Proxy and Digest Authentication Issues

I have a problem with Proxy and Digest authentication. My web server provide proxy to another web server using Lighttpd mod_proxy.

Structure like this.

PC: eth 1 - 192.168.37.200

Server 1: eth 1 - 192.168.37.100, eth 2 - 192.168.50.100

Server 2: eth 1 - 192.168.50.101

[PC] <------------------> [Server 1] ------------------- [Server 2]

Client                    Proxy server                   Target server

Proxy url like this: http://ift.tt/2i1jGmz

Server 1 and server 2 need another digest authentication.

But web browser fails to distinguish authentication information between two servers. So, browser shows login popup again and again.

How can I solve? Please your help.