We’ve talked about the ongoing work at the Jet Propulsion Society on the Sun’s gravitational focus at some length, most recently in JPL Work on a Gravitational Lensing Mission, where I looked at Slava Turyshev and team’s Phase II report to the NASA Innovative Advanced Concepts office. The team is now deep into the work on their Phase III NIAC study, with a new paper available in preprint form. Dr. Turyshev tells me it can be considered a summary as well as an extension of previous results, and today I want to look at the significance of one aspect of this extension.

There are numerous reasons for getting a spacecraft to the distance needed to exploit the Sun’s gravitational lens – where the mass of our star bends the light of objects behind it to produce a lens with extraordinary properties. The paper, titled “Resolved Imaging of Exoplanets with the Solar Gravitational Lens,” notes that at optical or near-optical wavelengths, the amplification of light is on the order of ~ 2 X 1011, with equally impressive angular resolution. If we can reach this region beginning at 550 AU from the Sun, we can perform direct imaging of exoplanets.

We’re talking multi-pixel images, and not just of huge gas giants. Images of planets the size of Earth around nearby stars, in the habitable zone and potentially life-bearing.

Other methods of observation give way to the power of the solar gravitational lens (SGL) when we consider that, according to Turyshev and co-author Viktor Toth’s calculations, to get a multi-pixel image of an Earth-class planet at 30 parsecs with a diffraction-limited telescope, we would need an aperture of 90 kilometers, hardly a practical proposition. Optical interferometers, too, are problematic, for even they require long-baselines and apertures in the tens of meters, each equipped with its own coronagraph (or conceivably a starshade) to block stellar light. As the paper notes:

Even with these parameters, interferometers would require integration times of hundreds of thousands to millions of years to reach a reasonable signal-to-noise ratio (SNR) of ? 7 to overcome the noise from exo-zodiacal light. As a result, direct resolved imaging of terrestrial exoplanets relying on conventional astronomical techniques and instruments is not feasible.

Integration time is essentially the time it takes to gather all the data that will result in the final image. Obviously, we’re not going to send a mission to the gravitational lensing region if it takes a million years to gather up the needed data.

Image: Various approaches will emerge about the kind of spacecraft that might fly a mission to the gravitational focus of the Sun. In this image (not taken from the Turyshev et al. paper), swarms of small solar sail-powered spacecraft are depicted that could fly to a spot where our Sun’s gravity distorts and magnifies the light from a nearby star system, allowing us to capture a sharp image of an Earth-like exoplanet. Credit: NASA/The Aerospace Corporation.

But once we reach the needed distance, how do we collect an image? Turyshev’s team has been studying the imaging capabilities of the gravitational lens and analyzing its optical properties, allowing the scientists to model the deconvolution of an image acquired by a spacecraft at these distances from the Sun. Deconvolution means reducing noise and hence sharpening the image with enhanced contrast, as we do when removing atmospheric effects from images taken from the ground.

All of this becomes problematic when we’re using the Sun’s gravitational lens, for we are observing exoplanet light in the form of an ‘Einstein ring’ around the Sun, where lensed light from the background object appears in the form of a circle. This runs into complications from the Sun’s corona, which produces significant noise in the signal. The paper examines the team’s work on solar coronagraphs to block coronal light while letting through light from the Einstein ring. An annular coronagraph aboard the spacecraft seems a workable solution. For more on this, see the paper.

An earlier study analyzed the solar corona’s role in reducing the signal-to-noise ratio, which extended the time needed to integrate the full image. In that work, the time needed to recover a complex multi-pixel image from a nearby exoplanet was well beyond the scope of a practical mission. But the new paper presents an updated model for the solar corona modeling whose results have been validated in numerical simulations under various methods of deconvolution. What leaps out here is the issue of pixel spacing in the image plane. The results demonstrate that a mission for high resolution exoplanet imaging is, in the authors’ words, ‘manifestly feasible.’

Pixel spacing is an issue because of the size of the image we are trying to recover. The image of an exoplanet the size of the Earth at 1.3 parsecs, which is essentially the distance of Proxima Centauri from the Earth, when projected onto an image plane at 1200 AU from the Sun, is almost 60 kilometers wide. We are trying to create a megapixel image, and must take account of the fact that individual image pixels are not adjacent. In this case, they are 60 meters apart. It turns out that this actually reduces the integration time of the data to produce the image we are looking for.

From the paper [italics mine]:

We estimated the impact of mission parameters on the resulting integration time. We found that, as expected, the integration time is proportional to the square of the total number of pixels that are being imaged. We also found, however, that the integration time is reduced when pixels are not adjacent, at a rate proportional to the inverse square of the pixel spacing.

Consequently, using a fictitious Earth-like planet at the Proxima Centauri system at z0 = 1.3 pc from the Earth, we found that a total cumulative integration time of less than 2 months is sufficient to obtain a high quality, megapixel scale deconvolved image of that planet. Furthermore, even for a planet at 30 pc from the Earth, good quality deconvolution at intermediate resolutions is possible using integration times that are comfortably consistent with a realistic space mission.

Image: This is Figure 5 from the paper. In the caption, PSF refers to the Point Spread Function, which is essentially the response of the light-gathering instrument to the object studied. It measures how much the light has been distorted by the instrument. Here the SGL itself is considered as the source of the distortion. The full caption: Simulated monochromatic imaging of an exo-Earth at z0 = 1.3 pc from z = 1200 AU at N = 1024 × 1024 pixel resolution using the SGL. Left: the original image. Middle: the image convolved with the SGL PSF, with noise added at SNRC = 187, consistent with a total integration time of ?47 days. Right: the result of deconvolution, yielding an image with SNRR = 11.4. Credit: Turyshev et al.

The solar gravity lens presents itself not as a single focal point but a cylinder, meaning that we can stay within the focus as we move further from the Sun. The authors find that as the spacecraft moves ever further out, the signal to noise ratio improves. This heightening in resolution persists even with the shorter integration times, allowing us to study effects like planetary rotation. This is, of course, ongoing work, but these results cannot but be seen as encouraging for the concept of a mission to the gravity focus, giving us priceless information for future interstellar probes.

The paper is Turyshev & Toth., “Resolved imaging of exoplanets with the solar gravitational lens,” available for now only as a preprint. The Phase II NIAC report is Turyshev et al., “Direct Multipixel Imaging and Spectroscopy of an Exoplanet with a Solar Gravity Lens Mission,” Final Report NASA Innovative Advanced Concepts Phase II (2020). Full text.