1. Introduction

Diffuse optical spectroscopy (DOS) is a non-invasive technique capable of providing concentrations of oxygenated and de-oxygenated hemoglobin, water, and lipid in deep tissue non-invasively, without the use of ionizing radiation [1,2]. Quantitative recovery of these properties is dependent upon the accurate and precise recovery of the absorption and scattering of tissue. Some techniques, such as continuous wave-diffuse optical spectroscopy are commonly employed for measurements of these properties but are unable to separate the effects of scattering and absorption when using single optode and low wavelength count systems. Therefore, they are often limited to only monitoring changes in concentration and requiring assumptions of scattering based on published literature [3,4]. With additional information from multiple source-detector pairs and multiple wavelengths, continuous-wave data can be used to recover both absorption and scattering [5]. Alternatively, continuous wave light sources can be used to perform spatial frequency domain imaging, which has been shown to achieve relatively accurate and fast recovery of optical properties in a large field of view [6]. Recent work has also explored the use of wavelength modulated systems to extract optical properties in biological tissue [7]. Alternatively, diffuse optical spectroscopy systems can be modified to collect information regarding the pathlength of light through tissue. Frequency domain-diffuse optical spectroscopy (FD-DOS) and time domain-diffuse optical spectroscopy (TD-DOS) are two such methods. In FD-DOS, laser sources are amplitude modulated at frequencies in the range of 50-1000 MHz. From this modulated source, both the alternating current (AC) amplitude reduction and phase shift of the detected signal are used to recover absorption and reduced scattering coefficients [8]. In TD-DOS, short pulses of light on the order of 10s of picoseconds are launched into tissue, and the temporal point spread function is measured some distance away. This information is then used to recover the optical properties of the sample [9]. Of these two, FD-DOS is more commonly employed for measuring optical properties as it can provide reasonably accurate recovery with relatively simple instrumentation and data processing, as well as light sources and detectors that are low-cost.

As stated previously, FD-DOS commonly uses amplitude modulated sources in the 50MHz-1 GHz band and measures both the amplitude and phase of the detected signal to provide information regarding attenuation and the pathlength of light through tissue [10]. This additional data enables the recovery of both optical absorption (${\mu _a}$) and the reduced scattering coefficient ($\mu _s^{\prime}$), therefore providing much more accurate measurements of concentration. However, this information provided by the radio frequency (RF) modulation of the light amplitude results in increased cost and complexity of the hardware involved. Since its inception, FD-DOS instrumentation has seen tremendous advancement in its accuracy, speed, and usability. Many unique designs have been described in the literature detailing ways to reduce cost, increase measurement speed, improve ease of use in the clinic, and increase the accuracy of recovered optical properties. A more detailed overview of FD-DOS instrumentation, principles, and methods may be found in Refs. [2,11]. Early implementations of heterodyne systems typically used benchtop signal generators to create the unique frequencies required and lock-in amplifiers to provide accurate measurement of amplitude and phase [12]. Though beneficial due to their ease of use and configurability, these units are bulky and often provide more functionality than is necessary, which results in a higher than necessary development cost. Since then, more purpose-built and compact designs have been introduced. Roblyer et al. investigated the use of direct-digital synthesis for versatile software controllable signal generation as well as, high-speed analog-to-digital converters to directly sample the detected RF signal [13]. Later, Zimmerman et al. expanded this approach to include phase-locked loop (PLL) based signal generation and efficient, field programmable gate array based frequency decoding [14]. No et al. designed and tested a highly compact and low-cost, custom miniature frequency domain system that performed high speed multi-frequency measurements removing the need for expensive network analyzers [10]. However, the complexity of these systems is such that they are more suited towards commercial development, as novices in electronics may find building the system troublesome. In this paper we propose a novel design that reduces system cost and complexity, while also providing excellent control for the user.

As related areas of industry and research spur the creation of integrated circuits for applications such as laser imaging, detection, and ranging (LIDAR), optical telecommunications and radio, we are inadvertently provided with tailor-made solutions to the issues often created when using analog circuitry. An example being the use of direct-digital synthesis for clock signal generation which provides greater flexibility than the more traditionally used connectorized crystal-oscillator modules. In this work, we propose another method for generating FD-DOS clock signals using two phase-locked frequency generator integrated-circuits that provide a low-cost, low-component count, and highly versatile method for source signal generation that can be mounted directly on an Arduino Uno (Arduino LLC, Turin, Italy). We also implement laser modulation using integrated circuits that remove the need for combining direct current (DC) and high-frequency alternating current (AC) signals through a bias-tee, which can make it difficult to quickly change laser intensity output without greatly compromising the modulation depth. Finally, we have incorporated the compact and versatile OpenSiPM design, which provides high sensitivity by using a silicon-photomultiplier (SiPM) as the detector. This system, as presented, provides a low-cost, easily expandable blueprint to build an FD-DOS system that provides programmable source output intensity, clock frequencies, and detector gain, that can be constructed using basic lab equipment with little knowledge of electronics, for under $\$$600 when using a single source-detector configuration.

2. Methods and materials

2.1 System overview

A typical heterodyne FD-DOS system consists of a signal generator, capable of generating frequencies somewhere in the 50MHz-1 GHz range, laser diode light sources, high-speed photodetectors, frequency mixers for demodulation, and an analog to digital converter to record signals. In our system, we have made multiple modifications to the traditional heterodyne system architecture including source generation, laser diode driving, choice of detectors, and reference signal generation. A block diagram showing the components of the new design and how they are interconnected is provided in Fig. 1(a) along with the layout of a more traditional heterodyne system, shown in Fig. 1(b) that was made by referencing designs found in [11,12].

 

Fig. 1. Block diagram of (a) the novel heterodyne FD-DOS system and (b) a more traditional heterodyne system adapted from [11,12]. LO: Local Oscillator, IF: Intermediate Frequency, Ref: Reference, LD: Laser Diode, PD: Photodiode, DAQ: Data Acquisition, CV: Control Voltage, D: Demodulator, LPF: Low pass filter, BPF: Band pass filter, Amp: Amplifier.

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In this newly designed system, we have made several changes from traditional setups. Firstly, driving of the laser diodes avoids use of bias-tees and instead uses a fully integrated circuit that also provides control of laser output intensity. Secondly, we use the integrated photodiode inside the laser diode package as our reference signal, providing an excellent phase-locked reference that also gives access to source output amplitude data. Thirdly, we have adopted the OpenSiPM design for a low-cost and highly sensitive detector. Lastly, we implement all signal generation using low-cost, digital, clock signal generators. The design is intended to be modular and increase the amount of control the user has over different aspects of the system. For instance, gain of the optical detector, frequency generation, and laser diode output amplitude is all controllable over USB. In doing so, aspects of the system such as issues of saturation or low signal to noise ratio (SNR) at short or long source-detector separations, can be adapted to more easily.

2.2 Signal generation

Historically, heterodyne systems have been constructed using two phase-locked benchtop signal generators, or expensive network analyzers. In this setup, generation of the two RF waveforms needed is achieved using two Si5351A (Skyworks inc., Irvine, CA) integrated circuits (IC). For ease of use, we have designed the printed circuit board (PCB) that generates these RF signals as a shield that is mounted on an Arduino Uno [Fig. 2(a)]. This allows all frequency generation control to be performed in software with the Arduino integrated development environment using established libraries [15]. These ICs can be programmed to output a complementary metal-oxide semiconductor (CMOS) digital output signal at any frequency from 8kHz to 200 MHz and require few additional components to be operated [16]. Each IC is capable of outputting a unique frequency. However, when generating frequencies with a small offset, crosstalk may become apparent in the output signals at a low level. This crosstalk can be reduced by using two Si5351A locked to the same crystal oscillator. This is easily achieved by providing the crystal oscillator reference to one Si5351A, then enabling the oscillator fanout option to create a copy of the oscillator output on one of this Si5351A’s outputs. This output is then fed into the clock input of the second Si5351A [Fig. 2(b)]. The currently used PCB provides 2 unique frequency outputs. In its current configuration these are 130.000 MHz and 130.001 MHz. A frequency of 130 MHz was chosen as a balance between when the laser diode driver began to display decreased modulation depth and when high order harmonics from the square wave modulation became visible in the laser diode output. However, with improved filtering the system should be usable down to 50 MHz or lower. If necessary, additional copies of these signals can easily be acquired through either the use of a fanout buffer or the signal can be amplified and then fed through a power splitter. As the Si5351A provides direct-current (DC) offset digital outputs, two of these are alternating-current (AC) coupled for use as the local oscillator (LO) reference of the demodulators. The 3^rd output is DC coupled for use with the laser diode driver (See Fig. 1(a)).

 

Fig. 2. (a) Arduino (bottom, teal PCB) with shield using dual Si5351A clock generators (top, green PCB) and (b) a block diagram showing the key components of the signal generator shield and how they interconnect. I2C: Inter-Integrated Circuit, Clk: Clock

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The shield plugs directly into an Arduino Uno and uses the native inter-integrated circuit (I2C) lines to provide real time software control over the frequency generation. A single pole double throw switch is used to control each Si5351A independently as they share the same I2C address and the native Arduino 5 V logic is translated to 3 V logic before being sent through the switch. Power can be supplied either via the USB connected to the Arduino, or separately through a low noise supply if desired.

2.3 Laser diode driver

Traditionally, FD-DOS has used bias-tee configurations to modulate laser diodes at the desired frequency, typically between 50 MHz to 1 GHz. Bias-tees enable the combination of DC currents with AC waveforms. While this method can provide excellent results, it can also introduce greater complexity into the design and result in poor efficiency and control. Most RF signal generators are designed to work with 50$\mathrm{\Omega }$ systems while a typical laser diode used for FD-DOS may have an active impedance of only a few ohms. This results in a large impedance mismatch. The simplest method to improve the mismatch is to insert a series resistor, on the order of 47$\mathrm{\Omega }$s close to the laser diode. However, in doing so only a fraction of the power supplied to the load is dissipated in the laser diode. By utilizing a dedicated IC capable of directly modulating the laser diode based on an RF control signal, we can significantly improve the efficiency of the laser diode modulation and provide greater control.

Figure 3 shows the laser diode driver circuit which uses the iC-HK (iC-Haus, Germany). The DC-coupled output from the signal generator board provides the control signal. This control signal is used internally by the IC to switch the current to the laser diode on and off creating the required RF amplitude modulated laser output. To suppress harmonics that may be present in the laser diode output, the IC is driven at 130 MHz. This puts any unwanted harmonics well outside the bandwidth of the iC-HK (DC - 155 MHz), providing a relatively pure sinusoidal modulation. Lower frequencies can be used but will increase the frequency content at harmonics outside of the operating frequency band. However, decreasing the frequency will also result in an increased response from the SiPM detector.

 

Fig. 3. (a) The front and (b) the back of the laser diode driver providing amplitude control and monitoring of the laser diode output signal. (1) Laser-photodiode package, (2) iC-HK, (3) Power & control, (4) Modulation signal input. (c) is a block diagram showing the laser diode control and use of integrated photodiode for use as the reference arm. Amp. Cont.: Amplitude Control, LD Enable: LD CMOS logic modulation signal.

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The iC-HK drives the laser diode at defined low and high current levels based on resistor configurations. In our design we have set these resistors to provide the greatest modulation depth, defined as $MD = ({{V_{peak - to - peak}}/2} )/mean({{V_{peak - to - peak}}} )$, where V is voltage. However, these levels can be easily modified if desired. The laser diode output amplitude can also be easily varied by changing the DC voltage applied to a control input. Increasing this voltage increases the laser diode amplitude output and vice versa (to be shown in Fig. 6). This means that the laser diode output can be easily controlled via software. If desired, the output level can even be swept in real time to increase the dynamic range of the system considerably.

Traditionally, the reference arm of a heterodyne system is a phase locked copy of the system intermediate frequency (IF) frequency. As the 785 nm laser diode (DL-7140-201S, Sanyo, Osaka, Japan) is driven in constant current mode, the integrated photodiode in the package is available for monitoring. In our design this photodiode signal is used as the reference arm for phase measurement in the system. The output is sent through a low pass filter (RLP-137, Mini-Circuits, New York, NY) over coaxial cable to an RF amplifier based on a PGA-103+ (Mini-Circuits) before being demodulated to 1kHz with a mixer and measured with the analog to digital converter (ADC). Not only does this ensure the reference signal is phase locked to the laser diode source, but it also enables measurement of the source amplitude. This can be used to correct for any drift in power output caused by the laser diode and to compare relative source levels if the power output is varied by altering the DC control level.

2.4 Detector

The detector used in this system is a silicon photomultiplier (SiPM) Model S14420-3025 MG (Hamamatsu, Bridgewater, NJ). SiPMs were first investigated for use in FD-DOS systems by Kitsmiller et al. [17,18]. Their work established the SiPM as a promising component capable of detecting the low signals associated with FD-DOS while also investigating methods of expanding their sometimes limited dynamic range. SiPMs show great promise as replacements for photomultiplier tubes (PMTs). Being made up of thousands of individual single-photon avalanche diodes in parallel, SiPMs are able to provide high levels of gain (${\sim} {10^6}$) while operating at much lower voltages (∼50 V). They are resistant to damage caused by exposure to high light intensity, and can be obtained for only a fraction of the cost of a PMT. The design used in this work is taken directly from the OpenSiPM project available on Github [19] which has been thoroughly discussed and validated by Ching-Roa et al. [20]. This design provides the necessary control over bias voltage for the SiPM as well as conditioning of the output signal. The design is compact, fitting in a standard SM1 tube system (Thorlabs, Newton, NJ) and is controllable via USB-C connection. SiPMs provide excellent sensitivity through their high gain and are therefore well suited to the low signals requiring measurement at long source-detector separations. This high gain enables their use, even when operating well outside their relatively low 3 dB bandwidth. This bandwidth is significantly improved through the application of current-domain pole-zero cancellation as described in [20]. Briefly, this method allows separation of a large “slow” or low frequency component from the SiPM output signal. This component arises due to operation of SiPMs which generate their high gain output by summing together the pulses generated by many parallelized avalanche photodiodes, each of which makes up a single SiPM “pixel”. After being triggered by a photon, the recharging of an individual pixel’s junction capacitance through its respective quenching resistor results in a large slow component at the output. It should be noted that the OpenSiPM module was designed for use in microscopy, and as such it was designed for a lower bandwidth requirement. Additional tuning of the pole-zero compensation circuit and/or moving to a higher gain bandwidth-product operational amplifier would significantly improve the 3 dB bandwidth.

2.5 Demodulation and acquisition

As the RF modulated light signals are well outside the bandwidth of the low-cost DAQ used (USB-6009, National Instruments, Austin, TX), they must be demodulated before quantization of the signal with the onboard ADC as shown in Fig. 1(a). The demodulator used is the ADE-1LH from Mini-Circuits (New York, NY). This demodulator is relatively low-cost at less than $\$$10, while providing good isolation between ports, and high compression points. To suppress any out of band noise, a simple first order, passive, low pass filter is placed on the PCB at the output of the mixer to improve data quality before being acquired by the DAQ. This DAQ not only provides measurement of the laser diode amplitude and the detected light amplitude and phase, but also is used to supply the laser diodes DC control voltage. In all cases the DAQ samples signals at 21kHz for a period of 100 ms.

2.6 Component testing

To ensure the instrument works as designed, we have performed a series of validation experiments. These consist of network analyzer characterization of the detector, fast photodiode reference measurements, dynamic range measurements, optical property recovery of liquid phantoms, and long-term stability measurements. From the results of these measurements, we can conclude the instrument can provide accurate measurements of optical properties across a wide range of values with excellent long-term stability.

Dynamic range measurements were performed by coupling the laser diode source through optical fibers to two, series connected attenuators (VOAMMF, Thorlabs). The output from these attenuators is connected to a 90:10 fiber splitter (TM200R2F1A, Thorlabs). The 90% branch of this goes to an optical power meter (818-SL, Newport, Irvine, CA), while the 10% branch goes to the detector branch of the system. This setup allows us to sweep the power on the detector while recording proportional changes in power using the power meter. It should be noted that the power incident upon the power meter is not equal to exactly nine times the power falling on the SiPM detector. This is because the SiPM was overfilled, as such we are only providing a measure of the dynamic range of the system and not the minimum optical power sensitivity. The detector was overfilled to ensure an accurate measure of the system’s maximum achievable dynamic range in its current configuration. Any amount of underfilling would negatively affect this measurement by ignoring available microcells of the SiPM. Therefore, by overfilling the SiPM detector we avoid any underestimation of the system dynamic range, and by normalizing the measured values from the SiPM detector we cancel out any imbalances from the optical splitter. To emphasize this, we have normalized the data from the power meter to the maximum recorded intensity value. Using MATLAB (MathWorks, MA, USA) the amplitude and phase of the detected light are calculated using the Hilbert transform ($\cal{H}$) as,

SiPMs provide excellent sensitivity but at the cost of limited bandwidth. However, the high gain of the detector means that even with losses from operating well outside the 3 dB bandwidth the SiPM still provides a high SNR signal. To observe the frequency response and to ensure the SiPM had been correctly built, we performed a measurement with a network analyzer (8712ET, Agilent, Santa Clara, CA, USA) based system and compared the results with the original publication describing the OpenSiPM modules specifications. This network analyzer was used to modulate a laser diode through a bias-tee using 201 evenly spaced frequencies between 5 MHz and 300 MHz with the laser diode was attenuated to a point corresponding to the midpoint of the detector’s dynamic range to ensure good SNR without saturation, and the output was connected to a network analyzer. The measured frequency response was then normalized to the maximum response.

To test the ability of the laser diode to maintain good modulation depth across a range of output intensity control voltages, we performed measurements using a silicon photodiode detector (DET02-AFC, Thorlabs) terminated with $50\mathrm{\Omega }$ in a 200 MHz oscilloscope. The use of this detector and the oscilloscope ensures that the measurement is unaffected by components of the system other than the laser driver. With the laser diode set at a fixed distance from the photodiode, the laser diode driver control voltage was varied. At each discrete control voltage, we calculated the modulation depth.

2.7 Validation using tissue mimicking phantoms

To test the ability of the system to accurately recover optical properties, we performed a series of liquid tissue phantom experiments. Liquid phantoms were constructed from a mixture of nigrosine ink to provide absorption, Intralipid 20% (Fresenius, Germany) to provide scattering, and water. In each of these experiments the laser diode and SiPM are protected with a layer of Saran Wrap and placed directly in contact with the liquid phantom surface. In the first set of measurements, 5 liquid phantoms were constructed with a constant reduced scattering coefficient of $10c{m^{ - 1}}$ and absorption coefficients ranging from $0.05c{m^{ - 1}}$ to in steps of $0.025c{m^{ - 1}}$. In the second set of phantom measurements the absorption was fixed at $0.1c{m^{ - 1}}$, while the reduced scattering coefficient was varied from $8c{m^{ - 1}}$ to $12c{m^{ - 1}}$ in steps of $1c{m^{ - 1}}$. In each experiment, a single phantom was used to provide a reference measurement to calibrate the amplitude and phase measurements of all other liquid phantoms. For both the absorption and the reduced scattering titrations the reference phantom had values of ${\mu _a} = 0.1c{m^{ - 1}}$ and $\mu _s^{\prime} = 10c{m^{ - 1}}$. All measurements were repeated a total of 5 times and each time the source and detector were completely removed from the phantom then replaced on the surface. In doing so, we ensure the effect of system placement on the phantom does not influence the accuracy of the results. All measurements used a source-detector separation of 3 cm with each data point representing the mean of the 5 measurements while the error bars correspond to ${\pm} $ the standard deviation.

Measurement stability was assessed by placing the source and detector directly in contact with a solid tissue mimicking phantom constructed from silicone, titanium dioxide for scattering, and nigrosine ink for absorption. The phantom had optical properties of ${\mu _a} = 0.06c{m^{ - 1}}$ and $\mu _s^{\prime} = 7c{m^{ - 1}}$ and the source and detector were separated by 3 cm. Data was collected at a sampling frequency of 21kHz, every other second for a continuous period of two hours and from this data we calculate the phase and amplitude.

2.8 Correction of SiPM amplitude nearing saturation

SiPM detectors offer the high gain necessary for making accurate measurements of phase and amplitude in turbid media, however at higher photon rates the SiPM output exhibits nonlinearities. Though not an issue in every scenario, when performing measurements with large, expected differences in optical properties or when varying source-detector separation distance this may cause errors in the recovered optical properties. To improve the measured linearity of the detector output we calibrated our measured data using the data collected in our dynamic range measurement. To perform this calibration, we fit a line to the lower, more linear part of the system dynamic range curve and a high order polynomial to the measured dynamic range data. Then the ratio between the ideal fitted line and the fitted dynamic range data is taken. This ratio tells us the correction that is needed as the SiPM deviates from linearity and begins to go into saturation.

3. Results

The dynamic range measurements showing the number of decades of changing light intensity (x-axis) that the detection branch of the system will be able to respond linearly to (y-axis) is shown in Fig. 4. In this figure, the power meter reading (x-axis) is normalized to the maximum value as the exact power incident on the SiPM is not known and only the relative change in power is, due to the fact that the fill factors were not measured. As the bias voltage applied to the SiPM is increased (e.g., from 45 V to 49 V), we are able to shift the minimum detectable signal to lower levels while the dynamic range remains the same, as is expected. The SiPM displays the expected nonlinear response at higher optical powers however, the linear range is still sufficient for use with a large range of optical properties. To ensure measurements are taken in this linear range, the gain of the SiPM and the amplitude of the laser diode source can be varied. Dynamic range is not currently limited by the SiPM detector at the lower end but due to a combination of the ADC used and the lack of additional amplification after demodulation of the detected signal. Incorporating a higher resolution and lower full scale voltage ADC, as well as additional amplification of the intermediate frequency output should significantly improve this range. The quantization noise encountered gives the data a staircase function appearance and is visible in Fig. 4 before the SiPM output voltage flattens out at low optical powers.

 

Fig. 4. (a) Experimental setup for dynamic range measurement. (b) Dynamic range measurement with various levels of bias voltage for the SiPM. In (b) the power meter reading was normalized to the maximum value to illustrate this is only a measure of dynamic range and not the minimum and maximum optical powers the system can detect before either insufficient SNR or detector saturation occurs.

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The frequency response of the SiPM module is shown in Fig. 5. The results agree with the original publication [20] which demonstrated a 3 dB bandwidth of 60 MHz. As previously mentioned, this bandwidth can be significantly increased by additional tuning of the pole-zero compensation and/or choosing an op amp with a greater gain bandwidth-product. The data illustrates how the SiPM operates well outside this bandwidth at our operating frequency of 130 MHz. However, due to the incredibly high SiPM gain of almost ${10^6}$, even if our response is decreased by 30 dB at 130 MHz the remaining gain is still much higher than that achievable with a typical avalanche photodiode. This enables us to obtain high signal to noise measurements at relatively long source-detector separations.

 

Fig. 5. Normalized frequency response of OpenSiPM from 5 MHz to 300 MHz showing good agreement with the original publication [20].

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Measurement of the laser diode driver’s ability to control the laser diode output amplitude is shown in Fig. 6. This measurement was taken by coupling the laser diode output, modulated at 130 MHz, directly to a high-speed silicon photodiode (DET02-AFC, Thorlabs, Newton, NJ), which was then terminated with $50\mathrm{\Omega }$ on a 200 MHz bandwidth oscilloscope. This was done to ensure characterization of the true laser diode output and not how it is affected by the smaller bandwidth of the SiPM or other components in the system. As the 12-bit analog output of the USB-6009 varies the control voltage from 1.3 to 1.6 V, the laser diode output power increases by more than 5 times. At higher control voltages the modulation depth decreases, but never drops below 70%, illustrating the ability of the circuit to tailor laser diode output to measurement requirements while not requiring modification to supplied DC or AC signals as would be the case in a bias-tee based system.

 

Fig. 6. Laser diode amplitude control measurements. The output at each specified control voltage (CV) was captured with a fast silicon photodiode using an oscilloscope and then the modulation depth (MD) calculated.

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Results of the liquid phantom experiments are shown in Fig. 7. The FD-DOS system is able to accurately recover both variations in absorption, as well as the reduced scattering coefficient. Every data point on the plot was acquired from 100 ms worth of data at a 3 cm source-detector separation with the ADC sampling at a rate of 21kHz. Ultimately, our system was able to recover all optical properties with good accuracy and repeatability with an average error of <4% for both scattering and absorption coefficients. The largest error occurs in the recovery of the reduced scattering coefficient. These are overestimated below the reference measurement level and overestimated above the reference measurement level. The fit to varying absorption shows excellent agreement between the fitted and expected values. In the experiment varying $\mu _s^{\prime}$, all measured values of ${\mu _a}$ were recovered to within 5% of their true value. In the experiment varying absorption the largest error, which occurs at the phantom with ${\mu _a} = 0.15 c{m^{ - 1}}$ is less than 4%. The exact reason for the system’s more accurate recovery of ${\mu _a}$ as opposed to $\mu _s^{\prime}$ is currently unknown. It is possible that the noise in the phase measurement is much greater than that of the amplitude measurement, or that the error is due to the dynamic range of the system in its current state. Future studies and improvements of the system will attempt to elucidate and address this imbalance.

 

Fig. 7. Liquid phantom measurements. (a) displays the results of the absorption variation experiment, (b) shows the results of the reduced scattering coefficient variation experiment.

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The measurement stability data is shown in Fig. 8. In this experiment, the laser diode and SiPM detector were both placed in direct contact with a silicone tissue-mimicking phantom while data was collected continuously, every other second, for two hours. After first turning the system on, we allowed it to warm up for 25 minutes. This time is needed for the SiPM to reach operating temperature which is required for a stable output as variations in temperature result in changes in gain. The distance between the source and detector was 3 cm. Every data point is plotted and two red lines on each plot indicate ${\pm} 2\%$ of the mean value. For amplitude data 99.9% of data falls in this range while for phase data 93.1% of data is within the range indicating minimal long-term drift that may otherwise negatively affect measurements.

 

Fig. 8. Instrument stability measurements. (a) The amplitude and (b) the phase, as recorded over the 2-hour continuous data collection period on a solid silicone phantom.

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In Fig. 9 we show the process for calibrating the SiPM to obtain a more linear response in amplitude as it enters saturation. Figure 9(a) shows the ideal line that was used to correct the measured amplitude. The ratio of the ideal line and the polynomial fitted to the measured dynamic range of the detection branch of the system is applied to the measurements to help correct for the effects of decreased output amplitude. The purpose of fitting a polynomial to the measured data is to reduce experimental noise and variations in the recovered correction factor. Figure 9(b) shows the improved recovery of optical properties after it was applied to the experiment in which ${\mu _a}$ was varied while holding $\mu _s^{\prime}$ constant. The error in recovered optical properties has been reduced, most notably, for phantom #1 which has the lowest values of absorption and scattering which will result in the highest light intensity on the SiPM. To emphasize the improvement due to calibration we calculated the root mean squared error (RMSE) as, $RMSE = \sqrt {\sum {{({{\mu_i}_{measured} - {\mu_i}_{expected}} )}^2}/N} $, where $\mu $ is the optical property in question (either $\mu _s^{\prime}$ or ${\mu _a})$ and N is the number of measurements. This was calculated for both the calibrated and uncalibrated optical property datasets. Prior to calibration the RMSE for ${\mu _a}$ was $2.93\ast {10^{ - 3}}\; c{m^{ - 1}}$ and after calibration it was reduced to $2.24\ast {10^{ - 3}}\; c{m^{ - 1}}$. For $\mu _s^{\prime}$, the RMSE before calibration was $0.29\; c{m^{ - 1}}$ and after calibration it was reduced to $0.18\; c{m^{ - 1}}$.

 

Fig. 9. SiPM calibration method. (a) is the fitted SiPM dynamic range data (orange) and the ideal linear response (black). (b) is the ratio between the ideal linear response and fitted data which will be the calibration factor. (c) shows the optical properties recovered from the original ${\mu _a}$ variation experiment with no calibration. (d) is the corrected optical property recovery using the recovered calibration factor.

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4. Discussion

We have detailed the design and characterization of a low-cost, heterodyne FD-DOS instrument. This instrument incorporates advancements from related fields to improve laser diode driving, signal generation, and light detection. All components were tested individually and as a whole system to illustrate their ability to make accurate measurements of absorption and scattering in tissue-mimicking phantoms. The system affords the user improved software-based control of system features such as detector gain, operating frequency, and laser diode output amplitude. With this improved control, it also reduces system cost and complexity enabling users with little expertise in electronics to build the system.

Dynamic range of this system, while more limited than some systems is sufficient for many applications. In the case where one is performing measurements at long and short source-detector separations, such as when attempting to separate the effects of superficial and deep tissue contributions, smaller dynamic range may prove problematic as collected intensity can vary significantly. However, the increase in the level of control over the system means the saturation point of the detector can be avoided by decreasing the source amplitude or decreasing the SiPM gain, and low SNR signals can be improved by increasing the source amplitude or the SiPM gain if operating near the maximum permissible light intensity. All of this may be done in real time during measurements. Additional increases to the system dynamic range can be achieved by either acquiring a higher resolution and lower full scale voltage ADC or additional amplification of the IF signal prior to measurement by the ADC. Ultimately, although the dynamic range is small relative to many other systems, it is sufficient for measurements on a wide range of optical properties as shown in Fig. 7. In future experiments we will allow the output amplitude of the source to vary and investigate how this can enable extension of the dynamic range and also investigate alternative SiPMs that can provide larger dynamic range.

Frequency response of the OpenSiPM detector is presented in Fig. 5. The data was collected on a 1.3 GHz network analyzer in the frequency range of 5 MHz – 300 MHz. This result provides confirmation that the SiPM is operating correctly. It also illustrates how the high gain of the SiPM compensates for operation well outside the 3 dB bandwidth of the detector. In the future, improvements to this design can be made by incorporating a faster operational amplifier and modified tuning of the current-domain pole-zero cancellation circuit. This will lead to improved SNR as well as allow operation at higher frequencies with lower loss.

Most FD-DOS systems to date have used bias-tee configurations to modulate laser diodes at the relatively high frequencies required. While this does provide a setup with better frequency response, it often comes at the cost of decreased control, and decreased efficiency. Through the use of an integrated high speed laser diode driver we decrease cost and are able to provide high modulation depth signals with greater control. Increases in efficiency occur as the RF signal input into the driver is not used to modulate the laser diodes directly, but instead is used as a control signal to switch the laser diodes on and off. This removes the need for amplification of RF signals to a high level prior to injection into a bias-tee. The circuitry involved is simple, relying on few additional components and can therefore be made quite compact. The version tested in this work was constructed on a 1-inch diameter printed circuit board for use in an SM1 tube system (Thorlabs), similar to the OpenSiPM module. In the future, the higher speed iC-HG laser diode driver from iC-Haus could be used to drive multiple laser diodes at once and increase the operating frequency of the system.

Two experiments used optical phantoms to establish the ability of the system to accurately recover absorption and reduced scattering coefficients. As there was only a single source detector separation used in these experiments a single measurement from each was used as a calibration reference. The results display the ability of the system to recover a wide range of biologically relevant optical properties with good accuracy and repeatability. The accuracy of the system being <5% on average for the recovery of all optical properties is comparable with many other published systems, although direct comparisons of accuracy are made difficult by differences in experimental setups [17,21]. All measurements were performed at a single frequency and source power. The recovered optical properties could theoretically be improved by performing additional measurements at various frequencies by simply programming the signal generator to do so. However, this additional data would likely come at the cost of greater acquisition time than the currently employed 100 ms.

The stability of the system was determined by performing continuous data acquisition at a source-detector separation of 3 cm on a tissue-mimicking silicone phantom. Each datapoint recovered is plotted in Fig. 8(a) and 8(b). The red lines in each plot, indicating ${\pm} 2\%$ of the mean value, contain nearly every datapoint recovered during the two hours of continuous monitoring. For the recovered amplitude data 99.9% of datapoints fell within ${\pm} 2\%$ of the mean value and for phase data 93.1% fell within this range. This level of drift makes it comparable with other published results although variations in experimental setups make direct comparisons difficult [14,18]. This high level of stability illustrates the low drift that occurs even when measurements are performed with considerable amounts of time between them. It is important to note that 20 minutes of data from the beginning was discarded as it was during the system warm up period. This period of time is necessary to allow the SiPM signal output to stabilize as temperature variations can cause significant changes in the SiPMs overvoltage, and therefore, its gain. In the future, SiPMs with built-in thermoelectric coolers, such as the S14422-3025DG, will be used to further improve thermal stability and decrease dark noise.

Lastly, we have demonstrated a simple method to improve the linear response of the SiPM module. The method only requires dynamic range measurements at the desired gain, which is easy to obtain. From this data we are able to recover the ideal measured amplitude should the SiPM not go into saturation. As the important information captured in this calibration is simply how the SiPM output tails off as it approaches saturation, it should only need to be measured once as long as the same gain is used, the fill condition on the detector active area is kept constant, and temperature remains relatively constant. In fact, the dynamic range data used to recover the correction factor applied to the phantom measurements shown in this paper was taken weeks after the phantom experiment it was applied to. Using this method, we reprocessed the phantom experiment in which absorption was varied while the reduced scattering coefficient was held constant. The improved results reduce the error in optical properties as shown by the reduction of the root mean square error as described in the results section. The most notable improvement being the phantom with the lowest scattering and absorption which corresponds to where the SiPM is closest to saturation.

Table 1. Approximate pricing for each system module at the time of construction not including laser diode, cables, and wiring for interconnection of modules.

View Table

Ultimately, this paper has described a low-cost and highly flexible method for development of an FD-DOS instrument. Table 1 shows the approximate price for each of the system modules at the time of construction. Almost half of the total cost comes from the digital acquisition (DAQ) device used. Therefore, the addition of another laser driver (excluding laser diode), demodulator, and detector to the system adds only ∼$\$$160 if one is to expand the current system to two wavelengths and two detectors. This low-cost per channel combined with the compact nature of the components is highly advantageous for the development of high-density diffuse optical tomography (DOT) systems. Specifically, in the case of DOT covering the whole head, this system design would drastically decrease total cost, overall system size, and likely decrease power supply requirements that currently make high-density DOT systems difficult to realize. In the future, additional upgrades to the system will be undertaken to improve challenges of scaling to high-density DOT imaging. Ideally, these would include an improved DAQ with a greater number of analog input and outputs. The DAQ module currently used can handle a maximum of eight analog inputs which would limit the number of detector channels that may be added. The exact number of channels that could be used with this system depends on the number of reference signals and whether differential or single-ended inputs are used. For example, if two source wavelengths are used, a maximum of six detector channels can be added. If the number of detectors required is significantly greater, either a different DAQ should be employed or additional DAQs may be added into the design. Other improvements would include laser drivers that accommodate multiple wavelengths, and modification of the SiPM power supplies to be able to drive multiple detectors.

5. Conclusion

In this work, we have presented a novel method for constructing a low-cost heterodyne FD-DOS system. The system utilizes novel methods for signal generation, driving of laser diodes, and detection. We have exhibited its ability to accurately recover optical properties, its high level of controllability, and its excellent stability. The system can easily be expanded for use with additional source and detector channels, enabling its use in clinical applications. All while maintaining a low-cost at less than $\$$600 for a single source-detector pair system as well as complexity that can decrease the level of knowledge needed to construct the system. In the future, an expanded version of this system would prove useful to be applied in the realm of high-density DOT due to its compact source and detector modules, increased level of control, and its low-cost per channel count.