CIRCULAR POLARIZER
The biggest bang for your buck are B+W Circular Polarizers. I believe you need 72mm filters for your AF-P 10-20mm DX lens...
$64.50.... B+W 72mm "MRC" C-Pol, standard 1 to 2 stops light reduction, 8-layer multi-coating, German Schott glass in brass frame.
$68.95.... B+W 72mm "F-Pro" C-Pol, high transmissive (.75-1.5 stops), finer Kaesemann type, edge sealed, otherwise same as the above.
$77.95... B+W 72mm "XS-Pro" C-Pol, same as above, except 16-layer Nano MRS coatings (easier to clean, dust/scratch resistant), and a slimmer frame.
You can find some multi-coated C-Pol that are slightly less expensive, but they aren't the same quality... using "no name" glass, aluminum frames, etc.
Most are a little to a lot more expensive, even though they might not be the same quality (certainly aren't any better). For example...
$129.95.... Hoya 72mm EVO C-Pol... 16-layer multi-coatings... but no-name glass, not not high transmissive, nor Kaesemann type foils, aluminum frame (more likely to get stuck on lenses with metal threads), and not "slim".
$139.95... Tiffen 72mm HT C-Pol... high transmissive and "ColorCore" glass... but unknown coatings, "military grade" and "extra hard" (whatever that means), titanium? frame.
$158.00... Zeiss 72mm T* C-Pol... "quality glass", "T* coating" (singular?), slim
The most comparable to B+W specification...
$139.00... Breakthrough Photography 72mm X4 C-Pol... Schott glass, high transmissive, 15- or 16-layer multi-coatings, brass frame.
$172.70... Heliopan 72mm SH-PMC C-Pol.... almost identical specs as B+W XS-Pro (but Heliopan offers choice of standard or slim mount for same price).
Note: Any circular polarizer will in some situations give an uneven effect on an ultrawide lens like yours. For example, a broad expanse of clear blue sky may darken more in one area than in others. This is because a polarizing filter's effect is strongest 90 degrees from the light source (i.e., the sun), and it gradually diminishes as the angle is closer to 0 or 180 degrees. Ultrawides simply encompass such a broad scene, that you are likely to see this occurring at times. It's not necessarily a bad thing (can even be useful)... just don't be surprised when you see it and rest assured it's not a fault of the lens or the filter. All polarizers do this when used on ultrawides.
NEUTRAL DENSITY FILTER
As to the ND Filter (not "circular" ND... although it's a round filter), well it's not so clear cut.... You'll probably want a fairly strong 8 or 9 stop for "waterfall" effects.
$66.40 (on sale)... Formatt Hitech 72mm ND 2.4 (8 stop)... Schott glass, 15-layer multi-coating, slim frame (aluminum)
B+W offers choice of 10-stop or 6-stop or weaker ND. Instead of a single, strong ND filter such as above, for still photos of moving water (or large apertures in bright light conditions) you might prefer two less strong that can be used separately or combined when stronger effect is wanted. For example...
$97.95... B+W 72mm MRC 106M 6-Stop ND... Schott glass, 8-layer multi-coating, brass frame. And...
$114.00... B+W 72mm MRC 103M 3-Stop ND... same specifications.
(B+W also offers the same in cheaper "SC" or "single coated" and in more expensive "XS-Pro" 16-layer MC, slim versions.)
This can be useful, giving you three different strength ND to work with in different situations. However, I'm not certain if stacked filters would cause vignetting problems at the wider settings of your lens. It's possible they would. You'll almost have to try it and see. "Slim" filters might work, if standard frames don't. However, I usually try to avoid slim unless necessary, because they can be a little more difficult to thread onto and off the lens, and may be more prone to getting stuck.
If you were considering them, I don't recommend Variable ND filters. Those are basically two polarizers stacked on top each other and they often give uneven effects and some even add ugly color casts to images. The "better", multi-coated ones also tend to be very expensive. And a Variable ND isn't really necessary for still photography (might be needed for video, tho, where there are fewer means to adjust exposure).
I don't think you'll see any vignetting problem with any of the B+W C-Pol, using them alone on that lens. Even the "standard" B+W frame is pretty slim. Their "slim" version is just a little more-so.
By the way, a C-Pol can also serve as a "weak ND" or in combination with an ND filter if you need around 1 to 2 stops of light reduction. However, it also will reduce reflections, which may not always be desirable.
CIRCULAR POLARIZER br br The biggest bang for you... (
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