PRR said:
If you mix omni and bi-di, just-right (including frequency responses), you have cardioid.
Olson did it this way.
At least he had good intentions and tried to materialized those ideas in commercial products. With all due respect to the genius of Harry Olson, while his earlier products (like 77C) because of combination/mixing two different patterns (fig8 and omni) had much better pattern control, unfortunately, his later mics (with mechanical shutters) in terms of the "tightness" and pattern integrity were quite mixed. Indeed, his search for "reducing production costs" inevitably reflected on a quality of the product (of course, it has nothing to do with commercial success).
In those RCA's the only "solid" pattern was an omni, while fig8 was quite asymmetrical and cardioid all over the place. Because of very loose production tolerances it is almost impossible to find two even remotely matched pairs in the cardioid. IF one would like to have those matched there should be taken painstakingly time consuming mechanical adjustments.
The more "specialized" cardioid ribbons had much better and consistent patterns. The notable mics to mention here would be BeyerDynamic M320 and M360. Both had labyrinths, but the transformers had quite a bit of low end roll off, so while pretty rare those did not get deserved respect. Later M160 is a double ribbon and in fact, is a very nice hyper cardioid. The problem with all of those is for the ribbon they used Duralum, which tends deteriorate and be serviced every 10-20 years, depending on the climate conditions.
Another line is RCA KU3--terrific mic--very expensive and scarce--the source of inspiration for many VO talents, widely used in Disney classics production, and BK5--an OK cardioid mic with some "weirdness" going on in the mids and in the especially lower mids, many people are complaining about.
One of my favorites is Oktava ML19--combines acoustic labyrinth, quite a big back chamber, and acoustical resonator. Can be had for quite cheap ( I found both of mine for $190 and $200 respectively on ebaby) and sonically beat socks off the BK5s with a good margin, for at least third of the price. The problem with those is ever deteriorating foam used for time delay. In many cases need to be serviced. Still, one of my absolute favorite cardioid ribbons.
Another classic would be Shure 330-333. In the bass department and overall probably not as nice as Oktavas, but still a terrific classic, with very carefully and nicely designed horn to preserve a full range response and provide a wonderful performance for many applications.
There are some others, much more scarce models, however, all of them share the same approach to the concept.
Best, M