With Sphere microphone modeling technology it is possible to select any one of nine polar patterns even if the original mic doesn’t have all of those options. Pretty cool, huh?
Typical multi-pattern microphones allow adjustment of the polar pattern by electrically blending different amounts of front and rear cardioid capsule outputs. An omnidirectional pattern is created by summing the front and rear outputs in equal proportion. Figure-8 is created by subtracting (i.e., phase inverting and summing) the rear output from the front. Cardioid is attained simply by using only the front output.
Hypercardioid can be created by blending cardioid with figure-8 in equal proportion. And supercardioid is an equal blend of cardioid and hypercardioid. Subcardioid is created by blending omni with cardioid.
Interestingly, once you know the response of the omni and figure-8 patterns you can interpolate to find any intermediate pattern, such as cardioid or supercardioid. Sphere uses this fact to synthesize nine patterns even when the original mic being modeled only has a couple of pattern options. These intermediate patterns are actually very close to what would occur if the mic electronics were physically modified to create these additional patterns.
For example, a Neumann U87 microphone has omni, cardioid, and figure-8 patterns, but a Sphere model of that mic also allows for subcardioid, hypercardioid, and four other intermediate patterns. This is basically equivalent to modifying the circuit of an actual U87 so that it can produce hypercardioid.
The cardioid setting of a Neumann U47 is actually somewhere between super and hypercardioid, even though Neumann calls it cardioid. So just like the actual mic, when you select a 47 model with a cardioid pattern you actually get this supercardioid-ish pattern. In actuality, this is not quite so simple because polar patterns are always at least somewhat frequency dependent, so even though a U47 has a nominally supercardioid pattern, it moves towards omni at low frequencies and becomes even more directional at high frequencies.
Small diaphragm condensers often come with multiple interchangeable capsules to achieve different patterns. For example, the AKG C451 series mic can be fitted with either omni, cardioid, hypercardioid or figure-8 capsules. With Sphere, you can select any of these four patterns, but additionally any one of five other intermediate patterns, such as supercardioid, that are not possible with the original mic.
It is even possible to approximate all polar patterns from the cardioid response, since it is made up of equal proportions of omni and figure-8. But generating other patterns from just omni or from just figure-8 is much more of a creative exercise, because you can't determine the omni response from just figure-8 and vice versa. For example, there is no physically meaningful way to take a figure-8 ribbon mic and make it omni. In these cases, the on-axis frequency response is combined with a generic pattern, which effectively creates a new type of microphone.
If you do really want to create an omni or cardioid mic with a typical figure-8 ribbon sound, for example, then read up on the Off-Axis Correction™ feature, which allows you to do just that.