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The rental store only has 16X (4-stop) ND Filters, and I'd ideally like to get at least 8-10 stops of filtration. How many filters can I stack on top of one another before the image starts to significantly become affected?
I'm on a 5D Mark III with a 16-35mm f/2.8L (mark I)
Well, there are other reasons not to stack so many filters. First, with a full frame camera, you will likely run into detrimental vignetting fairly quickly...it wouldn't take more than a couple of standard (non-slim, which are not stackable) filters to cause several-stop vignetting.
Vignetting aside, filters, even the best of the best, tend to be of lower optical quality than the glass in the lens itself. Even a single filter, including those of high quality, WILL have an impact on IQ. It is usually low enough that it doesn't undermine the value of using the filter in the first place. Filters also tend to have less capable coatings on them to prevent flare and ghosting. Modern lenses (not sure about the EF 16-35mm I) often have nanocoatings, which are vastly superior to multicoatings. Midrange and lower end filters often have only a single coating, and cheap ones at that. Flare can become a significant problem when stacking filters.
The issues aside, assuming you do not run into flare, the vignetting caused by deeply stacked filters can actually be used to an artistic end. I've found a number of ultra long exposures on 500px and 1x that had extremely deep vignette that I actually found quite pleasing. Any tool can be used to good effect, so long as you know what to expect and put the outcome to good use. ;)
Other than the cumulative effect of each additional optical element placed in the light path with the resulting effect on overall image quality (i.e. sharpness, flare/ghosting, etc), the primary concern with stacking multiple filters will be vignetting. Since the EF 16-35mm f/2.8 L requires a filter to be weather sealed, the design would presumably allow one filter without any additional vignetting caused by the filter ring. How many filters may be used before seeing additional vignetting and how much vignetting is too much will depend on several factors:
The lens used. Some lenses vignette more than others. Zoom lenses will vignette differently at different focal lengths. Wide open, the EF 16-35mm f/2.8 L vignettes the most in the corners at the 16mm end, vignettes the least in the middle of the zoom range, and then vignetting increases again through the 35mm long end. The lens in question is designed to accept one filter for weather sealing and shouldn't experience increased vignetting with a single filter. With some lenses, even one filter will increase vignetting, especially with wider focal lengths. Once the filter ring is in the optical path of light that would otherwise make it through the lens to the sensor, each additional filter will cause the vignetting to reach further into the frame.
The aperture selected. In general, narrower apertures will reduce vignetting compared to the same lens at a wider aperture. The EF 16-35mm f/2.8 L follows this paradigm. When shooting with a wide open aperture, adding a single UV filter did not affect vignetting in this test. Once the filter ring is in the light path each additional filter will cause more vignetting at wider apertures than it will at narrower apertures until the point the lens is stopped down so that none of the light being blocked by the filter ring(s) would have been allowed to pass the diaphragm had the filter ring(s) not been obstructing the light.
The artistic intent. Sometimes vignetting is a desired quality, sometimes it is not. Sometimes it is added in the post production process, sometimes it is removed. Removing vignetting caused by filter rings could be more difficult to accomplish than the normal vignetting caused by a lens' characteristics that are often included in lens correction profiles.
This article on the lens rental.com blog shows an extreme case of stacking a lot of filters. The image quality degradation is severe.
http://www.lensrentals.com/blog/2011/06/good-times-with-bad-filters
For a one-time rental, I would not worry about it. If you find you need this radical level of filter often, I'd buy one that does exactly what you want. I picked up a B+W 9 stop ND filter, it works and is high quality, but you can't see through the viewfinder and the autofocus on my Canon 50D won't work.
