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Illumination is a separate dimension to size and contrast, so they can be considered all together in three-dimensional space.

So, how do we represent changes in illumination on the CSF? Having different illuminations means dealing with different CSF plots, so to help me understand what’s going on I like to consider them arranged together in sequence, darkest-to-brightest, in a 3D space.

Multiple CSFs arranged in order of illumination

Note: Again, it’s really hard to display the brighter illumination levels convincingly on a graphic like this. The brightest plot (at the back) ought to be really-really bright, but it’s limited by the brightest white on your screen, which is the same as the background of the web page, so it doesn’t look that bright. So you’re just going to have to use your imagination for that.

If we connect up the bottom of each plot (the maximal contrast part of each plot), then we get this, as forming two walls of a space:

Contrast gradient vs brightness gradient

I know representations of 3D shapes can be ambiguous — so, just to be clear, the two top walls are the back walls of the space, with the bottom wall being like the floor. Looking towards the right wall is kind of like looking towards the sunrise on a misty day — very bright at the horizon, with the brightness fading into haze above, while behind you shades into night.

Plotting CSFs in 3D

Remember this image? CSF plots for normal healthy eyes over a range of illumination levels?

Let’s plot (some of) them in the 3D space:

Selected CSF curves arranged in order of brightness

Notice that I’ve modified the left side of each curve (the part that represents high spatial frequency, aka ‘big things’) so that they don’t dip down. I’m doing that because I’m planning to use this mostly for discussion of making text readable, and since the print/background junction is abrupt rather than gradual there isn’t the reduction in visibility.

CSF in Very Bright Conditions

There’s also one plot missing, the very back one. That should represent the really bright conditions we normally encounter — let’s say outside on a bright sunny day. At that point things are too bright, we’re suffering discomfort glare, and so we don’t see as well (until we put on our sunnies). That doesn’t appear in the graph from the study we were looking at, but we can predict what it will look like — something somewhat worse than the optimal, anyway. For low vision work it’s important to consider those high illumination levels, so let’s add that in now:

Adding in one more curve, at maximal illumination

Can you see how these all start to form a framework for a 3D surface? Considered all together, they create what I call a Visual Volume (VV).

The full Visual Volume for normal vision


Note: For the purposes of all the following pages, I’m considering levels of illumination only from mesopic or the low photopic and up. I’m not considering scotopic vision at all. Maybe it’s something I’ll tackle later… Anyway, if you’re moving into the scotopic then there should be a long low volume, not including any high spatial frequencies. See the discussion on Achromatopsia later.

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