I read more about ambisonic microphones. I'll be happy if someone corrects me. Maybe it will also be useful for someone else.

The easiest way to understand the ambisonic principle is a 1st order microphone (eg TetraMic). If someone is starting to read about ambisonic, it is best to first thoroughly read how Mid/Side of a coincident stereo pair works. When we understand Mid/Side, then understanding 1st order ambisonic is easy.

The 1st order microphone is made of four coincident directional capsules evenly angled in space. From their signals, it is possible to get any pattern of the 1st order (omni, fig.8 or their combination - cards, hypercards, ...) and we can angle this pattern arbitrarily in space. Everything is built on the basis of summing and subtracting coincident directional microphones (eg cardiode):

-when we sum the signals from two coincident directional microphones rotated 180 °, we get omni.

-when we subtract these signals from each other, we get fig. 8.

-when we sum two coincident directional microphones that have an angle of less than 180 °, the result is a less directional microphone in their axis.

(explanation - each directional pattern contains a certain ratio of the components omni and fig. 8., it's just composing fig.8s and summing the omnis.)

By summing and subtracting the signals of the four coincident cardiodes evenly angled in space, we obtain one omni and three figs. 8 in the perpendicular directions X, Y, Z. This is the 1st order B-format. And to get the final pattern from the B-format, we use the following manipulation. The sum of the signals of three fig. 8 (X, Y, Z) in the corresponding ratio is resulting to fig.8 in the desired spatial direction. And when we add the omni signal in a certain ratio to the resulting fig.8, we get the resulting desired directional pattern rotated in the desired direction.

The principle of higher order ambisonic microphones (eg OctoMic) is different. There are multiple microphone capsules that are distributed on a spherical surface (imaginary or rigid) and a mathematical model is used to evaluate their signals. The mathematical model is based on the fact that the values of acoustic pressure on a spherical surface can be expressed using the sum of the infinite number of spherical harmonics. And these spherical harmonics correspond to our polar patterns.

The input to the mathematical model are signals from individual capsules. A matrix operations are performed with these signals and the output are spherical harmonics. 1st order spherical harmonics and their combinations correspond to the generic microphones patterns. Higher orders and their combinations are ambisonic specialties. The more microphone capsules we have, the higher spherical harmonics we can derive.

The principle of the higher order microphone (capsules on a spherical surface/space + mathematical model) is different from the principle of the 1st order microphone (combination of 4 coincident cardiodes). It would be interesting to hear their comparisons, eg TetraMic vs OctoMic with 1st order patterns.