Alpha mask in cycles

I have created a black and white alpha mask for use in Cycles, and applied it to an object as you can see in this picture:

The object which I have applied the alpha mask to has has a solidify modifier and the “fill rim” option has been checked. The problem is that only the rims on the edges of the mesh are filled while the rims on the inside of the mesh are empty… Is there any way to fill the inside rims and solve this problem?

We are dealing with surface type modeling paradigm and what you did there was make the surfaces have transparent areas. If you want surfaces in the holes too, you have to model them, use a volumetric material, or use extra objects and double mask it with dynamic paint. Easiest to model them.

I was hoping to use this method on many surfaces, and I was afraid that modeling the holes or using a boolean modifier would dramatically increase the render times… I think I’ll just make the space between the surfaces narrower and hope that the results will be good enough.

Thanks for the advice!