Neuro fuzzy prediction of laser fluence based on photoacoustic signal analysis in different gas mixtures


Available online 24 January 2023, 112533

MladenaLukićaŽarkoĆojbašićbDraganMarkushevcaFaculty of Occupational Safety, University of Niš, Čarnojevića 10a, Niš 18000, SerbiabMechanical Engineering Faculty, University of Niš, Aleksandra Medvedeva 14, Niš 18000, SerbiacInstitute of Physics, University of Belgrade, Pregrevica 118, Belgrade-Zemun 11080, Serbia

Received 17 October 2022, Revised 19 January 2023, Accepted 21 January 2023, Available online 24 January 2023.

Intro to the article by Dr Beck

In 1988, we published an article on the theory and application of optoacoustics (photoacoustics) in gases, based on my PhD thesis at UIC. It involved the relaxation properties of SF6 in argon buffer gas. SF6 is a huge absorber of IR photons and a greenhouse gas. Since those early studies, many groups and researchers have interpreted photoacoustics using our approach of Green’s Function analysis of the waveform. This study is the most advanced, and utilizes a neural fuzzy logic approach to decipher the laser fluence.


Photoacoustic spectroscopy achieves high sensitivity and selectivity using high-power lasers. Variations of parameters such as laser beam spatial profile and fluence can alter precision of photoacoustic measurements. Numerous commercial instruments aren’t usable for high Φ values measurement, due to possible harmful effects. To estimate high values from photoacoustic signals in time domain we applied computational intelligence method: adaptive-network-based fuzzy inference system (ANFIS).

Experimental photoacoustic signals are generated in two different gas mixtures: SF6+Ar and C2H4+Ar, for values ranging from (0.2 – 1.4) . Obtained results indicate that different absorption characteristics of examined molecules and various signal intensities don’t influence ANFIS prediction, due to its adaptation ability and error tolerance in dealing with imprecise and noisy data. Furthermore, robustness, high learning capability and self-correction, make this technique computational effective and recommendable for in situ photoacoustic measurements. Aside from many advantages, limitations of the proposed method are also discussed.


Photoacoustic spectroscopy (PAS) is laser-based spectroscopy technique applicable in environmental, biological, medical, industrial, agriculture, and other fields [1], [2]. The leading process in PAS is energy absorption by molecules in a gas sample and its conversion to a local heat. Establishing laser as conducive radiation source, PAS has developed as modern techniques with high sensitivity, selectivity, large dynamic range and, detection limit below parts-per-trillion [3], [4], [5]. Highly sensitive PA devices use different radiation sources, chamber designs and detectors, to improve qualitatively PA detection, and increase dynamic range of measured concentration [6], [7], [8], [9], [10], [11]. Due to proportionality between PA signal amplitude and power of the incident radiation, high-power lasers are crucial for eminent PAS potential. Interaction between intense infrared (IR) laser radiation and molecules in a sample creates phenomenon known as multiphoton absorption (MPA), the physical basis in PAS. Multiphoton absorption for different polyatomic molecules is a function of laser fluence  (the time integral of the radiation intensity defined for a certain pulse duration) [12]. For absorber concentrations used in this study, intensity of PA signal is directly proportional to absorbed energy . Energy absorbed by the sample  is defined by average number of absorbed photons per molecule  which is fluence  dependent quantity [13]. Unforeseeable  variations during the experiments may cause incorrect interpretation of absorption efficiency for different trace gases and measurement inaccuracy altering calibration procedure [14], [15]. In our previous research it was concluded that exact knowledge of the laser beam spatial profile is crucial for the analysis of PA signal temporal shapes, vibrational to translational relaxation time () determination and consequently trace gases detection [16], [17], [18]. Commercial instruments for laser beam profile and fluence  determination have some restrictions for high  values, because of possible degradation of device performances [19], [20], [21]. Knowledge of  values is crucial for quantitative study of molecular absorption, particularly in experiments performing in real environment, where  may vary much less controllable than in the laboratory. Many practical applications of PA effect such as signal analysis in PAS and image analysis in photoacoustic imaging (PAI), strongly imply reconstruction algorithms dependency on incident fluence and fluence distribution in a tissue [22], [23], [24]. Numerous algorithms for fluence estimation and correction have been proposed for clinical applications [25], [26], [27], [28]. However, many image reconstruction techniques are based on ideal assumptions, and time demanding procedures don’t support real-time applications. Pelivanov et al. [29] develop method for quantitative image reconstruction that simultaneously estimated and compensated variations of optical fluence. For simultaneous determination of the laser beam spatial profiles and molecule relaxation time, Rabasovic et al. [16] used mathematical algorithm developed for photoacoustic tomography (PAT). Although, the PAT algorithm is very accurate for laser profile reconstruction, due to high computational cost, the method can be applied only as correction procedure after the completed experiment. To promote PAS potential for real-time monitoring (precision and real time operation) we proposed computational intelligence (CI) for inverse problem solving. Recently we have applied several optimization algorithms and artificial neural networks to enhance precision and accomplish real-time determination of PA signal parameters [30], [31], [32], [33], [34], [35]. Using artificial neural networks (ANN) we determined simultaneous and in real-time four parameters of theoretical/experimental PA signals: the laser beam spatial profile , vibrational-to-translational relaxation time (), distance from the laser beam to absorption molecules in the photoacoustic cell  and laser fluence [31]. Although, results were encouraging regarding accuracy and real time operation, the key issues for network performances – selection of ANN topology and network training, remain demanding task especially when our a priori knowledge of experimental parameters is limited, and data (PA signals) are ill-defined (due to difficulty to noise control for in situ measurement). In this paper we proposed a technique suitable for inverse problem solving, adaptable to dynamic environment and capable to dealing with fuzzy, vague data: adaptive-network-based fuzzy inference system (ANFIS) [36], [37]. In last two decades estimation of primarily for clinical application attracts attention of many researchers, who proposed numerous deep learning algorithms for inverse problem solving and image reconstruction [38], [39], [40]. Based on our previous studies [30], [31], [32], [33], [34], [41], [42], we chose ANFIS as technique capable to predict  values from PA signal in a straightforward manner. Unlike complex deep learning architecture, ANFIS has simpler topology, doesn’t require large amounts of labelled data and substantial computing power. ANFIS is a combination of the adaptive control technique, artificial neural network, and the fuzzy inference system with advantages of both fuzzy and neural networks technique, offering superior training results in comparison to other methods. ANFIS provides real time operation and possibility to adjust appropriate fluence  values between two consecutive lasers pulses, using ambiguity of human perception and decision to solve problems under undetermined circumstances. Fluence dependent PA signals were dataset for ANFIS training. Experimental PA signals are generated in two gas mixtures: SF6 + Ar and C2H4+ Ar for five different  values ranging from (0.2 to 1.4)  [43]. To test ANFIS performances and generalization capabilities for future application, we chose absorbers SF6 and C2H4, with remarkably different MPA features and consequently PA signal intensities.

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