Implementation of continuous filtering frequency comb Vernier spectroscopy for continuous acquisition of spectra in a flame

UME˚ A UNIVERSITY

Implementation of continuous filtering frequency comb Vernier

spectroscopy for continuous acquisition of spectra in a flame

by

Adam Edlund

Master’s thesis in Engineering Physics

Faculty of Science and Technology Department of Physics

November 2017

This thesis is written as a requirement for the Master’s degree in Engineering Physics.

Master’s degree in Engineering Physics, 30.0 ECTS. Department of Physics, Ume˚ a University, Sweden.

Author: Adam Edlund, adam92edlund@gmail.com Supervisor: Alexandra Johansson,

Department of Physics, Ume˚ a University Examiner: Aleksandra Foltynowicz Matyba,

Department of Physics, Ume˚ a University

To my father

ii

Abstract

In this project laser absorption spectroscopy was performed on a flame in a Fabry- P´ erot cavity, using an optical frequency comb. Optical frequency comb spec- troscopy is a technique that allows broadband ultra-sensitive detection of molec- ular species in gas phase. Optical frequency combs are generated by femtosecond mode-locked lasers, which generate short pulses and whose spectrum consists of a comb of sharp laser lines covering a broad spectral range. Doing spectroscopy with optical frequency combs can hence be compared to measurements with thousand of synchronised continuous wave lasers simultaneously, which enables broadband sensitive measurements in short acquisition times. A Vernier spectrometer uses the filtering ability of the cavity to allow sequential transmission of parts of the frequency comb spectrum. Its technical simplicity and robustness make it a good candidate for measuring in turbulent environments.

The aim of the project was to implement continuous-filtering Vernier spec- troscopy in a setup for measuring absorption spectra in air and in a flame. This was done by using an Er:fiber femtosecond laser emitting in the near-infrared wavelength range and a Fabry-P´ erot cavity containing the flame. The cavity, which consists of two highly reflective mirrors, lets the light of the comb inter- act with the molecules in the flame for each of the many round-trips it perform;

thus increasing the sensitivity to absorption. An active locking mechanism was implemented to stabilize the coupling of the optical frequency comb to the cavity.

The locking allowed multiple measurements to be averaged which reduced noise.

A galvanometer scanner was added to the system which was used to measure a broad part of the comb spectrum. Hot water absorption lines were detected in the swept comb spectrum and a candidate absorption peak for OH absorption was recorded.

The spectrometer today has opportunities for improvements. A frequency

calibration should be implemented which is essential for making estimates of re-

actant/product concentrations in combustion processes.

Popul¨ arvetenskaplig Sammanfattning

Spektroskopi med optiska frekvenskammar anv¨ ands som ett medel att detektera molekyl¨ ara ¨ amnen i gasfas med mycket h¨ og k¨ anslighet. Optiska frekvenskammar genereras av femtosekund modl˚ asta lasrar som ger korta pulser. I frekvensdom¨ an ger detta en kamlik struktur med skarpa linjer ¨ over ett brett spektrum. Optisk frekvenskamspektroskopi har ett brett optiskt frekvensomr˚ ade med en h¨ og spektral uppl¨ osning som g¨ or det m¨ ojligt att m¨ ata flera molekyl¨ ara ¨ amnen samtidigt under kort m¨ attid. Detta kan j¨ amf¨ oras med att m¨ ata med flera tusen synkroniserade lasrar samtidigt. Dessa egenskaper g¨ or optiska frekvenskammar eftertraktade inom industriell processkontroll, medicinsk diagnostisering och inom milj¨ overvakning.

I detta projekt anv¨ andes frekvenskamspektroskopi f¨ or att m¨ ata absorption- slinjer fr˚ an hett vatten och OH i en eldsl˚ aga. Tekniken bygger p˚ a att f˚ anga in n¨ ara infrar¨ ott ljus fr˚ an laserkammen i en resonator best˚ aende av tv˚ a speglar och en br¨ annare. Speglarna l˚ ater ljuset fr˚ an kammen interagera med molekylerna i l˚ agan ¨ over en l¨ angre str¨ acka n¨ ar ljuset passerat gasen vid varje runda vilket ¨ okar absorptionsk¨ ansligheten.

En Vernierspektrometer ¨ ar en till¨ ampning p˚ a frekvenskamsspektroskopi. Den anv¨ ander sig av resonatorn f¨ or att filtrera frekvenskamsspektrumet. Dess tekniskt simpla konstruktion och robusthet g¨ or den l¨ amplig att anv¨ anda vid turbulenta milj¨ oer.

M˚ alet med detta projekt var att ˚ aterst¨ alla en tidigare uppst¨ allning av spek- trometern samt att ut¨ oka med en aktiv l˚ asning av lasern till resonatorn med hj¨ alp av reglerteknik. Den nya l˚ asningen gjorde det m¨ ojligt att m¨ ata flera m¨ atserier och medelv¨ ardesbilda signalen. Ett vridspoleinstrument gjorde det m¨ ojligt att vrida ett gitter f¨ or att m¨ ata ett bredare spektrum ¨ an vad som var tidigare m¨ ojligt.

Absorptionslinjer av hett vatten samt OH kunde detekteras med spektrometern.

Spektrometern har utrymme f¨ or f¨ orb¨ attringar. Ett n¨ asta steg ¨ ar att kallibrera frekvensen p˚ a det m¨ atta spektrumet vilket ¨ ar en v¨ asentlig del i att kunna m¨ ata koncentrationen av produkt och reaktanter vid f¨ orbr¨ anningsprocesser.

iv

Acknowledgements

I would like to thank Aleksandra Foltynowicz for the opportunity to work on this project and the insightful advice you have brought me. My sincerest thanks to Alexandra Johansson my supervisor for your kind support and patience helping me with technical questions during these weeks. Your kindness and cheerfulness seem to know no bounds.

I would like to thank my mother and father for supporting me during my studies, for whom without I would never have made it this far. Thank you for your unconditional love and support during all these years. A big thank you to my beloved brother Noa who’s creativeness keeps me inspired. Last but not least, thanks to my best friend and wife Angelica for all the joy you have brought to my life.

v

Contents

Abstract iii

Popul¨ arvetenskaplig Sammanfattning iv

Acknowledgements v

List of Figures viii

Nomenclature x

Abbreviations xii

1 Introduction 1

1.1 Background . . . . 1

1.2 Scope of the project . . . . 1

1.3 Outline of this thesis . . . . 2

2 Theory 3 2.1 Laser absorption spectroscopy . . . . 3

2.2 Fabry-P´ erot cavities . . . . 4

2.2.1 Cavity parameters . . . . 6

2.3 Optical frequency combs . . . . 6

2.4 Continuous filtering Vernier spectroscopy . . . . 8

2.4.1 Perfect match . . . . 8

2.4.2 Continuous filtering . . . . 9

2.5 Stabilising the laser frequency . . . 10

2.5.1 Block diagrams and transfer functions . . . 10

2.5.2 Basic control theory . . . 11

2.5.3 PI controller . . . 12

3 Setup of the spectrometer and measurement procedures 14 3.1 Building the high finesse Cavity . . . 15

3.2 Mode-matching the laser to the cavity . . . 17

3.3 Laser actuators . . . 17

vi

CONTENTS vii 3.4 Locking the comb to the cavity . . . 19 3.5 Measuring in air . . . 21 3.6 Measuring with a flame . . . 22

4 Results 23

4.1 One sweep . . . 23 4.2 Averaging multiple spectra . . . 25 4.3 Normalising and scaling . . . 27

5 Discussion 30

6 Summary and conclusions 33

References 34

A Voltage vs. Vernier Orders 36

B CO ₂ absorption lines in air 37

C Position sensing detector 38

List of Figures

2.1 A schematic of a simple direct laser absorption spectrometer. The light from the laser source is partially absorbed by the sample and the transmitted light is recorded by a photodetector. . . . . 3 2.2 A schematic illustration of the Fabry-P´ erot cavity with intracavity

index of refraction n r . . . . . 5 2.3 Three consequtive modes transmitted through the cavity. . . . 6 2.4 (a) Time representation of an optical frequency comb. (b) Fre-

quency domain representation . . . . 7 2.5 A schematic illustration showing the perfect matching between the

comb modes (red bars and cavity modes (black curve). Each comb mode is matched to a cavity mode. . . . 9 2.6 A schematic illustration of the continuous-filtering Vernier scheme.

There is a small mismatch between the cavity and comb. Several groups of comb modes are transmitted. . . . 9 2.7 A simple negative feedback control loop is shown in the block diagram. 11 2.8 The block diagram of the PI controller. . . 12 2.9 The amplitude of the transfer function of the PI controller. . . 13 3.1 Illustration of the continuous-filtering Vernier spectrometer setup,

where BS is the 50:50 beamspliter, f ₁ -f ₄ are the lenses, M ₁ -M ₅ are mirrors, TS are translation stages, M ^cav ₁ -M ^cav ₂ are the wedged cavity mirrors, PD ₁ -PD ₂ are two photo detectors, Ph is a phase shifter and HVA is a high voltage amplifier. Note that the beam has to enter the cavity at an angle due to the wedge which is not shown in the illustration. . . 16 3.2 Simplified schematic of the internal parts in the comb laser. The

actuators of the comb laser are labeled in blue [16]. . . 18 3.3 Schematic of the f _rep controller. The servo controllers are coupled

in series. . . 18 3.4 Open-loop error signal for three consequtive Vernier orders around

k = −19. The signal was recorded as the cavity length was scanned linearly with the grating position fixed. . . 20 3.5 Open-loop error signal for a single Vernier order. The signal was

recorded with a fixed position of the grating. The sweep of the cavity length was decreased to resolve only one VO. . . 20

viii

LIST OF FIGURES ix 3.6 a) Open-loop error signal for VO k = −19, recorded as the cavity

length and the grating position was scanned simultaneously. The sweep of the cavity length and grating position are slightly out of synchronisation and the left side of the signal is close to the unlinear turning point of the sweep. b) The corresponding closed-loop error signal recorded with the integrators on. . . 21 4.1 A single measurement of the spectra when the flame is off, in air

(blue curve) and with the flame on (red curve). The HAB was 2 mm 24 4.2 Air spectrum (flame off) in blue and spectrum when the flame is

on in red HAB = 2 mm. . . 24 4.3 a) The recorded signal for air, b) measured signal for three different

heights when the flame is on, HAB= 2, 2,5 and 5 mm. The signal shows an average of 100 measured spectra. . . 25 4.4 Flame spectra for number of averages, N = 1 (black), N = 20 (red),

N = 100 (blue). The signal to noise ratio is greatly improved by the averaging. . . 26 4.5 Averaged comb spectrum with the flame on at HAB = 2 mm for

number of averages N = 100 (blue) and N = 5 (red). The averaged recording of the comb spectrum in air for N = 100 sample (black) is also plotted, showing an etalon fringe pattern. . . 27 4.6 Normalised intensity signal of the comb spectrum in the flame for

HAB = 2 mm (blue), HAB = 2,5 mm (red) and HAB = 5 mm (black). All are averaged N = 100 times. . . 28 4.7 Normalised intensity signal of the comb spectrum with the flame for

different HAB, scaled to get an overlap. A suspected OH absorption line is seen to the right. . . 28 A.1 The peak intensity of the Vernier signal is shown as it drops when

shortening the cavity length with integer numbers of k. . . . 36 B.1 Suspected CO ₂ absorption lines atmospheric air. . . 37 C.1 The active sensing area of the position detector divided into four

quadrants. . . . 38

Nomenclature

Roman symbols

I _T transmitted intensity W/m ²

I ₀ intensity of incident light W/m ²

N ^abs population density of absorbing molecules molecules/cm ⁻³ S ˆ integrated molecular line strength cm ⁻¹ /molecule/cm ⁻² n _r index of refraction inside the cavity dimensionless

L cavity length m

t _i transmission coefficient dimensionless

r _i reflection coefficient dimensionless

l _i loss coefficient dimensionless

I _R reflected intensity W/m ²

I _c intra cavity intensity W/m ²

F SR free spectral range Hz

E ˜ ₀ incident electric field Vm ⁻¹

E ˜ _R reflected electric field Vm ⁻¹

E ˜ _T transmitted electric field Vm ⁻¹

F cavity finesse dimensionless

OP L optical path length m

f ₀ laser offset frequency Hz

f _rep laser repetition rate Hz

r distance from the optical axis m

z ₀ Rayleigh range m

R(z) radius of curvature m

L _{P M} perfect match length m

x

NOMENCLATURE xi

k Vernier order dimensionless

F SR _V Vernier free spectral range dimensionless

Greek symbols

ν frequency Hz

α(ν) frequency dependent absorption coefficient cm ⁻¹ χ ^abs area normalised absorption lineshape function cm

ω angular frequency rads ⁻¹

λ ₀ wavelength of incident light m

ν _q cavity resonant frequency Hz

Γ _c cavity mode-width Hz

∆φ _ce phase shift dimensionless

ω ₀ beam waist radius m

Γ _V Vernier resolution Hz

Abbreviations

OFC Optical Frequency Comb NIR Near-Infrared

DAS Direct Absorption Spectroscopy EM Electro Magnetic

FSR Free Spectral Range

FWHM Full Width Half Maximum OPL Optical Path Lenght

TEM Transverse Electric Mode

CF-VS Continuous Filtering Vernier Spectroscopy PZT Piezo Electric Transducer

PM Perfect Match

PML Perfect Match Length

VO Vernier Order

PI Proportional Integral DAQ Data Acquisition SG Signal Generator

CW Continuous Wave

EOM Electro-Optic Modulator HAB Height-Above Burner SNR Signal to Noise Ratio

xii

Chapter 1 Introduction

1.1 Background

Spectroscopy is the science of studying the interaction between electromagnetic waves and matter. In this project a special type of spectroscopy technique called Vernier spectroscopy was used to detect molecular species in gas phase. The project was ordered by Optical Frequency Comb Spectroscopy Group at the De- partment of Physics at Ume˚ a University. The group works with development of optical frequency comb spectroscopy which can be used for broadband highly sen- sitive detection of trace gases [1]. The optical frequency combs are produced by femto-second mode-locked lasers whose spectrum consists of a comb like struc- ture of sharp laser lines. The spectrum covers a broad spectral range and allows sensitive detection of many molecular species in short acquisition times. Doing spectroscopy with optical frequency combs is equivalent to measuring with thou- sand of synchronised continuous wave lasers simultaneously. The technique has therefore a chance of becoming an industry standard for process control or medical diagnostics such as breath analysis.

In the work for this thesis optical frequency comb absorption spectroscopy is used to detect broadband absorption spectrum of water and OH in a flame. A technique called continuous-filtering Vernier spectroscopy (CF-VS) was used to record a broad spectrum of an optical frequency comb in short acquisition time.

Its technical simplicity and robustness make it a good candidate for measuring in turbulent environments.

1.2 Scope of the project

The aim of the project was to improve on a previously built Vernier spectrometer, by adding an active locking and a grating sweep to enable fast continuous mea- surements and averaging of recorded comb spectra. The goal of the project was to build a continuous-filtering Vernier spectrometer capable of measuring multi- ple spectra in a flame. The project did not include analysis of reactant/product concentrations in the reaction in the flame.

1

Chapter 1 Introduction 2

1.3 Outline of this thesis

The disposition of this thesis is as follows: Chapter 1 gives an introduction to the

subject of this thesis and the background of the project. Chapter 2 covers the

general theory of laser absorption spectroscopy. The theory section has a large

emphasis on the cavity and how light interacts with it, it plays a central role of

understanding the concepts of the Vernier technique. The theory section thus

covers a large portion of this thesis. Chapter 3 presents the experimental setup

and procedures. In Chapter 4 are the results of the measurements done with the

spectrometer. Chapter 5 discusses the result and the reasoning behind some of the

measurements. Chapter 6 gives a brief conclusion to the work done in this project

and the results presented in the thesis. This thesis assumes some knowledge of

optics and laser physics for which reference [2] covers the basics.

Chapter 2 Theory

The theory in this chapter starts with a short introduction to laser absorption spectroscopy and continues with how light interacts with cavities. A large portion is spent on describing optical cavities, namely the Fabry-P´ erot cavity. Furthermore there is an introduction to optical frequency combs, the continuous filtering Vernier spectroscopy technique and the chapter is concluded with a brief mentioning of the basics of control theory.

2.1 Laser absorption spectroscopy

Spectroscopy is a science of studying how electromagnetic waves interact with matter. Three interactions commonly studied in spectroscopy include absorption, emission and scattering. In absorption spectroscopy the absorption of incident radiation is measured as its frequency is varied [3]. The irradiated matter, com- monly referred to as a sample, is in this case a sample of molecules in gas phase.

When a laser is used as a source of electromagnetic-radiation (EM-radiation), it is referred to as laser absorption spectroscopy or laser absorption spectrometry (AS).

The simplest form of laser based AS is direct absorption spectrometry (DAS). In DAS the sample is put directly in the path of a laser beam. F IGURE 2.1 shows a set-up where the absorbing sample has a length L.

Figure 2.1: A schematic of a simple direct laser absorption spectrometer.

The light from the laser source is partially absorbed by the sample and the transmitted light is recorded by a photodetector.

According to the Lambert-Beer law, the intensity I _T (W/m ² ) of light transmitted through an absorbing sample is

3

Chapter 2 Theory 4

I _T = I ₀ e ^−α(ν)L , (2.1)

where α(ν) is the frequency dependent absorption coefficient (cm ⁻¹ ) and I 0 is the incident intensity [4]. The absorption coefficient of the sample α(ν) is given by

α(ν) = ˆ SN ^abs χ ^abs (ν), (2.2) where ˆ S is the integrated molecular line strength (cm ⁻¹ /molecule/cm ⁻² ), N ^abs is the population density of absorbing molecules (molecules/cm ⁻³ ) and χ ^abs (ν) is the area normalised absorption lineshape function (cm) [1]. The sensitivity to absorption is increased by increasing the interaction length. [1]. We can also increase the sensitivity by choosing a strong absorption line (that is choosing a proper wavelength range for a specific atom or molecule) or using noise reduction methods (such as modulation techniques [1]).

The absorption coefficient can be calculated from the interaction length and the intensities of the incident and transmitted light

α(ν) = 1 L ln I ₀

I _T (ν) , (2.3)

We may also define the relative (or normalised) absorption as ∆I(ν)/I ₀ [1], where

∆I(ν) = I ₀ − I _T (ν) is the change in intensity due to the absorption. If the absorption is small [α(ν)L  1], we can Taylor expand the exponential function in (2.2) and get

I _T (ν) ≈ I ₀ [1 − α(ν)L], (2.4)

and by simple algebra we have

∆I(ν) I 0

≈ α(ν)L. (2.5)

Hence according to the Lambert-Beer law (equation (2.1)) the transmitted light is to first approximation (and for small absorption) proportional to the integrated molecular line strength, the density and the cavity length. We can increase the optical pathlength through the sample by introducing multipass cells or resonant cavities. This is the topic of the following section 2.2.

2.2 Fabry-P´ erot cavities

A Fabry-P´ erot cavity is an arrangement of mirrors that allows EM-radiation to resonate. Resonance cavities are commonly used to increase the interaction length of the EM-radiation between the light source and the sample, referred to as a cavity enhancement [5].

One commonly used cavity design is the Fabry-P´ erot cavity shown in F IGURE

2.2 below.

Chapter 2 Theory 5

Figure 2.2: A schematic illustration of the Fabry-P´ erot cavity with intracavity index of refraction n r .

The cavity is built from two concave mirrors separated by L, where the index of refraction of the medium inside the cavity is n _r . Each mirror has an associated transmission, reflection and loss coefficient (defined for the intensity of light) t i , r i , l _i , respectively. By the principle of energy conservation t _i + r _i + l _i = 1. The optical intensities of the incident, reflected and transmitted light are denoted by I ₀ , I _R and I T . The incident, reflected and transmitted electric fields are given by ˜ E 0 , ˜ E R

and ˜ E _T respectively. The intensity inside the cavity is denoted by I _c . In depth calculations of the electrical fields and intensities and cavity transmission functions can be found in [4]. When light enters the cavity it gets partially reflected by the cavity mirrors. The waves that are reflected interfere constructively if a multiple integer q times the wavelength of the incident light, λ ₀ , is equal to the round-trip optical length of the cavity, qλ 0 = 2n r L. What follows is an increased intracavity intensity, I _c . Moreover the effective interaction length is longer than the physical length of the cavity, L, as for each round-trip the light passes the sample multiple times. The electrical field will resonate at cavity resonant frequencies, ν q that is

ν _q = qc

2n _r L , (2.6)

where, c is the speed of light. The frequency spacing between two resonant fre- quencies is what is known as the free spectral range (FSR) of the cavity and is given by

FSR = c

2n r L . (2.7)

Some of the electric field inside the cavity leaks out through the cavity mirrors

at each round-trip. The results of the constructive interference is a repetitive

structure in the transmitted intensity at the resonating frequencies ν _q . This is

known as cavity modes [6] and is depicted in F IGURE 2.3.

Chapter 2 Theory 6

Figure 2.3: Three consequtive modes transmitted through the cavity.

2.2.1 Cavity parameters

There are some important parameters describing the cavity such as the cavity res- onant frequencies, ν _q and FSR described earlier. Two other important parameters are the cavity finesse, F , and the full width at half maximum (FWHM) of the cavity modes, Γ _c . The FWHM (also known as the cavity mode-width) is given by [4]

Γ _c = (1 − √

r ₁ r ₂ ) FSR π √

r ₁ r ₂ , (2.8)

where the width of the cavity modes is assumed to fulfil Γ _c  FSR. The finesse, F , of the cavity is defined as

F = FSR

Γ _c = π √

r ₁ r ₂ 1 − √

r ₁ r ₂ . (2.9)

For two identical mirrors (r ₁ = r ₂ = r), equation (2.9) simplifies to F = π √ r/(1 − r).

2.3 Optical frequency combs

Optical frequency combs (OFCs) can be produced by various laser sources such as mode-locked lasers, indirect comb sources and continuous wave (cw) lasers.

Common mode-locked lasers for comb spectroscopy are Ti:sapphire laser, Yb:fiber laser and Er:fiber laser. They generate pulses with a duration of femtoseconds [7].

In F IGURE 2.4(a) is an illustration of a pulse train in time domain generated by

a mode-locked laser and (b), the frequency representation of the OFC.

Chapter 2 Theory 7

Figure 2.4: (a) Time representation of an optical frequency comb. (b) Fre- quency domain representation

In the frequency domain there are many equidistant narrow modes. The separation of these modes are given by the repetition rate of the laser f _rep = 1/τ _rep . The comb has an offset f ₀ from an multiple integer of f _rep . Due to intracavity dispersion the pulses are not completely identical. The electric field oscillation has a phase shift ∆φ _ce with respect to its envelope [7]. The offset frequency is

f ₀ = f _rep ∆φ _ce

2π . (2.10)

By performing a Fourier transform of the time series of the pulses we get an expression for the frequency, ν _n , of the n ^th line of the frequency comb as

ν _n = nf _rep + f ₀ , (2.11)

where n typically is in the order of 10 ⁵ − 10 ⁶ (for mode-locked femtosecond lasers) [1].

The mode-locked Er:fiber lasers generate combs around a wavelenght of 1.55 µm

[8]. Since this is the main telecommunication wavelength, they use relative inex-

pensive and accessible technologies.

Chapter 2 Theory 8

2.4 Continuous filtering Vernier spectroscopy

The previous sections defined the general terms and the fundamental equations regarding optical cavities and optical frequency combs. This section presents the concept of CF-VS. The CF-VS technique is relatively new [9]. It allows acquisition of broadband and cavity-enhanced comb spectra with medium to high resolution.

A measurement can be performed in tens of ms using a robust and compact detection system. But first we need to address the principle of frequency matching the comb modes to the cavity.

2.4.1 Perfect match

The modes of the cavity and the modes of the OFC share a similar structure.

Hence to transmit the comb through the cavity, the optical frequencies of the comb need to match the resonance frequencies of the cavity. An intuitive way of coupling two comb structures together is to match them by adjusting their frequency spacing and offset. With the actuators on the OFC source it is possible to tune the f rep and f 0 . Even though the f rep of the comb is constant over the whole bandwidth of the laser, the FSR of the cavity changes with frequency due to the dispersion inside the cavity. This limits the bandwidth of effective matching between the cavity and the OFC [1].

In general we have a perfect match (PM) locally when

mf _rep = q FSR, (2.12)

where m and q are positive integers and when f ₀ is tuned to match the offset of the cavity modes. The length of the cavity at perfect match is called the perfect matching length (PML). A trivial case of perfect matching occurs when m = q = 1.

F IGURE 2.5 illustrates perfect matching for m and q = 1 while not considering

dispersion. Here the comb modes are shown with vertical bars in red as the width

of the comb modes is typically a lot thinner than the widths of the cavity modes

shown in black.

Chapter 2 Theory 9

Figure 2.5: A schematic illustration showing the perfect matching between the comb modes (red bars and cavity modes (black curve). Each comb mode is

matched to a cavity mode.

2.4.2 Continuous filtering

The Vernier filtering scheme uses the cavity to filter the comb. The filtering also enables sequential detection of the entire bandwidth using a photodiode. The filtering of the comb modes is produced by mismatching the cavity modes and comb modes from PM by a slight detuning of the f _rep of the comb from the FSR.

It transmits groups of comb lines, each group is called a Vernier order (VO) [10].

F IGURE 2.6 shows two consecutive Vernier orders resulting from the groups of comb modes that are transmitted.

Figure 2.6: A schematic illustration of the continuous-filtering Vernier scheme.

There is a small mismatch between the cavity and comb. Several groups of comb modes are transmitted.

Let us assume that we have an OFC and an enhancement cavity at perfect matching FSR _{P M} = f _rep such that n = 1 and q = 1 in equation (2.12), where FSR _{P M} = c/2n _r L _{P M} and L _{P M} is the perfect match length (PML) of the cavity.

Now the cavity length, L is detuned from the PML by a value |∆L| < L _{P M} /F ,

Chapter 2 Theory 10 such that L = L _{P M} + ∆L, where ∆L can be either positive or negative. The cavity FSR is then changed to

FSR = c

2n _r (L _{P M} + ∆L) = f rep

1 + ∆L/L _{P M} , (2.13) and the created Vernier orders are centred at frequencies ν _k [10] given by

ν _k = c(k − δf ₀ /f _rep )

2n _r |∆L| , (2.14)

where k is an integer number of the order and δf ₀ is the mismatch between the cavity and the comb offset frequencies. For high Vernier orders (k  1) the center frequencies can be simplified to ν _k ≈ ck/2n _r |∆L|.

Consecutive Vernier orders are separated in the frequency domain. This sep- aration is given by the Vernier free spectral range,

FSR _V = c

2n _r |∆L| , (2.15)

and their width (resolution) is

Γ _V = FSR _V

F = c

2n _r F |∆L| . (2.16)

To acquire a spectrum the Vernier orders needs to be separated spatially. The integrated intensity of a selected Vernier order is tuned over the comb spectrum by scanning the length of the cavity with ∆L. An alternative is to scan the f _rep of the comb. Scanning the length is usually preferred in practise as it can usually be done over a greater range than the f _rep [10]. Detuning by shortening is also the typical choice as it results in a higher contrast in the normalised transmitted intensity spectrum [11]. Being able to adjust the f rep and ∆L allows for stabilisation of the Vernier order frequency by controlling them both.

2.5 Stabilising the laser frequency

In order to keep the matching between the cavity and the comb an active locking is needed in order to compensate for thermal drift and vibrations. This locking is a stabilisation process that requires some form of error signal to tell when and how to correct the eventual mismatch [12]. This section will go through the basic terminology and concepts of control theory.

2.5.1 Block diagrams and transfer functions

Block diagrams are schematic illustrations representing a complex system without

going into the specific details of how the different parts operate. Block diagrams

are used as a visualisation tool for understanding transfer functions. A transfer

function is in this context a function that connects the input and output signal

in a system. If we denote the input signal with X _in and let X _out be the output

Chapter 2 Theory 11 signal, then the transfer function H relates the two by X _out = HX _in . The transfer function represents the gain or loss of the system and may be unit-less. A block in the block diagram depicts how the output from the block is related to its input and the diagram itself shows how it is all linked together.

2.5.2 Basic control theory

In control theory there is typically a system that needs to be controlled for the process to work properly. This requires negative feedback. When using negative feedback the output signal, X, of the system is compared to a reference signal, X _ref by subtraction. The resulting error signal, X _err is fed through a controller and back into the system under control. F IGURE 2.7 shows a schematic diagram of the system where G(f ) is the transfer function of the controlled system, H(f ) is the transfer function of the controller, X _corr is the correction signal and X _dist is a disturbance signal [12].

Figure 2.7: A simple negative feedback control loop is shown in the block diagram.

The output of the system in a closed loop configuration can be expressed as [4]

X = G(f )(X _dist − X _corr ), (2.17) where the correction signal is

X corr = H(f )(X − X ref ) = H(f )X err . (2.18) We can therefore express X in terms of the reference signal and disturbance

X = G(f )H(f )

1 + G(f )H(f ) X _ref + G(f )

1 + G(f )H(f ) X _dist . (2.19) The factor that occurs in front of the reference signal is the closed loop transfer and the factor in front of the disturbance is the disturbance propagation function [4]. This can be rewritten as

X = 1

1 + 1

G(f )H(f )



X ref + 1

H(f ) X dist



, (2.20)

Chapter 2 Theory 12 which means that if the open loop transfer function, H _open = G(f )H(f ), is much larger than 1, then X is close to the reference X _ref , and any disturbance is de- creased by the inverse of the transfer function controller namely 1/H(f ). So if we design a control loop we should aim for as high open loop gain and controller gain as possible.

The control loop is unstable if the open loop transfer function H _open (f ) is equal to −1, as seen from equation (2.20) the denominator approaches infinity and the system starts to oscillate. The open loop transfer function can generally be written as [12]

H open (f ) = A(f )e ^{iΦ(f )} , (2.21) where A(f ) is a frequency dependent amplitude and Φ(f ) is the phase shift be- tween the input and output signals. When the phase in equation (2.21) is −180 ^◦ , H _open (f ) is close to −1 for unity gain amplitude A(f ). In order to keep the system from oscillating a margin is implemented called a phase margin of at least 30 ^◦ at the point of unity gain (0 dB). Another thing is to keep a gain margin of at least 3 dB for when the phase angle inevitably passes −180 ^◦ .

2.5.3 PI controller

A Proportional Integral (PI) controller can be used to control a system through negative feedback [13]. The proportional part in the PI controller has constant gain. In order to handle slow drift in the system an integrator part is used. F IGURE

2.8 shows a block diagram showing a model of the PI controller. Signals in the time domain are denoted by small letters whilst their capital counterpart is their Laplace transform. Here x _err (t) is the error signal and x _corr (t) is the correction signal.

Figure 2.8: The block diagram of the PI controller.

Chapter 2 Theory 13 In time domain the proportional block act on the input signal as

x ^p _corr (t) = K _p x _err (t), (2.22) where K _p is a constant, and the integral block is

x ⁱ _corr (t) = K _i Z t

0

x _err (t ⁰ )dt ⁰ (2.23) where K _i too is a constant. If we take the Laplace transform of equations (2.22) and (2.23), where s is the complex frequency, we get

X _corr ^p (s) = L{K _p x _err (t)}(s) = K _p X _err (s), (2.24) and

X _corr ⁱ (s) = L

 K i

Z t 0

x err (t ⁰ )dt ⁰



(s) = 1

s K i X err (s). (2.25) If we add together the results of equations (2.24) and (2.25) we get

X _corr (s) = X _corr ^p (s) + X _corr ⁱ (s) =



K _p + K _i s



X _err (s) = H(s)X _err (s), (2.26) where H(s) is the collective transfer function. If we look at the transfer function in complex frequency domain such that s → i2πf we get

H(f ) = K _p + K _i

i2πf . (2.27)

F IGURE 2.9 shows a schematic illustration of the amplitude of the transfer function in frequency domain. In the illustration the PI corner is marked as a transfer region between where the proportional term dominates over the integral term.

Figure 2.9: The amplitude of the transfer function of the PI controller.

Chapter 3

Setup of the spectrometer and measurement procedures

A schematic illustration of the experimental setup is shown in F IGURE 3.1. The experimental setup was a recreation and expansion of the setup done perviously by [14]. For the experiment an Er:fiber femtosecond laser (Menlo Systems) was used with a repetition rate of 250 MHz and a power of 20 mW. The laser spectrum covered 100 nm between 1.5 and 1.6 µm with a bandwidth of 12000 GHz. The beam was sent through a polarisation maintaining optical fiber to an open-air optical cavity with a finesse of 1000. Two mode matching lenses with focal lengths f ₁ = 35 mm and f ₂ = 50 mm were used to couple the Gaussian laser beam to the cavity transverse electric modes (TEM). The second mode matching lens f ₂ was mounted on a horizontal translation stage T S. The cavity mirrors M ₁ ^cav and M ₂ ^cav were mounted on two horizontal translation stages. The latter translation stage allowed the back mirror M ₂ ^cav to be moved with a 10 µm precision. A piezoelectric transducer (PZT) was mounted on the former translation stage holding the front cavity mirror M ₁ ^cav . This PZT was used to scan the cavity length. The PZT was fed a signal from a signal generator that was amplified by a high voltage amplifier (HVA). See section 3.1 for more details on the cavity and section 3.2 for the alignment procedure.

Betweeen the two cavity mirrors, below the laser beam, was a premixed air/methane flat flame burner based on the design of [15]. The burner itself was mounted on a multi-directional translation stage to allow adjustments with 10 µm precision. The burner was operating at a stoichiometric ratio of 1 and 10 l/min for methane and air flow, respectively.

Three flat adjustable mirrors M ₁ , M ₂ , and M ₃ were used to align the beam to the cavity. Two similar mirrors M ₄ and M ₅ were mounted behind the cav- ity to align the transmitted beam onto a ruled diffraction grating (Thorlabs, 600 grooves/mm). The grating was used to separate the Vernier orders spatially.

The grating was designed for a wavelength of 1600 µm. It was mounted on a galvanometer scanner (Thorlabs, GVS001), which made it possible to sweep the grating to scan across the comb spectrum. The beam diffracted by the grating was split by a 50:50 beam splitter. Half of the beam was focused by a lens with f ₃ = 25 mm onto a position sensitive detector PD ₁ (Thorlabs, PDQ30C InGaAs quadrant photodiode). The difference signal from PD ₁ was used as an error signal.

14

Chapter 3 Setup of the spectrometer and measurement procedures 15 The difference signal is calculated as the difference between the sum of two quad- rants on opposite sides of the y-axis from the sensing areas of PD ₁ (see Appendix C). The other half of the split beam, was sent through a focusing lens f ₄ = 50 mm onto a photo detector PD ₂ (Thorlabs, PDA 10CS-EC InGaAs) with adjustable gain. The signal from PD ₂ was then recorded on a PC using a data acquisition (DAQ) card and yielded the Vernier signal.

The signal from the positioning detector PD ₁ was used as the error signal to create negative feedback for stabilizing the laser (see section 2.5). The control segment is labelled f _rep controller in the figure. The signal from PD ₁ was sent to a servo controller (New Focus, LB1005). The output of the servo was fed to a second identical servo controller. The two servos were controlling the current and PZT actuators of the laser. Section 3.3 further below goes into more detail of these laser actuators.

Two apertures Iris ₁ and Iris ₂ were placed to help with the alignment of the beam to the cavity. Another pair of apertures Iris ₃ and Iris ₄ were used to select one Vernier order out of the many orders diffracted by the grating. Aperture Iris 3

and Iris ₄ blocked unwanted VOs from reaching PD ₁ and PD ₂ respectively.

Finally a signal generator (SG, Agilent 33210A) was used to simultaneously scan the grating and the cavity PZT with a 20 Hz sine wave. The signal to the cavity PZT was adjusted with a phase shifter and amplification to match the sweep of the grating. These components were used to get a good starting point for the locking by letting the signal be imaged by the grating over a longer period of time (for further details of the synchronised simultaneous scan see section 3.4).

3.1 Building the high finesse Cavity

To achieve sufficient enhancement of the absorption to study OH and water spectra

in the flame the cavity was designed using concave mirrors with reflectivity of

99,70 ± 0,10% and radius of curvature R = 5 m. The finesse was approximately

1000 using equation (2.9). The mirrors are coated with alternating dielectric

materials and have a wedge of 3.0 ± 0.1 ^◦ on the outside of the cavity mirrors to

avoid interference within the substrate of the mirror [14]. To get the appropriate

length of the cavity equation (2.7) was used together with the perfect match

condition equation (2.12). The PML is L = 60 cm for f _rep = 250 MHz.

Chapter 3 Setup of the spectrometer and measurement procedures 16

Figure 3.1: Illustration of the continuous-filtering Vernier spectrometer setup, where BS is the 50:50 beamspliter, f ₁ -f ₄ are the lenses, M ₁ -M ₅ are mirrors, TS are translation stages, M ^cav ₁ -M ^cav ₂ are the wedged cavity mirrors, PD 1 -PD 2 are two photo detectors, Ph is a phase shifter and HVA is a high voltage amplifier.

Note that the beam has to enter the cavity at an angle due to the wedge which

is not shown in the illustration.

Chapter 3 Setup of the spectrometer and measurement procedures 17

3.2 Mode-matching the laser to the cavity

Careful positioning and alignment of the mirrors were needed to couple the laser comb to the cavity spatially. The positions of the collimator, M 1 , M 2 , f 1 , f 2 and the optical length to the first cavity mirror were reused from the previous setup [14]. A mobile pinhole was used to get the correct alignment of the mirrors. The requirement for transmitting the comb through the cavity is to have completely parallel beams inside the cavity. The length of the cavity L, and thereby the FSR, can be coarse tuned with the translation stage. It can be fine tuned via the PZT attached to the front cavity mirror M ₁ ^cav to match the cavity resonance frequencies to the comb lines. Furthermore the PD ₂ was temporarily placed directly behind M ₂ ^cav to capture the light of a continuous wave (CW) laser (1550 nm) sent through the same polarisation maintaining fibre and collimator. The CW laser was used first in place of the OFC to more easily see modes when the cavity length is close to but not at PML. By walking the beam by adjusting the rotation of mirrors M ₂ , M 3 , M ₁ ^cav and M ₂ ^cav and tuning L, the higher order transverse modes were reduced until their peaks were below 1% of the TEM ₀₀ signal.

3.3 Laser actuators

The OFC used in this setup was an Er ³⁺ fiber laser that was pumped by a CW

diode laser. The comb laser consisted of a number of parts shown here in a

schematic illustration F IGURE 3.2 [16]. The three actuators controlling the repe-

tition rate are the current actuator, the PZT actuator and the electro-optic mod-

ulator (EOM). Two actuators were used to lock the comb to the cavity; the pump

diode laser current and the PZT. The current actuator controlled f ₀ and f _rep with

a bandwidth of approximately 200 kHz. The PZT changes the f rep by changing

the laser cavity length. The PZT is limited by it’s response time to a bandwidth

of approximately 10 kHz [12]. F IGURE 3.3 shows the two servo controllers where

the correction signal of the first servo (Current cotroller) is fed to the second

servo (PZT controller) as an input error signal. The control signals from the servo

controllers are sent to the actuators of the laser.

Chapter 3 Setup of the spectrometer and measurement procedures 18

Figure 3.2: Simplified schematic of the internal parts in the comb laser. The actuators of the comb laser are labeled in blue [16].

Figure 3.3: Schematic of the f rep controller. The servo controllers are coupled

in series.

Chapter 3 Setup of the spectrometer and measurement procedures 19

3.4 Locking the comb to the cavity

To lock the OFC modes to the cavity, L was shortened from PML until Vernier order k = −19 was visible which corresponds to a ∆L of −15 µm. The cavity length and grating position were swept simultaneously with the sine wave from the signal generator. The error signal was measured by the position sensitive detector PD 1 as a difference signal between two sides of the detector. The difference signal is zero when light hits the detector equally on both sides of the detector. Appendix C shows in detail how this difference signal is measured on the detector. The error signal from PD 1 was monitored with an oscilloscope. The sweeping angle and offset of the grating; the alignment of M ₄ and M ₅ , together with the irises and lenses f ₃ and f ₄ were adjusted such that only a single VO hit the detectors. The sweep of the cavity length was tuned in phase and amplitude until the width of the error signal was maximised in time duration. This ensured a good initial stability so that the servos mainly correct for small deviations in the sweep. The gain transfer functions of the open and closed loops for the servos were simulated in MATLAB to get a starting point for the settings of the PI-controllers. The grating and cavity length were scanned simultaneously. The servo controllers were set to ”low frequency gain limit”, corresponding to proportional correction, which locked the comb to the cavity. Finally the integrators of the servo controllers were turned on.

The settings of the PI-controller gain, PI-corner and gain limits were tested until the servos could maintain a stable locking. The PI corner of the current servo was set to 100 kHz. The low frequency gain limit was set to 50 dB. The gain of the current servo was 4.4 dB. For the PZT servo the PI corner was set to 1 kHz. The low frequency gain limit was set to 40 dB and the gain was 3.8 dB.

F IGURE 3.4 shows the open-loop error signal for three consequtive Vernier

orders around k = −19 measured in air. The signal was recorded with the grating

fixed and while scanning the cavity length with the PZT. The grating resolves

the successive Vernier orders but does not resolve their width Γ _V . The zero-

crossings of the open loop signals from the orders are seperated by FSR _V = 10

THz, according to equation (2.15). The separation between the extrema of one

VO is determined by the size of the beam hitting the position detector PD ₁ and

the grating dispersion. By assuming a linear relationship between the time and

frequency domains one can calculate the slope of the error signal in time domain

[10], by dividing the difference in the extrema divided by the time separation. The

slope of the middle VO is here 2.3 kV/s which is recalculated to 1.1 µV/MHz by

using the separation of the zero-crossings of the error signals in the time domain,

that is 4.8 ms which corresponds to F SR _V = 10 THz.

Chapter 3 Setup of the spectrometer and measurement procedures 20

Figure 3.4: Open-loop error signal for three consequtive Vernier orders around k = −19. The signal was recorded as the cavity length was scanned linearly

with the grating position fixed.

F IGURE 3.5 shows the open-loop error signal for one Vernier order with fixed grating position. The sweep of the cavity length was decreased until only one VO was imaged on the detector.

Figure 3.5: Open-loop error signal for a single Vernier order. The signal was recorded with a fixed position of the grating. The sweep of the cavity length

was decreased to resolve only one VO.

F IGURE 3.6 a) shows the open- and closed-loop error signals when the position

of the grating was swept simultaneously with the cavity length. The open loop

Chapter 3 Setup of the spectrometer and measurement procedures 21 error signal is widened in time domain compared to F IGURE 3.5. This suggest that the Vernier order is kept on the detector over a longer period of time. F IGURE

3.6 b) shows the closed-loop error signal. The standard deviation of the noise on the signal is 280 µV. This gives a frequency stability of 252 MHz, calculated by dividing with the slope of the error signal [10]. The frequency stability is thus equal to 2.5% of its resolution (Γ _V = 10 GHz) which is slightly worse than the result achieved by [10].

Figure 3.6: a) Open-loop error signal for VO k = −19, recorded as the cavity length and the grating position was scanned simultaneously. The sweep of the cavity length and grating position are slightly out of synchronisation and the left side of the signal is close to the unlinear turning point of the sweep. b) The

corresponding closed-loop error signal recorded with the integrators on.

3.5 Measuring in air

The Vernier signal was measured with PD ₂ . F IGURE A.1 in Appendix A shows

the results of the decrease in peak intensity when the order is increased. The

length of the cavity was purposefully mismatched from PML by ∆L = −15 µm

in order to look for CO ₂ absorption in air. The expected resolution according

to equation (2.16) was approximately 10 GHz corresponding to k = −19. The

data was recorded by using a DAQ card (National Instrument) and a LabView

program. The number of data points were 40000 recorded with a sampling rate of

1 Msamples/s with 1 MOhm impedance. An external trigger sent from the signal

generator was used to trigger at 1.8 V. A hundred samples were recorded. The

recorded data was then averaged in MATLAB. The measurement for air was used

as a baseline to normalise the spectrum for the measurement in the flame. Each

measured data lacks a proper frequency scale as implementing such lay outside

Chapter 3 Setup of the spectrometer and measurement procedures 22 the scope of this project. The measurement is instead presented as a function of time.

3.6 Measuring with a flame

The burner was equipped with a cooling flow of water and a co-flow of nitrogen that kept the flame stable. The flow rates of the methane and air were controlled with two flow controllers. The flow rate of methane was 1 l/min and the flow rate for air was 10 l/min. When the flame was on a lot of heat is added to the cavity which changes the index of refraction. The alignment of the back cavity mirror was tweaked by adjusting the vertical alignment slightly to compensate for the change of the optical path length (OPL). The flame was placed in the center of the cavity using a multi-directional TS. The height above the burner (HAB) was adjusted to record data for HAB = 2, 2,5 and 5 mm. Due to the change in index of refraction inside the cavity when the flame is on, the Vernier order was changed with respect to when the flame was off. In order to change the VO ∆L was tweaked by a slight adjustment of the offset on the HVA feeding the cavity PZT.

The correct Vernier order (k = −19) was found by looking for the same intensity

for when k = −19 ± 1 without the flame. The measured data was analysed in

MATLAB. The data was normalised to the air spectrum to look at the relative

absorption lines of the products when methane reacts with oxygen. The products

are H ₂ O, CO ₂ and OH. Finally the data was scaled in amplitude to look for OH

absorption lines in hot water absorption lines spectrum similar to [17].

Chapter 4 Results

The data presented in this section is all measured for the Vernier order number k = −19 ± 1. The VO corresponds to a detuning from PML by ∆L = −15 µm and a resolution of 10 GHz. The recorded signal is for measurements in atmospheric pressure air and in a flame with different HAB. When the data is not referred to as air it denotes the use of the burner to record the absorption spectrum of the products of the combustion: hot water and OH.

4.1 One sweep

F IGURE 4.1 shows the result of one recorded sample for measurements in air (blue curve) and in a flame with a HAB of 2 mm (red curve). The figure displays the intensity (V) of the Vernier signal versus time (ms). The swept spectrum is recorded two times; one on the way up and one on the way back down. F IGURE 4.1 shows the Vernier signal recorded in one direction of the sweep with the turning point of the grating sweep at 13 ms. The second turning point of the sweep is occurs after 35 ms. The signal peaks near 160 mV.

If one compares the recordings of the two spectra in F IGURE 4.1 one can see some hot water absorption lines present in the sample when the flame is on (HAB

= 2 mm, red dots). The signal near the turning point (at 13 ms) is oscillating slightly. The peaks located between 20 ms and 35 ms are recorded at the most linear part of the scan of the grating and cavity.

23

Chapter 4 Results 24

14 16 18 20 22 24 26 28 30 32 34

Time [ms]

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Intensity [V]

Air Flame

Figure 4.1: A single measurement of the spectra when the flame is off, in air (blue curve) and with the flame on (red curve). The HAB was 2 mm

F IGURE 4.2 shows a zoomed version of the previous figure between 20 ms and 35 ms.

20 25 30 35

Time [ms]

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Intensity [V]

Air Flame

Figure 4.2: Air spectrum (flame off) in blue and spectrum when the flame is

on in red HAB = 2 mm.

Chapter 4 Results 25 There are visible hot water absorption lines in Figure 4.2. The signal is oscillat- ing slightly around 25 ms, indicating issues with the stability of the gain of the controllers when locking the laser comb to the cavity modes.

4.2 Averaging multiple spectra

A set of N = 100 recorded spectra were averaged. F IGURE 4.3 shows the recorded averaged signal of air and with the flame on at different heights above the burner.

The Vernier signals were averaged 100 times.

14 16 18 20 22 24 26 28 30 32 34

Time [ms]

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Intensity [V]

Air k=19 HAB 2 mm HAB 2.5 mm HAB 5 mm

Figure 4.3: a) The recorded signal for air, b) measured signal for three different heights when the flame is on, HAB= 2, 2,5 and 5 mm. The signal shows an

average of 100 measured spectra.

The spectra taken at different HAB have a slight difference in intensity, mainly caused by small changes in the OPL inside the cavity when the HAB is varied.

The difference at the peak is approximately −8 mV between the HAB = 2 mm and HAB = 5 mm.

The flame spectrum measured at HAB = 2 mm was studied in more detail

by varying the number of averaged samples. F IGURE 4.4 shows 1000 data points

recorded over 1 ms between 27 and 28 ms. The measured data points in the figure

are connected by lines to make the peaks more distinguishable.

Chapter 4 Results 26

27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9 28 Time [ms]

0.057 0.058 0.059 0.06 0.061 0.062 0.063 0.064 0.065 0.066 0.067

Intensity [V]

N=1 N=20 N=100

Figure 4.4: Flame spectra for number of averages, N = 1 (black), N = 20 (red), N = 100 (blue). The signal to noise ratio is greatly improved by the

averaging.

The recorded Vernier signals shows three absorption lines for a single sweep (black curve) and signals averaged 20 times (red curve) and 100 times (blue curve). The signals for a single sweep have a lot of noise. The signal to noise ratio is improved as the number of averages are increased. For N = 100 in blue the noise is strongly reduced.

The comb spectrum for the flame with HAB = 2 mm, with N = 100 (blue

curve) and N = 5 (red curve) were plotted together with the recorded averaged

N = 100 samples of the comb spectrum in air. The result of the recorded signal

can be seen in F IGURE 4.5 recorded between 25 to 35 ms.

Chapter 4 Results 27

25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30

Time [ms]

0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08

Intensity [V]

HAB 2 mm, N=5 HAB 2 mm, N=100 Air, N=100 Etalon fringes

Figure 4.5: Averaged comb spectrum with the flame on at HAB = 2 mm for number of averages N = 100 (blue) and N = 5 (red). The averaged recording of the comb spectrum in air for N = 100 sample (black) is also plotted, showing

an etalon fringe pattern.

The two spectra in F IGURE 4.5 in the flame with N = 100 and N = 5 are plotted together. The recorded signal for air is showing the etalon fringes which are not distinguishable in the recorded signal with the flame. The absorption lines are on top of the etalon fringes.

4.3 Normalising and scaling

For three different HAB, the averaged signal of 100 samples with the flame on was

normalised to the recorded averaged signal of the comb spectrum in air. The result

can be seen in F IGURE 4.6 which shows a part of the spectrum between 20 and 30

ms. The relative intensity is calculated by using the intensity of the air spectrum

as the background reference. The normalisation improves the readability of the

absorption lines.

Chapter 4 Results 28

20 25 30 35

Time [ms]

0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1

Relative intensity

HAB 2 mm HAB 2.5 mm HAB 5 mm

Figure 4.6: Normalised intensity signal of the comb spectrum in the flame for HAB = 2 mm (blue), HAB = 2,5 mm (red) and HAB = 5 mm (black). All are

averaged N = 100 times.

In order to reduce the noise to a level where the absorption peaks can be compared in relative intensity difference an averaging of N = 100 is needed. The values of the relative intensity for HAB = 2,5 mm and HAB = 5 mm in F IGURE 4.6 are scaled in amplitude by multiplying with two arbitrary constants until the lines overlap vertically. F IGURE 4.7 shows the spectra measured at different HAB, when they have been multiplied with arbitrary constants to make them overlap.

20 25 30 35

0.86 0.88 0.9 0.92 0.94 0.96 0.98 1

Relative Intensity

HAB 2 mm HAB 2.5 mm HAB 5 mm

OH-absorption

Figure 4.7: Normalised intensity signal of the comb spectrum with the flame for different HAB, scaled to get an overlap. A suspected OH absorption line is

seen to the right.

Chapter 4 Results 29

At the fourth peak from the right in the figure (at 33 ms) the normalised intensity

differs noticeably between HAB = 2 mm (blue dots) and HAB = 5 mm (black

dots). This result is similar to the result presented in [17]. This is a suspected OH

absorption line. The relative absorption of H ₂ O is expected to stay fairly constant

with a small increase of the HAB. The absorption of OH is expected to decrease

with increased HAB according to the results of [17].

Chapter 5 Discussion

From the results of the single sweep presented in F IGURE 4.1 it is clear that there are some oscillations near the endpoints of the sweep. This is due to the fact that the gain limit of the servo controllers are reached. Near the peak of the comb spectrum there are large amplitude changes in the spectrum. It is difficult to lock the spectrum if there is nearly no light on the detector. At the turning points of the grating sweep the movement is the least linear stemming from the use of a sine wave for the sweep. Therefore the most valuable region of study is expected to be the region in the center of the scan.

The noise on the error signal is estimated by looking at flat part of the air spectrum and taking the standard deviation over a few data points. It was mea- sured to 1.8 mV where the peak signal of the spectrum was 160 mV for the sum signal of the PD 2 . The signal to noise ratio (SNR) was roughly estimated to about 100 for one average N = 1. The estimate is crude but gives an indication that the signal to noise ratio is slightly lower than what was previously achieved in [14]. It is possible to lock the comb to the cavity to scan over a wider region of the comb spectrum than what was previously possible.

F IGURE 4.2 shows data for the most linear region of the scan and thus the one of most interest. The absorption lines are visible, however the details of the lines are not clear, due to low signal to noise ratio and oscillations. The spectra over the whole range is interesting as it shows there are water absorption in the entire swept range. In an earlier testing phase the Vernier signal was recorded with the position detector PD ₁ by using the sum signal that it provides. This was the originally planned to be used exclusively for both the Vernier and error signal. However there was a travelling noise spike picked up in the sum signal of the position detector. The travelling noise spike repeated itself with a regular interval. As a solution the beamsplitter was introduced to pick up half the signal.

This improved the signal to noise ratio from 67 to 100. The error signal was recorded after some capacitors were introduced acting as a low pass noise filter.

The SNR of the error signal for the open loop was 578. The closed-loop error signal reaches 20 mV at the peak of the comb spectrum. The frequency stability of 2.5% of the Vernier resolution is close to the results by [10].

F IGURE 4.3 shows the flame spectra for different HAB. The signal for the flame when the HAB was 5 mm is lower by 8 mV compared to the signal for HAB

= 2 mm. A hypothesis is that it was recorded at a higher VO k = −20. This

30

Chapter 5 Discussion 31 agrees with the measured intensity drop between Vernier order k = −19 and −20.

If the hypothesis is correct the spectrum was recorded with a slightly different resolution. This is not of great concern when looking at the recorded spectrum of the relative intensity as the difference in resolution is small. When measuring at different heights, turning the servos on and off would often lock to another VO.

Locking anew in the flame and assuring that the same VO was used was somewhat difficult. The lock could differ up to 2 VO from VO k = −19.

F IGURE 4.4 shows the recorded flame spectra for different number of averaged samples. What is interesting is how the system is stable enough to allow for averaging with a great number of averages. The improvement on the SNR by increasing the number of averages can not be made indefinitely. At some point the absorption lines are expected to be broadened by the averaging due to frequency instability. At N = 100 samples the peaks are visible and broadening can not be seen clearly. The averaging seems to reduce the noise by a good degree. There is a trade off between low noise (many averaged spectra) and broadening of the absorption lines. If the frequency stability of the locking is improved, and if the signal was recorded at a higher VO (higher resolution): sharper peaks and less broadening is to be expected. In order to make good averages a frequency calibration is needed.

Visible in F IGURE 4.5 is the measurements for both air and in a flame with a HAB of 2 mm. In the figure there are visible etalon fringes in the spectrum of air.

The fringe pattern is produced by some optical component. The absorption lines are on top of the fringe pattern and can not be seen in the flame spectra. In order to more easily see the effect of the absorption the normalised intensity is calculated and plotted. The result seen in F IGURE 4.6 shows that the absorption peaks occur at the same sample time. However the relative intensity differs between the different HABs. The noise is low thanks to the averaging. The normalisation against the air spectrum allows the relative absorption peaks to be seen. The chosen region has a relative constant trend over the range between 20 and 35 ms. This is expected to be the most linear region of the sweep of cavity and grating. The intensity was scaled in F IGURE 4.7 to make the curves overlap vertically. According to the results presented in [17] the hot water absorption lines are expected to stay constant with a slight increase of the HAB. The OH absorption is expected to decrease with increased HAB. This seems to be the case for the fourth rightmost peak in F IGURE 4.7. The work on the Vernier spectrometer was deemed finished at this point as the initial goals had been met.

It is difficult to make good use of the data without a proper frequency cal- ibration. One way to further develop the instrument is to add a Fabry Perot etalon with a known FSR and another detector to make a frequency callibration of the recorded spectrum, similar to the works of [10][11]. The source of the etalon fringes visible in F IGURE 4.5 and their FSR are unknown. There is noise from the position signal PD ₁ . Improvements to the SNR could be made if the noise of the detector were lower. One suggestion is to check the expected noise level of the detector to see if the device is malfunctioning. At the time of writing this thesis the expected noise level is not specified by the producer.

Measuring the whole comb spectrum is not possible with this setup. The

servos can not lock the comb laser modes to the cavity modes if the amplitude of

Chapter 5 Discussion 32 the error signal is too small. To keep a robust lock with the servos the spectrum swept with the grating was limited to assure that there would always be light hitting the position detector.

In the combustion process when methane reacts with oxygen it produces water and CO ₂ . The absorption lines of CO ₂ are not identified in recorded signal of the comb spectrum with the flame. The expected relative absorption of CO ₂ is small [14]. In Appendix B in F IGURE B.1 are measurements done in air averaged over 5 samples in an attempt to find carbon dioxide absorption.

The built Vernier spectrometer is stable enough to allow many samples to

be averaged. It can continuously acquire more of the spectrum than what was

previously possible. One sweep back and forth is recorded in 25 ms.