FABRY-PEROT INTERFEROMETER Roberto Bartali

ABSTRACT

Spectroscopy is a technique based on the separation of light. Chemical and Physical phenomena can be studied by the analysis of the quantity of absorbed, emitted or reflected photons of some particular wavelength. Normally this is done using filters with narrow or broad band pass, depending on the information we are looking for. If the filter band pass is narrow, more precise measurements can be done, because we have the capacity to isolate photons, of a very specific wavelength, which are produced by some particular phenomenon or circumstance. The selection of a particular wavelength, from the whole incoming light, can be done using a technique developed by Fabry and Perot in late 1800. This work is devoted to the description of such technique, called, precisely, Fabry-Perot interferometer. BACKGROUND

August Comte (1798-1857), a French philosopher known as the creator of the Positivism [Wikipedia 2006] stated that something that people would never know is the chemical composition of stars, because they are so far that we could never go there to get a sample and bring it back on Earth for analysis [U-Maryland]. Maybe we will never travel to stars, but we do

not need to do that to know how stars works and their composition. Spectroscopy is the technique of the analysis of light emitted, reflected or absorbed by objects. A spectrum (discovered by Newton) is the decomposition of light into each constituent wavelengths, for example, in the case of our Sun, it is the rainbow (visible spectrum) plus all other invisible wavelengths. A spectrum is obtained by passing the light

through a prism (figure 1-a) or a diffraction grating (figure 1-b).

Fraunhofer in 1814 (observing Sun spectra with a magnification lens) discovered a series of dark lines (figure 2) in the solar spectra, but nobody know what they are until 1859, when Kirchhoff and Bunsen figured out that chemical elements produces a unique pattern of spectral lines, like their own fingerprint. This way we can know the exact chemical composition of materials and of

course stars, just spreading the light we receive from them into a spectrum. Light is an electromagnetic radiation (an electric and a magnetic field perpendicular one to each other, moving, in the vacuum, at the speed of light, or at different speed depending on the medium) and behave as a particle and as a wave (but not at the same time). Photons (the particles of light) are generated when an energized electron return to its normal no energized state (falls down to it original energy band in the atom). Due to its duality, it shares all the properties of a wave and a particle and it carries energy because it moves. If we see light as a wave, we can represent it by the wavelength λ (the distance from two successive crest), the quantity of crests that succeed in a second is the frequency (f). The energy is then, the frequency multiplied by the Planck constant (h). We can observe this energy in the Photoelectric effect, which is the way a light act as a particle. We have seen the application of the photoelectric effect in CCD and Photomultiplier tubes. We are interested, now, in the wave properties of light. Waves suffer from interference which can be constructive or destructive [Olympus 2006, Wolfram 2006]. The former is when two or more waves are in phase (both crest are of the same sign, positive or

negative), the maximum effect is when both crest pass at the same time from the same place, so they are added together (figure 3-a). The latter is when the waves are out of phase (one is positive and the other is negative), the maximum effect is when the crest of one wave coincide, in the same place at the same time with the trough of the other, in this case the amplitude of the resulting wave is zero (figure 3-b). Waves of different wavelength and phase create a complicated pattern when interact (figure 3-c). Another important concept we need, for the understanding of this discussion about interferometers, is that a star emit light as a blackbody object (which is an idealized object that absorb all radiation falling on it and do not reflect any. A blackbody does not emit any electromagnetic radiation, all the radiation emitted is only thermal radiation) and obey Wien and Stephan-Boltzman laws for blackbody radiation. [ESA 2005] . The light (electromagnetic radiation) we receive from a star could be seen directly, through a cloud of gas and dust or scattered by that cloud (figure 4) [U-Maryland].

• If the light is received directly from the star, we perceive a continuous spectrum, when it pass through a prism (figure 4-a). A continuum spectrum shows all the wavelength emitted by the object.

• If the light pass through a gas cloud, some wavelengths are absorbed (depending on the atoms that constitute the gas). The spectrum is called an absorption spectrum and show (figure 4-b) dark lines corresponding to the wavelengths absorbed (not transmitted by the gas cloud).

• If the gas cloud is not aligned with our line of sight, we perceive the light that it scatter. The scattering effect depends on the gas composition. The resulting spectrum show a series of bright lines corresponding to the elements which interact with the gas and emit photons (figure 4-c).

• If we superimpose the absorption and the emission spectrum, we get the continuum spectrum again, because photons of wavelengths absorbed by the gas, energize its atoms and photons at those precise wavelengths are now emitted depending of course of the characteristics of each atom.

After this brief explanation of key concepts, we will enter in the field of interferometry, which is the study of wave interference, and in its application in spectroscopy and imaging. INTERFEROMETER BASICS

Interferometry is a technique that combine various beams of light to achieve a greater resolution. It is used to made very precise spatial measurements like diameter of stars. Due to the complexity of the technique, it is applied from visible to radio wavelengths of the electromagnetic spectrum (optical and radio interferometry). Some examples of radio

interferometers are the Very Large Array [VLA] and the Australia Radio Telescope [ATNF] (figure 5-a). Some examples of optical interferometers are the European Southern Observatory Very Large Telescope [VLT] (figure 5-b) and the Keck twin telescopes [Keck].

It consists of capturing waves, coming from a single object, by two or more different and separated instruments. The separation between instruments is called the baseline. The resolution of the image is the same that would be obtained by a single instrument which diameter is equal to the baseline; but the light collecting power is, obviously, much less because the diameter of each instrument is much less than the baseline, even more, it is lesser than the one of a single instrument with a collecting surface approximately equal to the sum of the collecting areas of each instruments conforming the interferometer. Waves reach each instrument at slight different time, so to obtain useful information from an interferometer we need to record each one with a very precise timing, for very long baseline interferometry in the radio spectrum, an atomic clock is used to synchronize every signal. Optical interferometry is much more complex, due to the shorter wavelengths involved, light path from each telescope must be compensated (with a maximum difference of a fraction of a wavelength) before to be combined. An interferometer is not an instrument intended to capture images in a direct form, like a telescope equipped with a CCD, instead of an image, it show a complex interference pattern (captured by a conventional CCD) that must be processed to obtain the image of the object of interest. Many kinds of interferometers were developed, each one for a different application, in this work we are interested only in one of them, developed by Fabry and Perot in late 1800 []. FABRY-PEROT APPARATUS The Fabry-Perot apparatus (figure 6) [Dickmann 2003, FP1, FP2, FP3, FP4, FP5] consist of two semitransparent mirrors (plane or curved) placed at some distance (t), which is in the order of the wavelength to be observed. The medium between both mirrors has a refractive index of n. Light (λ) from the object under study must enter at certain angle θ

with respect to the optical axis, through the mirror on the left side. Light inside the mirrors suffer from a series of constructive and destructive interferences because it is reflected many times from one mirror to the other because they are semitransparent. If the mirror separation (t) is an entire multiple of the wavelength, of the incoming

light, a constructive interference reinforce that light and it is the one that can pass through the second mirror (the one on the right). Instead, if the distance (t) is half a wavelength of the incoming light, destructive interference occurs and no light of that wavelength pass through the second mirror. Conceptually simple to fabricate, but very difficult to do in practice because of the extremely small dimension of the distance between mirrors, the flatness or surface accuracy of them must be very high, the refractive index of the inter-mirror medium must be very uniform as the reflectivity of both mirrors. This two mirror

configuration is also called an optical cavity because is an optical resonator. Another name, coined by Fabry and Perot is Etalon, word that means something like the “measuring gauge” of the light.

An output wavelength can be obtained if the conditions or the status of (t, θ and n) met the Fabry-Perot Equation depicted in the blue box of figure 6. It is obvious that this is a tunable optical filter. Tuning can be performed by varying any of the two main parameters: distance between mirrors (t) and the angle of the incident light. If the angle of incidence is zero i.e., perpendicular to the mirror, no interferences are produced inside the mirrors and the exiting light is the same as the incident one [FP1, TecOptics 2006]. Tuning the filter moving one of the mirrors respect to the other (incrementing or decrementing

the distance t), it is possible to calculate an unknown wavelength with the relation: λ=2t/n; where lambda is the unknown wavelength, t is the distance between mirrors and n is the fringe order. The latter is the number of fringes counted outward from the centre of the

image (figure 9), to do this a photodiode or a photomultiplier tube are best suited (it is more or less the same as counting white and black lines in a barcode). The resolution of a Fabry-Perot Etalon is known as the Finesse and it is proportional to the reflectivity of the mirrors (figure 7) [Dickmann, FP4]. Higher the reflectivity, smaller the pass-band of the output wavelength. This imply that if we want to separate (fine tuning) a narrow band from a complex or a wider set of wavelengths the reflectivity of the mirrors can be as high as possible (figure 8). In that figure we can see the effect of the reflectivity, if the curve is steeper, the intensity of the wavelength transmitted by the

filter is higher. This imply that the resolution is better than for a low reflectivity mirror. Recalling the interference theory, if the light is reflected more times, the constructive interference reinforce that wave more times too. At the same time, the undesired wavelength suffers from destructive interference more times, so the intensity of the output

wave is very low or null. The distance from fringes (peaks in figure 8) is d=c/(2t), where c is the speed of light and t is the separation between mirrors. The output of the Fabry-Perot filter is focused by a lens and directed to a conventional optical sensor like a CCD or a photomultiplier tube. The resulting image is a series of concentric circles [Hyperphysics] with the higher order one toward the centre (figure 9). The advantage of a Fabry-Perot interferometer is its extremely high resolution at the expense of a very complex manufacturing process.

Some of the critical figures that can degrade its performance if not well calculated and manufactured are: parallelism between mirrors, flatness of the mirrors, uniformity of the refractive index of the medium between mirrors, differences in the reflectivity of one mirror respect to the other, impurities in the mirror material and movements of the mirrors. APPLICATIONS Astronomy is just one of the multiple applications of this kind of interferometer. Communication technologies, laser (modern lasers could be not manufactured without Fabry-Perot technology) and medicine uses it extensively. The main application of a Fabry-Perot interferometer in Astronomy is spectroscopy. Thank to its high resolution, it is possible to isolate a specific wavelength and measuring its intensity, to know precisely the quantity of some specific element present or absorbed. It is a part of a spectrometer, the light from a slit is diffracted by a diffraction grating and is directed to the etalon. The light from the etalon is then focused on a CCD.

A precise measurement of the position of the lines in the spectrum of an object (like a galaxy) permit the calculation of the velocity of that object due to the Doppler effect. In this field, a Fabry-Perot interferometer is more accurate than an ordinary spectroscope. A precise three dimensional velocity curve profile (figure 11,12) can be made with Fabry-Perot interferometry giving the possibility to understand the morphology of galaxies and

their star forming region developments specially when there are imaged looking for HII regions using the Halpha emission line (figure 10). Figure 13 is the galaxy NGC1672 in Halpha light just for comparison, to better understand the interferometric images. Solar research can take also advantage to the high resolution of these interferometers because very narrow lines can be measured.

REFERENCES General Wikipedia 2006-1, Auguste Comte: http://en.wikipedia.org/wiki/Auguste_Comte ESA 2005, Stellar radiation and stellar types: http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=35774&fbodylongid=1696 VLT: http://www.eso.org/paranal/ Keck: http://www.keckobservatory.org/ VLA: http://www.vla.nrao.edu/ ATNF: http://www.atnf.csiro.au/ Dickmann 2003, Fabry-Perot Resonator, Experiment03, 2003. FP1: http://www.ee.byu.edu/photonics/Fabry_Perot.phtml FP2: http://www.micronoptics.com/telecom_ffp.htm FP3:http://www.cfht.hawaii.edu/Instruments/Spectroscopy/Fabry-Perot/mosaicfp5.html#finessecalc FP4: http://www.chem.uic.edu/tak/chem524/Spring2001/notes6/figureN_1.gif FP5: http://www.phy.davidson.edu/StuHome/cabell_f/diffractionfinal/pages/Fabry.htm#Theory TecOptics 2006: http://www.tecoptics.com/etalons/index.htm Wikipedia 2006-2: Fabry-Perot Interferometer: http://en.wikipedia.org/wiki/Fabry-Perot U-Maryland, The tools of Astronomy: http://www.umuc.edu/virtualteaching/module1/umuc_ex/content/mod2.html#1.1 Olympus 2006, Microscopy Resource Center: http://www.olympusmicro.com/primer/lightandcolor/java.html Wolfram 2006, Interferences: http://scienceworld.wolfram.com/physics/Interference.html Hyperphysics, Fabry-Perot Interferometer: http://hyperphysics.phy-astr.gsu.edu/Hbase/phyopt/fabry.html Applications Puerari I., Valdez-Gutierrez M, Rosado M., A Fabry-Perot study of Scd I galaxy NGC5457, 2002, astro-ph/0202013 v1.

Debattista V., Williams T.B., Fabry-Perot absorption line spectroscopy of NGC7079: kinematics and bar pattern speed, 2004, Astrphysical Journal 605:714-724. Soh M., et al, Short wavelength infrared tuneable filters on HgCdTe photoconductors, 2005, Optics Express 9683, vol 13 num 24. The Electronic Universe Project, University of Oregon Allen Gary G., CIV vacuum ultraviolet Fabry-Perot interferometer for solar research, 2006: http://solar.physics.montana.edu/ IMAGE CREDITS Figure 1-a Prism: adapted from http://www.cglapocatiere.qc.ca/techno/banque%20de%20photos/prism.jpgFigure 1-b Diffraction grating: adapted from http://oco.jpl.nasa.gov/images/grating_spec-br.jpgFigure 2 Solar spectrum: http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=35774&fbodylongid=1699Figure 3-a Constructive interference: http://scienceworld.wolfram.com/physics/ConstructiveInterference.htmlFigure 3-b Destructive interference: http://scienceworld.wolfram.com/physics/DestructiveInterference.htmlFigure 3-c Interference pattern diagram: Interference pattern picture: http://en.wikipedia.org/wiki/Image:2006-01-14_Surface_waves.jpgFigure 4-a,4-b,4-c Kind of spectrum (adapted from): http://hal.physast.uga.edu/~rls/1020/ch6/Figure 5-a ATNF: http://www.narrabri.atnf.csiro.au/Figure 5-b VLT: http://www.eso.cl/paranal.phpFigure 6 FP diagram: http://www.cfht.hawaii.edu/Instruments/Spectroscopy/Fabry-Perot/mosaicfp5.html#finessecalcFigure 7 Finesse: http://upload.wikimedia.org/wikipedia/en/a/a3/Etalon-finesse-vs-reflectivity-2.pngFigure 8 Finesse: Dickmann 2003, Fabry-Perot Resonator, Experiment03, 2003.

Figure 9 Fringes: http://www.mellesgriot.com/glossary/wordlist/glossarydetails.asp?wID=279Figure 10 NGC1672 HII regions: http://zebu.uoregon.edu/fp2.htmlFigure 11 Curve map of NGC1672: http://zebu.uoregon.edu/fp2.htmlFigure 12 Velocity profile of NGC1406: http://zebu.uoregon.edu/fp2.htmlFigure 13 NGC1672: http://zebu.uoregon.edu/fp2.html