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Oh! I am *so* glad you asked that question! Thread incoming:
1/ If you want to make an experimental astronomer cringe, here are two good ways to do it:

1) Touch an eyepiece with your bare finger.

2) Say the words "flat field".
2/ Every digital camera (including the ones used in telescopes) is composed of a grid of millions of pixels. These pixels are, fundamentally, just semiconductor devices for turning light (photons) into an electric signal (electrons) that a computer can read.
3/ The number of electrons generated by a single photon strike is called the gain. So if a pixel has a gain of 1, it means one electron is generated for every photon that hits the pixel.
4/ But we can't manufacture a grid of 25 million pixels and expect them all to have *exactly* the same gain. In reality, some pixels are going to be slightly better/worse at turning photons into electrons (i.e. have a higher/lower gain) than others.
5/ So we need a way to know the gain of every single pixel in a detector. If we don't, then we are at risk of thinking an astronomical target (say, a star) is brighter than it actually is, simply because it had the bad luck to fall on a pixel with a higher gain.
6/ What this means is that *before* we can image a target, we need to image something else that is:

1) Big enough to expose all the pixels on the detector
2) Bright enough to generate a statistically large number of photons
3) Uniform enough to expose all the pixel equally.
7/ This type of image is called a flat field, and the process of taking one is called flat fielding. ("Flat" because it is uniform) and these (along with dark frames and bias frames) are the 3 calibration exposures that astronomers need to take along with their actual data.
8/ Sidenote: Even the camera in your phone has hot and cold pixels, it's just that no one cares if your IG feed has on a pixel that is 0.1% brighter than its neighbor. But astronomers (who's entire job might be summed up as "find out how bright this thing is") *absolutely* care.
9/ So we need an object that is big, bright, and uniform that we can point our telescope at. No problem right?

In theory, no. But in practice, it is actually *incredibly* hard to find an object that meets these criteria to the level of precision that astronomers need (<1%).
10/ The problem is that generating a photometrically flat light source is *incredibly* hard. The difficulty of doing it has led to the proliferation of all sorts of different flat fielding methods. Here are some:
11/ Dome flats: Illuminate a specially painted panel on the inside of the telescope's dome with a bunch of lamps, and then point the telescope at the inside of your dome. (image is from the Univerity of Wyoming infrared observatory)
12/ Twilight flats (aka sky flats): Just after sunset, while the sky is still slightly illuminated, point the telescope at a patch of sky near the zenith that doesn't have any bright stars in it. (image is one of mine taken at the Vassar College Observatory when I was a senior)
13/ Lamp flats: Back illuminate a translucent piece of paper or frosted glass with a grid of LEDs, and point your telescope at it. (Image credit: Sky and Telescope)
14/ Further complicating this issue is that gain is a function of wavelength (i.e. color), temperature, dust grain locations, and the capricious whims of gremlins who live in your telescope. But we have to do it. There is just no way around it.
15/ So how does Hubble take flat fields? Well, Hubble had a series of ground flats taken with before it launched (here is one, credit STSCI). But after ~30 years of thermal cycling and radiation exposure, how do we know if these flats are still accurate?
16/ One way is to point Hubble at a bright star (or star cluster) and then move the telescope around (which astronomers call "dithering") to smear the signal across multiple pixels (aka Star Flats).
17/ But stars don't make for great flat fields, because they are point sources. At some wavelengths, the easiest way for Hubble to generate a new flat field is just to point it *down*.
18/ Earth is a poor flat field because of its clouds and terrain features, but at some wavelengths (UV especially) it is actually possible to generate a flat field that is good enough to cross-check the ground flats. These are called Earth Flats (image credit: Mark Clampin, NASA)
19/ And that's it! Thanks for coming down this deep well with me. The takeaway you should have at this point is that flat fielding is *maddeningly* difficult to get right, especially because it's insidiously difficult to detect when you've got it wrong.
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