Here is my work-a-round ;o)
I can’t find a way to have objects in the same “glass/water-sphere” and some are refracted more than others. Imagine for a moment this option were given, three parts in a glass sphere would have no, a strong positive and one a strong negative value, that sounds to me like “Scotty— beam us three up”, only to arrive as a Kraken on board, with six arms and six legs, etc. In other words, the mix would be difficult to separate or even to adjust. ;o) Sorry about the weird example.
The simplest idea would be to take the object apart and render in sessions. Half-spheres front, logo, half-sphere back, masks, object buffer, comp etc. Well, sounds like a lot work and perhaps a little change and the whole thing needs to be done again. So: nope.
I thought as well of a sphere with a sphere hole in the middle which contains a little bit smaller sphere for the logo. Since I have no data about the logo size, I can’t really test this. The logic would be to work in the smaller sphere in a different way than on the outside. Again, not tested with the right size
My suggestion might be kind of complex on first sight, but is pretty simple once you read one time through.
The sphere should reflect in many ways, inside and outside, for that I have used the Sphere.mirror. Simple and with nearly no or little refraction. (yes, little—read on…)
The next sphere (called Sphere) has a ‘flat nose”, adjustable with the Correction Deformer, and here with the Falloff>Offset>Y [second value, currently at 118cm]. This flat nose looks always to the camera and does not reflect, but the refraction is lower in the center, where the nose is the most flat. So, the logo/icon is less distorted, but everything else, especially the “ring” around the logo is. This Sphere has a material with NO reflection, but with refraction, adjust to your liking.
You can move the camera, and all looks fine. Who can really say that the snow-particles are less refracted in the middle area? However, I dialed in a little bit of refraction here to soften the trasition and have a good feel anyway. Keep the snow in the inner sphere, but perhaps you test both options.
The orange figure is the placeholder for the logo, the pale bluish cage used here as an indicator for the refraction.
I hope that will work for you.
All the best
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