The Tracking Resonance Frequency Method for Photoacoustic Measurements Based on the Phase Response
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One of the major issues in the use of the resonant photoacoustic cell is the resonance frequency of the cell. The frequency is not stable, and its changes depend mostly on temperature and gas mixture. This paper presents a new method for tracking resonance frequency, where both the amplitude and phase are calculated from the input samples. The stimulating frequency can be adjusted to the resonance frequency of the cell based on the phase. This method was implemented using a digital measurement system with an analog to digital converter, field programmable gate array (FPGA) and a microcontroller. The resonance frequency was changed by the injection of carbon dioxide into the cell. A theoretical description and experimental results are also presented.
KeywordsPhase response Photoacoustic Photoacoustic measurements Synchronization to the resonance frequency
the resonance frequency change can be calculated from the measured temperature ,
inside the cell, there is a speaker [9, 10, 11] which is used to determine the frequency response of the cell. The PA resonance frequency can be either directly measured or calculated from another mode since the ratio between modes is constant for the same cell ,
- (c)the resonance frequency can be determined by estimating maximum amplitude based on the amplitude response obtained by:
by producing a PA signal based on the PA generator method [16, 17]. In this method, the intensity of the light beam is driven by the PA signal in the feedback loop. The stimulating frequency is self-adjusting to the actual conditions of the PA cell.
2 The Description of a Proposed Method
The standard PA measurement system is presented in Fig. 1a [12, 18]. It is based on a PA cell which contains the measured sample, a light source (eg., laser or LED) with an externally triggered optical modulator and an acoustic sensor connected to the cell. The acoustic signal induced by the photoacoustic effect is changed by an acoustic sensor (eg., microphone) into an electrical signal. In order to increase the level of the photoacoustic signal, a preamplifier is used. Then, the signal is changed into a digital one by an analog to digital converter (ADC). In most PA systems, the stored samples are processed by a digital signal processor (DSP) which calculates the amplitude response and controls the function generator frequency.
The PA cell is stimulated by a light beam from a light source which signal is modulated by the function generator. In certain applications, the lock-in amplifier is used instead of a control unit and a data acquisition module (DAQ) [19, 20]. Such a solution is presented in Fig. 1b.
The proposed method describes another approach to the control and data acquisition module. To track or monitor the resonance frequency of the cell, the phase relation between stimulating and measured signal is used instead of the amplitude response. This approach uses the phase which value is zero at the resonant frequency. Moreover, the relation between the phase and the amplitude response is constant and is independent of temperature and gas mixture. The example of the amplitude and phase response of the PA cell is presented in Fig. 2. At the same time, while the amplitude is obtained, the phase can also be determined. The described method uses input samples to calculate the amplitude, which is proportional to the absorption, and also phase to determine the correction of the stimulation frequency. If the phase is negative, then the stimulating frequency is increased; otherwise, the frequency is decreased.
3 Measurement Concept Based on Phase Response
The proposed method is based on the IQ demodulation technique. The block diagram of the method is presented in Fig. 3. As the figure shows, the PA signal is converted into the digital one by an ADC. This digital signal is connected to the input of two mixers (digital multipliers) where each mixer has two inputs and one output. The signal at the output is a multiplication of the signal at inputs. The input signal from the converter is mixed with the signal generated by the numerical control oscillator (NCO).
A typical PA cell was used to evaluate the proposed method. This cell is similar to the one used earlier in the measurement of the PA generator . The block diagram of a photoacoustic system is presented in Fig. 1a. In the figure, instead of the block control & DAQ have been used two digital development boards and a custom-made analog board. Digital development board with field programmable gate array (FPGA) DE0-Nano was used to perform all signal processing operations. While the board with the microcontroller (STM32F411 Nucleo) was responsible for the communication between PC computer and a signal processing circuit.
The clock for the signal processing unit was set to 50 MHz and each processing signal block operated with the same frequency. The whole circuit worked in such a way that the processing speed was sufficient to finish all mathematical operations before processing next sample from an analog to digital converter. An analog custom-made board consisted of the ADC, an amplifier and analog filters. The signal from the microphone passed through the amplifier in order to increase the amplitude of the signal. And then this signal is passed through the analog filter to reduce its bandwidth. After the whole process, the analog signal was converted into a digital one by the 18-bit ADC and went to the FPGA board.
In this paper, a new approach to overcome problem of the tracking resonance frequency of the PA cell was proposed. This method is based on the measurement of the phase difference between the stimulating light source and the signal from the microphone. Depending on the phase between both signals, the stimulating frequency increases or decreases. The method tries to maintain the constant zero phase between both signals. Measuring of both the amplitude and the phase can be performed using the same data. Moreover, our approach allows us to use low-pass filters and the average algorithm on the calculated phase and amplitude. Similar signal processing algorithms are used in lock-in amplifiers; thus, the SNR can be improved and the detection sensitivity can be enhanced in this way.
The performed measurements allowed us to verify the proposed method. The PA cell was filled with nitrogen, and later carbon dioxide was injected into the cell five times. So, consequently every gas injection changed the resonance frequency. Each time the stimulating frequency was adapted to the resonance frequency of the cell based on the phase response.
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