ADVANTAGES OF USING DIRECT ABSORPTION METHOD FOR TDLAS MEASUREMENT

Jie Zhu, Alan Cowie, Anatoliy Kosterev, Don Wyatt Yokogawa Corporation of America – Laser Analysis Division

910 Gemini Street Houston, TX 77058, USA

KEYWORDS

Tunable Diode Laser Absorption Spectroscopy, Direct Absorption Spectroscopy, Wavelength Modulation, Relative Intensity Noise, Line Shape

ABSTRACT

Direct absorption spectroscopy (DAS) and wavelength modulation spectroscopy (WMS, typically 2nd harmonic detection or 2f) are the two main measurement methods for tunable diode laser absorption spectroscopy (TDLAS). Wavelength modulation was widely adopted before the last decade as it could improve the signal to noise ratio (SNR) by modulating and demodulating the absorption signal at a high frequency. With advances in electronics, especially the availability of cheap powerful processors and high-speed high-resolution analog to digital converters, direct absorption method can achieve the same SNR as wavelength modulation. Meanwhile, the measurement of true (un-distorted) absorption spectra together with advanced spectroscopic algorithms allows direct absorption method to have better accuracy, wide dynamic range and many attractive analyzer features such as calibration free, online validation, etc. This paper gives practical application examples to demonstrate the advantages of using direct absorption method for TDLAS measurements.

INTRODUCTION

Tunable diode laser absorption spectroscopy (TDLAS) has been proven to be one of the better techniques for on-line process gas analysis in many industrial fields with great merits of fast, sensitive, nonintrusive, in-situ, path averaging measurement, low maintenance, etc. Direct absorption spectroscopy (DAS) [1] and wavelength modulation spectroscopy (WMS) [2] are the two most popular detection methods for TDLAS. Both have very simple optical configuration that the laser beam passes through the measurement gas onto a photodiode. This paper first

compares the basic principles of the two methods, and then focuses on the advantages of using DAS over WMS for on-line process analysis.

DIRECT ABSORPTION SPECTROSCOPY

To better explain the principle of TDLAS measurement, it is necessary to first introduce the main characteristics of a tunable diode laser (either vertical cavity surface emitting laser ‘VCSEL’ or distributed feedback laser ‘DFB’). Figure 1 shows 3 important characteristics of a typical tunable diode laser. The laser output is single mode with ultra-narrow line width. The wavelength has linear relationship with injection current (Figure 1-a) and case temperature (Figure 1-b). Because the wavelength tuning response is much faster for injection current than case temperature, the laser temperature is typically controlled at a constant value and the injection current is ramped and scanned across the target absorption feature. The output laser power increases with injection current after threshold current, but the relation is usually not linear as illustrated in Figure 1-c.

FIGURE 1. TYPICAL CHARACTERISTICS OF A TUNABLE DIODE LASER: A) CURRENT TUNING, B) TEMPERATURE TUNING, C) OUTPUT POWER

In a DAS scheme, as shown in Figure 2-a, zero (or below threshold) current is first applied to the diode laser for a short time before a ramp current scans the laser output wavelength 𝜆 or frequency 𝜈. The period for the laser control pattern is usually shorter than 1 millisecond. The output laser intensity 𝐼0(𝜈) and detected light intensity after measurement volume 𝐼(𝜈) are presented in Figure 2-b. 𝐼0(𝜈) can be obtained from a reference photodiode either embedded in the laser package or after an external beam splitter. It is also the detected light intensity when no absorption gas is available, for example during zero calibration. According to Beer’s Law: 𝐼(𝜈) = 𝑇𝑟 ⋅ 𝐼0(𝜈) ⋅ 𝑒−𝑆(𝑇)⋅𝜙(𝜈)⋅𝑃⋅𝑥⋅𝐿 + 𝑅 (1) Where 𝑇𝑟 = laser transmission at non-absorbing region 𝑆(𝑇) = absorption line strength as a function of gas temperature 𝑇 𝜙(𝜈) = absorption line shape Voigt function 𝑃 = gas pressure

𝑥 = absorption gas concentration 𝐿 = optical path length through measurement gas 𝑅 = background radiation

FIGURE 2. OPERATION PRINTCIPLE OF DIRECT ABSORPTION SPECTROSCOPY MEASUREMENT: A) LASER DRIVING AND WAVELENGTH SCAN, B) LASER OUTPUT INTENSITY AND DETECTED LIGHT INTESNITY BY PHTODIODE, C) TARGET GAS ABSORPTION SPECTRUM

As the laser is tuned much faster than the fluctuation of measurement gas, we can assume that gas pressure, temperature, concentration, transmission, and background radiation are constant during one laser scan. The absorption spectrum is calculated after digitization and averaging of amplified photodiode signals: 𝛼(𝜈) = ln � 𝐼0(𝜈)

𝐼(𝜈)−𝑅� = 𝑆(𝑇) ⋅ 𝜙(𝜈) ⋅ 𝑃 ⋅ 𝑥 ⋅ 𝐿 − ln (𝑇𝑟) (2)

The absorption spectrum is plotted in Figure 2-c, with baseline offset −ln (𝑇𝑟). Theoretically gas temperature and pressure can be calculated by studying the line shape function 𝜙(𝜈). But in this

paper we only consider gas concentration measurement. Since 𝜙(𝜈) is a normalized function ∫𝜙(𝜈) ⋅ 𝑑𝜈 = 1, measurement gas concentration can be calculated with the following equation: 𝑥 = ∫[𝛼(𝜈)+ln(𝑇𝑟)]⋅𝑑𝜈

𝑆(𝑇)⋅𝑃⋅𝐿= 𝑃𝑒𝑎𝑘 𝐴𝑟𝑒𝑎

𝑆(𝑇)⋅𝑃⋅𝐿 (3)

With gas temperature and pressure input from external sensors, optical path length is fixed and known, and line strength available from HITRAN (or other) database or experimental data, concentration is simply proportional to the absorption peak area (shaded portion) in Figure 2-c.

WAVELENGTH MODULATION SPECTROSCOPY

In late last century when TDLAS became an emerging technology, DAS faced challenges to provide accurate measurement, especially for trace level concentrations. To measure weak absorption signals in a large laser power sloping and radiation DC offset background, high-resolution analog-to-digital converter (ADC) is required to cover the full photodiode signal for low quantization noise. Additionally, fast laser scanning and a large number of scan averages are needed to reduce laser relative intensity noise (RIN, inversely proportional to the scan frequency) and other noises, which further requires the ADC to have fast sampling rate. High-speed and high-resolution ADCs were very expensive or not available with industrial packaging grade at that time. Balanced detection [3] can cancel the laser ramp background and reduce laser RIN as they are detected by both measurement and reference photodiodes. However, the strict requirement of two detector signal ratio makes this technique suitable for only lab environment rather than aggressive field measurement. 2f wavelength modulation appeared to be a good method by shifting the signal to higher frequency and detecting the background-free second harmonic component. Some technical papers claim that peak area of DAS is difficult to integrate when the absorption peak is broad under a high-pressure condition, and adjacent absorption peaks may have interference effect. The second derivative absorption signal made 2f-WMS seemingly more attractive for TDLAS. In contrast to DAS, WMS laser injection current has an additional sinusoidal modulation to the ramp scan as shown in Figure 3-a. The laser output frequency 𝜈(𝑡) can be expressed as: 𝜈(𝑡) = 𝜈(𝑡) + 𝑎 ⋅ cos (2𝜋𝑓𝑡) (4) Where 𝑖(𝑡) = laser center frequency 𝑎 = modulation amplitude 𝑓 = modulation frequency Figure 3-b shows the laser output power and the light intensity detected by the photodiode. A lock-in amplifier (LIA), either analog or digital, detects the 2nd harmonic component of the photodiode signal. With weak absorption and negligible amplitude modulation assumptions, the 2f signal is similar to 2nd derivative of a direct absorption peak shown in Figure 3-c. The math expression is derived from Fourier Transform:

𝐻2(𝜈, 𝑎) = −𝑇𝑟⋅𝑆(𝑇)⋅𝑃⋅𝑥⋅𝐿𝜋 ∫ 𝜙(𝜈 + 𝑎 ⋅ cos𝜃𝜋

−𝜋 ) ⋅ cos2𝜃 ⋅ 𝑑𝜃 (5)

FIGURE 3. OPERATION PRINTCIPLE OF SECOND HARMONIC WAVELENGTH MODULATION SPECTROSCOPY MEASUREMENT: A) LASER DRIVING AND WAVELENGTH SCAN, B) LASER OUTPUT INTENSITY AND DETECTED LIGHT INTESNITY BY PHTODIODE, C) 2F ABSORPTION SIGNAL

Unlike DAS, the whole 2f spectrum information is needed to calculate gas concentration because the line shape function 𝜙(𝜈) cannot be eliminated in equation (5). The algorithm could be very complicated, for example, fitting the 2f signal to a stored spectral database calibrated with standard gases.

DAS NOISE REDUCTION

As described earlier, a high-speed and high-resolution ADC is needed to digitize the detector signal to achieve sensitive measurement for DAS. High-speed allows detection of fast laser scan to reduce the laser 1/f RIN noise. Large amount of samples can be averaged at the DAQ to further reduce the random noise. High-resolution lowers quantization noise so that small

absorption signal in the large sloping background can be identified. Then what is the minimum ADC specification requirement? The simulation by Lins, et al [4] concludes that, for RIN = -150 dB/Hz, an ADC of 13-bit resolution and 1 MHz sampling rate is good enough to achieve the same SNR performance as 2f WMS. His experiment with 200 Hz laser scan frequency further supports the statement [5]. It is believed that oversampling, noise dithering and averaging lead to an increase of the effective ADC resolution. Independently, experimental evaluation has been done in this work. The gain of the amplifier before digitization is adjusted so that the span of the amplified detect signal is portion of the ADC input range. With negligible amplifier noise, smaller portion of ADC input range is equivalent to reduced ADC resolution as most significant bits are zeros. Other test setup configurations are: 1 kHz laser scan, 50 MHz ADC sampling rate and 5-second averaging time. The result in Figure 4 shows that ADC with 11-bit or higher resolution has the same noise performance, which is about 1.5·10-5 absorption.

FIGURE 4. ADC RESOLUTION EFFECT ON ABSORPTION SPECTRUM NOISE With current advances in electronics, ADC chips with such specification are easy and cheap to acquire from the market. The performance for both DAS and WMS is limited by optical etalon noise. Since the typical optical noise has similar frequency response with the absorption feature, WMS cannot help reduce the optical noise. So from the sensitivity (detection limit) point of view, there is no disadvantage for DAS compared with WMS.

ADVANTAGES OF DAS OVER WMS

As explained in the last section, the biggest claimed WMS advantage, better sensitivity, is not correct any more with appropriate DAS electronics design. Now the advantages of using DAS over WMS for on-line process analysis are discussed in the following paragraphs.

TRUE ABSORPTION MEASUREMENT “True” means the obtained absorption feature has no distortion for DAS. The absorption spectrum is strictly calculated based on Beer’s Law, where log-ratio is applied to the laser output and transmitted intensity signals. This property enables DAS to give most accurate concentration results with fundamental and proven signal processing algorithms. For DAS, absorption saturation starts to happen when the absorption blocks almost all the laser light at the center wavelength. Usually 𝛼(𝜈) = 2 is used for DAS saturation limit, allowing 5 decades (105) dynamic measurement range. An example would be the ability of DAS method to measure large CO excursions in large scale industrial combustion process (Refinery Heater or Ethylene Cracking Furnace), such as 3,000ppm CO with 75ft optical path length at 2200oF. However WMS is a transmission based detection. At weak absorption 𝛼(𝜈) ≤ 0.05 , the approximation expressed in equation (6) is correct. 𝐼(𝜈)𝐼0(𝜈)

= 𝑒−𝛼(𝜈) ≈ 1 − 𝛼(𝜈) (6) But at higher absorption, the error is greater. This leads to the linearity issue and narrow dynamic range for a WMS analyzer. It is possible to improve the linearity issue with the same modulation on both measurement and reference laser beam and calculate the absorption before demodulation [6], but the system will be much more complex for both hardware and software. As indicated by equation (5), the 2f signal line shape depends on modulation amplitude 𝑎. For a Lorentzian line profile, 2f signal has highest SNR when modulation index 𝑚 = 𝑎

Δ𝜈≈ 2.2 (where

Δ𝜈 is the half width at half maximum of the absorption peak). As the modulation is optimized during laborious calibration, the actual measurement at different conditions will yield unquantifiable error. Another undesirable distortion of WMS comes from laser intensity modulation, often referred as residual amplitude modulation (RAM) [2], causing asymmetric 2f line shape. The phase shift between intensity and wavelength modulation makes the signal distortion more complicated and hard to interpret. Additional DC or even 1f spectrum is needed to normalize the 2f signal, which further complicates the scheme. Due to the first principle nature of DAS, the possibility of calibration free or self-calibration of TDLAS can be achieved to further enhance reliability, performance, and ease of maintenance. PEAK AREA METHOD As in equation (2), line shape function 𝜙(𝜈) is a Voigt function, convolution of Gaussian and Lorentzian. It is dependent not only on gas temperature and pressure, but also on gas composition. Different molecules have different collisional broadening coefficients. Figure 5

shows the DAS and WMS absorption spectra of 10% oxygen in different background gases (nitrogen, helium, and methane) under standard conditions of 1 meter optical path length, 25°C and 1 atmospheric pressure. This has some representation of flare line oxygen measurements whereby the background gases can have unknown compositional variation. The areas of the 3 DAS absorption peaks are constant, which can be used for concentration calculation. WMS usually involves much more complicated algorithms such as width compensation (very sensitive to noise) or special fittings to the calibrated spectral database. With above described spectral distortions, WMS typically has greater errors on the result than DAS.

FIGURE 5. DAS AND WMS ABSORPTION SPECTRA OF 10% OXYGEN IN THE BACKGROUND OF NITROGEN, HELIUM, AND METHANE UNDER STANDARD CONDITIONS (1 METER, 25°C, 1 ATMOSPHERIC PRESSURE)

The peak area method doesn’t simply mean the numerical integration of all the data points in the DAS absorption spectrum. In fact, there will be a big error on the integrated peak area when the absorption peak is broad as part of absorption tails is outside the wavelength scan range. Also necessary baseline flattening process can further reduce the apparent peak area. One popular technique is to peak-fit the absorption feature with a Voigt or Lorentzian function. The low-order baseline coefficients can be added to the fitting function, which simultaneously compensate the baseline fluctuations caused by particulate scattering, beam steering, mechanical vibration, etc. The peak area can be extracted from the fitting result. For example, the peak area of a Lorentzian profile equals (𝜋 ⋅ ℎ𝑒𝑖𝑔ℎ𝑡 ⋅ Δ𝜈). Tests have been done that DAS with peak fitting algorithm can achieve accurate oxygen measurement under gas pressure range of 0.02~15 barA (0.3 ~218 psiA). FAST SCAN CAPABILITY Fast wavelength scan is important for the measurement of dynamic processes, such as coal-fired power plants, waste incinerators, thermal oxidizers, etc. The fast flying particles in the process gas produce rapid fluctuations for the detected laser transmission and thermal radiation. Field data has proved that the required wavelength scan frequency needs to be higher than 1 kHz to obtain negligible process interference.

DAS method can easily achieve laser wavelength scanning between 1 kHz and 10 kHz, without shrinking the wavelength scan range. During one scan, laser transmission and thermal radiation can be treated as constant values. Only DC offset appears on the averaged detector signal and absorption spectrum. Fast laser scan also reduces the 1/f laser RIN, and allows large amount of averaging numbers within a few seconds to further improve the SNR (proportional to square root of averaging number). For WMS, it is not easy to have fast wavelength scan because the sinusoidal modulation needs to be much faster. This causes big phase shift between wavelength modulation and laser intensity modulation, which distorts the 2f signal in these particulate laden applications. LINEAR/ADDITIVE PROPERTY Thanks to Beer’s Law, DAS has a great linear property that the total absorption is the sum of all the individual gas absorption contributions. This property is expressed in the following equation: 𝛼(𝜈) = ∑ 𝑥𝑖 ⋅ 𝑠𝑖(𝜈)𝑖 (7) Where 𝑥𝑖 = concentration of gas 𝑖 𝑠𝑖(𝜈) = absorption of gas 𝑖 with unit concentration With this linear property of absorption, many attractive on-line process analyzer features can be implemented. Online validation is one of the desirable and demanding features. During normal TDLAS process analyzer operation, a known measurement gas (for example, instrument air for oxygen analyzer) is introduced to the non-process optical path. So the total absorption is the sum of that from process gas and non-process gas. By subtracting the process gas absorption before and after validation from the total absorption, the non-process gas absorption is known. By applying non-process optical path length, temperature and pressure to equation (3), the calculated validation gas concentration is available. The analyzer online span validation is implemented by comparing the known and calculated validation gas concentration values. This on-line validation routine can therefore be automated and easily integrated into a process analyzer maintenance and/or statistical quality control (SQC) program. It also serves as a very useful feature for SIS/SIL loop instrument routine verification. Another good feature is that zero absorption optical purge gas is not required for some applications. For example, some plants only have instrument air instead of nitrogen gas available for oxygen TDLAS operation. DAS allows the known non-process absorption subtracted from the total measured absorption to derive the residual process absorption. This ensures accurate measurement of the process gas concentration. The DAS based on-line process analyzer can incorporate software parameters that allow the non-process parameters to be configured accordingly to ensure optimal performance with I/A purge gas.

Linear property of absorption can be used to eliminate the spectral interferences and further implement multi-component measurement with the help of statistical algorithms. Equation (7) can be converted to matrix format: 𝐴 = 𝑋 ⋅ 𝑆 (8) Where 𝐴 = vector of mixture gas absorption (measured absorption spectrum) 𝑋 = vector of concentration values of absorbing gases 𝑆 = matrix consisting of parent spectra of unit concentration absorbing gases (calibration) All the absorption gas concentration can be calculated with the following matrix conversion, which is also known as classical least squares method (CLS). 𝑋 = 𝐴 ⋅ 𝑆𝑇 ⋅ (𝑆 ⋅ 𝑆𝑇)−1 (9) Figure 6 plots a CLS model for typical cracked gas samples. The concentrations of all the components can be calculated simultaneously by equation (9). The fast response of optical measurement makes TDLAS a great potential replacement for traditional process gas chromatography.

FIGURE 6. SPECTRAL MODELING FOR CRACKED GAS MEASUREMENT

CONCLUSION

As the SNR of DAS achieves an equal to or better than level of WMS due to the advances of modern electronics and signal processing, there is no advantage of WMS. However, DAS shows many unique merits that WMS cannot offer. The advantages of using DAS over WMS for on-line process analysis are summarized below:

• DAS measures true absorption features without any induced spectral distortion. This gives opportunities of accurate and linear measurement over wide dynamic range and implementation of analyzer calibration-free feature.

• Peak area method allows for a concentration measurement that is not affected by changing background composition. Known process conditions including gas temperature and pressure can be easily compensated.

• The fast laser scan capability improves the spectrum SNR, and also eliminates the interference from fast fluctuations of transmitted laser light and background radiation.

• The linear property of absorption spectrum makes it possible to implement many practical field analyzer features, such as online validation (spiking/bump-checks), flexible purge gas requirement, reduced spectral interference and simultaneous multi-component measurement.

REFERENCES

1. Teichert, H., Fernholz, T. and Ebert, V., “Simultaneous in situ measurement of CO, H2O, and gas temperatures in a full-sized coal-fired power plant by near-infrared diode lasers”, Applied Optics, Vol. 42, No. 12, 2003, pp. 2043-2051.

2. Schilt S, Thevenaz L., and Robert P., “Wavelength modulation spectroscopy: combined frequency and intensity laser modulation”, Applied Optics, Vol. 42, No. 33, 2003, pp. 6728-6738.

3. Hobbs, P., “Ultrasensitive laser measurements without tears”, Applied Optics, Vol. 36, No. 4, 1997, pp. 903-920.

4. Lins B., Zinn P., Engelbrecht R., and Schmauss B., “Simulation-based comparison of noise

effects in wavelength modulation spectroscopy and direct absorption TDLAS”, Applied Physics B, Vol.100, Issue 2, 2010, pp. 367-376.

5. Lins B., Engelbrecht R., and Schmauss B., “Software-switching between direct absorption

and wavelength modulation spectroscopy for the investigation of ADC resolution requirements”, Applied Physics B, Vol. 106, Issue 4, pp. 999-1008.

6. US Patent No. 7,957,001.