New Horizons is a spacecraft headed to Pluto. It launched nearly a decade ago, but it will arrive in July of this year and do a fly through the system. Doing lots of amazing science.
One of the instruments is LORRI, a long-focal-length camera that will be the prime imager for much of the mission because it will be able to take the highest spatial resolution images. It will also be used (was being used and is being used, too) for optical navigation — make sure we’re headed in the right direction.
Just a few minutes ago, on the anniversary of Clyde Tombaugh’s birth (the guy who discovered Pluto), NASA released the first image from LORRI of Pluto and its main satellite, Charon, taken during the Approach Phase. There’s a lot going on here – one point in particular that I just know is prone to misunderstanding later on – so I want to talk a bit about this image.
I am involved with the New Horizons mission. I am not a NASA employee. This is my personal blog and everything on it is my opinion, are my words, and is done completely independently (time-wise, resource-wise, person-wise) from my work on New Horizons. In fact, it is on record that this blog is legally distinct from my professional work. Nothing I say here should be taken as an official statement by NASA or the New Horizons team.
Resolution / Pixel Scale
That out of the way, let’s get to the meat of this post. Also, I’m going to use “resolution” and “pixel scale” a bit loosely here, so pedants need to forgive me right away.
LORRI is an amazing camera. It is a 1024×1024 pixel detector, and each pixel has an effective angular size of 4.95 µrad (micro radians, or about 1.02 arcsec). 1 arcsec is about the width of a human hair from 10 meters (33ft) away. (source)
At the moment, New Horizons is around 200,000,000 km away from Pluto. That’s okay, it still has 5.5 months to get there. Pluto is approximately 1180 km in radius. That means, from some simple trigonometry (remember SOHCAHTOA?), Pluto is about 1.2 arcsec in radius, or 2.4 arcsec in diameter. Charon is very roughly half Pluto’s diameter, so it’s around 1.2 arcsec in diameter. Charon and Pluto orbit on opposite sides of their center of mass, which means they are around 8.6 Plutos away from each other, or around 9.1 arcsec separated.
Okay, lots of numbers there. Basically, that means that right now, if we had perfect optics, Pluto is about 2 pixels across, Charon 1, and they’d be around 8 pixels away from each other, max (since their orientation on the plane of the sky is not perpendicular to the spacecraft right now).
(No) Perfect Optics
No such thing exists. Given the best, most perfect optics ever, you can never get infinitely fine details. This is because light will behave as a wave, and give rise to Airy disks and patterns meaning that the light will spread out as it travels through the optics. Unless you had an infinitely wide optical system.
When you factor everything together about the optics and system and detector and other things, from a point source of light, you get a point-spread function (PSF). This is the practical, measured spreading out of the light. In astronomy, we often measure the PSF based on fitting a Gaussian distribution to a star, since a star should be a point source and just cover one, single pixel.
With a telescope aperture of 208mm for LORRI, and a passband of light centered around 0.6 µm (red light), the Airy disk should be around 1.22*0.0006/208 = 6.8 µrad. That’s around 1.4 LORRI pixels. Amazing coincidence!
Actually, not. When designing an instrument, you typically want to just about over-sample the Airy disk. You don’t want to under-sample because then you’re losing valuable resolution and information. You don’t want to over-sample because then you’re just wasting money on a detector that is too “good” for your optics, and other issues that come about when you have small pixels. So, designing a system that’s around 1-3 pixels per Airy disk is good.
When you go to a practical PSF, it’s going to be a bit bigger just because no system is perfect.
What’s the Point?
Oh yeah, back to Pluto.
First New Horizons Image of Pluto and Charon from Approach Phase (©NASA/APL/SwRI)
Let’s put these parts together: Right now, Pluto should be around 2 pixels across, Charon 1, and a separation of around 7-8 pixels. But, add in the PSFs due to the laws of optics. That means that the light should now be spread out a bit more.
And that is why this image looks like it does. It’s also been enlarged by 4x, such that each original LORRI pixel has now been resampled. So, if you look at the image NASA released, and you blow it up a lot, Pluto looks like it’s around ten pixels across, and Charon around five.
To repeat: The released image shows Pluto to be around 10 pixels wide, and Charon around 5. Despite the theoretical values now (2 pixels and 1 pixel, respectively). That’s because (1) the PSF spreads the light out because we live in a world with real and not ideal optics, and (2) the released image was enlarged by a factor of 4.
New Horizons is zipping quickly along. In May, it will surpass all previous images taken and we will truly be in new territory and a new era of discovery (so far as imaging the Pluto system — note that the other instruments have already taken a lot of data and are learning new things). That best image that exists so far of Pluto shows Pluto to be approximately 8 pixels across.
And that’s why I started this post out by stating, “one point in particular that I just know is prone to misunderstanding later on.” So, today, NASA released an image that shows Pluto with as many pixels across as what it will take in late May, when it will have that number of pixels across.
See why I wanted to bring this up now? I can just hear the pseudoscientists claiming that NASA is lying about the power of the New Horizons telescopes, they’re deliberately down-sizing images (later, based on images released now), and various other things. While they’ll still almost certainly say that, at least you know now why that’s not the case, and what’s really going on now versus then.
There are only 2 (well, about 4, since it’s 2×2) “real” pixels in the Pluto disk right now, the others are interpolated based on expanding the size to make the image look nice for this release, celebrating the image and Clyde Tombaugh’s birthday. In four months, we’ll have all these pixels, but they won’t be based on a computer algorithm, they’ll be “real” pixels across Pluto taken by LORRI. Convolved (“smeared”) with a PSF that’s about 1.5-2 pixels.