The Scott Manley video The Only Pilot to Shoot Down A Spacecraft - A Space Ace talks about the ASM-135 ASAT and its successful test launched from an F-15.
He shows images from the page The F-15 ASAT story, by Gregory Karambelas, edited by Sven Grahn. As mentioned in the video, the spacecraft rotated at about 35 RPM.
The target sensor operated at liquid helium temperature (about 4.2 Kelvin or a little above) and according to the linked page was a cross of four logarithmic spiral patterns as shown below. I'm guessing that "NB" is really Nb or niobium, a superconductor at this temperature and would be very sensitive to tiny amounts of heat from infrared radiation imaged to a spot by the folded Gregorian telescope described.
In space, after the missile was launched, these cryo lines were retracted, and then two spin motors located on the spin bearing assembly of the interceptor were fired and the interceptor was spun up. It is important to note that the interceptor did not work while not spinning. This was not a staring array. I have attached a crude drawing of the strip detector layout. Those spiral lines were symmetrical logarithmic spirals (spirals of archimedes as I recall). Some simple geometry and trigonometry would enable us by recording the time of the detector crossing, calculate the objects location in the sensor field of view.
Question: I can understand how the relative timing between the four pulses as the spot passed over the four arms of the cross could be used to calculate the direction to the target, but I don't see why a cross of four straight line segments wasn't used. Why the logarithmic spiral?