How to create a differential backup considering the base the previous differential backup in SQL Server? I am studying differential backups. I know that I can create a differential backup which will contain all the modified data from last full  backup.
I wonder isn't it possible to create a backup from the last differential backup?
I mean to create a base full backup, then differential backup1, which contains all the data modified from full backup, then create backup2 which contains modified data from backup1, not full backup.

If it is possible how can I do it? Also can I do the same only with Log file backups?

Thanks for your time.
You are essentially asking for incremental, which is pretty much what a log backup is.  So your Diff1 and Diff2 would actually be log backups, which still gets you point in time restores.

Why are you trying to do this...purely academic reasons?