Going with the idea that the tricorder should automatically access ship's sensors, it should also access any other tricorders and miscellaneous sensing devices on the planet. But, instead of having spheres of sensing that can overlap and which suddenly cut off, it would be great to use the inverse square law. The system should have active devices have an emission strength value divided by r^2. At twice the base distance signal strength will be four times weaker, and at three times the signal will be nine times weaker, four times it will be 16 times weaker, and so on. I think it should be signal/(r^2) and not signal/(4*pi*r^2) because radar sweeps the beam, they don't emit omnidirectional, it's also a simpler formula. Actually signal/(2r^2), as I'll explain below.
Using the inverse square law allows active sensors to have a signal range and sensing range. For the sensing range you double the radius, because it is going to the target then back, covering the radius twice. The signal range is used by other tricorders, they measure the distance from the other tricorder to a particular target, then the range of the target to itself, and that is the radius used when measuring incoming signal strength from the other tricorder. That strength, and all other active tricorders in range have their strength added to the tricorder's own strength to create a combined signal strength. Each tricorder will have a maximum receivable signal resolution, so within a certain radius tricorders won't need to do this, but outside that radius it will allow tricorders to combine their output to increase their maximum full detail scanning range.
Signal strength can be directly related to sensor resolution. Point blank scanning detail may have sub-atomic detail measured in attometers (10^-18). DNA can be measured with a nanometer resolution (10^-9). That's a difference of 1 000 000 000 times, and for resolution to decrease by that much the scanner would have to be about 31,600 times further away. If the tricorder can read sub atomic particles at 1 cm away, then it could read DNA 316 meters away if signal strength is directly proportional to resolution. Wait, that's if the signal traveled one way, if it travels two ways, and it would, then the actual range would be 158 meters. It would have 1 meter resolution at 5 000 kilometers, so at 500 km it should have cm resolution, because the signal travels from A to B, then back to A. Please, please check my math, it's almost 1 AM and I don't do much math as it is.
If we go with this kind of resolution signal sharing would be completely pointless, except for scanning DNA, and we might as well go back to the original idea of the ship sharing anything it detects with the tricorder automatically. The signal range/sensing range thing doesn't seem worth while now. Maybe we could have sensor shadows so sensor overlap makes more sense. Trees and normal rocks shouldn't cause sensor shadows, tricorders can penetrate quite some dirt over a few hundred meters at least. Large masses of material should cause sensor shadows, as should sensor blocking minerals, certain shields, and otherwise specially designed facilities.
There's something good in here but it needs more thought.
Now I realize at least with radar the resolution has to do with the wavelength used, not the signal strength. I don't care, I like the signal strength thing and there must be something to it. People need binoculars and stuff.
