Laser beams can be used to precisely measure an object’s position or velocity. Normally, however, a clear, unobstructed view of this object is required — and this prerequisite is not always satisfied. In biomedicine, for example, structures are examined that are embedded in an irregular, complicated environment. There, the laser beam is deflected, scattered, and refracted, often making it impossible to obtain useful data from the measurement.
However, researchers have now been able to show that meaningful results can be obtained even in such complicated environments. Indeed, there is a way to specifically modify the laser beam so that it delivers exactly the desired information even in a complex, disordered environment — and not just approximately, but in a physically optimal way. Nature does not allow for more precision with coherent laser light. The new technology can be used in very different fields of application, even with different types of waves.
“You always want to achieve the best possible measurement accuracy — that’s a central element of the natural sciences,” says Stefan Rotter from TU Wien. “Let’s think, for example, of the huge LIGO facility, which is being used to detect gravitational waves. There, you send laser beams onto a mirror, and changes in the distance between the laser and the mirror are measured with extreme precision.” This only works so well because the laser beam is sent through an ultra-high vacuum. Any disturbance, no matter how small, must be avoided.
But what can you do when you are dealing with disturbances that cannot be removed? Imagine a panel of glass that is not perfectly transparent, but rough and unpolished like a bathroom window. Light can pass through, but not in a straight line. The light waves are altered and scattered, so we can’t accurately see an object on the other side of the window with the naked eye. The situation is quite similar when you want to examine tiny objects inside biological tissue: the disordered environment disturbs the light beam. The simple, regular straight laser beam then becomes a complicated wave pattern that is deflected in all directions.
However, if you know exactly what the disturbing environment is doing to the light beam, you can reverse the situation. Then it is possible to create a complicated wave pattern, which gets transformed into exactly the shape needed to correct for the disturbances, and hits right where it can deliver the best result. To achieve this, you don’t even need to know exactly what the disturbances are, it’s enough to first send a set of trial waves through the system to study how they are changed by the system.
The researchers developed a mathematical procedure that can then be used to calculate the optimal wave from this test data. It can be shown that for various measurements there are certain waves that deliver a maximum of information such as, for example, on the spatial coordinates at which a certain object is located.
Take an object that is hidden behind a turbid pane of glass: there is an optimal light wave that can be used to obtain the maximum amount of information about whether the object has moved a little to the right or a little to the left. This wave looks complicated and disordered but is then modified by the turbid pane in such a way that it arrives at the object in exactly the desired way and returns the greatest possible amount of information to the experimental measuring apparatus.
The fact that the method actually works was confirmed experimentally at Utrecht University (Utrecht, Netherlands). Laser beams were directed through a disordered medium in the form of a turbid plate. The scattering behavior of the medium was thereby characterized. Then the optimal waves were calculated in order to analyze an object beyond the plate — this succeeded, with a precision in the nano-meter range.
Then the team carried out further measurements to test the limits of their method. The number of photons in the laser beam was significantly reduced to see whether one then still gets a meaningful result. In this way, they were able to show that the method not only works but is even optimal in a physical sense. They found that the precision of their method is only limited by the so-called quantum noise. This noise results from the fact that light consists of photons — nothing can be done about that. But within the limits of what quantum physics allows for a coherent laser beam, we can actually calculate the optimal waves to measure different things. Not only the position, but also the movement or the direction of rotation of objects.