We have seen that there are lines of evidence for both homology and non-homology of compound eyes within insects and crustaceans. 

For homology, evidence is primarily focused on the morphology of intricate details present in the structure of the ommatidia. For non-homology, there doesn't currently seem to be much evidence out there. However, through molecular evidence, there has been one lineage of crustaceans that has supposedly independently evolved compound eyes: the Myodocopid Ostracods. 

It is important that we look into more specific groups of insects and crustaceans, especially those whose common ancestor did not originally have compound eyes, like in the case of the ostracods.

This will help us further understand how these amazingly complex visual systems we see today have evolved through evolutionary time!

Some research suggestions could include:

1. Embryology, development, and cell fate of compound eyes.

2. How age and habitat/environment may influence the structures and functions of compound eyes.

3. Miniature compound eyes (like in the Ostracod study), as most studies focus on significantly larger species with compound eyes.

4. The structure and function of the corneal surface in different groups.

5. Compound eye sexual dimorphism (Meyer-Rochow, 2015).