[...]It's pretty tough to capture the design issues in a letter, but...
Basically, a seeker head is a complex search device with a swiveled head. On the head can be one or more sensors. The inner gimbal swivels and is serve-controlled to search or point, depending on whether it has seen a target or not. Sensors and their associated processing should be on the inner gimbal if possible, although the IG is small, setting up a major design conflict.
The picture [refer to a sketch, an associated function(?) diagram and a design process flowchart ] shows that the sensor often has optics associated with it, adding weight and inertia as well as some optics design issues like aperture, focal length, and field of view. All of these want to be large so that faint distant targets can be acquired. Of course, the inertia adds to the problem of searching and locking on.
The tracking problem is to keep the seeker aimed at the target while the missile maneuvers under it so that it intercepts the target. So the bandwidth of the gimbal must exceed that of the guidance and maneuvering servo system of the missile itself. A typical seeker bandwidth spec. might be 10 Hz. This is typically much fast than that of the missile, an obvious requirement. However, there is not much room for servo motors on the gimbals, so torque is not easy to come by.
If you look in Applied Optimal Control by Bryson and Ho you will find a description of the seeker missile homing problem. Basically one wants to servo on the rate of change of the line of sight angle between the seeker and the missile, driving this rate to zero. (As sailors say, if the other guy appears not to be moving with respect to you, you are on a collision course.) This means, among other things, that you need to measure this angular rate. Both the missile and the seeker therefore have rate gyros on them.
Most seekers have infrared sensors which must be kept at liquid nitrogen temperatures. So there must be a supply of liquid N2, and plumbing to feed it up to a little Dewar flask that surround the detector on the IG. This plumbing must be flexible enough to permit the IG to move as needed.
Most seekers must fit into small missile packages, typically 5" or so in diameter. This typically means that seeker designs are space-constrained. Real estate on the IG is especially valuable but of course this is the smallest region of all. On it must be a least one sensor and rate gyro, plus bearings. On the outer gimbal and base must be one each of gimbal servo motor and angle readout. All power and signal wires must be snaked out along the gimbal structures and cannot be allow to pull tight within the normal swing range of the seeker, which is typically +/- 45 degrees in both directions.
Seeker gimbals are measuring instruments. One reads out the angles from the two gimbals in order to find out the direction in which the target lies. Accurate operation of the seeker requires that the inner and outer gimbal axes be orthogonal and intersect, and that they intersect on the missile's centerline. The boresight line of the sensor(s) must also intersect the axes' intersection, preferably at right angles to them.
For dynamic purposes, the CG of the entire gimbal system must also lie on at the intersection of these axes. Otherwise there will be cross-torques between gimbals every time you try to reorient the gimbal or between the gimbals and the missile anytime the missile maneuvers. The latter event is especially hard to counteract given the weak gimbal motors. Imagine 10 Gs or more resulting from missile maneuvers.
If a good simulation model is made that permits non-orthogonal axes, non-intersecting axes, CG located somewhere else, etc., that is, if all the geometric and optical tolerance errors are put into the sim, then an appreciation of the required tolerances can be obtained by running the sim. An analytical model could also be made but I'm not sure how long that would take.
So, summing up, there are dynamic, optics, controls, cryogenics, geometric accuracy, and space allocation problems here in full measure.
Ask someone at Lockheed or TI to talk more to you about seeker requirements. The problem won't be interesting from the design point of view unless these issues are taken into account.