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Int J Thermophys (2017) 38:53
DOI 10.1007/s10765-017-2188-8
CPPTA3
The Tracking Resonance Frequency Method for
Photoacoustic Measurements Based on the Phase
Response
Mariusz Suchenek1
Received: 24 October 2016 / Accepted: 2 February 2017 / Published online: 20 February 2017
© The Author(s) 2017. This article is published with open access at Springerlink.com
Abstract 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.
Keywords Phase response · Photoacoustic · Photoacoustic measurements ·
Synchronization to the resonance frequency
1 Introduction
Photoacoustic (PA) spectroscopy is widely used for tracing gas analysis [1,2]. The
influence of noise becomes more significant when the concentration of target gas
decreases. Any acoustic fluctuation picked up by the acoustic sensor (typical micro-
phone) might be recognized as a PA signal. It can be a signal either from the measured
Selected papers from Third Conference on Photoacoustic and Photothermal Theory and Applications.
B Mariusz Suchenek
M.Suchenek@elka.pw.edu.pl
1 The Institute of Electronic Systems, Warsaw University of Technology, Nowowiejska 15/19,
00-665 Warsaw, Poland
123
53 Page 2 of 8 Int J Thermophys (2017) 38:53
sample (gas, solid, liquid) or from external acoustic noise. One of the most com-
mon methods used to improve the signal-to-noise ratio (SNR) is to place measured
specimens into the cell [3,4]. In this method, the cell is sealed both electrically and
acoustically; thus, the measured gas and the acoustic sensor are separated from exter-
nal interferences. In this way, the sample is isolated from the acoustic signals from
the surrounding environment and the level of the background noise is also reduced. In
PA constructions, two approaches are used. The first one is to operate at the frequency
located far away from the resonant frequency of the cell [5,6], while the second one, on
the contrary to the previous one, operates at the resonant frequency [7]. Both solutions
have their advantages and disadvantages. The first approach does not require tuning
of the stimulating frequency; however, it also does not use the cell resonance proper-
ties. The cell allows the amplitudes at frequencies around the resonance frequency to
pass through and attenuates amplitudes at frequencies outside the resonance. Hence,
the selectivity of frequencies can be used to attenuate amplitudes of external noise
and to allow amplitudes of measured PA signal to pass through. The second solution
requires knowledge of the actual resonant frequency of the cell and follows it by the
stimulating frequency. This solution increases sensitivity significantly. However, the
resonance frequency is affected by the environmental parameters (temperature) and
the chemical composition of the gas mixture. That is why, its variations may become
a significant problem. So several methods are used to determine the actual resonant
frequency and a tracking method in PA systems. In these methods:
(a) the resonance frequency change can be calculated from the measured temperature
[8],
(b) inside the cell, there is a speaker [9–11] 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 [12],
(c) the resonance frequency can be determined by estimating maximum amplitude
based on the amplitude response obtained by:
• measuring amplitudes at selected frequencies [13], frequency by frequency,
• the pulse technique [14] measuring the amplitudes at several frequencies at the
same time by using either the chirp technique [15] or by sweeping frequency,
(d) 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.
The last presented solution uses the PA signal from the microphone to drive the optical
modulator which stimulates the PA cell. Such a system automatically adjusts the
stimulating frequency to the resonant frequency of the cell. However, the PA generator
requires a strong PA signal from the measured sample to produce oscillation. This
phenomenon limits generator practical application.
123
Int J Thermophys (2017) 38:53 Page 3 of 8 53
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 acquisi-
tion 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. More-
over, 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).
The input signal from the ADC yRF (t) can be described as:
yRF (t) = ARF · sin(ωRF · t + ϕRF ) (1)
and the signal from the NCO is described as:
yLO(t) = ALO · sin(ωLO · t + ϕLO) (2)
123
53 Page 4 of 8 Int J Thermophys (2017) 38:53
the mixer output is described as [21]:
yI F (t) = yRF (t) · yLF (t)
= 0.5 · ALO · ARF · (sin [(ωRF + ωLO) · t + (ϕRF + ϕLO)]
+ sin [(ωRF − ωLO) · t + (ϕRF − ϕLO)]) (3)
where
ω = 2 · π · f (4)
The mixer output contains two frequencies fRF + fLO and fRF − fLO , and since the
stimulating frequency (NCO) and measured frequency are the same, the fRF = fLO
and Eq. 3 have the form
= 0.5 · ALO · ARF · (sin [2 · ωLO · t + (ϕRF + ϕLO)] + sin(ϕRF − ϕLO)) (5)
The low-frequency component is responsible for the phase difference and is extracted
by the low-pass filters (LPF). The Cartesian representation enables us to calculate the
amplitude as:
A =
√
I ′2 + Q′2 (6)
and a phase difference as:
ϕ = a tan
(
Q′
I ′
)
(7)
To change the stimulation frequency, the phase difference is used to determine the
frequency corrections for the NCO. In order to improve SNR, a dedicated module
which implements low-pass filtering and averaging (LPF & AVG) was added. This
module allows to set the average number in the presented method. Depending on it,
the phase difference measurement may be more accurate, which is important for the
measurement of very weak PA signals. The control module checks the phase and
depending on its value changes the frequency of the NCO. The output of the NCO is
connected to the digital comparator (CMP) which drives the laser by a digital signal
with 3.3-V level.
4 Verification
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 [17]. 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
123
Int J Thermophys (2017) 38:53 Page 5 of 8 53
Fig. 1 Block diagram of a standard photoacoustic system (a), a system with the lock-in amplifier (b)
1.1 1.3 1.5 1.7
−150
−50
50
150
Frequency, kHz
P
ha
se
, d
eg
re
es
1.1 1.3 1.5 1.7
20
60
100
140
Frequency, kHz
A
m
pl
itu
de
, a
. u
.
(a) (b)
Fig. 2 Measured frequency dependence of amplitude (a) and phase (b) of the photoacoustic cell
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.
The picture of the described measurement setup is shown in Fig. 4. In order to verify
a proposed method, graphite powder was placed into the cell to cause an absorption
of the light. At the beginning of tests, the PA cell was filled with nitrogen, and after
a few seconds measurements were started. The resonance frequency of the cell filled
with nitrogen was stabilized at 1395 Hz. In order to evaluate the proposed method, the
speed of sound in the cell was changed by portion of carbon dioxide injected into the
cell. This procedure was repeated five times. During all tests, the resonance frequency
and the phase were recorded and obtained results are shown in Fig. 5. Every time after
injection, the phase suddenly changed and then after a few seconds returned to the
initial value. The variance of the phase in each test was in the range of 1 degree while
the resonance frequency changed from 1089 Hz to 1395 Hz.
123
53 Page 6 of 8 Int J Thermophys (2017) 38:53
Fig. 3 Block diagram of proposed method
PA cell with
microphone
Laser
microcontroller
board
FPGA and
ADC board
Fig. 4 Photograph of the measurement setup
100 300 500 700 900 1100
1.05
1.15
1.25
1.35
1.45
Time, s
G
en
er
at
ed
 fr
eq
ue
nc
y,
 k
H
z
CO2 injection
CO2 injection
CO2 injection
CO2 injection
CO2 injection
100 300 500 700 900 1100
−5
0
5
10
15
20
25
30
Time, s
P
ha
se
, d
eg
re
es
(a) (b)
Fig. 5 Generated frequency of the light beam source (a), the phase difference between measured from the
photoacoustic signal and set from reference measurement (b)
123
Int J Thermophys (2017) 38:53 Page 7 of 8 53
5 Conclusions
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.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 Interna-
tional License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license, and indicate if changes were made.
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123


The Tracking Resonance Frequency Method for Photoacoustic Measurements Based on the Phase Response

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Nagalingam et al. Breast Cancer Research  (2017) 19:39 
DOI 10.1186/s13058-017-0829-2ERRATUM Open AccessErratum to: Honokiol activates
AMP-activated protein kinase in breast
cancer cells via LKB1-dependent pathway
and inhibits breast carcinogenesis
Arumugam Nagalingam1, Jack L. Arbiser2, Michael Y. Bonner2, Neeraj K. Saxena3 and Dipali Sharma1*Erratum
After the publication of this work [1], an error was
noticed in Fig. 1b. An incorrect image was inadvertently
shown for the soft-agar colony for MDA-MB-231 cells
treated with 5.0 uM Honokiol. The correct figure is
shown below. This error did not affect the findings or
conclusions of the article.
Author details
1Department of Oncology, Johns Hopkins University School of Medicine and
the Sidney Kimmel Comprehensive Cancer Center at Johns Hopkins,
Baltimore, MD 21231, USA. 2Department of Dermatology, Emory University
School of Medicine, Winship Cancer Institute, Atlanta, GA 30322, USA.
3Department of Medicine, University of Maryland School of Medicine,
Baltimore, MD 21201, USA.
Received: 6 March 2017 Accepted: 6 March 2017
Reference
1. Nagalingam A, et al. Honokiol activates AMP-activated protein kinase in
breast cancer cells via an LKB1-dependent pathway and inhibits breast
carcinogenesis. Breast Cancer Res. 2012;14(1):R35.* Correspondence: dsharma7@jhmi.edu
1Department of Oncology, Johns Hopkins University School of Medicine and
the Sidney Kimmel Comprehensive Cancer Center at Johns Hopkins,
Baltimore, MD 21231, USA
Full list of author information is available at the end of the article
© The Author(s). 2017 Open Access This artic
International License (http://creativecommons
reproduction in any medium, provided you g
the Creative Commons license, and indicate if
(http://creativecommons.org/publicdomain/zele is distributed under the terms of the Creative Commons Attribution 4.0
.org/licenses/by/4.0/), which permits unrestricted use, distribution, and
ive appropriate credit to the original author(s) and the source, provide a link to
changes were made. The Creative Commons Public Domain Dedication waiver
ro/1.0/) applies to the data made available in this article, unless otherwise stated.
Fig. 1 Honokiol inhibits clonogenicity and anchorage-independent growth of breast cancer cells. a MCF7 and MDA-MB-231 cells were treated
with various concentrations of honokiol (HNK) (as indicated) and subjected to clonogenicity assay. Untreated cells, denoted with the letter “U”.
Colonies containing >50 normal-appearing cells were counted. *, P < 0.005, compared with untreated controls. b Breast cancer cells were
subjected to soft-agar colony-formation assay in the presence of various concentrations of honokiol for three weeks. Untreated cells are denoted with
the letter “U”. Results are expressed as average number of colonies counted (in six micro-fields). *, P < 0.001, compared with untreated controls
Nagalingam et al. Breast Cancer Research  (2017) 19:39 Page 2 of 2


Erratum to: Honokiol activates AMP-activated protein kinase in breast cancer cells via LKB1-dependent pathway and inhibits breast carcinogenesis

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