Why does this add shader create so much noise?

Question

This question is based on the shader in this answer. When I render the scene using plain glass for the material ball, it takes about 500 samples to converge. Here is the node setup and the result at 512 samples:

When I use the dispersion glass material, however, it produces a large amount of noise. Here is the node setup and the result at 2048 samples (4 times as many samples, which should be more than enough to make up for using 3 glass nodes).

Using mix shaders with 3x brighter glass produces the same result. The image does eventually converge after around a hundred thousand samples, but that's obviously not practical for real-world renders. Here is an overnight render at 65536 samples:

I can get a similar, but slightly different, result in far fewer samples by rendering 3 separate images and combining the color channels in an image editor:

But that leaves me with two questions: first, why does using the add shader produce so much more noise than expected? Second, why does it give a different result than a normal glass shader? Specifically, where does the black band at the bottom of the material ball come from?

Here is the .blend file, for reference:

All of this is observed in the material ball scene as of Blender 2.76. There are no lamps in the scene, and enabling/disabling multiple importance sampling of the world background doesn't have any significant effect on the noise. I haven't tested it in other scenes or other versions of Blender/Cycles.

Update: Based on the discussion of Rich Sedman's answer, I experimented with a hybrid shader which uses diffractive glass for the first ray bounce and standard glass for subsequent bounces:

It seems this may be the best we can do within blender, without either using the compositor, or getting a way to generate a per-ray random value within Cycles. Here's the result at 4096 samples, rendered using Blender 3.5.1:

And here is the result if I randomize the IOR of the standard glass as well:

Answer 1

The difference is all due to light path.

Consider your 'composite' method - you're essentially just rendering each wavelength of light separately and then combinine the results. This is really simple and for each bounce the wavelength of light considered in the bounce does not change.

In your 'add shader' method, however, Blender will split the ray at each bounce and that resultant ray may or may not be the same "wavelength" on each bounce (Blender is forced to pick one of the IORs for the ray - this is effectively the "wavelength"). If the wavelength for the entire path is the same then your light gets through. However, if the choice of IORs differs over that path then your shader is effectively filtering out the light (eg, a'Red' bounce filters out everything but red light. If that's followed by a 'Green' bounce then that will filter out all the Red and Blue and you've got no light contributed from that ray).

Essentially, on each bounce your shader is discarding two-thirds of the rays. This means you need to really ramp up the samples to give any rays the chance of getting through and contributing to the final image.

For example, consider just 5 bounces. For your composit method, every ray would be considered over its whole path. For the multiple glass shaders method, the chance of a ray not being filtered out becomes 0.333 * 0.333 * 0.333 * 0.333 * 0.333 = 0.004 - ie, you're effectively getting only 0.4% of the rays to contribute to the image.

The solution...? Use the 'composit' method so that you consider each 'band' of colour separately.

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EDIT: I've been playing around with this a little bit. Here's my initial take on a dispersion glass material using a single Glass Shader :

And here's the result :

Rendered using the 'out of the box' Blender 3.5.0 Cycles default settings.

The ranger of IOR is controlled via the second Map Range node (in this case 1.40 to 1.50) and the corresponding light for that IOR range is defined in the Color Ramp. This setup is a bit of a fudge in that you need the Vector Scale 3.0 to adjust the brightness and to manually adjust the colour of the glass by manually varying the amount of RGB in the Color Ramp node.

I've got some ideas for other solutions (such as rendering as separate images and recombining in the compositor) which I'll update as I can.

Answer 2

It looks like by splitting out into three glass shaders you're getting three times the caustics, and they're tricolor making them difficult to resolve.

Unfortunately cycles is not great with glass, there are other types of renderers that use algorithms like Metropolis Light Transport to find the most likely refraction angles and bias rays in those directions.

LuxCoreRender might be a place to start.

Answer 3

This method can be used for every 3d program: you render 1 sample 200 times at same spot and combine using average mode.