I don't have that Oldham blade, but I have not trouble making 1/16" by 1/16"
pieces, generally from holly and ebony for inlay.

With almost any really good blade, Forrest, Freud, Amana, whatever, and a well
tuned saw (whcih really does not take all that long, if you knwo what to do),
you should be able to rip perfectly. Ripping is what a table saw DOES.