# Einstein, Princess Leia, and the Telephone Hologram

Imagine you having a long stick in your hand – a veery long stick, one that reaches all the way to the moon. There, on the lunar surface, is a good friend of yours who holds the other end of the stick. At the same time, an important football match is broadcasted on TV, which your buddy on the moon doesn’t want to miss at all cost. Although he can watch it (the NASA kindly allowed him to bring a (battery-powered and portable) television set on his moon walk), he really misses the “real-time feeling” due to the time delay. (Remember, it takes about 1.2 seconds for the light to travel from the Earth to the moon.) For that reason, you agreed with your friend upon shaking the Earth-sided end of the stick everytime his favorite team scores. In doing so, he would already know about the course of the game – full 1.2 seconds before the TV would show him. Thus, the information was transmitted with a speed faster than the speed of light.

But stop! – This clearly contradicts Einstein’s theory of relativity, according to which nothing (not even any kind of information) can propagate with a speed beyond light speed. Something is wrong here! (And, as you may have already guessed, it’s not the theory of relativity! 😉 )

Instead, the fallacy lies in the way the signal travels along the stick: The “information of shaking” cannot go faster than light either. When you shake one end of the stick, a wave starts to travel along it – with a speed slower than light. As long as the wave hasn’t arrived at the man in …uumm…on the moon, your buddy wouldn’t even know about your shaking. Moreover, it actually takes longer for the “stick signal” to arrive at the moon than it does for the TV signals. (So this whole stick project wasn’t really worth it, was it?! 😉 )

So we found a consequence of the theory of relativity: There are no physical bodies which are absolutely stiff and inelastic. Everything in the universe has to be elastic and malleable, at least to some extent. Otherwise, a transmission of information faster than light would be possible.

However, as we know from our day-to-day lives, there are countless object which seem completely solid. If we applied some force, however small, to them, they would have to be deformed, consequently. Is this really true?

Not let’s assume that you – just hearing about the impossibility of superluminal information transmission – call your friend on the moon in order to bring him these bad news. After some explanations about the interferometry experiments performed by Albert Abraham Michelson and Edward Morley, which strongly suggested the constancy of the light speed in all frames of reference, and numerous digressions on the nature of Lorentz transformations, you disappointedly replace the receiver on the telephone set.
In doing so, you realize that your whole telephone set must actually deform a little bit under the weight of the receiver. You ask yourself if there would be any way of making these small deformations visible.
The answer to this question is: Yes, there’s a way indeed! And today, in this article, I want to present a method which enables us to visualize tiniest deformations.

This is a telephone set from the 1970s. It gets along just fine without WhatsApp.

If physics and our physiology wouldn’t put a spoke in our wheel, we would be able to directly see the phone’s deformations due to the receiver weight. But given such small force influences, these deformations might be smaller than the wavelength of the light which is reflected by the object before reaching our eyes. For this very reason, the resolution of the received image is just too small to see subtle surface structures or deformations.

So let’s reach deeply into the physicist’s bag of tricks! Let’s explore the method of holographic interferometry!

Princess Leia as a hologram. (Scene from Star Wars, Episode IV – A New Hope)
(Source unknown)

When it’s about holograms, many of you might think of the Star Wars scene in which the droid R2-D2 delivers the emergency call of princess Leia in the form of a hologram.
Some, however, might rather think of the more realistic forms of holograms which is impressively shown in the following video.

In order to understand the core topic of this article – the holographic interferometry – I will now write some words about holograms in general.

The “inventor” of the holography is considered to be the engineer Dennis Gábor who received the Nobel Prize in Physics in 1971 for the concept of the holography. The motivation behind his “invention and development of the holographic method”, rather than depicting objects three-dimensionally, was to improve the resolution of microscopes. The technological realization of the holography, though, wasn’t fully possible until the invention of light amplification by stimulated emission of radiation – or, in short: the laser.

Conventional black-and-white photographs are made by exposing, e.g., sensitive coatings to light. At it, the photographic film gets blackened on places where light hits it. The degree of blackening depends on the light’s intensity and the length of exposure. Color photos, in addition to the information about the degree of blackening, also contain informations about the wavelengths (= color) of the light.
Nevertheless, light holds even more informations than just intensity and color. In the case of conventional photos, the full information about the incoming light’s phase gets lost. The phase of a light beam strongly depends on its distance travelled. So if we intend to depict a three-dimensional picture on a two-dimensional film, we will have to additionally store some information about the object’s “spatiality”. The basic principle for doing this is quite simple: If we can somehow manage to additionally capture the phase of the incoming light beams, we will know how long the light has travelled before it hit the photographic film. More precisely, what we want to do is to compare the phases of the light beams which were reflected by the object with the phases of light beams coming directly from the light source without ever being reflected. The result, then, are just the phase differences between the reflected light beams and the “reference light beam”. This information is actually enough to reconstruct the three-dimensional image of the object, as we will see soon.

But let’s take it one step at a time for now!

The following picture schematically shows the setup which is required in order to create a hologram.
They grey cube on the upper right should be depicted on the photographic plate on the lower right. Therefore, a laser beam is sent into the arrangement. Laser beams are especially “coherent” which, in our case, just means that the phases of the light waves are known to a high degree. Right at the beginning, the laser beam is split up and it isn’t until the individual beams reach the photographic plate that they are brought together again. What happens in between is crucial for the successful development of the hologram.

Schematical setup for creating a hologram.
(Credit: Bob Mellish, via Wikimedia Commons)

The light is scattered and reflected at the object and a wave subsequently propagates from the object to the photographic plate. We shall call this wave “object beam”. The phases within this object beam are varied since some of the beam’s photons were reflected at places farther apart from the plate as others. When the object beam reaches the photographic plate, it meets the reference beam which still has the original and known phases. Since the phases of the object beam now differ from the reference beam’s phases (because the photons within the object beam have different run times due to the reflection on the object), it comes to interferences.
The picture arising on the photographic plate could, for example, look like this:

Hologram of a checkered pattern.
(From H. Nassenstein: Z. Angew. Physik 22, 37-50 (1966))

Great!” you might think “And this lousy picture should be worthwhile?!
Well, this confused diffraction pattern contains a lot of information! Since the scattered wave from an individual object point is distributed across the whole film in the process of generating the hologram, every segment of the holographic film holds the information of the entire object, which is fundamentally different from conventional photography. You can actually fully reconstruct the image of the object from just a cut-off piece of the hologram. (Only the image resolution suffers from that.)
In order to reconstruct the picture of the object, one has to light the holographic plate with a “reconstruction beam” – a light beam of the same frequency which has been used in the process of creating the hologram. In this way, the “encrypted” informations on the plate are diffracted on the patterns of the film and thereby “decrypted”. What’s left is the three-dimensional image of the object.
As distinguished from the 3D pictures which are commonly known from cinema halls, holograms in a way allow the viewer to “look around” the depicted object up to a certain point. This is possible due to the fact that holograms indeed contain informations on the “spread” of the object – they don’t just lead us to believe in having these informations, which of course happens in ordinary 3D (movie) technology.

We want to make these deformations visible to the naked eye. To do just that, we first create a hologram of the telephone set when the receiver is not placed onto it. What we get is a nice three-dimensional picture of it – everything works analogously to the above-described method. Now, we put the receiver on the apparatus and make a hologram again. The crucial point here is that we don’t change the photographic plate! The plate gets exposed twice!
Since the phone’s casing is a little bit deformed due to the receiver’s weight when we take the second “picture”, the phases within the object wave are now different from the ones of the unloaded and receiver-less telephone set of the first shot. The resulting interference pattern just looks different from the first one and it is written on top of the first pattern.
When we reconstruct the wave field using a (unchanged) reconstruction wave, only the differences between the first and the second holographic picture become visible. These differences in our case are the deformations of the casing due to the influence of the receiver’s weight force.

In my opinion, the result is absolutely stunning!!

Deformation of a telephone set due to the weight of the receiver.
(Source: Website of Jakob Woisetschläger)

Naturally, a cup of slightly changes its shape when being filled with a hot liquid:

Deformation of a cup after being filled with hot liquid.
(Source: Website of Jakob Woisetschläger)

The method of the holographic interferometry has a wide variety of applications. For example, it’s used in medicine to holographically survey a patient’s head and determining the spatially resolved structure of the soft tissue through comparing the hologram with an X-ray image of the skull.
It’s also possible that, in the future, holographic memories will gain in importance – after all their information density seems to be huge, according to present insights.
In stating just these two examples, the application areas of the holographic interferometry aren’t nearly covered. I’ll come back to this later in another blog post, possibly.