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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 $d^2$ (the inverse square law), while received radar signal is proportional to $d^4$ (inverse square law applied twice), with $d$ being the distance to the contact.

Reasoning from first principles, I would expect the extra $d^2$ 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 $d^4$ 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.

Some of the differences I'm aware of:

property radar infrared advantage for
path type reflected, signal proportional to $d^4$ emitted by contact, signal proportional to $d^2$ infrared
emission power tens of kW, but only a fraction being reflected by the contact 10s to 100s of kW? A jet engine consumes megawatts worth of fuel when cruising, I'd expect a substantial portion of that is converted into heat. infrared
transmission directionality transmitter is very directional, but reflection is omnidirectional omnidirectional ?
detector aperture radar antennas are typically much larger than IR sensors If this was an issue IR sensors could be made much larger radar
detector sensitivity I think radio receivers are more sensitive, in terms of min. picowatts being detectable. Not sure Advanced photodetectors have a significant probability of detecting an individual photon. But IR has a lot more energy per photon than radar. radar?
angular resolution Radar, being longer wavelength, gives a much lower angular resolution for the same aperture IR, being much shorter wavelength, gives a higher angular resolution infrared
background noise low the atmosphere also emits some infrared, though it being very cold high up I don't expect it is a lot radar
atmospheric attenuation very low depends on wavelength, but for some wavelengths it is quite low radar
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  • $\begingroup$ Military radars can by many kW of transmit power. The infrared signature is much less than that. Then there is the whole radio vs infrared propagation in the atmosphere. $\endgroup$
    – Jon Custer
    Nov 7, 2023 at 13:10
  • $\begingroup$ JWST is a big IR sensor with a very long range, only topped in the microwave with the CMB (btw, passive microwaves are also a thing). Here on earth, GEO is loaded with IR sensors looking down. Finally, I think the EHT has the best angular resolution of anything? $\endgroup$
    – JEB
    Nov 7, 2023 at 15:37
  • $\begingroup$ @JEB Big IR telescopes is certainly a thing in space, but for some reason not within the atmosphere. I've never seen an AWACS-style boeing with a big infrared telescope mounted on top instead of a radar dish. Also, despite those big telescopes, we also do radar mapping of asteroids, which is apparently better than just looking at them with the telescopes. $\endgroup$
    – JanKanis
    Nov 7, 2023 at 15:48
  • $\begingroup$ 'stroid range doppler has the resolution equivalent to resolving a quarter (25 cents) in NY, from LA....with active illumination. On IR in space: en.wikipedia.org/wiki/Space-Based_Infrared_System $\endgroup$
    – JEB
    Nov 7, 2023 at 17:00

2 Answers 2

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Active radar and passive IR operate on fundamentally different principles.

Active radar is a coherent system in the sense that a replica of the transmitted signal is directly and explicitly compared to the received one, so that when subtracted one from form the other ideally there be nothing but pure noise or other errors left. Especially some older radars only compared the only the amplitude modulation in the transmitted signal with its received replica and ignored the phase modulation but that was for its simpler and cheaper receiver not for lack of interest...

A passive IR receiver is a power detector that cannot distinguish one kind of power received from another, it measures background power and compares it with the received one.

Every other consideration is a secondary issue to this including range or transmitted power. For example, a wideband spread spectrum radar tries to blend its transmitted signal in the background noise to be as inconspicuous to power detectors as possible. But in detection, be it coherent (amplitude and phase) semi-coherent (amplitude), what matters is not the received power but the received energy that is the coherently integrated power over time.

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  • $\begingroup$ This is to say the radar signal can be crafted to boost signal-to-noise by e.g. pulsing the signal and using lock in detection? I assume you can get many orders of magnitude increased sensitivity this way. $\endgroup$
    – Jagerber48
    Nov 7, 2023 at 14:49
  • $\begingroup$ @Jagerber48 lock-in detection is a way to move the received near dc signal away from the high noise - low frequency region by shifting it around a desired a carrier frequency around which the detector noise is less. Radar's modulated RF signal is at a frequency that is primarily determined by the available RF bandwidth, the antenna and transmitter. Radar shapes the transmitted signal to avoid detection and jamming meanwhile be as wide bandwidth as possible for good range resolution and be as long in time as possible to have good velocity resolution. $\endgroup$
    – hyportnex
    Nov 7, 2023 at 15:18
  • $\begingroup$ This is the crucial point: The detection performance of a radar in wideband noise is independent of its signal power (amplitude) but is directly dependent on its received energy over the coherent time. The relevant SNR is $\frac{E_p}{\mathcal N_0}$ where $E_p$ is received energy and ${\mathcal N_0}$ is the receiver's background noise power spectral density, if the latter noise is thermal then ${\mathcal N_0}=k_B T_{eff}$. $\endgroup$
    – hyportnex
    Nov 7, 2023 at 15:22
  • $\begingroup$ It looks like this might be the answer I'm looking for, but I'm having trouble understanding all of it. e.g, how does that SNR equation compare to the SNR equation for a passive IR receiver? $\endgroup$
    – JanKanis
    Nov 7, 2023 at 15:56
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    $\begingroup$ You thought correctly but if you have a faithful local copy of the transmitted signal, amplitude and phase and locally you can compare it completely with the received signal you will have extracted the most information. This is called coherent detection in radar parlance. If the target moves then you have to shift the frequency of the local copy to match the two up in phase during the coherent reception time, a "Doppler" measurement. $\endgroup$
    – hyportnex
    Nov 7, 2023 at 16:05
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I'm not an expert in radar or IR imaging. Here's my uninformed response (aka my guess):

  • I think your estimate for the amount of thermal radiation emitted by a target may be an overestimate. With Radar we can always boost the power by emitting more radar from our antenna. With IR the amount of power is fixed by the thermal radiation coming from a target. The exact quantitative details should be worked out here.
  • You say atmospheric attenuation is "very low" for radar but "quite low" for "some wavelengths". What is "very low" and "quite low" in these cases? Maybe targets don't emit thermal radiation in the "quite low" attenuation bands. The exact quantitative details should be worked out here.
  • I understand that radar can bounce of the atmosphere so you don't need line of sight to your target to image it. I doubt thermal radiation bounces of the atmosphere in this way. So to get more range you need your sensor higher and higher up in elevation. When were talking about ranges of 100s of km I'd expect this effect to be very important. I guess this is due to an index of refraction step at the ionosphere for radio waves.

My last point is an underlying physics difference between the two. The first two are arguably "details of specific radar or infrared systems" which is something you say you aren't looking for. But "why does radar have longer range than infrared systems" is an engineering question. Not a physics question. The answer will probably involve physics, but it will probably also involve engineering. If you get a different planet with more favorable atmospheric attenuation and the possibility for thermal radiation atmospheric refraction then maybe thermal imaging would have a longer range. In engineering the specific details might matter and can't be glossed over.

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  • $\begingroup$ I'd love to find out how much thermal IR jet aircraft actually emit, but I haven't found that yet. Maybe I'm overestimating, but then again the amount of radar power re-emitted from a target is also tiny compared to the transmitter beam. $\endgroup$
    – JanKanis
    Nov 7, 2023 at 14:53
  • $\begingroup$ The atmosphere has narrow absorption bands spread over the infrared spectrum. Thermal emissions are wideband, even for a single source at one temperature. For aircraft they range from around 10 µm for the fuselage to 1 µm for the hot jet exhaust. So the thermal emissions cover many absorption and transmission bands. The frequencies in the absorption bands won't be very useful of course, but there will be plenty in the transmission bands. According to the graphs on en.wikipedia.org/wiki/Electromagnetic_spectrum#Microwaves, the transmission band at 10 µm has an attenuation of <0.1 dB/km. $\endgroup$
    – JanKanis
    Nov 7, 2023 at 15:15
  • $\begingroup$ I haven't found numbers on the attenuation of radar yet, but reading from the very crude atmospheric opacity graph on the wikipedia page they are lower. I don't think curvature of the earth is very important for this question. High flying aircraft at 9-10 km have a distance to the horizon of several 100 km, much further than their IR sensor ranges. $\endgroup$
    – JanKanis
    Nov 7, 2023 at 15:18

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