Calibration-free 1f and 2f wavelength modulation spectroscopy with in-situ measurement of laser parameters

Over the past few decades tunable diode laser spectroscopy (TDLS) has established itself as a highly

reliable technique for the measurement of gas parameters, specially in systems that require high

sensitivity, high specificity and rapid in-situ measurements. In TDLS a narrow linewidth tunable

diode laser is tuned across the rotational-vibrational absorption line of the target gas. The relative

transmission obtained is used to infer the gas parameters. A variant of TDLS known as wavelength

modulation spectroscopy (WMS) where a high frequency sinusoid superimposed on a low frequency

ramp is used to modulate the laser. The information bearing signal is shifted to its baseband with

the help of a lock-in amplifier (LIA) resulting in an improvement in the signal-to-noise ratio (SNR)

by about two orders. Initial WMS methods were not calibration-free and were not suitable for field

measurements in harsh environments. Over the last decade several calibration-free WMS methods have

been proposed which have enabled the deployment of TDLS based gas sensors in harsh environments.

However, there were some limitations of these techniques. The calibration-free first harmonic (1f)

WMS methods such as residual amplitude modulation (RAM) method and phasor decomposition (PD)

methods were limited to low modulation index values (m-values) and suffered from the problem of

large absorption independent background RAM which lead to the early saturation of the detection

electronics. These methods were extended to high m-values by replacing the Taylor series analysis

with the Fourier analysis of the transfer characteristics of the absorption signal. Also, the RAM nulling

methods were able to remove the large absorption independent background accompanying the RAM

signal. However, these methods were not immune to rapidly varying absorption independent losses

such as those due to vibrations and beam steering. Second harmonic (2f) WMS methods such as 2f/1f

method were able to overcome both these issues. The 2f/1f WMS signal had a negligible absorption

independent background and was immune to the absorption independent systematic losses. However,

this method relies on the pre-characterized laser parameters for the simulation of the 2f-WMS signal.

These laser parameters may drift due to temperature variation and aging and would lead to an error

in the measurement. The frequency modulation (FM) component of the 2f-WMS signal which is

main measurement signal of the 2f-WMS methods, is always weaker than the FM component of the

corresponding 1f-WMS signal. Despite this compromise in SNR, 2f-WMS methods were preferred

over 1f-WMS methods because of low absorption independent background accompanying these signals.

Hence different WMS techniques in their present form suffer from different types of limitations and

there is a need to overcome these limitations either by making changes in the existing WMS methods

or by proposing new methods that can overcome these limitations.

This work can be broadly divided into three parts, in the first part we have optimized the RAM

method by operating at the phase quadrature modulation frequency ( fq) of 125.5 kHz. In the RAM

method only a component of RAM signal is used for the measurement when operating at any other

frequency instead of fq. The PD method overcomes this problem and uses the full RAM signal.

However, this method relies on the measurement of the phase between the intensity modulation (IM)

and the FM of the laser which is susceptible to errors for lower concentrations and for smaller phase

difference between the IM and FM. Hence operating at the fq has the advantage that full RAM signal is

used for the measurement of the gas parameters, without any limitations being imposed by the accuracy

of measurement of phase between the IM and the FM of the laser. Although this advantage of operating

at fq was known for a long time but it had not been utilized because the fq reported earlier were of

the order of 1MHz. The cost of the supporting electronics when operating at such high frequencies

increases. Along with operating at this low fq, optical RAM nulling was used to remove the absorption

independent background RAM. In optical RAM nullling the laser output is divided into two parts. The

light output in the first part known as gas arm is transmitted through the absorbing gas sample and a

polarization controller. The other part goes through a delay arm comprising of a single mode fiber of

appropriate length, a variable optical attenuator and a polarization controller to generate an absorption

independent RAM signal equal in magnitude but 180° out of phase with the absorption independent

RAM signal in the gas arm. When operating at a fq =125.5 kHz the length of the fiber in the delay arm

is 0.814 km which is much greater than the typical coherence lengths. In contrast when operating at a

fq of the order of 1 MHz this length would be close to 100 m and would lead to an optical interference

when the signals from the gas arm and delay arm recombine in a 3dB coupler. Thus by operating at the

fq and implementing RAM nulling at this frequency to remove the absorption independent background

RAM and using Fourier analysis of the transfer characteristics, RAM method was fully optimized.

In the second part of this work a new calibration-free 2f-WMS method was proposed and its

detailed description was provided. In this method all the relevant laser parameters are measured from

the signals captured in traditional WMS, that is the transmitted output, the LIA output and the resonator

output. Therefore any change in experimental WMS signal due to variations in these parameters

because of the non-absorbing losses are incorporated in the simulated signal as well. Hence this method

is immune to the rapidly varying non-absorbing losses such as those due to vibrations, beam steering

and fouling of the coupling optics. It is also immune to the slowly varying absorption-independent

systematic losses such as those due to drift, aging and temperature variation. The applicability of this

new method has been established by implementing it on three different types of lasers, namely 5250

nm continuous wave distributed feedback quantum cascade laser (cw-DFB-QCL), 2004 nm vertical

cavity surface emitting laser (VCSEL) and 1650 nm edge emitting distributed feedback (DFB) laser

for the measurement of nitric oxide, carbon dioxide and methane respectively. If there is significant

nonlinearity in the intensity versus current characteristics of the laser such as for the cw-DFB-QCL

laser used in this study, the 2f-WMS signal can be accompanied by a significant background RAM

signal. The WMS signals for higher harmonics are weaker in signal strength but their signal to the

absorption independent background ratio increases. Therefore for such lasers it would be advantageous

to use higher harmonics. By extending this technique to third harmonic for the three lasers used in this

study, it has been established that this technique is not limited to 2f-WMS and is applicable to higher

harmonics as well.

Using the same technique of in-situ real-time measurement of laser parameters a new calibrationfree

1f-WMS method which uses the magnitude of 1f-WMS signal as the measurement signal was

proposed. The large absorption independent background of the 1f-WMS signal was removed through a

new RAM nulling method proposed in this work. In this method the transmitted signal detected by the

photo-detector is divided into two parts. One part goes through a microcontroller that uses a software

LIA of large dynamic range to generate a signal which is equal in magnitude but 180° out of phase with

1st order IM signal received at the photo-detector. The other part combines with the signal generated

by the microcontroller through an analog summing amplifier. The output of the summing amplifier

which is free from the absorption independent 1f background RAM is given as an input to a second

LIA that has a much smaller dynamic range. Since the full dynamic range of the second LIA is used

to measure the absorption dependent signal it leads to an increase in sensitivity of measurement. The

quantization noise present in the output of the summing amplifier does not affect the final measurement

because this noise is filtered by the second LIA as it is outside the bandwidth of the second LIA. This

method obtains the RAM component, the FM component and the magnitude of the 1f-WMS signal.

Since the FM component of the 1f-WMS is always stronger than the FM component of the 2f-WMS

signal this method would provide a larger SNR as compared to 2f-WMS techniques. The RAM signal

can be stronger or weaker than the FM signal, depending upon the operating modulation frequency

and the tuning coefficient. However, it is demonstrated that the magnitude of 1f-WMS signal is the

strongest WMS signal. Therefore this method would always provide a higher SNR as compared to

other WMS methods. The new WMS schemes have been validated by implementing them on different

types of lasers for the measurement of different gases at various concentration and pressure values. A

detailed explanation of each of these techniques has been provided. The advantages and limitations ofeach of these schemes have been discussed in detail.