Filters for Digital Cameras

Graduated Neutral Density Filters

Grad ND filters are used when the dynamic range of a scene exceeds the capabilities of the camera (film or digital) to record detail in both the brightest and darkest part of the scene. The go from clear on one side to a neutral .6D (2 stop) or 0.9D (3 stop) neutral filter on the other. A typical use is to record detail in a bright sky (or mountains) while simultaneously recording detail in a foreground in shadow. You have to hope that the dark/light transition is a straight line though, since that's what a grad ND filter is designed to cope with.

Grad ND filters are available with "soft" and "hard" transitions between the two halves and they are available in a number of sizes with a variety of different holders. The filters are typically much larger than the lens diameter to allow then to be positioned with the transition at any angle and any position in the frame. Typical sizes might be 84mm x 120mm (84mm is the width of a standard Cokin filter holder).

You can also get round grad ND filters which screw into a lens like a normal filter, but unless you always want your dark/light transition running across the exact center of the frame, they may not be ideal.

The above shows the effect of an ND grad. On the left is the "straight" shot. On the right is the effect of an ND grad with the transition across the horizon and the ND part over the upper half of the image.

Note that you can duplicate the effects of ND filters by making multiple exposures and combining them in software. However that means taking multiple images and if you have a moving subject that could lead to problems. For landscape work though (which is where an ND grad is most often used), the digital stitching of multiple images taken with different exposures may be just as effective (even maybe more effective), though it probably requires more effort than just taking the shot using a filter.

InfraRed Filters

Just about all digital cameras use a filter in front of the sensor which allows visible light to pass but blocks almost all (but not quite all) of the infrared. This is needed because typical sensors are very sensitive to infrared and if it was allowed to reach the sensor it could mess up both exposure and color balance. Since you can't see in IR, you don't need (or want) IR response for general purpose photography. 

However if you want the special IR effects (black sky and white foliage) you can use a filter such as the Hoya R72, which blocks all of the visible light while allowing IR to pass though it. Though the camera's IR blocking filter will remove most of this IR light, some will get through, and since the visible light is now blocked, a long exposure will record an image in IR light. In most cases the image will need a long exposure at wide aperture and high ISO settings and so the image will be noisy. There are companies who will remove the IR blocking filters from the camera to enable much better IR response, but this isn't cheap (typically around $500) and will void any warranty on the camera as well as making it tricky to use for normal photography.

Special Effect Filters

The effects of most of these can actually be duplicated digitally. You can do very good soft filter effects for example. Maybe there are a few effects like "starbursts" or multiple images that might be easier to do with a filter than in software, but personally, if I really wanted such effects, I'd probably go the software route since the effects are more controllable.

Why filters (and other optical elements) need to be anti-reflection coated

Below is a diagram of what happens when a ray of light passes through a filter:

Light comes in as a ray [1] and hits the filter surface at point [a]. Most of the light is refracted to point [b], but a small amount is reflected as ray [3]. This is light reflected from the filter surface and it does no harm except to make the ray passing though the lens slightly dimmer.

At point [b] a small amount of the light is reflected back to point [c] but most is refracted and emerges from the filter as ray [2]. This is the main light ray, the one that we want and it's where most of the light goes.

Most of the light reflected back to point [c] is refracted and emerges from the front of the filter as ray [4] and goes off into space,  again doing no harm, but a small amount is reflected back to point [d].

So far, no problems, but it's here where we see the first hint of trouble. Some of the light reflected from [c] to [d] gets reflected back again, but most of it emerges from the filter along ray [5] and heads off towards the camera where it isn't wanted.

The process repeats (see the green rays) and so you get a number in increasingly faint rays heading back into the camera. All we want is ray [2], the other rays just cause problems. The same thing happens at every glass/air interface in the lens, so you can see that by the time the light has passed though all the elements in the lens (usually between about 6 and 20), there are all sorts of unwanted rays bouncing around inside the lens. With digital sensors, there's also light which refects off the sensor and may eventually end up coming out of the front of the lens, as well as  bouncing around and ending up headed back to the sensor again!

By using anti-reflection coatings on all air/glass surfaces the intensity of all these extra rays can be greatly diminished. The main effect of these extra rays is to reduce image contrast by causing flare. There are so many reflections that the light essentially gets "scrambled" and so doesn't form an image. It's very low level light, but it can be enough to noticeably drop contrast.

With no anti reflection coating at all, about 4% of the light gets reflected at each glass/air interface. This means that ray [2] has about 92% of the original intensity of ray [1] and that ray [5] has about 0.15% of the intensity of ray [2]. Not much, but enough to cause problems. If the lens elements were not coated, you'd lose 1/2 the light after passing though 8 elements!

For a single layer antireflection coating, reflection can be reduced from 4% to 2.5%. Multilayer coatings reduce reflection even more. A typical multicoated surface might only have 1.5% reflection and the best coatings, like the 12 layer coatings on the Hoya Pro 1 series filters, lower reflection losses to around 0.15% per surface.

Which Filters

So assuming you want a polarizer, UV or ND filter, which one should you buy? Actually it's more of which one shouldn't you buy. You shouldn't buy an uncoated filter or a monocoated filter if you can avoid it for the reasons described above and you shouldn't buy the cheapest filter you can find since it's important that the glass be flat and the sides be parallel - and that's not something you're likely to find in the cheapest filters. I've been happy with Tiffen filters, though they are sometimes hard to find in multicoated versions.. I've also been happy with Hoya filters. Hoya is probably the major manufacturer of multicoated and supermulticoated filters at reasonable prices. Their filters are very good and their Super Multicoated Pro 1 series have the lowest reflectivity coatings of just about any filter on the market. B+W and Heliopan also make good filters, though they tend to be more expensive then equivalent Hoya filters.

Glass ND grads are available in a number of sizes and from a number of  suppliers, for example Singh-Ray (84mm x 120mm) and Tiffen (3"x3" and 3"x 4")   Hi-Tech and Cokin make "optical plastic" filters which are considerably cheaper, but which are more susceptible to scratching. The Cokin filters are "graduated grey" and may not be fully neutral. The square or rectangular ND grads attach to lenses using a custom adapter (the Cokin adapters are inexpensive and quite popular).

IR filters are available which transmit different wavelengths of IR. Probably the most useful for DSLR work is the Hoya R72 which blocks just about all visible light but transmits near IR light above 720nm which will (with some attenuation) pass through the camera's IR blocking filter. There are stronger IR filters like the 87C, but these work better with IR film than DSLRs since they only transmit longer wavelength IR which is totally blocked by the digital camera's built in IR blocking filter.