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Is there a filter or material that allows a variable amount of light through based on intensity? So the brightness of highlights would be reduced, while shadows would be less, or not at all, affected. If such a filter were to exist, it would result in increased dynamic range.

I am not referring to ND filters because, if I understand correctly, they cut light uniformly across a scene. (See Do ND filters increase the dynamic range that a camera can 'see'?)

A serious problem with this idea that I did not consider earlier is that a filter made from such a material, if it does exist, would ultimately behave as an ND filter because light passes through the filter from all directions (as pointed out by @RomeoNinov).

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Yes, there is such material. You can check this article in Wikipedia about it.

But the material is slow, it react in minute to the change of light intensity. And mostly it is sensitive to UV waves.

But the main challenge to create such filter is the filter "receive" light from all directions in front of it. Which mean you do not have only light, coming from front. Of course you can add veeery deep hood, but this will make entire construction much more unbalanced and vulnerable to the wind. Also such hood with enough deep will make strong and huge vignetting.

So yes, it is possible. No, it is not practical (IMHO)

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    \$\begingroup\$ Interesting thought! Maybe one could construct a sensor with a thin layer of such material as part of the sensor stack. \$\endgroup\$
    – mattdm
    Jul 13, 2018 at 21:12
  • \$\begingroup\$ @mattdm, sure this is possible. I see few technical and optical challenges. But nothing which can't be resolved :) \$\endgroup\$ Jul 13, 2018 at 21:15
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    \$\begingroup\$ @RomeoNinov I think what you are talking about is what some eyeglasses use? So that they get darker when one walks outside than when one is indoors? That would reduce everything at any given point in time. The question seems to be looking for something that would only reduce highlights while not reducing shadows at the time an image is captured. \$\endgroup\$
    – Michael C
    Jul 13, 2018 at 22:07
  • \$\begingroup\$ @MichaelClark, correct. Such glass is used in eyeglasses. But m idea is to make with hood kind of tunnel with only parallel beans, which will darken only part of the glass. \$\endgroup\$ Jul 14, 2018 at 4:08
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    \$\begingroup\$ It won't work on the outside of the lens. Light from each point in the FoV strikes the entire surface of the front of the lens. \$\endgroup\$
    – Michael C
    Jul 14, 2018 at 4:13
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There are filters that limit the spectrum of light that goes through, like infrared filters or hydrogen-alpha filters, but that's probably not what you're looking for.

There are 2 types of filters I know of that might do what you need, depending on the situation.

The first is a polarizing filter, which will reduce bright reflections and darken things like the sky during the day. See https://en.wikipedia.org/wiki/Polarizing_filter_(photography) for some examples of how it can be used.

The other is a graduated nd filter, which is generally used in sunrise or sunset pictures, when part of the scene is much brighter than the other part.

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