Measuring distance sensor in short range to soft materials like wool, fabric and hair?
Light travels about 1 foot/nanosecond.  So it takes about 1/3 nanosecond to go 10 centimeters and 1/30 nanosecond to go 1 centimeter.  Thus a ranging system based on light would have to use extremely high speed circuitry to meet your requirements.  Sound, on the other hand, travels 1 foot in about 0.9 milliseconds or 0.3 milliseconds to travel 10 centimeters. I don't know what "average precision" means but let's assume 0.1 centimeter is sufficient.  Then you would have to resolve about 3 microseconds in travel time.  You don't say what the minimum range needs to be (0 is impractical). Assume 0.5 centimeter is adequate. For 0.5 centimeter the round trip travel time is about 30 microseconds. You could use a pulse width of 10 microseconds (hopefully sufficiently short to allow receiving a return after the transmission ends) and a frequency of say 500 kHz (which would allow 5 cycles per pulse). Sonic transducers at this frequency are available.  However, the materials you need to work with are not good sonic reflectors since their acoustic impedance is not that much different from air (I assume air is the propagating medium since you didn't specify that).  You don't say how thick these materials will be.  If they are thin enough, most of the sound energy will simply penetrate them and not reflect. You will probably need to experiment to see if you can get an adequate return.  You also need to specify your requirements in more detail for a better answer.