Perfect!
If that 10uF/16V electrolytic happens to be the problem, be sure to replace the others of the same value as well (e.g. the one right beneath the label 'C250'). Similar caps in similar positions from the same batch frequently have a similar life expectancy. Electrolytics don't have an infinite lifespan to begin with.
Sadly these caps are the more challenging ones to replace. There are two ways that come to mind:
1: With a regular soldering iron, get hold of some "litze"/desoldering braid, which is a copper mesh that will wick up solder. Fold a bit of the braid in an angle, press that against one of the contacts of the capacitor, then hold your soldering iron against it until most/all of the solder is wicked into the braid. While doing this, you can try to push the body of the cap away from the contact that you're sucking dry to see if it will lift off the PCB. Then do the same for the opposite contact. Temperature setting on the soldering iron will depend; this is likely already done with lead-free solder, so temperature will need to be fairly high. I generally set it to over 300C for a task like this, but you'll have to experiment. It helps to apply some flux to the contact before you start wicking up the solder, so buy some of that too. Any flux will do. A small to mdeium-sized chiseled soldering tip will work best for this.
2: If you have (or are willing to purchase) a hot air rework soldering station, just set it to a conveniently high temperature (350-400C for this job sounds like a decent starting point), with a broad aperture bit and high airflow. See if you can heat the entire thing in one go and try to pick it up with a pair of tweezers. Once the contacts are hot enough, the cap should lift right off the PCB without any effort. Make sure to blast the hot air
away from the AD9822 chip.
Re-soldering the electrolytic cap is actually easier than removing it. With a normal soldering iron (option 1), I'd suggest melting some soldering tin onto both pads first so you have a nice bead. I prefer a leaded type of 60/40 or thereabouts, which will work just fine here, but manufacturers aren't allowed to use it as per RoHS. Apply some flux, then hold the capacitor to the pads and solder the contacts one by one, while pressing the capacitor down towards the PCB so that its contacts are ensured to be dipped into the tin puddle you made their.
Observe proper polarity; the black wedge on the top of the electrolytic capacitor should be on the same side as the original one you remove. Mounting the new one in the wrong orientation will likely cause fireworks (the new cap will pop/explode) and possible damage to other components.
With a hot air gun, re-soldering the part can be done in a similar way; first wet the contact with a nice quantity of tin, apply some flux, press down the part with tweezers and heat the contacts until the capacitor 'melts' into place. But I prefer r(e)soldering these caps with a regular iron and a decently fine tip.
If replacing the 10uF/16V electrolytic capacitor helps anything, I'd also suggest replacing the bigger 100uF/6V caps. For instance C198 and C200 by the looks of it provide filtering for the analog 5V supply of the AD9822 and their performance is absolutely critical for a clean signal (the same is true for the smaller C196 discussed below).
See if replacing that electrolytic (and similar ones elsewhere in the device; see earlier remark) solves the problem. I have a feeling it might not, but who knows. If it doesn't help, I'd be tempted to also replace the smaller 0.1uF decoupling capacitors. These are the tiny tan-colored boxes. In particular you would want to replace the three little caps near the label 'C213', the single one just below the AD9822 labeled 'C196' as well as its sibling immediately above the AD9822 (to the right of the U117 label, between the 10uF/16V electrolytic and the AD9822 chip). Finally, C197 (to the left of the AD9822) should be replaced if you're going to do the all of the small decoupling caps.
Capacitor C201 of a similar function as the ones mentioned above is far less critical and unlikely to present a problem.
For the smaller capacitors (the tan ones), removal is relatively easy. With a regular soldering iron, take a decently large chiseled tip, set temperature to 300C or so and hold the tip against the length of the capacitor so that it touches both contacts. You may want to add some more tin to each of the contacts so that there's more surface area for the soldering iron to work with. Heat up the part and lift it off with tweezers. Shouldn't take more than a few seconds to get this done. Don't worry about destroying the part if you're going to replace it anyway. I often find the contacts dislodge or the body of the cap fractures a bit if force is applied; no worries. Just keep the replacement in one part (which is easy enough)!
With hot air, even easier: heat up, lift off with tweezers, done.
Resoldering with a regular iron and fine tip: wet one of the contacts with a little bead of tin. Press the part against the contacts, then tack the part into place by melting the bead of tin you've just deposited. The cap will now remain in place and you can solder the other contact by applying some tin to it.
With a hot air gun: apply some tin to both contacts, stick the capacitor to the contacts using some flux (or hold it with a tweezer), apply hot air until tin melts and the cap will 'magically' slide into place.
Don't even think of undertaking this if you do not have a soldering iron that with temperature control or a hot-air smd rework soldering station. Devices like soldering irons without temperature control, hot-air guns for automotive or general purpose use, 'soldering guns' used for plumbing or miniature gas flame soldering devices are NOT appropriate for this work.
Without the right tools this job WILL turn into a
nightmare, whereas with the proper tools, it takes a few minutes and the result will be clean.
Good luck and let me know if you have any questions.
PS: there are millions of videos on YouTube about soldering SMD parts. Be sure to have a look at some. Some will do it the same way I described above, some will be subtly different. There are many ways; the above is what works for me.
The three small caps to the center right of the AD9822 are the input capacitors between the AD9822 and the actual CCD. I don't expect them to be faulty; the problems would look different and be far worse. When doing work around the IC, make sure to not damage these little capacitors and also not to overheat them, as this may degrade their performance.
Removing the small tan caps is similar to the electrolytics. It's easy with a hot air station, where you just heat up the entire part and pick it up with tweezers.
PS: if you have a working knowledge of electronics, I'd recommend studying the datasheet of the AD9822 chip which you'll find here:
https://www.analog.com/media/en/technical-documentation/data-sheets/ad9822.pdf
Especially the application circuit on page 17 is relevant as you'll be doing work that relates to the components listed on it. It looks like Nikon's implementation follows these instructions closely (as it should!)