i want to change the redirect location URI protocol to https if that is using, so i tried to configure like this:

proxy_redirect ~*^http://$host(/.*)?$ $scheme://$host$1;

but that didn't work, so i change it to:

proxy_redirect http://$http_host $scheme://$http_host;

then, it works. I suspect that the variable in regular expressions is treat as a string, hence my former directive failed, am I right?
Is there any way to make variables effect in regular expressions?