FLIR Systems, Inc.
`IPR2014-00411/IPR2015-00065
`FLIR v. LSI
`Exhibit 1042-00001
`
`Development of infrared spectroscopy techniques
`for environmental monitoring
`
`Jonas Sandsten
`
`Lund Reports on Atomic Physics
`LRAP-257
`
`Doctoral Thesis
`Department of Physics
`Lund Institute of Technology
`August 2000
`
`ISBN 91-7874-055-X
`
`

`

`T0 Maria and Erik
`
`Exhibit 1042-00002
`Exhibit 1042-00002
`
`To Maria and Erik
`
`

`

`Exhibit 1042-00003
`
`Contents
`
`Abstract
`List of papers
`
`1. Introduction
`
`2. Infrared radiation sources
`2.1 Natural background radiation
`2.2 Artificial infrared radiation
`2.3 Near-infrared diode lasers
`2.4 Difference-frequency generation with near-infrared diode lasers
`2.5 Passive versus active remote-sensing methods
`
`3. Infrared spectroscopy
`3.1 The gas-correlation principle
`3.2 The two-dimensional extension to the gas-correlation principle
`3.3 Gas concentration calibration
`3.4 Aerosol particle scattering
`
`4. Infrared image detectors
`4.1 Thermal detectors
`4.2 Photon detectors
`
`5. Optical design considerations
`5.1 Gas-correlation telescopes
`5.2 Gas-filter cell design
`5.3 Aerosol particle sensor optics criteria
`5.3 Difference-frequency generation criteria
`
`6. Image processing
`6.1 Gas visualization
`6.2 Noise in gas-correlated images
`6.3 Gas flow evaluation by cross correlation in time
`
`7. Applications
`7.1 Gas visualization
`7.2 Aerosol particle sensor
`7.3 Diode laser spectrometer
`
`8. Summary of papers
`
`Acknowledgements
`References
`
`6
`7
`
`9
`
`12
`12
`14
`15
`16
`17
`
`18
`25
`27
`28
`33
`
`39
`39
`40
`
`42
`43
`47
`48
`51
`
`53
`53
`56
`57
`
`58
`58
`63
`63
`
`64
`
`65
`66
`
`5
`
`

`

`Exhibit 1042-00004
`
`Abstract
`
`Infrared spectroscopy techniques have long been utilized in identifying and
`quantifying species of interest to us. Many of the elementary molecules in the
`atmosphere interact with infrared radiation through their ability to absorb and emit
`energy in vibrational and rotational transitions. A large variety of methods for
`monitoring of molecules and aerosol particles by collecting samples or by using
`remote sensing methods are available. The objective of the work presented in this
`thesis was to develop infrared spectroscopic techniques to further enhance the
`amount of useful information obtained from gathering spectral data.
`
`A new method for visualization and quantification of gas flows based on gas(cid:173)
`correlation techniques was developed. Real-time imaging of gas leaks and
`incomplete or erratic flare combustion of ethene was demonstrated. The method
`relies on the thermal background as a radiation source and the gas can be visualized
`in absorption or in emission depending on the temperature difference.
`
`Diode laser spectroscopy was utilized to monitor three molecular species at the
`same time and over the same path. Two near-infrared diode lasers beams were
`combined in a periodically poled lithium niobate crystal and by difference(cid:173)
`frequency generation a third beam was created, enabling simultaneous monitoring
`of oxygen, water vapor and methane.
`
`Models of aerosol particle cross sections were used to simulate the diffraction
`pattern of light scattered by fibers, spherical particles and real particles, such as
`pollen, through a new aerosol particle sensing prototype. The instrument, using a
`coupled cavity diode laser, has been designed with a ray-tracing program and the
`final prototype was employed for single aerosol particle sizing and identification.
`
`6
`
`

`

`Exhibit 1042-00005
`
`List of papers
`
`This thesis is based on the following papers which will henceforth be referred to by
`their Roman numerals, I-V.
`
`I
`
`II
`
`III
`
`IV
`
`V
`
`J. Sandsten, H. Edner, and S. Svanberg, "Gas imaging by gas-correlation
`spectrometry," Optics Letters 23, 1945 (1996).
`
`J. Sandsten, P. Weibring, H. Edner, and S. Svanberg, "Real-time gas(cid:173)
`correlation imaging employing thermal background radiation," Optics
`Express 6, 92 (2000); http://www.opticsexpress.org/opticsexpress/tocv6n4.htm
`
`J. Sandsten, H. Edner, and S. Svanberg, "Gas visualization of industrial
`hydrocarbon emissions," Manuscript for Applied Physics B, (2000).
`
`U. Gustafsson, J. Sandsten, and S. Svanberg, "Simultaneous detection of
`methane, oxygen and water vapor utilizing near-infrared diode lasers in
`conjunction with difference frequency generation," Applied Physics B, in
`press.
`
`J. Sandsten, U. Gustafsson, and G. Somesfalean, "Single aerosol particle
`sizing and identification using a coupled-cavity diode laser," Optics
`Communications 168, 17 (1999).
`
`7
`
`

`

`Exhibit 1042-00006
`
`1. Introduction
`
`Humans make decisions based on information gathered by the senses. Information
`with high quality makes it easier to take the correct measures in complex decision
`situations. The development of instruments enhancing the sense of sight makes it
`possible for us to monitor species invisible to us. Greenhouse gases and aerosol
`particles are examples of species that we are able to sense with optical instruments
`through absorption and scattering of light. Several instruments have been employed
`during the last century to monitor gases and aerosol particles emanating from a
`variety of both natural sources, like volcanoes and sea spray, and manmade sources
`like those related to combustion of fossil fuel. Some of the most useful instruments
`are based on the remote sensing techniques, [1]. The principles that the instruments
`rely on are called passive if natural radiation sources are used, such as thermal
`background radiation or the sun, and they are called active if the rely on an
`artificial source of radiation, like a lamp or a laser. The most widely spread passive
`optical technique is visible light photography, as illustrated in the upper left corner
`of Fig. 1. The sun is used as a light source and objects can be imaged by the
`spectrally reflected light. The upper middle box in Fig. 1, illustrates a situation
`where the thermal background is radiating behind a gas cloud. This radiation is also
`called infrared light and it can be used to monitor many molecules in the
`fundamental infrared region (2. 7-20f.Lm) due to their strong absorption by
`vibrational- and rotational transitions. The energy absorbed by the molecules can
`also be emitted and observed against a cold background, as depicted in the upper
`right box in Fig. 1. In the lower left box an artificial source of radiation is utilized,
`e.g. an incandescent lamp, a laser or a glow bar. The spectral brightness of such a
`source can easily be more than a million times higher than the brightness from a
`passive source. Instruments based on active techniques are therefore suitable as
`trace gas detectors and the path-integrated absorption can be measured to ppt levels
`(ppt = 1 part in 1 012). Differential optical absorption spectroscopy, DOAS [2],
`Fourier transform infrared, FTIR [3-5], and diode laser spectroscopy [6] are all
`active transmission techniques, and by increasing the path-length between the
`source and the instrument, minute amounts of trace gases in the atmosphere can be
`measured. However, the number of particles, water droplets and absorbing
`molecules other than the measured molecules in the path between the instrument
`and the source will decrease the visibility. At sea, the mariners use the visibility to
`describe horizontal atmospheric conditions. A normal weather condition is in this
`context, defined as having a transmission of74% or a visibility of 10 nautical miles
`(18.52 km). A mist has a visibility of 1 km or a transmission of 60% and a perfect
`transmission of 100% never prevails in the atmosphere. This limits the practical
`distance of active measurements with ppt detection limits to a few kilometers in
`urban areas. In the lower middle box in Fig. 1, a pulsed laser beam is directed out
`in the atmosphere and the backscattered light from aerosol particles is collected by
`a telescope. If the laser beam frequency is alternately tuned on and off a molecular
`absorption line, the influence of other slowly frequency varying absorbing
`
`9
`
`

`

`Exhibit 1042-00007
`
`molecules and particles will not affect a differential on/off signal. Range resolved
`measurements can be performed by gating the detector and thus collecting light
`from scattering particles along the beam path. Light detection and ranging, LIDAR,
`and the described extension, DIAL, differential absorption lidar, are techniques
`utilizing aerosol back-scattering [7-9].
`
`Absorption
`
`Emission
`
`Passive
`
`Active
`
`Transmission
`
`Back -scattering
`
`Target back-scattering
`
`(Y--EY,
`
`Fig. 1. Passive and active remote sensing techniques.
`
`If a diffusely scattering target is used as a background, as shown in the lower right
`box, a stronger backscattered signal is obtained but the range resolution is lost and
`the path-integrated measurement is performed over the whole laser beam.
`Topographic differential absorption LIDAR has recently been extended to an
`imaging mode and this technique is called differential backscatter-absorption gas
`imaging, BAGI [10-15]. This technique is requiring a large laser system as an
`illuminating source. Other gas imaging systems utilize a heated background and
`view the gas in absorption with an infrared camera equipped with a bandpass filter
`[16,17]. A Fabry-Perot etalon, an acousto-optic filter or an interferometric
`correlator can be used instead of the bandpass filter to enhance the contrast in gas
`visualization [18-21]. DOAS, FTIR and LIDAR are all line-of-sight instruments,
`meaning that if we would like to create a cross-sectional image the instrumental
`field-of-view must be swept over the scene. Measurements performed from
`satellites are based on passive methods and a vertical column of air through the
`whole atmosphere is the most common line-of-sight mode. The Terra satellite with
`the Measurements of Pollution in The Troposphere (MOPITT) instrument onboard,
`released the first scientific data and images in April2000. The instrument makes it
`possible to create global maps of methane and carbon monoxide utilizing a gas(cid:173)
`correlation technique [22-27].
`
`The new gas-correlation imaging technique, which is presented in this thesis, is a
`compact and straightforward passive imaging method where the natural thermal
`background radiation is employed, either in an absorption mode or in an emission
`mode [Papers I-III]. Presently, the applications where the gas-correlation imaging
`
`10
`
`

`

`Exhibit 1042-00008
`
`can be most beneficial are when the molecular concentrations are localized as in
`the case of leak searching and flare combustion monitoring. The gas-correlation
`imaging system is based on an infrared sensitive camera, a gas-correlation
`telescope with a gas-filter cell and a filter wheel with different spectral filters tuned
`to
`specific gas absorption bands. The camera system
`is depicted
`in
`Fig. 2.
`
`Fig. 2. The gas-correlation camera system.
`
`The diode laser based instruments developed during this work are active
`transmission and scattering instruments. One is a tunable spectrometer capable of
`detecting three species (methane, water vapor and oxygen) simultaneously [Paper
`IV] and the other one is an aerosol particle sensor based on extinction and
`diffraction of near-infrared diode laser light inside a coupled cavity [Paper V].
`
`The following chapters will cover complementary issues of relevance to the
`technique development and applications presented in Papers I-V. In Chapter 2 the
`laws describing natural background radiation are recapitulated and the near(cid:173)
`infrared diode laser sources are discussed in connection with passive and active gas
`monitoring. Infrared spectroscopy, absorption, emission and scattering issues is
`discussed in Chapter 3. The gas-correlation imaging principle will be explained and
`simulations of diffraction patterns from models of aerosol particles will be
`presented. A survey of infrared imaging detectors to come and those used in this
`work will be presented in Chapter 4. The optical design considerations, when
`constructing the gas-correlation telescope and the aerosol particle sensing
`instrument using a ray-tracing program, are discussed in Chapter 5. Gas image
`processing aspects will be described in Chapter 6 together with noise issues and
`gas detection limits. In Chapter 7, examples are given of some applications where
`we have found the gas-correlation imaging particularly useful. Specific gases
`especially suitable for detection and imaging with the gas-correlation methods are
`tabulated and some future applications will be discussed.
`
`11
`
`

`

`Exhibit 1042-00009
`
`2. Infrared radiation sources
`
`2.1 Natural background radiation
`
`Electromagnetic radiation is a wide-reaching concept with many names. The
`wavelength is the only primary difference between radiation towards the left and
`right in Fig. 3. The interaction of electromagnetic radiation with matter is,
`however, strongly wavelength dependent, and causes different secondary effects
`which we observe with our sensors. Another aspect of short- or long-wavelength
`radiation is that the resolution of an image created with electromagnetic radiation is
`inversely proportional to the wavelength. Thus, the resolution of an infrared image
`is less than the resolution of a visible image.
`
`10-6
`
`10-5
`
`10-4
`
`10-3
`
`10-2
`
`10-1
`
`Wavelength (J.tm)
`
`Fig. 3. The electromagnetic spectrum.
`
`Radiation impinging on a surface can either be reflected, absorbed or transmitted,
`processes which are characterized by the coefficients r-. , a-. and t._ , respectively.
`Independent of the wavelength (A.) and according to energy conservation
`considerations:
`
`(2.1)
`
`i.e., all the radiation interactions probabilities sum up to one. If the reflectance and
`the transmittance coefficients are both zero, all the energy will be absorbed and the
`temperature of the object will increase. Objects in thermal equilibrium with the
`surrounding will have to emit exactly the same amount of energy as they absorb; in
`other words, the spectral emissivity is equal to the spectral absorptance at any
`specified temperature and wavelength. The emissivity, e, is defined as the ratio of
`the spectral radiant power from an object to that from a blackbody at the same
`temperature and wavelength. A blackbody with a natural background temperature
`of 300 K radiates energy according to the Planck's radiation law with a spectrum
`peaking at 10 Jlm. The Planck radiation law is
`
`12
`
`

`

`Exhibit 1042-00010
`
`(2.2)
`
`where dl;. IdA is the spectral radiant exitance in W/m3 at the wavelength A, h is
`Planck's constant with a value of 6.626·10"34 Js, c is the speed of light, k is
`Boltzmann's constant with a value of 1.38·10"23 J/K and Tis the temperature of the
`blackbody. Curves of blackbody radiation in the temperature range 223-313 K are
`shown in Fig. 4. These curves reflect the background temperatures prevailing when
`passive gas monitoring is performed.
`
`45
`
`40
`
`~ 35
`... ~ 30
`~
`~ 25
`...
`"' c
`.. ...
`~ 20
`-; 15
`...
`
`0
`
`0
`
`-~--------------~---------------------
`
`---~3!3K - - - -
`
`10
`
`20
`Wavelength ( JliD)
`
`30
`
`40
`
`Fig. 4. Blackbody radiation from 223 K to 313 K. Notice that the peak spectral
`radiance is shifted towards shorter wavelengths with increasing temperature.
`
`An object having an emissivity of 1 is a blackbody radiator by definition. If the
`emissivity is a constant less than 1, the object is called a gray body and if the
`emissivity varies over an extended wavelength region, as is the case for real
`objects, then the object is denoted a selective radiator. The total power/area
`produced by a radiator at a temperature Tis given by the Stefan-Boltzmann law
`
`(2.3)
`
`13
`
`

`

`Exhibit 1042-00011
`
`where E has the dimension W/m2, e is the emissivity and a has a value of 5.67·10-8
`W/m2 K4 • Stefan-Boltzmann's law is derived by integrating the Planck radiation
`law over the wavelengths from zero to infinity. The total rate of emission of
`photons/area produced by a radiator at temperature Tis
`
`(2.4)
`
`where N has the dimension photons/s m2, and aph has a value of 1.5202·1 015
`photons/s m2 K3• Eq. 2.4 is obtained by dividing the Planck radiation law with the
`energy of a photon and then integrating over the wavelengths.
`
`The color of heated objects is not depending on the object material but on the
`temperature of the surface. Wien's displacement law describes that the peak power
`is shifted towards shorter wavelengths if the object is heated;
`
`(2.5)
`
`where A, is the wavelength in J..lm where the Planck radiation curve has its
`maximum value and the constant, C, is 2898 J..lm K.
`
`At background temperatures (300 K), the materials do not glow in the visible
`region. The contrast in visible light photography is governed by the differences in
`reflectance and transmittance of the objects. An important aspect of infrared
`imaging is that the contrast is governed by the temperature distribution of the
`objects but also by the wavelength dependent emissivity of the objects. To use
`natural background radiation for imaging is always favorable both in visible light
`photography and in infrared radiation imaging (thermography). By combining a
`visible image with an infrared image, very useful information is frequently
`obtained.
`
`2.2 Artificial infrared radiation
`
`An ordinary incandescent lamp is also an infrared radiation source. The tungsten
`filament inside the lamp glows at 3000 K and the power spectrum is peaked
`according to the Wien formula at around 970 nm. According to Planck's radiation
`law, we expect to find powerful infrared radiation in a tail for longer wavelengths.
`This is not what is observed, however, because the optical crown glass of the lamp
`only transmits radiation with wavelengths between 400 nm and 2 Jlm. The
`observed infrared power spectrum peak, at approximately 8 J..lm, is instead
`originating from the heated glass surface. The Nernst glower is in principle an
`incandescent lamp without the glass, but this approach suffers from fast oxidation
`of the filament. Recently, work has been done to use the methods of lamp
`
`14
`
`

`

`Exhibit 1042-00012
`
`production to produce infrared lamps with sapphire and zinc selenide windows
`fused together with the lamp glass [28]. An infrared heater can be used as a large
`source of radiation. The heating component is made of a resistance alloy rod and it
`is optimized to give radiation in the same region as humans emit and absorb
`radiation, which is at a temperature of 300 K peaked at a wavelength of 10 f.lm.
`
`A completely different class of radiation sources is formed by lasers. The laser
`sources are frequently quite sophisticated and complex. The most used laser
`source, the semiconductor diode laser [29,30], has in its spectroscopic variety a
`need for a highly stabilized power supply and temperature control to 11100 of a
`degree. Lasers are monochromatic and this is an advantage in many cases but often
`also a problem due to the formation of interference fringes in an optical setup,
`especially in the infrared region. In the present work a near-infrared diode laser
`radiating at 780 nm has been used as the light source in an aerosol particle sensor
`and imager, and two near-infrared diode lasers radiating at 760 nm and 980 nm
`have been used to produce difference-frequency radiation at 3.4 f.lm in an
`experiment of simultaneous measurements of methane, oxygen and water vapor.
`
`2.3 Near-infrared diode lasers
`
`The development of diode lasers is mainly driven by the telecommunications and
`IT industries. The diode lasers are used to read and store data on mass storage
`media. A fast emerging market is the broad bandwidth data communication with
`optical fibers. We have explored the mass-produced compact disc diode lasers in
`spectroscopy applications, much because of their compact size and low price as
`compared to traditional lasers for spectroscopy.
`
`The near-infrared diode laser operating at 780 nm has a typical dimension of 1 x 3
`x 400 f.lm3• It is comprised of four integrated building blocks, a p-n junction, a
`waveguide and two laser resonator end facets. The diode laser capsule also
`includes a built-in photo diode, which is used for monitoring of the laser output
`power. The electromagnetic field output has a polarization ratio of 100 : 1, at the
`normal operating current. The population inversion needed for laser action is
`produced by reversing the polarity of the p-n junction, as shown in Fig. 5. The
`injected charge carriers recombine in the active region and photons with the same
`energy as the bandgap (Eg) are produced. The bandgap is the electric potential
`difference between the conduction band and the valence band and it can be tailored
`to a quantum well which confines the charge carriers. The statistical fluctuations of
`the bandgap potential are lowered as compared to a p-n junction without a quantum
`well. The net effect of creating quantum wells inside the bandgap is the resulting
`single mode lasing at a lower threshold current which is interesting for
`spectroscopy.
`
`15
`
`

`

`Exhibit 1042-00013
`
`p-doped region
`
`active region
`
`n-doped region
`
`(a)
`
`(b)
`
`... · . · ........... · ..
`
`···::: •:. ·= ~·· ·= • ••• ••
`
`Fig. 5. Energy band diagrams of a p-n junction, (a) at thermal equilibrium and (b)
`under high injection condition.
`
`Near-infrared diode lasers are based on an aluminum gallium arsenide (AlGaAs)
`crystal with a refractive index of 3.6, which makes the reflectance of the laser
`resonator facets to air ((3.6-1)1(3.6+1))2 = 0.32. GaAs has a direct bandgap,
`meaning that no lattice vibrations are needed to create a photon from the
`annihilation of charge carriers. When a photon is created in a direction inside the
`waveguide normal to the 1 x 3 J.tm2 facets, that photon will be reflected back and
`this starts the laser action, if the frequency is in resonance with the 400 J.tm long
`resonator. The created electromagnetic field emerging at the output facet is highly
`divergent (30° x 1 0°) due to the small dimension as compared to the wavelength,
`and it must be collimated by a lens to produce an elliptical laser beam. The infrared
`source is now ready to be used, it is monochromatic, it has a coherence length of a
`few mm, it diverges by 2 mrad after collimating and the power can be as high as
`0.3 W from a single-stripe diode laser.
`
`2.4 Difference-frequency generation with near-infrared diode lasers
`
`Two of these near-infrared diode lasers can been used to create an infrared beam in
`the mid-infrared region. In this work, quasi-phase matching in an PPLN
`(Periodically Poled Lithium Niobate) crystal was utilized [31-38]. The crystal is
`responding to the incoming near-infrared radiation by the polarizability of the
`material and the wave vectors must fulfill the energy conservation condition,
`1 I A.3 = 1 I A.2 + 1 I A.1• For efficient frequency conversion it is also necessary that
`
`16
`
`

`

`Exhibit 1042-00014
`
`the phase relationship between the waves is maintained over the whole interaction
`length, i.e. k3 = kz +k1• In Paper IV we used one laser at 'A3 = 760 nm and one at
`Az = 980 nm to produce a beam at 'A1 = 3.4 Jlm, for simultaneous measurements of
`oxygen, water vapor and methane.
`
`2.5 Passive versus active remote-sensing methods
`
`Successful passive gas imaging in the infrared region is depending on parameters
`that we cannot change, such as a high atmospheric transmittance, the integrated
`absorbance or emittance of several spectral lines, and as the driving force a
`temperature difference between the gas and the background. On the other hand, we
`can optimize the system response and the infrared radiation gathering power of the
`receiving telescope. A successful infrared thermographer will also work hard in
`finding
`the best perspective and object, in analogy with a visible light
`photographer. Two modes of operation are possible. If the gas is imaged against a
`cold background, we image the gas emission and if the gas is imaged against a
`warm background, we monitor gas absorption. The source of radiation is the
`natural background, and all our efforts can be put into the detection side, which
`makes the setup practical and compact compared to active techniques, where the
`source side often is complex and costly. The passive technique we have developed
`has a path-integrated absorption detection limit of a few ppm x m (1 part per 106
`times meter).
`
`Active laser techniques for gas detection uses an intense infrared source, which is
`frequently fine-tuned to a spectral line but it need not be one of the fundamental
`molecular vibrational-rotational transitions. The spectral radiance of a laser source
`is so large that the temperature difference between the gas and the source can be
`regarded as infinite. A 10 m W diode laser has approximately a million times higher
`radiance than the peak Planck radiation at 300 K. Monochromatic laser radiation is
`the key to gas concentration detection limits of a few ppb x m, but it is also
`responsible for interference fringes and, in the imaging case, speckle problems. The
`interference fringes can be handled by using optical isolators or by slightly tilting
`the optical components. For imaging purposes, the laser beam illuminates a gas and
`the background. Reflection from the background comes in phase with scattered
`light from some parts of the surface and out of phase from other parts of the
`surface. This results in a speckled image. The high output intensity from an
`illuminating laser makes eye safety a problem in for example an industrial site. The
`non-uniform far-field cross section of the laser beam is varying over distance and a
`special lens must be used to minimize this problem. The target back-scattering
`background should preferably be a diffusely scattering object. All these aspects
`together make practical active gas imaging questionable [14].
`
`17
`
`

`

`Exhibit 1042-00015
`
`3. Infrared spectroscopy
`
`The discovery of infrared radiation is credited to Herschel in 1800. The experiment
`he performed was beautiful in its simplicity. A glass prism was arranged to
`separate the colors in white light from the sun. He wanted to measure the
`temperature of the colors and discovered that the temperature was increasing from
`violet to red. After this observation, he decided to measure the temperature just
`beyond red and found that the temperature was even higher. The radiation he
`discovered was later called infrared. This was observed although it is known that
`the solar spectrum peaks at 500 nm, however, since the dispersion of a glass prism
`is very low at infrared wavelengths, all such wavelengths are concentrated into the
`same direction. The human eye cannot detect infrared radiation but the vicious pit
`snake, hunting mice against the cold desert sand during night, can. The human eye
`is sensitive to energy quanta in what we call the visible part of the spectrum ( 400-
`700 nm), corresponding to a molecular electronic transition, whereas molecules
`also absorb and emit infrared radiation quanta by transitions between vibrational(cid:173)
`rotational energy levels.
`
`E
`
`Electronic energy levels
`
`Vibrational- and rotational levels
`
`Fig. 6. The energy difference between electronic transitions and vibrational(cid:173)
`rotational transitions. The electronic energy levels are denoted by n. The
`vibrational energy levels are denoted by v and the rotational energy levels are
`denoted by J.
`
`18
`
`

`

`Exhibit 1042-00016
`
`The energy difference between an electronic transition and a vibrational-rotational
`transition is frequently one to two orders of magnitude, as exemplified in Fig. 6.
`
`E
`
`v=l
`
`v=O
`
`I
`
`J
`4
`
`3
`
`2
`1
`0
`
`4
`
`3
`
`2
`1
`0
`
`Fig. 7. Quantum vibrational/rotational transitions.
`
`P-branch
`
`R-branch
`
`An example of vibrational- and rotational transitions is shown in Fig. 7, and
`infrared absorption of photons create a spectrum as shown in the lower part of the
`figure. At natural background temperatures (300 K) the magnitudes of the spectral
`lines are distributed as shown in the figure. If the temperature increases, a
`redistribution of states to higher J quantum numbers occurs, and the resulting
`spectral line magnitude would be shifted to the left for the P-branch (M = -1) and
`to the right for the R-branch (ilJ = + 1 ). In order to simulate the absorption spectra
`of atmospheric gases, the molecular spectroscopy database HITRAN, which
`contains the absorption line strength parameters of about one million individual
`vibrational-rotational absorption lines of 37 gases, has been used during this work
`[39]. Each spectral line in the database contains 14 entries, and they are: the
`molecule formula, isotope type, transition frequency, line intensity, transition
`probability, air-broadened halfwidth, self-broadened halfwidth, lower state energy,
`temperature coefficient for air-broadened linewidth, upper and lower state global
`quanta index, upper and lower state quanta, error codes and reference numbers. An
`
`19
`
`

`

`Exhibit 1042-00017
`
`example of a simulated HCl spectrum is shown in Fig. 8(a). For comparison a
`FTIR spectrometer recorded spectrum from the database Qasoft is shown in Fig.
`8(b), [40]. The most abundant isotope 35Cl (76%) is responsible for the peaks of
`highest absorbance values and the less abundant isotope 37Cl (24%) is responsible
`for the peaks with lower absorbance values slightly shifted to the left. The
`molecule with the heavier isotope thus has less vibrational-rotational energy stored.
`
`0.05
`
`0.04
`
`0.03
`
`0.02
`v 0.01
`u
`§ -e 0
`:<
`
`0
`Ul 0.05
`
`0.04
`
`_l J I
`
`(a)
`
`J J
`
`(b)
`
`0.03
`
`0.02
`
`0.01
`
`0 2600
`
`l j l
`
`2700
`
`jL
`
`3000
`
`3100
`
`2900
`2800
`Wavenumber (cm- 1)
`
`Fig. 8. Simulated absorbance spectrum of 100 ppm x m hydrochloric acid, HCl,
`using HITRAN and Lorentz lineshape convolution (a). FTIR recorded HCl
`spectrum with a resolution of0.5 cm-1 of 100 ppm x min 1 atm N2 at 25°C (b) [40].
`
`The transmission of light through a medium can be expressed by the Beer-Lambert
`law
`
`(3.1)
`
`where I; is the incoming light intensity, It is the transmitted intensity after passing
`the medium and OD is the optical depth. The transmission and the optical depth are
`connected by T =It I I;= e-0 D.
`
`If the incoming light I(v) is monochromatic, i.e., v has a constant frequency (cm-1),
`and the light pass through a medium consisting of one molecular gas, we are able
`to write the light intensity change, di, through a gas path of length, dx, as
`
`20
`
`

`

`Exhibit 1042-00018
`
`di = -a(v)I dx,
`
`(3.2)
`
`where a(v) is the linear absorption coefficient (cm-1). The transmitted intensity It
`can be calculated by integrating over all the small intensity changes, dl, through the
`whole homogenous sample,
`
`I-=-I a(v)dx,
`
`I, di
`
`I, I
`
`L
`
`0
`
`(3.3)
`
`where L is the total path length. The situation is depicted in Fig. 9.
`
`L
`
`It
`-------·
`
`Fig. 9. The transmission of monochromatic light through a sample of absorbing
`molecules can be derived by dividing the sample into small slices, dx.
`
`The solution to Eq. 3.3 is the Beer-Lambert law for monochromatic light passing
`through one molecular gas,
`
`I =I . -a(v)·L
`; e
`t
`
`·
`
`(3.4)
`
`It is seen from Eq. 3.4 that the path-integrated intensity decrease exponentially with
`the thickness of the gas. If there are many different gases present in the sample then
`the total composite transmission is calculated by adding the individual optical
`depths,
`
`OD = (ai(v) +a2(v)+ .. .)-L.
`
`(3.5)
`
`A parameter of importance in this work is the absorbance, which is related to the
`optical depth as being equal to OD I lnl 0, or it can be related to the transmission as
`log(l/7). The essence of the Beer-Lambert law is that the absorbance is
`proportional to the path-integrated concentration.
`
`21
`
`

`

`Exhibit 1042-00019
`
`The absorption coefficient, a(v), is related to the absorption cross-section of the
`molecules, a(v), as
`
`a(v) = u(v)N,
`
`(3.6)
`
`where N is the absolute gas concentration in molecules/cm3 and the dimension of
`u(v) is cm2/molecule. The strength of a single absorption line is given by
`integrating the absorption cross-section over the frequency range of the line. The
`absorption cross-section can also be related to the molecular line strength, S, by
`
`fJ (v) = S g(v-vo),
`
`(3.7)
`
`where g(v-v0) is the normalized lineshape function, and v0 is the central frequency
`of the line. There are three main lineshape functions, namely the Lorentzian which
`is used for pressure broadening calculations, a Gaussian function is used for
`Doppler broadening and a Voigt profile is used for a c