Ok, let me explain. The true ambience portion of the bryce renderer functions as follows. Any object with an ambient value on the surface is immediately calculated. At any location where this object is reflected it is also calculated. Therefore, if the light is seen in a mirror it will have an 'ambient' value where the reflection is in the mirror. 'sphere' of influence is created at however many RPP with a certain falloff depending on the level of ambience in the material. This sphere of influence then reacts with other objects in its proximity, projecting the ambient levels onto that object. If this sphere of influence increases the ambient level of the secondary object, then that object in turn generates its own spheres of invluence (greater where it is effected by the other spheres) thus generating the caustics effect. You will notice that the same effect is generated with a white opaque surface.. The only two values taken into account by the true ambience render is the value for ambience and the color . Now, you mentioned that there is a 'caustics' effect on the transparent sphere. This is caused by the same phenomenon, look at the sphere, you will see that the basic 'refractions' in bryce cause the incident reflection/refraction of your white planeto be projected on both sides of the sphere.. one at the original incident reflection, and one on the other sides incident reflection+refraction. These 'reflections' shown on the sphere are treated as very ambient 'textures' by the true ambience renderer, thus they generate their own 'spheres' of ambient influence in these two incident locations (no volume refractions, only the front and the back of the sphere) which were then interpreted by you to be caustics. Hope this helps. Try doing that transparent sphere render with no reflection value and note the change in appearance.