofollow noreferrer">with rates around 100 in 17 million stars in the most recent surveys</a>.</p>
<p>Stellar densities (<span class="math-container">$\rho$</span>) around our solar system are on the order of 0.14 stars per cubic parsec. With such a low number density, microlensing does not pose any practical limitation on the resolution of radio telescopes. Lets do some scratch-pad estimates to see:</p>
<p>If we assume a synthetic aperture (<span class="math-container">$D$</span>) of 1AU (<span class="math-container">$4.84\times10^{-6}$</span>parsecs) , a wavelength (<span class="math-container">$\lambda$</span>) of 1mm (<a href="https://astronomynow.com/2017/06/30/see-the-sharpest-ever-view-of-giant-betelgeuse/" rel="nofollow noreferrer">similar to the view of Betelgeuse by the ALMA observatory</a>) , and a desired spatial resolution (<span class="math-container">$s$</span>) of 10,000 km at a distance <span class="math-container">$L$</span>:</p>
<p><span class="math-container">$$
\begin{align}
\frac{s}{L}  &amp;= 1.22 \frac{\lambda }{D} \\
L &amp;= \frac{sD}{1.22 \lambda } = 40\;\text{kilo-parsec}
\end{align}
$$</span></p>
<p>This is roughly the diameter of the milky way galaxy. So an interferometer operating in the 1mm wavelength with a 1AU baseline has a 10,000 km resolution at a distance of 40 kpc.</p>
<p>How many stars are between the 1AU-wide observatory and the target star? Using a cone of base diameter <span class="math-container">$D$</span> and height <span class="math-container">$L$</span> as a volume and the above stellar density, we get the average number of stars (<span class="math-container">$N$</span>) between our aperture and the observed star:
<span class="math-container">$$ N = \rho \frac{\pi}{12}D^2 L = 3 \times 10^{-8} \; \text{stars}$$</span></p>
<p>You would have to ramp <span class="math-container">$D$</span> up by a factor of <span class="math-container">$10^4$</span> before <span class="math-container">$N \approx 1$</span> and 'microlensing aberrations' were more than just an extremely rare event.</p>

CC BY-SA 4.0
2019-04-02T22:26:03.743Z
Thanks for your answer! Ah, it looks like I used the wrong term in my question. I was thinking of [weak gravitational lensing](https://en.wikipedia.org/wiki/Weak_gravitational_lensing), the collective effect of many small, static deflections. But I wrote microlensing by mistake. If there were no answers I could just make the correction, but now that you have answered based on microlensing, I need to honor your answer.
uhoh
CC BY-SA 4.0
2019-04-02T22:27:09.203Z
I can think of two ways to proceed 1) post a new question, similar to this one and pointing back here, but explaining that it asks about weak lensing instead, or 2) *add weak lensing* as a second effect to consider to this question, opening it up to additional answers. Do you have any preference?
uhoh
CC BY-SA 4.0
2019-04-04T03:37:34.060Z
I see you've been active on this site and so have seen my comments above. Since there's no objection, I've decided to go with option #2.
uhoh
CC BY-SA 4.0
2019-04-15T18:42:11.570Z
Related: https://astronomy.stackexchange.com/questions/30462/what-is-the-farthest-we-can-see-into-the-universe
Muze
CC BY-SA 4.0
2019-04-02T16:11:30.407Z
2022-08-15T00:38:30.553Z
2022-08-15T00:38:30.553Z
cms
<p>This is a theoretical question. </p>

<p><a href="https://astronomy.stackexchange.com/a/29088/7982">This answer</a> to the question <em>If we had the right technology could we see a distant star in detail?</em> (presumably space-based) primarily addresses the scaling of diffraction-limited resolution with aperture <span class="math-container">$D$</span>. For existing and near-future telescopes this is assumed to follow <span class="math-container">$\lambda/D$</span>.</p>

<p>Imagine a future optical or radio interferometric telescope of absurdly large <em>effective aperture</em> or baseline, say AU or even larger, operated similarly to the Event Horizon Telescope (local downconversion and timestamping, <a href="https://astronomy.stackexchange.com/q/20082/7982">interferometry performed offline</a>)</p>

<p>Could <a href="https://en.wikipedia.org/wiki/Weak_gravitational_lensing" rel="nofollow noreferrer">weak gravitational lensing</a> effects or <a href="https://en.wikipedia.org/wiki/Gravitational_microlensing" rel="nofollow noreferrer">gravitational microlensing</a> result in wavefront distortion that if not corrected, would result in <em>degraded resolution</em>? Note I'm not asking about distortion of the field, but instead a limitation to the resolution; degraded point spread function.</p>

<p>If so, would this problem be amenable to correction in the same way that atmospheric and ionospheric effects (visible and radio) are dealt with? Would it generally be static on the timescale of the observation?</p>

CC BY-SA 4.0
2019-01-09T18:19:52.977Z
Adaptive optic systems largely depend on a known "clean" reference source, so if your telescopes FoV can see even one star whose output is subject to significant grav microlensing then it could be corrected.
Carl Witthoft
<radio-astronomy><gravitational-lensing><interferometry><adaptive-optics><weak-lensing>
Can weak gravitational lensing or microlensing-induced wavefront distortion limit resolution of absurdly large aperture telescopes?
uhoh
# Can weak gravitational lensing or microlensing-induced wavefront distortion limit resolution of absurdly large aperture telescopes?

(Asked by: username_0 on 2019-01-09)

This is a theoretical question.

[This answer](https://astronomy.stackexchange.com/a/29088/7982) to the question *If we had the right technology could we see a distant star in detail?* (presumably space-based) primarily addresses the scaling of diffraction-limited resolution with aperture $D$. For existing and near-future telescopes this is assumed to follow $\lambda/D$.

Imagine a future optical or radio interferometric telescope of absurdly large *effective aperture* or baseline, say AU or even larger, operated similarly to the Event Horizon Telescope (local downconversion and timestamping, [interferometry performed offline](https://astronomy.stackexchange.com/q/20082/7982))

Could [weak gravitational lensing](https://en.wikipedia.org/wiki/Weak_gravitational_lensing) effects or [gravitational microlensing](https://en.wikipedia.org/wiki/Gravitational_microlensing) result in wavefront distortion that if not corrected, would result in *degraded resolution*? Note I'm not asking about distortion of the field, but instead a limitation to the resolution; degraded point spread function.

If so, would this problem be amenable to correction in the same way that atmospheric and ionospheric effects (visible and radio) are dealt with? Would it generally be static on the timescale of the observation?

**Tags:** radio-astronomy, gravitational-lensing, interferometry, adaptive-optics, weak-lensing

> **Comments:**
> **username_1**: Adaptive optic systems largely depend on a known "clean" reference source, so if your telescopes FoV can see even one star whose output is subject to significant grav microlensing then it could be corrected.  

---

## 1 answers

### Answer by username_2 on 2019-04-02. Score: 1

As far as *microlensing* is concerned:

### Not likely

This is a bit of a dodge on the question, but it is hard to come up with a scenario where microlensing becomes the dominant PSF term.

Microlensing occurs during conjunction with a stellar or planetary object, and results in a momentary (seconds-to-days timescale) increase in the brightness of the observed star. It is an extremely rare event, [with rates around 100 in 17 million stars in the most recent surveys](https://arxiv.org/abs/astro-ph/0002510).

Stellar densities ($\rho$) around our solar system are on the order of 0.14 stars per cubic parsec. With such a low number density, microlensing does not pose any practical limitation on the resolution of radio telescopes. Lets do some scratch-pad estimates to see:

If we assume a synthetic aperture ($D$) of 1AU ($4.84\times10^{-6}$parsecs) , a wavelength ($\lambda$) of 1mm ([similar to the view of Betelgeuse by the ALMA observatory](https://astronomynow.com/2017/06/30/see-the-sharpest-ever-view-of-giant-betelgeuse/)) , and a desired spatial resolution ($s$) of 10,000 km at a distance $L$:

$$
\begin{align}
\frac{s}{L} &= 1.22 \frac{\lambda }{D} \\
L &= \frac{sD}{1.22 \lambda } = 40\;\text{kilo-parsec}
\end{align}
$$

This is roughly the diameter of the milky way galaxy. So an interferometer operating in the 1mm wavelength with a 1AU baseline has a 10,000 km resolution at a distance of 40 kpc.

How many stars are between the 1AU-wide observatory and the target star? Using a cone of base diameter $D$ and height $L$ as a volume and the above stellar density, we get the average number of stars ($N$) between our aperture and the observed star:
$$ N = \rho \frac{\pi}{12}D^2 L = 3 \times 10^{-8} \; \text{stars}$$

You would have to ramp $D$ up by a factor of $10^4$ before $N \approx 1$ and 'microlensing aberrations' were more than just an extremely rare event.

> **Comments:**
> **username_0**: Thanks for your answer! Ah, it looks like I used the wrong term in my question. I was thinking of [weak gravitational lensing](https://en.wikipedia.org/wiki/Weak_gravitational_lensing), the collective effect of many small, static deflections. But I wrote microlensing by mistake. If there were no answers I could just make the correction, but now that you have answered based on microlensing, I need to honor your answer.  
> **username_0**: I can think of two ways to proceed 1) post a new question, similar to this one and pointing back here, but explaining that it asks about weak lensing instead, or 2) *add weak lensing* as a second effect to consider to this question, opening it up to additional answers. Do you have any preference?  
> **username_0**: I see you've been active on this site and so have seen my comments above. Since there's no objection, I've decided to go with option #2.  
> **username_3**: Related: https://astronomy.stackexchange.com/questions/30462/what-is-the-farthest-we-can-see-into-the-universe  

---

