Ah ... you are looking for the SR-6A or SR-6B antenna. I found out about this radar only on my last couple of trips to NARA. Recently, I'm finding a bunch of "Antenna Survey" photos from the 1950s. In 1948 there was a new Air Search Radar introduced and eventually installed on about 28 SUMNER/GEARING destroyers ... the SR-6 radar. The original antenna was similar to the old SC radar only different with a wave guide horn. I found a good photo of this antenna on a GEARING in a 1949 photo ... on DUNCAN actually ... in early March (see attachments below) and didn't recognize it so I looked it up in Friedman's Radar book. There WASN'T a photo of this radar's antenna in the book, but there was a description and discussion about it. According to Friedman, the SR-6 had terrible performance with this antenna. So they substituted the SPS-6A antenna and called the new combo the SR-6A or with a SPS-6B antenna and called it SR-6B. I suspect that is your radar. In photos you can't tell a SPS-6 or SR-6A apart.
Attached images:
I happen to have an image of your ship, USS DUNCAN (DDR-874) on a photo dated 28 June 1952.

A 1957 view of the SR-6B on USS BRINKLEY BASS on 1 November 1957.

A view of a "typical" SPS-6C radar on USS ROGERS (DDR-876) on 7 December 1957. Hard to tell the two apart.

Then for the record, below are smaller views of the 1949 SR-6 antenna on DUNCAN.