Archive | October, 2011

Detectors in Optical Astronomy

15 Oct

“Astronomy compels the soul to look upwards, and leads us from this world to another.” – Plato (4277-3477 BC), The Republic.

“Correctly understood, the stars were proof of a higher design in the Cosmos.”Plato, in Exploring Ancient: A Survey of Ancient and Cultural Astronomy, by David H Kelley, Eugene F. Milone, Anthony F. Aveny (Springer, New Yoork, 2011) 

Humankind always has sustained, since the dawn of times, a major interest in observing the sky and gaining new knowledge and insights on the working mechanism of Nature (and for some, a glimpse of God). For this reason astronomy is the oldest science developed by humankind and we have been using the discoveries made by the use of this science to improve our civilization, embedding this knowlegde in our culture, art, religion, and our present notions of space and time.

But, how can we access to this knowledge, understand how the universe looks like? The first mean we have is just the bare eye able to separate image details with about 3 minutes of arc. This is equivalent to to 1/10 of the moon diameter, or the airplane wing span (10 m) flying at 10 km high.


What is called angular resolution is the smallest detail detected by a telescope (or an eye), which is limited by aberrations and diffraction pattern (a series of concentric rings of light and darkness due to interference).

Fig. 1 -- Eye structure.

Why it is not possible to obtain an angular resolution with infinite value? Because unfortunately any optical detector (eye, telescope, camera,…) gives of a point light source a diffuse image of what it is called a diffraction pattern (Fig.2) caused by the light waves diffracted at the fringes of what is called the “apertures” (diaphragms that confine the circular beam area). Therefore, the view of the smallest point of the object emmiting light is limited by this pattern, which may be described by parameters such as the diameter of the inner structure (defined as the first zero of light intensity), and other parameters. But to simplify, usually it is prefered to use a new definition, actually a convention proposed firstly by Ernst Abbe in 1874:


Here, d is the size of the finest detail that can be resolved with a camera, lambda is the light wavelenght, and NA denotes the numerical aperture of the objective lens, which can be defined by the ratio:


This means that a telescope with 12 cm of diameter can separate at maximum stars distant one second of arc. The formula is this one:

AR(angular resolution)=250,000 x lambda/diameter

AR=250,000 x 6500Angstrom/0.12= 1.35 seconds of arc

We used for lambda the value 6500 angstrom=10^(-10) meters, a common value in the optical range. And what size eye (AR=1′, one minute) would you need to detect radio waves (lambda=0.1 m) ?

d=250,000 x 0.1/ 1’=450 m !

Sunset at the fingertips of my friend Americo Jones. The bridge links Lisbon to the South of Portugal and it is similar to the Golden Gate Bridge that cross San Francisco Bay.


That is, your eyes should be apart 450 meters to detect radio waves…, for which the atmosphere is transparent. Unfortunately, our eyes cannot strecht so much apart. Otherwise, human eyes, working together with the human brain, are extraordinary matural detectors in its range of color sensitivity, sensitivity to dim light and adaptability. Painters are highly sensitive to colors, see this article about impressionists French painters, and the eye was the principal help classical astronomers had before and served to observe planets and the most brilliant stars in the sky.


Hence, this represents a theoretical resolution, since atmospheric turbulence interposed between the star and the observer forbid this possibility. This is why telescopes are built at the top of mountains in order to gain a factor of 3 or 4 in this resolution. For example, at Mauna Kéa, Hawaii, at 4200 meters of altitude, it was built the world’s largest observatory for optical, infrared, and sub-millimeter astronomy. Among the equipment, France built a telescope 360 meters of diameter, so huge in order to increase the luminosity coming from the stars.

Mauna Kéa, Hawaii, tha world's largest observatory for optical astronomy. Image credit:

In the actuality, astrophysicists need more sensitive detectors to observe quantitatively very faint stars. But notice that at the end it is again the eyes that remain the ultimate detectors, since astronomers need to look at the pictures…


The next detector used in astronomoy is the analog camera. Although less sensitive than the eye, its advantage stays in the possibility to let the shutter open for a long time of exposure, it is simple to handle and possess a great capacity to stock information. But its main disadvantage is the difficulty to digitalize the image for computer analysis. For example a black-and-white roll film has one side more brilliant than the other.  The least brilliant side has an emulsion of gelatin with suspended array of silver halide crystals which determine the sensitive of the film to light exposure. The reaction taking place is the following:

Ag Br + h f -> Ag^+ + Br + e^- [when exposed to light with energy hf, Bromure is liberated and retained in the gelatine]

Ag^+ + e^- -> Ag  [the liberated silver atom is sequentially converted in metallic silver by electronc capture.]

In particular, the size of the grains determine the time of exposure necessary: larger grains needs faster exposure but gives a grainier appearance; smaller needs more extended time of exposure but the images are finer looking. The ISO factor traduces the graininess of the roll film, appearing as a multiple of 10 or 100. For example, lower ISO numbers produce finer grain but slower film, and vice versa.


However, nowadays the amateur and professional have acess to electronics registreurs, which has as precurseurs the electronographic camera invented by Prof. Lallemand and his team at the Observatoire de Paris in 1967. Although this detector was capable to detect just one photon and has a magnetic focalisation of the photo-electrons, it has a low performance. with the advent of integrated circuits (IC) and semiconductors, at 1970’s Williard S. Boyle (received in 2009 the Nobel Prize for this invention) and Smith invented a camera called CCD (charged coupled device) where successive metallic electrodes were capable to locally confine electric charge into silicium. See how it works here.

This operational mode allows that pratically each photon incident on the telescope can be enregistered and its properties made CCD cameras of great use in telescopes at the surface of Earth and in satellites.

After this short digression on the means to watch the sky by yourself, I invite you to watch these wonderful programs broadcast by BBC and presented by Sir Patrick Moore (here) along the great British traditions of scientific divulgation.

Do neutrinos move faster than the speed of light?

2 Oct

Quite recently, 23 Sept. 2011, CERN issued a press release reporting an anomaly in the time-of-flight of neutrinos.

The experiment, called Oscillation Project with Emulsion-Racking Apparatus (OPERA), aims to detect neutrinos obtained by smashing fast particles againts protons from the Europeans particle physics laboratory. The detector consists in a 1300-metric-ton particle detector.

Neutrinos travel underground from CERN to Grand Sasso in Italy along 732 km.

«As the particles hardly interact at all with other matter, they stream right through the ground, with only a very few striking the material in the detector and making a noticeable shower of particles.

Over 3 years, OPERA researchers timed the roughly 16,000 neutrinos that started at CERN and registered a hit in the detector. They found that, on average, the neutrinos made the 730-kilometer, 2.43-millisecond trip roughly 60 nanoseconds faster than expected if they were traveling at light speed. “It’s a straightforward time-of-flight measurement,” says Antonio Ereditato, a physicist at the University of Bern and spokesperson for the 160-member OPERA collaboration. “We measure the distance and we measure the time, and we take the ratio to get the velocity, just as you learned to do in high school.” Ereditato says the uncertainty in the measurement is 10 nanoseconds.»

Antonio Ededitato, a physicist at the University of Bern and the spokesperson of the 160 collaborators of the OPERA project, is prudent. He said “I would never say [that relativity is wrong]”. You can access the relevant papers published in the frame of the OPERA project in this site.

The problem of measuring speed is that we both need distance and time-of-flight. For the last one quantity the experimenters used the time given by Global Positioning System. The common GPS source of errors are:

  • Ephemeris errors: they occur when the satellite doesn’t correctly transmit its exact position in orbit;
  • Ionosphere conditions: when satellites travel through this region above the Earth their signal are slowed down due to the plasma medium that constitutes the ionosphere;
  • Troposphere region: it affects the signla propagation due to the variations of temperature, pressure, and humidity;
  • Timing errors: they may occur if the GPS receiver clock is not an atomic clock;
  • Multipath erros: the satellite signal can be reflected from any hard surface, sucg as buildings) and delay the travel time of the signal;
  • Poor satellite coverage.
Time and distance are measured by means of triangulation with 4 satellites. Diferent sources of errors are inherent to the method. Read here to learn more.

Science attempts to improve our vision of Nature and its working, and the speed of light is considered the maximum speed with which any meaningful signal may propagate in space. The apparent possibility that any object can travel faster than light reminds me of the famous mathematician Grothendieck, Field medal (the Nobel prize of mathematics), who disapeared sudenly in 1970 somewhere in village of the Pyrennés.

One story goes that Alexander Grothendieck is “convinced that the Devil is working to falsify the speed of light”.  Grothendieck told to Leila Schneps, wife of Pierre Lochak, both mathematicians at the Université de Paris-Jussieu, that he was willing to share his research into physics with her if she could answer one question: ‘What is a metre?’ …He refuses to work in physics sustaining that physics made possible the horror of Hiroshima. Alain Resnais made a dramatic and beautiful movie about the horror of it in his movie “Hiroshima, mon amour”, based on the work of the French writer Marguerite Duras. We always endure a catarsis when watching this movie (trailer here).

Grothendieck great contribution to mathematics  was to enlarge our concept of “geometric point”. This concept goes back to Leibniz for who the constituents of all things (material or spiritual) are monads without internal structure and it is their relationship that make the “structures”. Grothendieck concept of “point”. For this understanding we need the concept of space X: A space X described using the notion of topos T(X) of sheaves over X. A given point a is a point of X.

Despite the possible errors due to the method of measurment itself, or the methaphysical problems intrinsically related to the knowledge of the working mechanisms of nature, already some tentative explanations are advanced to explain the supraluminal effect, for example see this paper from Robert Alicki attempting to explain the effect on statistical grounds.

It is expected much ado about this effect, but for one thing I am sure, physics is well behind the development of mathematics and not taking due advantage of its progress.

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