I found many questions about Retina Display, but none of the answers were on the server side.
I would like to deliver a different image according to the screen, ex (
As you do not specify for what exact use-case you are needing this and i do not really see a use-case for the server knowing what resolution the client wants it's images in (in my opinion the client should decide) here is my suggestion:
Use something like Retina.js or use the srcset attribute 
This way you could also leverage browser caching of the images. which you can't do if you have one url for two different image sizes. Even if its an automatically created/updated image caching works using last-modified or etag headers.