Jitter

We live in an imperfect world. In any real system, there will be vibrations. Either from nearby machinery, people walking around, being buffeted by wind, distant traffic, or any number of other sources. Even just the ambient temperature of the environment can lead to unavoidable thermal motion. These vibrations will be transmitted to your beam pointer, and cause the beam to jitter slightly. This will make it harder to keep your beam at one spot on your target. In extreme cases (like long range shooting in space) it might make it uncertain that you can hit your target at all.

Engineers will, of course, try to minimize jitter. They can vibrationally isolate the beam pointer equipment. They can use active vibration control. They can try to keep noisy, vibrating equipment far away from the laser beam pointers. They can cool the beam directing equipment with liquid nitrogen. They can yell at the crew members to stop walking so loud and stomping their feet. All of this helps. But it can only take things so far. And the more you try to reduce the jitter, the more complicated and expensive the beam pointer becomes.

How much jitter?

How much of a problem is jitter, really? We can look at modern telescopes for some idea, because a telescope is really just a laser beam pointer operating in reverse. What we see is that for visible and near-visible colors of light, you can put in enough work to get the jitter angles close enough to the limits imposed by diffraction or turbulence that they are no longer a problem. If your diffraction-limited spot size is 1 cm across, no one will care if the point of aim is jumping around by 3 mm or so. This is not trivial, but it is achievable. And once they get the jitter control good enough, they stop trying to make it better because that would just be a needless expense. In extreme cases, they’ve taken astronomical telescopes mounted on airplanes, subject not only to the vibrations of the turbines but also being buffeted by near-sonic wind speeds, and made the jitter small enough that you could get more-or-less diffraction-limited pictures at most wavelengths of interest. So diffraction-limited operation of visible and near-visible colored lasers even in noisy and vibration prone environments looks to be achievable.

In addition, we have some data for actual laser weapons designed for actual space. Or at least actual laser weapon test beds, as these were part of the Strategic Defense Initiative and they never actually ended up getting launched. But the vibration reduction parts could be tested on the ground. The Space Integrated Controls Experiment (SPICE) project acheived a 77:1 reduction in jitter by using active vibration damping, 200 nanoradian jitter under quiescent conditions and 500 nanoradian jitter even in the worst atmospheric conditions. The Space Active Vibration Isolation (SAVI) project is reported to have achieved less than 100 nanoradians of jitter . However, we also find that this is under ideal static conditions. The Zenith Star project reported a 1.5 μrad jitter induced from slewing the aimpoint by 4° in approximately 2 seconds, or 65 μrad jitter if this slew is accomplished in approximately 1 second; although it is mentioned that optimal slewing techniques can be used to reduce the jitter to less than 1 μrad while completing the slew in one second.

But as your focusing ability becomes better and better, probably by going far into the ultraviolet or x-ray parts of the spectrum to limit diffraction or using low emittance particle beams, it becomes harder and harder to correct for the jitter relative to the ideal focused spot size. A long range beam may just have to deal with its focused spot of destruction wandering randomly around on its target - or, for very long ranges, wandering randomly around in the space near its target, hoping to trace across it at some point.

Instrument	Jitter (radians)
Keck Telescope	$3.9\times 10^{-7}$
Hubble Space Telescope	$3.4\times 10^{-8}$
Stratospheric Observatory for Infrared Astronomy (SOFIA)	$1.0\times 10^{-5}$
Space Integrated Controls Experiment (SPICE)	$2\times 10^{-7}$
Space Active Vibration Isolation (SAVI)	$1\times 10^{-7}$

If you really want to see just how far you can push jitter reduction, reference shows that most of the jitter for the Hubble Space Telescope is due to an approximately 60 Hz vibrational mode of the primary mirror, with significant additional contributions from just a few other modes. Active vibration damping of these structures could conceivably reduce the jitter by another factor of about 7, possibly leading to jitter angles on the order of 5 nanoradians.

Jitter from enemy weapons

The one source of jitter that will never cooperate with the engineers who try to get it from messing up sensors and weapons is enemy fire. Many other notions can be predicted, modelled, and measured. Dampeners with passive and active systems can isolate systems from a noisy enviroment - sensors in the larger structure can track distortions and vibrations and feed them to models and active controllers.

The moment an enemy weapon smacks into your hull, that paradigm gets disrupted violently. Even just thermal heating will cause parts of the hull to expand, and as the heat creeps into other parts of the structure, those parts too will expand, then contract as they heat and cool. We can track the heat moving using networks of temperature and stress sensors and feed it into a computer model. Special insulatory connections can stop the migration of heat into critical structural components, stand-by cooling systems can keep components within required tolerances.

The bigger problem after thermal load becomes shock. This can come from kinetic impacts, thermal vaporization from lasers or particle beams, or from outright explosive evaporation caused by strong energy fluxes - lasers, particle beams, the radiation off of nukes (thermal or ionizing). These will send vibrations and shockwaves through the armor, if they penetrate deeper the structure underneath too. A penetrating hit will induce vibrations whereever the resulting plasma can push on the structure. These events become unpredictable. You do not know from where enemy fire will come, generally, and precisely when. Furthermore the plasma dynamics are inherently chaotic, dependant on many factors. This makes predictive modelling complicated. Furthermore from where exactly the shockwaves come will not incorporate indefinitely with one's engineering efforts to isolate critical components. Penetrating hits will eventually cut past isolation points and firewalls and induce shock where it isn't supposed to be. Redundancies can of course be incorporated, but there are limits to everything. Structural integrity, mass, system complexity (all of this has to be serviced!)... it comes together. Eventually the vibrations will begin exceeding your carefully engineered tolerances and dampening systems capacity to fight them.

Jitter introduced by enemy fire appears to be the biggest (and hardest to quantify due to its complexity, also) influence on jitter and through this, sensor and weapons accuracy. Hulls rebounding with the aftershocks of enemy fire would likely find their sensors and weapons impaired. This has consequences for every other aspect of prosectuting an engagment. From long-range direct fire to sensor spotting to mid-range fire and point defenses. Even long-range narrow-focus comms may get messed up temporarily. All of this can compound itself, opening up weaknesses for approaching guided munitions, and/or make engagments at a certain range impossible since jitter is just too high to effectively lay weapons on target (in turn forcing a closer engagment range for direct-fire weapons - or taking them out of the field if the risk of guided weapons would become too great at a closer range.)

All that ugly math

If you know the amount of jitter $\sigma _{j}$ of your beam pointer in radians, at a range of $R$ the diameter of the spot your beam will wander over is

$S_{j}=2\,R\,\tan(\sigma _{j}).$

For small jitter angles (and if your weapon is going to be at all useful, the angles had better be small), this is approximately

$S_{j}\approx 2\,R\,\sigma _{j}.$

If your target has a profile area $A$ in your view, your chance of hitting with a single shot will be approximately

$p\approx {\frac {A}{(\pi /4)\,S_{j}^{2}}}.$

Credit

Authors: Luke Campbell and Sevoris