Can holograms be transported?

I guess the only case we can examine is The Doctor. Whenever The Doctor uses a transporter, what traveling: the lights or the mobile emitter?

There have been many cases which The Doctor has become solid so other solid objects can no longer pass through them. If the object we are seeing being beamed is the mobile emitter, then is it necessary for them to be on a separate pad? I imagine the person accompanying The Doctor could just hold the emitter instead.