What types of filter cannot be successfully emulated by digital post-processing?
Polarizing, obviously. and neutral density for depth-of-field control.
But what about UV filters? and are there other types that are best used on the camera rather than in the computer?
Any filter that changes properties of the light that isn't captured by the digital sensor (or film), is impossible to reproduce in post-processing.
So:
A polarising filter removes light beams with a specific angle. As the sensor doesn't record the angle of the light beams, it can't be recreated in post-processing.
An ultra violet filter reduces light above a certain frequency. As the sensor doesn't record this frequency range separately, it can't be recreated in post-processing. However, as digital sensors are less sensetive to UV light this is not a big problem for digital cameras.
A neutral density filter doesn't have any filtering effect, in the sense that it affects all light the same. The desired effect is to change the exposure time or aperture, and the effect of that can not be reproduced in post-processing.
Any filter that changes the path of the light, like starlight filters, is impossible to recreate exactly in post-processing.
However, some of the effects of those filters can be emulated, like getting the dark blue sky produced by a polarising filter, or getting something that looks very close to a starlight filter.
Some filter effects is actually easier to use in post-processing, like positioning a gradient filter exactly where you want it.
A lot of the time when filters are used, they are not used to achieve an effect, but rather optimal data in your RAW file.
I always prefer real filters over emulation, because emulation usually means visible artefacts (like halos around the edges where the modified and unmodified parts meet) in the photo. These artefacts are only amplified down the line (with sharpening for example).
In practice, for almost all photographers, the only filter effects you can't reproduce in post are:
There is doubtless a longer answer with more detail which would be more technically correct, but for practical purposes for most of us, this is the bottom line.
Well, I'd generally argue that doing it on camera is preferrable to post-processing primarily because it means you spend less time on the computer and more time behind the camera. However, many can be emulated in software, including graduated ND filters (with multiple exposures), warming, and color correction, the obvious ones that can't you've already mentioned. I'd suggest that some of the special effects ones, such as a starlight, would require some significant work to emulate and so it wouldn't be worth it, you may as well to a render instead of a photograph.
As for your specific question, the UV filter reduces haze and improves contrast which, to a degree, you can accomplish in post processing. However, digital cameras are not as sensitive to UV light as film is, so the need for its effect is little to none with a dSLR. Most common use of the UV filter at this point is lens protection, though the value of that is not completely agreed upon.
I carry three filters:
Circular Polarizer for reducing reflections on shiny objects and to darken skies. it's also useful as a neutral density filter with a +2 rating.
Neutral density filter to reduce incoming light. I typically carry a +3, which I can stack with the circular polarizer to lengthen shutter speeds to smooth out water flow and etc.
UV/Haze filters, because I'd rather replace a broken UV filter than the lens it's protecting. And Iv'e had that happen twice.
I used to carry graduated ND filters for landscape, and I no longer do; I do HDR or I do some form of post processing rather than try to handle that on site. The only filter effects I don't know how to handle in post are the polarization and ND effects. Everything else I can manage (and generally with better control) in post than in the field.
