Question

In the context of military aircraft and missiles, radars often have ranges of hundreds of kilometers, while thermal infrared sensors can only barely reach 100 km in the best of circumstances. But infrared radiation is emitted by the contact, while radar radiation is only reflected from the contact, leading to the received infrared radiation being proportional to d2

(the inverse square law), while received radar signal is proportional to d4
(inverse square law applied twice), with d
being the distance to the contact.

Reasoning from first principles, I would expect the extra d2
penalty of radar signals to dominate other differences in how both sensors work, and thus infrared sensors to have a longer range than radars. But that is obviously not the case. Why not?

(I am specifically looking for the underlying differences in the physics, not for the details of specific radar or infrared systems.)

I am aware of a number of differences that are favourable to one type of sensor or the other, but I have no idea which of these (or something else entirely) is responsible for overcoming the d4
radar signal handicap and causing radar to win in terms of detection range.

edit: As many of these differences are in orders-of-magnitude ranges, I expect that qualitative and order-of-magnitude numbers should be sufficient without needing to dive into detailed calculations. But I could be wrong.

Answer 1

Despite the inverse square laws favoring infrared sensors in theory, radar has a longer range due to better atmospheric transparency for radio/microwave frequencies, the use of powerful transmitters in active radar systems, and advanced radar technology that includes focused beams and high gain antennas that overall offset the mathematical range disadvantage when compared to passive infrared sensors.

Step-by-step explanation:

The question you've asked is rooted in the physics of how radar and infrared sensors operate and why radar can detect objects at greater distances despite the mathematical prediction that infrared should have a longer range. There are several physical reasons for this discrepancy.

First, the atmosphere has certain windows of transparency that are better suited to radio/microwave frequencies used by radar rather than thermal infrared frequencies. Water vapor, for instance, can absorb infrared radiation which limits its range, whereas radar waves can travel greater distances with less atmospheric attenuation.

Secondly, radar systems are actively emitting signals and can therefore use powerful transmitters to send out strong signals that can cover a larger range. Infrared sensors, on the other hand, are passive and can only detect the emission from objects, which are typically much weaker in strength compared to an active radar signal.

In addition, the power of infrared emissions is tied closely to the temperature of the objects (according to the T4 dependence), and not all targets present a strong enough temperature contrast to be detected at great distances.

Finally, technology has advanced radar systems to be highly sophisticated, allowing for focused beams and high gain in the receiving antennas which significantly improve the efficiency and the range of radar systems. In contrast, the detector technology for infrared is less advanced due to the shorter wavelengths, leading to lower resolution and range capabilities.