# What causes Hyabusa-2's close-up images of Ryugu to be dark in the corners?

The NYTimes' article Hayabusa2 Prepares to Drop Rovers on Asteroid Ryugu says

Sept. 19 Rock Hoppers

Hayabusa2 is preparing to deploy two small rovers this week, each about 7 inches wide. Ryugu’s gravity is so weak that the Minerva rovers will be able to slowly hop and float across the surface using internal rotors.

and includes the image below of a close-up view of the surface.

The images appear to be bright in the center and then become darker at the edges, especially in the corners.

I can think of three possible causes of nonuniform brightness in general (there could of course be more) though perhaps not all would apply in this case:

1. Optical vignetting
2. nonuniform fill of camera lights or flash, or $$1/r^2$$ illumination drop due to strong surface curvature
3. directional scattering of light (shadow-hiding) as is seen on the Moon

I don't think Hayabusa-2 is using flash photography, at it's furthest point from the Sun Ryugu is still only about 1.5 AU away.

And unless the camera has variable zoom optics pushed to their limits, I can't imagine that it would be designed with vignetting.

So are we seeing shadow-hiding here? Something else?

Question: What causes Hayabusa-2's close-up images of Ryugu to be dark in the corners?

See material at What's the story behind this Apollo-era image? for more background on this topic, and Are there ANY verified satellite images of visible light coherent backscattering from Earth? for the distinction between shadow-hiding and coherent backscattering.

What's the story behind this Apollo-era image?

below: "During an experiment to measure the asteroid’s gravity, the spacecraft took these images of the surface from less than a mile away." From here

update 2: I found one of the images on the Planetary Society page Hayabusa2 closeup on Ryugu from 1000 meters, 6 August 2018 where it says:

HAYABUSA2 CLOSEUP ON RYUGU FROM 1000 METERS, 6 AUGUST 2018

Surface of Ryugu photographed with the Optical Navigation Camera - Telescopic (ONC-T) from a height of about 1000 m. The image was captured on 6 August 2018 at around 22:57 UTC. Images of the entirety of Ryugu were taken at nearly the same time by the Optical Navigation Camera - Wide angle (ONC-W1, inset). The red frame corresponds to the region in the picture taken by the ONC-T.

also here is an excellent terrestrial manifestation of shadow-hiding

update 1: This tweet by JAXA's Hayabusa2 is stunning, and a great illustration of shadow-hiding (note the bright enhancement near the center:

• They applied Instagram filters Sep 21, 2018 at 9:15
• See wikipedia: " ONC-W1 and ONC-W2 are wide angle (65.24°×65.24°) panchromatic (485–655nm) cameras." But wide angle cameras a more prone to vignetting than telephoto lenses. Which cameras were used for the images in question? The "ONC-T is a telephoto camera with a 6.35°×6.35° field of view" or the ONC-W?
– Uwe
Sep 21, 2018 at 15:08
• @Uwe I'm not sure yet. The caption says the distance was "less than one mile away" and these have like 1 meter resolution roughly, so I can't guess if it's a really good wide angle system or not, but the darkening is over a distance of only a few tens of meters, which is would be less than 1 degree, no matter what kind of lens it was.
– uhoh
Sep 21, 2018 at 15:26
• @Uwe see "update 2"
– uhoh
Sep 21, 2018 at 15:36
• The images were taken at a distance of about 1 km. The diameter of Ryugu is about 0.9 km. The field of view of the images is 6.35° or about 110 m. Using Pythagoras I calculated the edges of the image to be about 6.9 m more distant than the center. I assumed a spherical Ryugu. But Ryugu is more like a diamond shaped body. Therefore the edges may be further away.
– Uwe
Sep 22, 2018 at 11:05

Something to keep in mind here: Lenses are round, AFIAK all current sensors are rectangular. This inherently means there will be a mismatch. There are only three possible choices:

• Make the lens big enough to cover the sensor. The sensor gets a whole image, extra light is projected beside the sensor and wasted. This is the choice made in most cameras, although some lenses in some realms, especially with filters attached, may still vignette. I've seen shots from extreme fisheye lenses that are round, not even dropoff in the corners.

• Make the sensor big enough to cover the lens. The result is major vignetting as these images show.

• Somewhere in between--some wasted light, some dark corners.

Remember that when we are dealing with spacecraft weight and data are king, pretty isn't that important and cost generally means little (because the big costs are going to be the engineering, testing, and the booster. To spend \$1000 to save an ounce on a deep space craft is a no-brainer decision.) While I do not know about the lenses on this spacecraft lenses are heavier than sensors. You'll get more data for a given weight by enlarging the sensor.

• Well making the CCD round is not going to suddenly make the image uniform. Any drop in intensity with distance from the optical axis will be the same no matter what shape an image sensor is. I still have a hunch this is shadow-hiding: atoptics.co.uk/fz611.htm
– uhoh
Sep 22, 2018 at 4:49
• There is another effect. The light rays at the center of the sensor are vertical to the sensor's surface, but the rays at the edges of the sensor are not perpendicular. Therefore light intensity received by the sensor is smaller at its edges. There are special lenses designed for digital imaging compensating this effect.
– Uwe
Sep 22, 2018 at 11:36