Alias with user authentication

Hello,

I use apache with authenticated users, and I would like to achieve the
following behavior:

When authenticated goes to https://my.site.com/perso/, apache
goes to /home//http/ on the server, where http is the UserDir
directory.

That is, I would like https://my.site.com/perso/ to be an alias for
https://my.site.com/~/.

I don't know if this is possible, as it requires prior user
authentication, and I couldn't find anything in the doc.

Could you tell me if there's one way to do this ?

Thanks,

AC