nginx auth_request - 在PHP脚本中进行身份验证后记录经过身份验证的用户

I have the following nginx config to authenticate /admin requests :

location /admin {
        auth_request     /auth;
        auth_request_set $auth_status $upstream_status;
        error_page 401 = @error401;
    }

    location = /auth{
        internal;
        proxy_pass              https://localhost/login/auth.php;
        proxy_pass_request_body off;
        proxy_set_header        Content-Length "";
        proxy_set_header        X-Original-URI $request_uri;
    }
    location @error401 {
            return 302 /login/;
    }

The authentication flow itself seems to work fine.

Question : How do I log the user that is authenticated in auth.php? I have tried setting up a header in PHP as follows:

    header("X-App-User: $user");

and then in nginx.conf :

   log_format combined_with_proto '$scheme $remote_addr $remote_user $sent_http_x_app_user [$time_local] '
                '"$request" $status $body_bytes_sent '
                '"$http_referer" "$http_user_agent"';

   access_log /var/log/nginx/access.log combined_with_proto; 

However that does not seem to work - the remote user is not logged in the access.log. What am I doing wrong?