Sep 262022
 

Putting aside Trumpism, woke-ism, the politics of the day, populism, the whole kaboodle, here’s something to contemplate.

Tonight, Russia is continuing its efforts to subjugate the independent nation of Ukraine, not refraining from committing serious, intentional, criminal acts against the country’s civilian population to further its goals.

Also tonight, the space agency of the United States, NASA, is conducting a ground-breaking experiment, the first of its kind testing a method that might one day avert a global disaster, protecting the entire planet from an asteroid impact.

DART: View of the asteroid Dimophos 20 minutes to impact

I think it speaks volumes about the different ways in which these countries see their respective roles in the world.

I almost long for Soviet times. The regime was assuredly brutal, but at least it professed to seek noble goals. Not anymore, I guess.

 Posted by at 7:18 pm
Sep 132022
 

Oops. It’s past midnight already, so technically it was yesterday but to me it is still today, September 12.

The sixtieth anniversary of John F. Kennedy’s famous “we choose to go to the Moon” speech. How many more years before another human sets foot on the Moon?

Oh, and it was thirty years ago that Ildiko and I became married.

Yup, that’s us; 1979 vs. 2019.

 Posted by at 1:54 am
May 232022
 

This morning, Google greeted me with a link in its newsstream to a Hackaday article on the Solar Gravitational Lens. The link caught my attention right away, as I recognized some of my own simulated, SGL-projected images of an exo-Earth and its reconstruction.

Reading the article I realized that it appeared in response to a brand new video by SciShow, a science-oriented YouTube channel.

Yay! I like nicely done videos presenting our work and this one is fairly good. There are a few minor inaccuracies, but nothing big enough to be even worth mentioning. And it’s very well presented.

I suppose I should offer my thanks to SciShow for choosing to feature our research with such a well-produced effort.

 Posted by at 7:22 pm
May 062022
 

A beautiful study was published the other day, and it received a lot of press coverage, so I get a lot of questions.

This study shows how, in principle, we could reconstruct the image of an exoplanet using the Solar Gravitational Lens (SGL) using just a single snapshot of the Einstein ring around the Sun.

The problem is, we cannot. As they say, the devil is in the details.

Here is a general statement about any conventional optical system that does not involve more exotic, nonlinear optics: whatever the system does, ultimately it maps light from picture elements, pixels, in the source plane, into pixels in the image plane.

Let me explain what this means in principle, through an extreme example. Suppose someone tells you that there is a distant planet in another galaxy, and you are allowed to ignore any contaminating sources of light. You are allowed to forget about the particle nature of light. You are allowed to forget the physical limitations of your cell phone’s camera, such as its CMOS sensor dynamic range or readout noise. You hold up your cell phone and take a snapshot. It doesn’t even matter if the camera is not well focused or if there is motion blur, so long as you have precise knowledge of how it is focused and how it moves. The map is still a linear map. So if your cellphone camera has 40 megapixels, a simple mathematical operation, inverting the so-called convolution matrix, lets you reconstruct the source in all its exquisite detail. All you need to know is a precise mathematical description, the so-called “point spread function” (PSF) of the camera (including any defocusing and motion blur). Beyond that, it just amounts to inverting a matrix, or equivalently, solving a linear system of equations. In other words, standard fare for anyone studying numerical computational methods, and easily solvable even at extreme high resolutions using appropriate computational resources. (A high-end GPU in your desktop computer is ideal for such calculations.)

Why can’t we do this in practice? Why do we worry about things like the diffraction limit of our camera or telescope?

The answer, ultimately, is noise. The random, unpredictable, or unmodelable element.

Noise comes from many sources. It can include so-called quantization noise because our camera sensor digitizes the light intensity using a finite number of bits. It can include systematic noises due to many reasons, such as differently calibrated sensor pixels or even approximations used in the mathematical description of the PSF. It can include unavoidable, random, “stochastic” noise that arises because light arrives as discrete packets of energy in the form of photons, not as a continuous wave.

When we invert the convolution matrix in the presence of all these noise sources, the noise gets amplified far more than the signal. In the end, the reconstructed, “deconvolved” image becomes useless unless we had an exceptionally high signal-to-noise ratio, or SNR, to begin with.

The authors of this beautiful study knew this. They even state it in their paper. They mention values such as 4,000, even 200,000 for the SNR.

And then there is reality. The Einstein ring does not appear in black, empty space. It appears on top of the bright solar corona. And even if we subtract the corona, we cannot eliminate the stochastic shot noise due to photons from the corona by any means other than collecting data for a longer time.

Let me show a plot from a paper that is work-in-progress, with the actual SNR that we can expect on pixels in a cross-sectional view of the Einstein ring that appears around the Sun:

Just look at the vertical axis. See those values there? That’s our realistic SNR, when the Einstein ring is imaged through the solar corona, using a 1-meter telescope with a 10 meter focal distance, using an image sensor pixel size of a square micron. These choices are consistent with just a tad under 5000 pixels falling within the usable area of the Einstein ring, which can be used to reconstruct, in principle, a roughly 64 by 64 pixel image of the source. As this plot shows, a typical value for the SNR would be 0.01 using 1 second of light collecting time (integration time).

What does that mean? Well, for starters it means that to collect enough light to get an SNR of 4,000, assuming everything else is absolutely, flawlessly perfect, there is no motion blur, indeed no motion at all, no sources of contamination other than the solar corona, no quantization noise, no limitations on the sensor, achieving an SNR of 4,000 would require roughly 160 billion seconds of integration time. That is roughly 5,000 years.

And that is why we are not seriously contemplating image reconstruction from a single snapshot of the Einstein ring.

 Posted by at 4:01 pm
Dec 242021
 

Although we are not religious, we celebrate Christmas.

And I still cannot think of a better way to celebrate Christmas than with the words of the astronauts of Apollo 8, and the sense of awe they felt when they became the first human beings ever in the history of our species to be completely cut off from Mother Earth, when their spaceship disappeared behind the Moon.

Earthrise from Apollo 8

Re-emerging, they read passages from the Book of Genesis to their audience, with Frank Borman concluding with the words:

[G]ood night, good luck, a Merry Christmas – and God bless all of you, all of you on the good Earth.

To me, this is the most beautiful Christmas message ever.

 Posted by at 2:38 am
Oct 242021
 

Thanks to streaming services, I occasionally stumble upon films and television series from foreign lands that otherwise I’d not even know about. And no, I don’t mean Squid Game, that explosively popular Korean series: I only watched the opening few minutes of the first episode so far, and I don’t yet know if it is my cup of tea. Rather, this time around it is a Russian movie that I came across on Amazon Prime: a 2017 film titled Salyut-7.

Salyut-7 was a Soviet space station. In 1985, the space station was dead, without power. The Russians launched a daring rescue mission, Soyuz-T13, which was not only able to dock with the derelict station but also able to revive and repair it.

Consistent with Soviet era secrecy, we knew very little about this mission and didn’t appreciate its significance back then.

The movie itself combined the actual story of the Soyuz-T13 mission with other events, such as the fire on board the Mir space station 12 years later or a nonsensical fictitious mission by the space shuttle Challenger to “steal” the station, for dramatic effect. In that, I think they did a disservice to the cosmonauts who pulled off this repair: perhaps less spectacular in terms of visual effects, what they accomplished was no less significant.

But otherwise, I found the movie fun to watch, very well done, with top notch special effects and (insofar as my inexpert eye can tell) excellent acting and directing. I enjoyed the movie. And its faults notwithstanding, I think it offers a worthy reminder that the USSR’s space program brought enormous value to all of humanity. It saddens me deeply when I think of how much of it went to waste in the turbulent years following the breakup of the USSR.

 Posted by at 12:11 pm
Apr 192021
 

This morning, a drone took flight. It successfully took off from the ground, hovered for a few seconds, and then landed safely.

What, you ask? How is this supposed to be a big deal? There are millions of drones out there, kids playing with them and whatnot.

Oh, but this drone is special, and not only because it carries a small piece of fabric from the Wright brothers’ very first airplane.

It is special because it flew on Mars.

 Posted by at 11:42 am
Mar 142021
 

The next in our series of papers describing the extended gravitational lens (extended, that is, in that we are no longer treating the lensing object as a gravitational monopole) is now out, on arXiv.

Here’s one of my favorite images from the paper, which superimposes the boundary of the quadrupole caustic (an astroid curve) onto a 3D plot showing the amplitude of the gravitational lens’s point-spread function.

I was having lots of fun working on this paper. It was, needless to say, a lot of work.

 Posted by at 9:18 pm
Feb 182021
 

I really cannot tell which impresses me more: The incredibly complex landing or the fact that there is now a de facto infrastructure in orbit around Mars, in the form of earlier spacecraft that provide communications relay capabilities for real-time tracking of the landing.

Or perhaps the fact that Perseverance also carries the Ingenuity helicopter. If successful, it will be the first drone to fly in the atmosphere of another planet.

The children of future settlers on Mars will be learning about these moments in school.

 Posted by at 4:06 pm
Sep 032020
 

Tonight, Slava Turyshev sent me a link to an article that was actually published three months ago on medium.com but until now, escaped our attention.

It is a very nice summary of the work that we have been doing on the Solar Gravitational Lens to date.

It really captures the essence of our work and the challenges that we have been looking at.

And there is so much more to do! Countless more things to tackle: image reconstruction of a moving target, imperfections of the solar gravitational field, precision of navigation… not to mention the simple, basic challenge of attempting a deep space mission to a distance four times greater than anything to date, lasting several decades.

Yes, it can be done. No it’s not easy. But it’s a worthy challenge.

 Posted by at 10:54 pm
Jul 312020
 

A few weeks ago, Christian Ready published a beautiful video on his YouTube channel, Launch Pad Astronomy. In this episode, he described in detail how the Solar Gravitational Lens (SGL) works, and also our efforts so far.

I like this video very much. Especially the part that begins at 10:28, where Christian describes how the SGL can be used for image acquisition. The entire video is well worth seeing, but this segment in particular does a better job than we were ever able to do with words alone, explaining how the Sun projects an image of a distant planet to a square kilometer sized area, and how this image is scanned, one imaginary pixel at a time, by measuring the brightness of the Einstein-ring around the Sun as seen from each pixel location.

We now understand this process well, but many more challenges remain. These include, in no particular order, deviations of the Sun from spherical symmetry, minor variations in the brightness of the solar corona, the relative motion of the observing probe, Sun, exosolar system and target planet therein, changing illumination of the target, rotation of the target, changing surface features (weather, perhaps vegetation) of the target, and the devil knows what else.

Even so, lately I have become reasonably confident, based on my own simulation work and our signal-to-noise estimates, as well as a deconvolution approach under development that takes some of the aforementioned issues into consideration, that a high-resolution image of a distant planet is, in fact, obtainable using the SGL.

A lot more work remains. The fun only just began. But I am immensely proud to be able to contribute to of this effort.

 Posted by at 7:41 pm
Oct 112019
 

I just saw the news: Alexei Leonov died.

Leonov was a Soviet cosmonaut. The first man to ever take a spacewalk (which, incidentally, nearly killed him, as did his atmospheric re-entry, which didn’t exactly go as planned either.)

Leonov was also an accomplished artist. Many of his paintings featured space travel. Here is a beautiful picture, from a blog entry by Larry McGlynn, showing Leonov with one of his paintings, in 2004 in Los Angeles.

So Leonov now joins that ever growing list of brave souls from the dawn of the space age who are no longer with us. Rest in peace, Major General Leonov.

 Posted by at 2:01 pm
Aug 072019
 

Yesterday, we posted our latest paper on arXiv. Again, it is a paper about the solar gravitational lens.

This time around, our focus was on imaging an extended object, which of course can be trivially modeled as a multitude of point sources.

However, it is a multitude of point sources at a finite distance from the Sun.

This adds a twist. Previously, we modeled light from sources located at infinity: Incident light was in the form of plane waves.

But when the point source is at a finite distance, light from it comes in the form of spherical waves.

Now it is true that at a very large distance from the source, considering only a narrow beam of light, we can approximate those spherical waves as plane waves (paraxial approximation). But it still leaves us with the altered geometry.

But this is where a second observation becomes significant: As we can intuit, and as it is made evident through the use of the eikonal approximation, most of the time we can restrict our focus onto a single ray of light. A ray that, when deflected by the Sun, defines a plane. And the investigation can proceed in this plane.

The image above depicts two such planes, corresponding to the red and the green ray of light.

These rays do meet, however, at the axis of symmetry of the problem, which we call the optical axis. However, in the vicinity of this axis the symmetry of the problem is recovered, and the result no longer depends on the azimuthal angle that defines the plane in question.

To make a long story short, this allows us to reuse our previous results, by introducing the additional angle β, which determines, among other things, the additional distance (compared to parallel rays of light coming from infinity) that these light rays travel before meeting at the optical axis.

This is what our latest paper describes, in full detail.

 Posted by at 9:10 pm
Jul 192019
 

The world is celebrating the 50th anniversary of one of the most momentous events in human history: the first time a human being set foot on another celestial body.

It is also a triumph of American ingenuity. Just as Jules Verne predicted a century earlier, it was America’s can-do spirit that made the Moon landing, Armstrong’s “one small step” possible.

And today, just like 50 years ago, their success was celebrated around the world, by people of all nationality, religion, gender or ethnicity.

But that’s not good enough for some New York Times columnists.

Instead of celebrating the Moon landing, Mary Robinette Kowal complains about the gender bias that still exists in the space program. Because, as we learn from her article, this evil male chauvinistic space program was “designed by men, for men”. Because, you know, men sweat in different areas of their body and all. Even in the office, temperatures are set for men, which leaves women carrying sweaters.

Sophie Pinkham goes further. Instead of celebrating America’s success on July 20, 1969, Pinkham goes on to praise the Soviet space program in a tone that might have been rejected even by the editors of Pravda in 1969 as too over-the-top. Because unlike America, the Soviets put the first woman in space! Their commitment to equality did not stop there: They also sent the first Asian man and the first black man into orbit. Because, we are told, “under socialism, a person of even the humblest origins could make it all the way up.”

Just to be clear, I am not blind to gender bias. We may have come a long way since the 1960s, but full gender equality has not yet been achieved anywhere: not in the US, not in Canada, not even in places like Iceland. And racism in America remains a palpable, everyday reality. Back in 1969, things were a lot worse.

But to pick the 50th anniversary of an event that, even back in the turbulent 1960s, had the power to unify humanity, to launch such petty rants? That is simply disgraceful. Or, as the New York Post described it, obscene.

The New York Post also makes mention of one of the female pioneers of the US space program, Margaret Hamilton, whose work was instrumental in making the Apollo landings possible. Yet somehow, neither Pinkham nor Kowal found it in their hearts to mention her name.

I have to wonder: Are columnists like Pinkham or Kowal secretly rooting for Donald Trump? Because they certainly seem to be doing their darnedest best to alienate as many voters as possible, from what appears to be an increasingly bitter, intolerant, ideological agenda on the American political left.

 Posted by at 6:49 pm
Jul 162019
 

Fifty years ago today, fifty years ago this very hour in fact, at 9:32 AM EDT on July 16, 2019, Apollo 11 was launched.

Moonbound Apollo 11 clears the launch tower. NASA photo

And thus began a journey that, arguably, remains the greatest adventure in human history to date.

I was six years old in 1969, hooked on the novels of Jules Verne. With Apollo 11, Verne’s bold imagination became the reality of the day.

 Posted by at 9:25 am
Jul 152019
 

Galileo is the world’s third global satellite navigation system, built by the European Union, operating in parallel with the American GPS system and Russia’s GLONASS. It has been partially operational since 2016, with a full constellation if satellites expected to enter service this year.

But as of early Monday, July 15, Galileo has been down for nearly four days, completely inoperative in fact:

As of the time of this writing, no explanation is being offered, other than one article mentioning an unspecified issue with Galileo’s ground-based infrastructure.

It really is difficult to comprehend how such a failure can occur.

It is even more difficult to comprehend the silence, the lack of updates, explanations, or any information about the expected recovery.

 Posted by at 12:59 am