HIGH SENSITIVITY INTERFEROMETER BASED ON FABRY - PEROT ETALONS : APPLICATIONS IN CHEMICAL ANALYSIS E. Fokitis*, P. Fetfatzisa**, V. Gikaa, G.Koutelierisa, S. Maltezosa, N. Maragosa, A. Aravantinosb a
Physics Department, National Technical University of Athens, 15780 Athens, Greece, bPhysics
Department, Technological Educational Institute of Athens, 12210 Athens, Greece. *e-mail:
[email protected] **Presenter
ABSTRACT We present a review of high spectral resolution spectroscopy based on recent progress in the design of a spectrometer based on a pair of Fabry – Perot (FP) interferometers with free spectral range 0.25cm -1, and 0.1cm
-1
respectively.
Using appropriate narrow band pass, less than 1nm, optical filters we select the wavelengths corresponding to the atomic or molecular line of interest. At the present, we plan to conduct studies in Hg elemental analysis in the atmospheric or liquid phase. In the present paper, we focus on the calibration of our system by using a natural low pressure mercury lamp. This work is extension of our several year instrumentation development works for atmospheric monitoring using the High Spectral Resolution LIDAR. In this work, we present modern opportunities of application of FP in the broad area of chemical analysis. This is done by presenting the capabilities, advantages and limitations of FP spectrometers.
Section 1. Introduction The NTUA group has studied in the last several years the application of the technique of FabryPerot interferometry in a variety of problems with emphasis in monitoring the optical properties of some fluids [1, 2], and atmospheric monitoring [3, 4]. Motivated, however, by the vast number of publications in the Fabry-Perot interferometry, we are presenting in this work, the possibilities of using this instrumentation in the topic of Chemical Analysis, and in particular try to present the challenges ahead. However, in the process of preparing this manuscript, we have made significant progress in the method of characterizing the etalon of the FP, in particular in measuring its free spectral range, and therefore we pay particular effort in presenting the method of this measurement. Μany important processes in nature include molecular dynamics expressed as the interaction of molecules with laser beams by displaying effect of molecular shift and broadening. In such case the Fabry-Perot interferometer may, very well be the most suitable experimental instrument for the study of velocity distributions of these molecular ensembles. During the last decade, we have the strong development of microsystems and nanotechnology, and in this respect the Fabry-Perot micromechanical structures play a more important role [5]. Therefore such microelectronic structures can be incorporated in chemical analysis optical devices. We present the various occasions where the Fabry-Perot interferometry is appropriate in Section 2. In Section 3, we explain and apply methods of characterization and validation the Fabry-Perot systems as well as the methods of data analysis. Finally, in Section 4 we present our Conclusions and Prospects. 1
Section 2. Areas of Application of Fabry - Perot (FP) Interferometry for Chemical Analysis One of the main advantages of FP interferometry is its capability for remote sensing. Thus, it allows Trace Species Detection in Troposphere. More specifically interesting areas which can be studied by FP include: 1. Ozone is a key oxidant in tropospheric photochemistry; ozone photolysis is one of the principal sources of the hydroxyl radical (OH), which is the most important radical species associated with the photochemical degradation of anthropogenic and biogenic hydrocarbons; 2. Exposure to enhanced levels of tropospheric ozone negatively impacts health, crops, and vegetation. 3. As a greenhouse gas it contributes toward radiative forcing and climate change. These three areas can be target of studies by FP interferometry in remote sensing. Earlier NASA sponsored research [6] has shown that a tropospheric ozone measurement capability can be achieved using a satellite - based nadir - viewing device making high spectral resolution measurements with high signal to noise ratio, and that a Fabry-Perot interferometer (FPI) is quite suitable for this task. Chemical analysis in star systems can be done, considering as example the reference [7], where singly ionized calcium is elegantly studied in stellar atmospheres. 4. Ιmportant role is reserved in FP interferometer in quantifying the column of CO2 in the Earth atmosphere with great accuracy [8] . In the case of chemical analysis in liquid phase, we cite as example matter of bio - molecules in solution studied inside a FP cavity [9]. Fabry - Perot line profile measurements have been used to obtain heavy particle temperatures and electron densities for an expanding cascaded arc plasma in argon [10]. Etalons are used as chemical sensors to monitor biological fluids [11]. However, we can mention at this point the many patents and commercial products available, based on combination of Fabry - Perot etalons and modern fiber optics [12] and adjusted to the telecommunication bands, near 1.5 μm. Finally, in chemical analysis, especially of solids, the Raman spectroscopy at high resolution requires the use of Fabry - Perot spectrometry [13]. In this specific case, a Fabry - Perot etalon was used to narrow the bandwidth to 0.03 cm-1. A very interesting work Ref. [14], explains very well the use of the technique CARS (Coherent Anti stokes Raman Spectroscopy) in combination with Fabry-Perot etalon, achieving a resolution 0.01 cm-1, very hard to achieve with grating based usual spectrometers.
Section 3. Methods of characterization, validation and data analysis of Fabry Perot systems 3a. Use of group of isotope lines of natural mercury Calibration of the FP has as first step, the calibration of its Free Spectral Range (FSP), given by the following formula, for a plane FP etalon: FSR = 1 / (2d ) where d is the spacer distance of the two mirrors of the etalon. For confocal type etalon, a procedure for calibrating the FSR is given in Ref. [15]. For a plane etalon, a comprehensive procedure is described in [16]. Another possibility to characterize this FP 2
etalon is by studying its response to the well known neutral atomic lines of oxygen in the Earth atmosphere. This possibility, i.e. to use the available infrastructure at NTUA Physics Department, may allow studies for chemical analysis include the study of molecular and atomic species either in a laboratory or in the atmosphere. These studies eventually lead to better understanding of the dynamics of the Earth atmosphere by measuring the distribution of neutral winds at a height of around 100Km, where we have large percentage of atomic oxygen. These are excited to states emitting radiations at 557.7 and 630.0 nm, and the velocity vector fields of these atoms can be measured using Fabry-Perot interferometer combined with optical telescopes [17]. Narrow optical filters at these wavelengths with pass band 0.3 nm preselect these radiations and then they are monitored at high resolution through Fabry-Perot etalon with 0.5 cm spacer, installed at a 250mm diameter Newtonian telescope. The challenge in this type of measurement is on the optimum use of CCD sensors to record the interference fringes from the above spectral lines. In order to make such measurements possible from the point of view of sensitivity we are planning to use CCDs either thermoelectrically cooled or operating near liquid nitrogen temperatures [3]. Incidentally, we have recorded the radiation at 557.7 nm with grating spectrometer but a lower spectral resolution, not allowing giving some estimation of the neutral winds. A second method for the calibration of the Fabry - Perot etalons available in our lab is by using standard spectral lines, with their frequencies known from the literature. The experimental apparatus is seen in Figure 1. There are many experimental parameters that may be defined appropriately so that the FP spectrometer has optimum performance. They are described in many publications. However, one key parameter to this measurement’s accuracy (and for that matter to all Fabry-Perot spectrometer’s measurements) is related to the angular or pinhole finesse. Τherefore, we discuss this effect in some more detail. The pinhole finesse can be defined in several different ways, but in any case, it is related to the, finite, angular size of the light source. This is most frequently defined by a pinhole just after the light source. The effect of the pinhole size on the finesse (or the visibility of fringes is treated elegantly by Francon [18]). According to some practical outcome from his analysis, the visibility of fringes is reduced rather abruptly when the angular size p′. Formally, this parameter is expressed as p'
2d nt
where θ is the angular size of the light source, nt the refractive index of the medium inside the etalon, d the etalon’s spacer distance. In our experimental conditions, if p’ becomes larger than p /100
(that is for a reflectivity of etalon mirrors of the order 92%, as is the case of our 20mm spacer etalon), we get high fringe visibility under the condition:
n 100 d
Therefore, for a focal length of input to etalon lens around 5 cm, etalon spacer length around 2 cm, for λ = 435.8nm, the light source size is estimated around less than 0.5mm. In practice, with such a pinhole just after the light source, one should obtain good visibility of fringes. Using these parameters, we discuss below the interferometric data with our low pressure natural mercury lamp. 3
3b. Data recording The light of a low pressure mercury lamp is made more homogeneous by a diffuser before exiting through the pinhole. Then, it was collimated by a lens of focal length 50 mm , it passed through an interference pass band filter and then transmitted through the 20mm spacer length etalon. A 300mm focal length lens projects the interference fringe pattern on the CCD image plane (Nikon D40 colored CCD). The interferogram is seen in Figure 2a. One already observes clearly the presence of “small” -“shoulder” that may be attributed to isotope shift structure. We discuss below the Fabry - Perot Interferometer modeling carried out in order to compare with interferometer data aiming eventually to extract the etalon parameter d. In order to interpret (analyze) the experimental results accurately the Fabry-Perot interferometer has been modelled taking values of shifts according to [21]. In Fig.2b one sees a preliminary simulation for the expected fringe pattern for the spectra of Hg at the 435.8 line(note that the data and calculations of [21] are also in agreement with [22]). Based on above reference and using the Airy function for all lines involved, we obtain the following formula
4
IT: transmitted intensity, Ic: calibration constant for the intensity, IR: experimental values for the relative intensities for each line, Np: CCD pixel number at the central row, No: CCD pixel number at the center of the central row, R: reflectivity of the Fabry-Perot mirrors, α: constant for the width of every line due to Doppler Broadening, n: refractive index of air, d: the Fabry-Perot spacer distance, λ: wavelength for every line due to isotopes, fL: focal length of the output lens, ε: phase shift parameter.
Due to isotope existence and the hyperfine structure this line splits to eleven (11) lines. Despite the general agreement of our data with the simulation based in [21], and [22], there is an uncertainty in the accurate wavenumber central group of isotopes, corresponding to even isotopes of Hg. Therefore, for the group of lines 196+198 we used the values of [32], and assumed the average values given for the lines of isotopes 200+202 (grouped together in ref.[21]). Due to these uncertainties, our simulation is very preliminary, and we have not been able yet to give values of spacer length d. From these experimental results of ours we can estimate the total Finesse of the interferometer which is quite low. The main reason for this is the Pinhole Finesse that can be reduced resulting in even better wavelength separation and the shot noise. The effect of overlap of the thirteen (11) wavelengths is present, as it can be noticed from the bottom simulation diagram in Fig.2. One can comment that we have studied (and we will be studying for more accurate data sets of Hg isotopic shift and hyperfine structure) in order to improve the simulation function. We even are studying large astronomical grating spectrometer Hg calibration spectra as explained in ref.[19]. A further comment is that lines of mercury within ±5 nm (the optical filter pass band) further complicate the data analysis. Further selection of more accurate literature data may improve the above agreement with our interferometric data. Finally, we may consider the prospect of fitting the FP etalon data with a function accurately representing the theoretical behavior. In this way, the 11 lines of the theory should give very strong constraints, and therefore, the spacer distance d should be determined with good accuracy. According to authors pioneering in the relevant analysis, one should conduct measurements with more than one spacer, and in particular, with spacer lengths differing
significantly (for instance by a factor of 5-10) [20]. Putting this in another way, one can put the question on the resolution of the FP interferometer and on the magnitude of the systematic errors related to it. In this respect, one can consider this question as a metrological issue since we have the here the potential to get an accuracy of the order of 10 -4 Å. A possible configuration for operation with two such separate etalons is seen in Figure below. We should note that these spectral lines, as components of isotope shift, suffer from the Doppler width, and this is a source of uncertainty. We could improve the data if we use a liquid nitrogen cooled lamp, as it has been done in ref. [23]. 3c. Use of lasers for characterizing the FP etalons Α further note about the potential of this method is explained in [24]. It can be fitted1 by the theoretical model of FP intensity response at the central fringe which is a function of the phase δ for a line of wavelength λ with finite natural width. In this expression, we have taken into account about 40 harmonic terms. This fitting function includes: R, the mirror reflectivity, L the coefficient of Lorentzian function, D the coefficient expressing the mirror flatness, G the Doppler broadening coefficient as a function of temperature T, NS and N A0 the finesse coefficients due to mirror spherical curvature and aperture area of the central fringe, respectively. We present in Figure 4, the results of fitting, based on above function I(δ), with the data on the response function of a pressure tunable Fabry-Perot interferometer using air as phase changing medium. In order that we introduce a fitting function to the experimental data, the longitudinal modes of He-Ne laser were assumed to be due to an effective cavity of length L, with refractive index of the active medium , n=1, and an etalon mirror reflectivity R. These two parameters, L and R, were entered as parameters in the fitting function. The resulting parameter L (effective length) was found to be =38.12cm. The statistical error of L was estimated at 0.14cm. Then, using for the longitudinal mode frequency separation from the formula, Δν = c / 2L. Thererore, Δν = 393.5ΜΗz with an uncertainty ±1.5 MHz. Despite these encouraging results, we have not enough documentation on the curvatures of the mirrors of the laser used, and as a result, there is a systematic error in the determination of Δν values. Thus, we are not yet in a position to use such a laser for determining the spacer length d, of the etalon and consequently its free spectral range. An alternative experimental method for calibration, using lasers, used in our lab, is to record spectrum of 532 nm SLM laser or He - Ne laser having well understood modes from previous work [4, 24]. A fourth method relies in using specific well known lines of Cadmium (Cd) lamp [25]. In discussing all these methods, one should point to the necessity of obtaining the so called excess fraction ε, corresponding to the exact relationship between each specific fringe diameter and the fringe order n. This needs, in general a complicated procedure which is facilitated significantly when the FP is crossed with a grating or prism spectrograph [26]. 3d. Tandem Fabry-Perot Interferometer measurements Some of the desired properties of the FP etalon include precision control of etalon plates to demonstrate accurate spectral tuning and parallelism control of the Low Resolution Etalon and High Resolution Etalon. The resolution of FP can achieve up to 0.002 cm-1 , allowing to probe very week phenomena of interest to chemistry such as effects of Van der Vaals forces
as described in Ref. [29]. We give below some examples of the potential of the Tandem FP spectrometer.Use of Tandem F-P system for daylight measurements: During the day, the light that can be collected in the spectral range of the FP etalon is comparable to the background. With the use of Tandem FP system, one can receive the true signal because due to the strong background rejection capability of this configuration[27]. This system needs certain conditions to achieve this coordination. The NTUA group has conducted some preliminary experiments with a Tandem FP with satisfactory preliminary results. To bring the two etalons in resonance with respect to the wavelength of interest simultaneously, one can use two alternative solutions. Another solution is obtained when the two etalons have a ratio of the two spacer lengths which is again a rational number. Then from the above Equation it can be seen that the two etalons resonate simultaneously. We have selected this procedure as it is much simpler and it does not require use of pneumatic systems. A further advantage of the Tandem FP spectrometer is that it effectively increases the free spectral range without compromising the spectral resolution. We discuss the data received with Tandem FP system at the end of the Section 4. Since 1930 Brillouin scattering (BS) using a Fabry-Perot interferometer (FPI) has been a well established method for the investigation of thermally excited sound waves in liquids and solids. However, it was early recognised in the field of Brillouin scattering that the standard Fabry-Perot interferometer has too low a contrast to allow weak Brillouin signals to be observed in the presence of the normally extremely intense elastically scattered light. This is automatically achieved by the scanning stage [28] which supports the scanning mirrors of both interferometers. In order to study this possibility, i.e. the increase of contrast in the FP data, a Tandem Fabry - Perot experimental test set up has been implemented. The experimental setup is similar to Fig.1, with only difference that two etalons, with spacer lengths 5 and 50 mm are in sequence. The results of this are in Fig.5. An He - Ne Laser has been employed to validate the systems performance from the separation between the longitudinal modes of such a Laser. Τhese data are very preliminary , and one has to apply a simulation program for the Tandem FP operation before some serious data analysis is made. One, however, expects some of the peaks of the short FSR etalon to be suppressed by the long FSR one, and at the same time, the contrast for these peaks remaining to be improved.
Section 4. Discussion, Conclusion and Prospects The operation of Fabry-Perot spectrometer has a need of appropriate software for imaging and analysing the interference fringes. This has been discussed in several recent works of our team [3,4]. One of the challenges ahead is to use the Fabry-Perot interferometer to study in great detail the temperature and pressure conditions during electrical discharges in air. Our group has managed to achieve such measurements from high spectral resolution measurements using grating spectroscopy. Studying this phenomenon by use of Fabry – Perot instrumentation we hope to compare with corresponding temperature measurements, and at the same time by analyzing the data to achieve pressure information. This study is in preparation phase. This work may be of interest in process monitoring through laser ablation applications. During these processes, the molecular nitrogen optical emission lines may be used as reliable probes of the thermodynamic parameters such as pressure and temperature [30]. We are also planning to use an optical instrumentation with one extra beam splitter and two separate etalons with different lengths in order to measure simultaneously the fringes from the same source. Finally, one can use FP etalons for studying rotational constants of simple molecules, as described in [31]. Αcknowledgements
The project is cofinanced 75% of public expenditure through EC – European Social Fund, 25% of public expenditure through Ministry of Development - General Secretariat of Research and Technology and through private sector, under measure 8.3
of OPERATIONAL
PROGRAMME "COMPETITIVENESS" in the 3rd Community Support Programme. We also greatly acknowledge Assoc. Professor Yiannis Raptis for kindly supplying the natural mercury spectral lamp.
References [1] Filippas et al, Precision measurements of gas refractivity by means of a Fabry – Perot interferometer illustrated by the monitoring of radiator refractivity in the DELPHI RICH detectors, T. A. NIM B, Volume 196, Issues 3-4, November 2002, Pages 340-348. [2] Fokitis E. et al, The Fabry - Perot Interferometer for the DELPHI Ring Imaging Cherenkov Detector , Nuclear Physics B - Proceedings Supplements, Volume 44, Number 1, November 1995, pp. 246-251(6). [3] E. Fokitis, P. Fetfatzis, A. Georgakopoulou, V. Gika, M. Kompitsas, Stavros Maltezos, I. Manthos, A. Papayannis and A. Aravantinos, “Review of High Spectral Resolution Techniques for Measurements of the Aerosol Phase Function and Application in Extensive Air Shower Detector Atmospheric Monitoring” Poster presentation at 31th ICRC-09 Conference, Lodz, Poland (2009). (http://users.ntua.gr/fokitis/icrc0768.pdf) [4] Fokitis E. et al. Design of a High Spectral Resolution Lidar for Atmospheric Monitoring in EAS Detection Experiments , Nuclear Physics B - Proceedings Supplements Volume 190, May 2009, Pages 261-265. [5] Kuhn, J. et al. Electro-mechanical Simulation of a Large Aperture MOEMS Fabry-Perot Tunable Filter,http://physics.gmu.edu/~satyapal/Projects/spie_fp_d000920.pdf [6] Larar, Allen et al. Airborne Imaging Fabry-Perot Interferometer System for Tropospheric Trace Species Detection:IIP Project Update, http://esto.nasa.gov/conferences/estc2003/papers/B4P2(Larar).pdf [7] Simpson J., Stellar elemental abundance determination using a Fabry - Perot Interferometer, Masters of Science Thesis, http://ir.canterbury.ac.nz/bitstream/10092/2684/1/thesis_fulltext.pdf [8] EL Wilson et al, Development of a Fabry–Perot interferometer for ultra-precise measurements of column CO2, 2007 Meas. Sci. Technol. 18 1495. [9] Mc Garvey T. et al. Finesse and sensitivity gain in cavity-enhanced absorption spectroscopy of biomolecules in solution. 30 October 2006 / Vol. 14, No. 22 / OPTICS EXPRESS 10441, http://minty.stanford.edu/papers/Publications/McGarvey06.pdf
[10] Meulenbroeks M.et al. Fabry-Perot line shape analysis on an expanding cascaded arc plasma in argon, J. Appl. Phys. 75 (6), 15 March 1994. [11] Minas G. et al. A 16 Fabry-Perot Optical-Channels Array for Biological Fluids Analysis using White Light, http://dei-s1.dei.uminho.pt/pessoas/higino/pampus/M2B1.pdf [12] http://www.micronoptics.com.cn/en/pdfs/FFP-SI.pdf http://www.micronoptics.com.cn/en/pdfs/FFP-SI.pdf, available from www.micronoptics.com [13] ABRAM Ι. et al., STIMULATED RAMAN SCATTERING EXPERIMENTS IN SOLID N2 AND H2 USING NITROGEN PUMPED DYE LASERS, Volume 52, number 1 CHEMICAL PHYSlCS LETTERS 15 November 1977. [14] Gillespie W. et al. Broadband D2 coherent anti-Stokes Raman spectroscopy for single-shot pressure and temperature determination with a Fabry – Perot etalon, p. 534 APPLIED OPTICS y Vol. 38, No. 3 y 20 January 1999. [15] Fletcher D. et al. Construction and calibration of a low cost Fabry - Perot interferometer for spectroscopy experiments, Colin D. Fletcher et al, Am. J. Phys., Vol. 73, No. 12, December 2005, p.1136.
[16] Haase A. et al. Lab Report on the Fabry-Perot-Etalon Anton Haase, Michael Goerz 4. October 2005GP II Tutor: M. Fushitani. http://users.physik.fu-berlin.de/~mgoerz/studies/gp2/FAP_report.pdf [18] Μ. Francon / Interferences, diffraction et polarization/ Fundamentals of Optics (Encyclopaedia of Physics.), Springer. [19] E.A. Mallia, Solar Physics, Springer, Vol.2,Number 3/Nov. 1967. [20] John M. BLANK, Interferometric Measurements of Wave - Lengths in the Spectrum of Mercury Isotope 198 , JOSA VOLUME 40, NUMBER 6 * Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts (Received February 23, 1950). [21] (Mitteilung aus dem Einstein-Institute, Astrophysikalisehes 0bservatorium, Potsdam.) Hyperfeinstrukturen und Kernmomente des Quecksilbers. Von H. Schiller in Potsdam und J. E. Keyston, Nottingham, England1), zurzeit in Potsdam, pp423-441. [22] Boggs and Webb 1935, Hyperfine structure Mercury Triplet, Physical Review, August 1, Vol. 48 [23] G H C Freeman et al Cu II spectral lines and their suitability as wavelength standards in the vacuum ultraviolet1977 J. Phys. E: Sci. Instrumentation 10 894. [24] E. Fokitis et al, Use of the Fabry-Perot Interferometer for atmospheric monitoring and night sky background in EAS Detection, E Fokitis et al (gre-fokitis-E-abs1-he15-oral) (http://icrc2005.tifr.res.in/htm/Vol-Web/Volume8_index.html).
[25] Davies T. et al. A NEW FABRY PEROT SPECTROMETER FOR THERMOSPHERIC AIRGLOW OBSERVATIONS ABOVE DAVIS STATION IN ANTARCTICA, Australian Institute of Physics 17th National Congress 2006 – Brisbane, 3-8 December 2006 River Phys. (http://www.aip.org.au/Congress2006/601.pdf). [26] K. Meissner , Interference Spectroscopy. Part I. JOSA,Vol.31,No.6, pp405-427, June 1941. [27] J.G.Dil et al, 1374 APPLIED OPTICS / Vol. 20, No. 8 / 15 April 1981 [28] R Mock, B Hillebrandst and R Sandercock, Construction and performance of a Brillouin scattering set-up using a triple-pass tandem Fabry-Perot interferometer J. Phys. E: Sci. Instrum. 20 (1987). [29] Bielski A. et al. Laser-induced fluorescence study of the influence of N2 and CH4 on the 114 Cd intercombination line.Eur. Phys. J. D 23, 217–222 (2003). [30] Maltezos S. et al. NITROGEN MOLECULAR SPECTRA OF AIR FLUORESCENCE EMULATOR USING A LN2 COOLED CCD, to appear at Proceedings of http://villaolmo.mib.infn.it/ICATPP11th_2009/accepted/Astroparticle/Maltezos.pdf
[31] Butcher R. et al. On the Use of a Fabry-Perot Etalon for the Determination of Rotational Constants of Simple Molecules-The Pure Rotational Raman Spectra of Oxygen and Nitrogen. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 324, No. 1557 (Aug. 12, 1971), pp. 231-245. [32]A. Melissinos and S. P. Davis, Dipole and Quadrapole Moments of Isomeric Nucleus Hg197*;Isomeric Isotope Shift*, Physical Review, Vol. 115, Number 1, Jul. 1959
FIGURES
Figure 1. Experimental arrangement of our FP 20mm etalon, CCD (Nikon D40) is on the right side of the optical table. On the left is the mercury (low pressure) spectral lamp. This etalon is between two positive lenses with the same (f = 300mm) focal length, the distance between the two lenses is about 185mm.
13
Counts
400
300
200
100
1800
1850
1900
1950
A
X pixel Number
B
Fig.3. A.The simulated fringe pattern for the 435.8337nm line Hg for the 13 lines passing the filter at 435.8 with 10nm FWHM. The total intensity is the black line and the colored ones are the isotopes constitutes. B. The measured interferogam, the half center fringes and the 1st one
14
Light Source
Beam Spliter HR Etalon
CCD1
L1 Beam Reduc er LR Etalon Plane Mirror
L2
CCD2
Figure 3. The simulated fringe pattern for the 435nm Hg, 11 of the 13 lines passing the filter at 435 with 10nm FWHM and the total intensity. Οne observes a general agreement with corresponding interferometer data but more accurate comparison would require using one fitting procedure.
15
Figure 4. Fit of the interferogram with 20 mm etalon versus pressure, with a theoretical curve describing the He - Ne laser longitudinal modes.
16
Figure 5. Right: The fringe pattern from a 50mm and a 5mm Tandem Fabry - Perot interferometer analyzing the He Ne Laser Longitudinal modes and Left: the corresponding intensity plot .
17
