Patent Publication Number: US-2021161389-A1

Title: Frequency domain diffuse optical spectroscopy device and optical detector calibration method

Description:
RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application No. 62/653,364, entitled “HANDHELD DIFFUSE OPTICAL SPECTROSCOPY DEVICE FOR BREAST CANCER RISK ASSESSMENT AND DIFFERENTIAL DIAGNOSIS,” filed Apr. 5, 2018, the entire contents of which is incorporated herein by reference. 
    
    
     BACKGROUND 
     Frequency domain diffuse optical spectroscopy (FD-DOS) is a non-invasive optical imaging technique for characterizing biological tissue. Current FD-DOS designs use Avalanche photodiodes (APDs) or photomultiplier tubes (PMTs) as optical detectors. However, supplying the high voltage bias needed for both APDs and PMTs requires the use of high-voltage modules with large footprints, which limits their practical use in portable FD-DOS systems. In addition, current FD-DOS designs are limited to scan the range of optical powers in which the optical detector has a linear response, which limits their dynamic range. 
     SUMMARY 
     A silicon photomultiplier (SiPM) provides equal or better performance in FD-DOS applications than an APD or a PMT, but operates at a lower voltage bias that can be supplied by a high-voltage module with a smaller footprint. Thus, the disclosure provides a frequency domain diffuse optical spectroscopy (FD-DOS) device that includes, in one embodiment, a radio frequency signal generator, a driver, a light source, a silicon photomultiplier, an analog to digital conversion circuit, and an electronic processing circuit. The driver is coupled to the radio frequency signal generator. The light source is coupled to the driver and is configured to generate modulated light at a plurality of different wavelengths and a plurality of different modulation frequencies. The light source is for emitting the modulated light at a sample. The silicon photomultiplier is configured to detect analog signals indicative of amplitude and phase of radio frequency modulation components of detected optical signals emanating from the sample in response to the modulated light. The analog to digital conversion circuit is coupled to the silicon photomultiplier and is configured to generate digital sample values from the analog detection signals. The electronic processing circuit is coupled to the analog to digital conversion circuit and is configured to determine absorption values and scattering values based on the digital sample values. The electronic processing circuit is also configured to determine concentration values based on the absorption values and the scattering values. The electronic processing circuit is further configured to determine an image stream based on the concentration values. 
     The disclosure also provides a method for calibrating an optical detector in a diffuse optical spectroscopy device. The method includes measuring a first sample with the optical detector to determine a measured power response. The method also includes determining an inverse response based on the measured power response and a predetermined power response of the first sample. The method further includes measuring a second sample with the optical detector to determine a first frequency response. The method also includes adjusting the first frequency response based on the inverse response to determine a second frequency response. The method further includes determining a third frequency response based on predetermined absorption and scattering coefficients of the second sample. The method further includes determining a plurality of correction factors based on the second frequency response and the third frequency response. 
     Other aspects of the invention will become apparent by consideration of the detailed description and accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram of a frequency domain diffuse optical spectroscopy (FD-DOS) device, in accordance with some embodiments. 
         FIG. 2  is a diagram of a radio frequency signal generator, a driver, and a light source included in the FD-DOS device of  FIG. 1 , in accordance with some embodiments. 
         FIG. 3A  are examples of oxy-hemoglobin (ctHb) images of breast tissue. 
         FIG. 3B  is an example of a handheld housing for an FD-DOS device, in accordance with some embodiments. 
         FIG. 3C  is a diagram of an FD-DOS system, in accordance with some embodiments. 
         FIG. 4A  is a graph that represents example signal to noise ratios of an avalanche photo diode and a silicon photomultiplier. 
         FIG. 4B  is a graph that represents example normalized frequency responses of an avalanche photo diode and a silicon photomultiplier. 
         FIG. 5  is a flowchart of a method for calibrating an optical detector, in accordance with some embodiments. 
         FIG. 6A  is a graph that represents an example of a measured power response of a continuously variable intensity filter. 
         FIG. 6B  is a graph that represents an example of a predetermined power response of a continuously variable intensity filter. 
         FIG. 6C  is a graph that represents examples of a measured and an adjusted frequency response of a known and controlled phantom. 
         FIG. 6D  is a graph that represents examples of an adjusted and a model frequency response of a known and controlled phantom, in accordance with some embodiments. 
         FIG. 7  is a flowchart of a method for calibrating a measured frequency response of an optical detector, in accordance with some embodiments. 
         FIG. 8A  is a graph that represents examples of a measured and an adjusted frequency response of an unknown phantom. 
         FIG. 8B  is a graph that represents examples of an adjusted and a corrected frequency response of an unknown phantom, in accordance with some embodiments. 
         FIG. 9  is a flowchart of a process for imaging a sample with frequency domain diffuse optical spectroscopy, in accordance with some embodiments. 
         FIG. 10  is a flowchart of a process for determining image data based on optical signals detected by an optical detector, in accordance with some embodiments. 
         FIG. 11A  is a graph of an example amplitude linearity from a noise floor to −1.5 dBM. 
         FIG. 11B  is a graph of an example optical property recovery of a digital DOS system and a reference system. 
         FIG. 12A  is a graph of an example Bland-Altman comparison of absorption coefficients recovered with a silicon photomultiplier and an avalanche photodiode. 
         FIG. 12B  is a graph of an example Bland-Altman comparison of scattering coefficients recovered with a silicon photomultiplier and an avalanche photodiode. 
         FIG. 13A  is a graph of example drift in recovered absorption coefficients over an hour long period on a single tissue simulating phantom at four wavelengths with a silicon photomultiplier. 
         FIG. 13B  is a graph of example drift in recovered scattering coefficients over an hour long period on a single tissue simulating phantom at four wavelengths with a silicon photomultiplier. 
         FIG. 14A  is a graph of example absorption optical property recoveries on a tissue-simulating phantom at a wavelength of 659 nanometers for multiple source/detector separations for a silicon photomultiplier and an avalanche photodiode. 
         FIG. 14B  is a graph of example reduced scattering optical property recoveries on a tissue-simulating phantom at a wavelength of 659 nanometers for multiple source/detector separations for a silicon photomultiplier and an avalanche photodiode. 
         FIG. 14C  is a graph of example signal to noise ratios as a function of source/detector separation for a silicon photomultiplier and an avalanche photodiode at three different frequencies. 
         FIG. 14D  is a graph of example signal to noise ratios as a function of frequency for a silicon photomultiplier and an avalanche photodiode at a 28 millimeter source/detector separation. 
     
    
    
     DETAILED DESCRIPTION 
     Frequency domain diffuse optical spectroscopy (FD-DOS) is a non-invasive optical imaging technique for characterizing biological tissue. FD-DOS exploits a region of the electromagnetic spectrum with relatively low absorption ranging from about 650 nanometers to 1,350 nanometers and achieves depth sensitivities up to several centimeters. The strongest molecular absorbers in this wavelength range, known as chromophores, are oxyhemoglobin, deoxyhemoglobin, water, and lipid. One advantage of FD-DOS compared to continuous-wave near infrared spectroscopy is the ability to directly measure tissue optical scattering, and thus provide a quantitative measurement of chromophore concentrations that can be compared longitudinally and between individuals. This functional information extracted from deep (up to three centimeter) tissue volumes has shown promise in areas including monitoring chemotherapy treatments of breast cancer, optical mammography, and brain imaging. For example, in breast oncology, FD-DOS is able to distinguish benign and malignant lesions by measuring concentrations of deoxy/Oxy-hemoglobin (Hb, HHb), water, and lipid levels. FD-DOS is also effective in quantifying breast density, which is critical considering women with dense breast tissue are four to six times more likely to develop breast cancer. An additional application of FD-DOS in breast oncology is monitoring response to neoadjuvant chemotherapy. 
     FD-DOS samples tissue volumes with radio frequency (RF)-modulated light (about 50 megahertz to 500 megahertz). Highly attenuated light, due to optical absorption and scattering, is detected at a fixed distance from the source in a reflection or transmission geometry with an optical detector. The overall sensitivity of an FD-DOS system is typically limited by the sensitivity and dynamic range of its optical detector. If the sensitivity and dynamic range of the optical detector in an FD-DOS system is increased, it enables detection of wider optical property ranges and increased source-detector (S/D) separations for higher depth sensitivity. 
     Some current FD-DOS designs use avalanche photodiodes (APDs) as optical detectors because of their small size and built-in amplification. APDs have an intrinsic gain of about 100× and low dark currents, leading to excellent signal-to-noise ratios (SNRs). APDs, however, require about 200 volts to 500 volts of reverse bias in order to achieve this gain. Other current FD-DOS designs use photomultiplier tubes (PMTs) as optical detectors because they have extremely high intrinsic gains of about 10 4 × to 10 9 × and low dark currents. PMTs, however, require a larger footprint size, are sensitive to magnetic fields, and require a high bias voltage (about 1 kilovolt). In both cases (APDs and PMTs), supplying a high-voltage bias requires high-voltage converters with large footprints (greater than 7 cubic centimeters), limiting their suitability for portable FD-DOS systems. 
     Some embodiments of the systems and methods described herein utilize silicon photomultipliers (SiPMs) (also known as multipixel photon counters, MPPCs) as an optical detector for FD-DOS. SiPMs are composed of many small microcells operating in single-photon counting mode known as single-photon avalanche diodes (SPADs), which are organized into larger arrays of about 500 to 58,000 microcells. The array is biased above breakdown voltage so that the optical detector operates in Geiger mode. SiPMs have similar high intrinsic gain (about 10 5 × to 10 7 ×), dark current, and signal-to-noise ratio as PMTs while operating at a much lower reverse bias (about 20 volts to 50 volts). This allows for high-voltage modules with extremely small footprints (about 0.1 cubic centimeters), which is advantageous for designing compact and portable FD-DOS systems. Further, SiPMs have about 10 to 30 decibels greater signal to noise ratios than comparably sized APDs while detecting about 1.5 to 2 orders of magnitude lower light levels, down to about 4 picowatts at 50 megahertz modulation. The greater signal to noise ratios of SiPMs as compared to APDs enables extended source-detector (S/D) separations and increased depth penetration. For example, SiPMs can accurately recover optical properties in a reflectance geometry at S/D separations up to 48 millimeters in phantoms mimicking human breast tissue. SiPMs can operate with optical wavelengths up to about 1,100 nanometers. 
       FIG. 1  illustrates an example embodiment of an FD-DOS device  100  with an SiPM. In  FIG. 1 , the FD-DOS device  100  directs modulated light at tissue  105 , and processes a detected optical signal that results from absorption and scattering of the modulated light by the tissue  105 . The FD-DOS device  100  illustrated in  FIG. 1  includes a radio frequency signal generator  110 , a driver  115 , a light source  120 , a silicon photomultiplier  125 , an analog to digital conversion circuit  130 , an electronic processing circuit  135 , a battery module  140 , orientation sensors  145 , and a communication module  150 . In some embodiments, the FD-DOS device  100  includes more or less components than the ones illustrated in  FIG. 1 . For example, in some embodiments, the FD-DOS device  100  may not include the battery module  140 , the orientation sensors  145 , and/or the communication module  150 . 
     The radio frequency signal generator  110  is coupled to the driver  115 , which drives the light source  120  for exposing the tissue  105  to modulated light at a plurality of different wavelengths and a plurality of different modulation frequencies. The silicon photomultiplier  125  detects optical signals emanating (for example, reflecting) from within the tissue  105  in response to the modulated light. The silicon photomultiplier  125  generates analog detection signals indicative of amplitude and phase of radio frequency modulation components of the detected optical signals. The analog to digital conversion circuit  130  is coupled to the silicon photomultiplier  125  and generates digital sample values from the analog detection signals. 
     In some embodiments, the light source  120  includes a plurality of lasers to generate modulated light to illuminate the tissue  105 . A radio frequency source and a direct current (DC) source are used together to drive the plurality of lasers to generate modulated light.  FIG. 2  illustrates an example embodiment in which the light source  120  includes four laser diodes  205 A through  205 D. Each of the four laser diodes  205 A through  205 D is configured to emit a distinct wavelength of light. For example, in some embodiments, the wavelengths of the four laser diodes  205 A through  205 D are 681 nanometers, 783 nanometers, 823 nanometers, and 850 nanometers, respectively. 
     The radio frequency signal generator  110  illustrated in  FIG. 2  acts as a radio frequency source and includes a direct digital synthesizer (DDS)  210  and an amplification circuit  215 . The DDS  210  is a current controlled device that outputs radio frequency modulation signals. In some embodiments, the DDS  210  communicates with the electronic processing circuit  135  (for example, via a serial peripheral interface link or another appropriate communication link) to select the output current and frequency. An example of the DDS  210  is the AD9912 DDS by Analog Devices, which generates an output current ranging from zero and 31.7 milliamps and a frequency ranging from zero and 450 megahertz. The maximum output power of the AD9912 DDS into a 50 ohm load is 7 decibal-milliwatts at 50 megahertz. The power output also may decrease with increasing output frequency. In some implementations, the plurality of laser diodes  205 A through  205 D need about 10 to 20 decibal-milliwatts of output power. Thus, in some embodiments, the amplification circuit  215  amplifies the output signal from the DDS  210 . Alternatively, or in addition, the radio frequency signal generator  110  is configured to increase the power of the radio frequency modulation signals as a function of frequency. For example, the amplification circuit  215  may increase power of the radio frequency modulation signals generated by the DDS  210  as the frequency increases, for example, to account for additional signal loss at higher frequencies. 
     The driver  115  includes a plurality of DC bias drivers that act as DC sources for the laser. In  FIG. 2 , the driver  115  includes four DC bias drivers  220 A through  220 D. Each of the four DC bias drivers  220 A through  220 D is configured to provide a DC signal for a corresponding one of the four laser diodes  205 A through  205 D. An example of the DC bias driver is the MLD230CHB laser driver by Thorlabs, which delivers up to 200 milliamps with a 3 volt compliance voltage. The MLD230CHB laser driver exhibits excellent stability with 12 microamp average root mean square current resulting in microwatt laser power stability. 
     The driver  115  also includes a radio frequency switch  225  to route the radio frequency modulation signal from the radio frequency signal generator  110  to each of the four laser diodes  205 A through  205 D. In some embodiments, the radio frequency switch  225  includes a plurality of cascade connected single pole, double throw switches that each route signals from one input to two output paths. Alternatively, the radio frequency switch  225  includes one or more multiport switches (or single pole, multiple throw switches) that each route signals from one input to three or more output paths. The driver  115  illustrated in  FIG. 2  also includes four bias tees  230 A through  230 D to isolate the radio frequency modulation signals from the radio frequency signal generator  110  and the DC signals from the four DC bias drivers  220 A through  220 D. 
     Returning to  FIG. 1 , the silicon photomultiplier  125  (also known as a multi-pixel photon counter) detects optical signals emanating from the tissue  105  in response to the modulated light generated by the light source  120 . The silicon photomultiplier  125  generates analog detection signals indicative of amplitude and phase of radio frequency modulation components of the detected optical signals. Unlike APDs which require additional amplification and high bias voltages, the silicon photomultiplier  125  does not require additional amplification and a much lower bias voltage which translates into a significant size reduction. As the bias voltage for the silicon photomultiplier  125  is low, an ultra-compact high voltage module can be used. An example high-voltage module is the C14156 high-voltage module by Hamamatsu Photonics, which has a footprint of 7×7×2 millimeters and is capable of providing up to 80 volts (2 milliamps) with only 1 millivolt peak-to-peak ripple. 
     The analog to digital conversion circuit  130  is coupled to the silicon photomultiplier  125  and includes an analog to digital converter (ADC) for sampling the analog detection signals generated by the silicon photomultiplier  125 . The analog to digital converter generates digital sample values from the analog detection signals (for example, via resistive termination). The analog to digital converter is also AC coupled to the radio frequency signal generator  110  to receive and sample the RF modulation signals generated by the radio frequency signal generator  110 . The analog to digital converter generates digital reference values from the radio frequency modulation signals. An example of the analog to digital converter is the AD9613 by Analog Devices, which is a 12 bit 250 MHz dual channel low voltage differential signal (LVDS) device with a 1.8 volt peak to peak input capability. The AD9613 has a dynamic range of about 70 decibels. In some embodiments, the analog to digital conversion circuit  130  is configured to under-sample the analog detection signals. Although the ADC sampling rate can be well below the Nyquist sampling frequency for the maximum system frequency (i.e., about 400 megahertz), the small bandwidth of the input signal allows the analog to digital conversion circuit  130  to meet the Nyquist-Shannon sampling criterion. 
     The electronic processing circuit  135  illustrated in  FIG. 1  includes a field programmable gate array (FPGA)  155  and memory  160 . The memory  160  is coupled to the FPGA  155 . The memory  160  includes read only memory (ROM), random access memory (RAM), an electrically erasable programmable read-only memory (EEPROM), other non-transitory computer-readable media, or any combination thereof. The FPGA  155  is configured to retrieve program instructions and data from the memory  160  and execute, among other things, instructions to perform the methods described herein. Alternatively of in addition, the memory  160  is included in the FPGA  155 . The FPGA  155  includes routines for transferring information between components within the electronic processing circuit  135  and other components of the FD-DOS device  100 . In some embodiments, in addition to (or in place of) the FPGA  155 , the electronic processing circuit  135  includes an electronic processor (for example, a microprocessor). 
     The electronic processing circuit  135  is coupled to the analog to digital conversion circuit  130  and receives digital sample values and digital references values from the analog to digital conversion circuit  130 . The electronic processing circuit  135  is configured to determine absorption values and scattering values based on the digital sample values. In some embodiments, in order to readily obtain amplitude and phase responses at each of the RF modulation frequencies, the FD-DOS device  100  obtains a large number of digital sample values for each set of RF modulation frequencies, and the electronic processing circuit  135  processes each set of digital sample values into a frequency domain representation using a Fourier transform. In some embodiments, the electronic processing circuit  135  uses a full fast Fourier transform (FFT) to determine the amplitude and phase responses from the digital sample values. Alternatively or in addition, the electronic processing circuit  135  uses a Goertzel algorithm to determine the amplitude and phase responses from the digital sample values faster than with a full FFT. 
     The electronic processing circuit  135  is also configured to determine concentration values (for example, chromophore concentrations) based on the absorption values and the scattering values. For example, the electronic processing circuit  135  determines chromophore concentration by using the Beer-Lambert law in combination with absorption values and predetermined molar extinction coefficients. The electronic processing circuit  135  is also configured to determine an image stream based on the concentration values. For example, the electronic processing circuit  135  uses the concentration values to build bi-cubic interpolated images.  FIG. 3A  are examples of oxy-hemoglobin (ctHb) images for breast tissue. The ctHb image on the left side of  FIG. 3A  is of cancerous tissue with an identifiable tumor. The ctHb image on the right side of  FIG. 3A  is of a healthy contralateral breast. In some embodiments, the electronic processing circuit  135  is configured to generate an image stream with a frame rate that is greater than thirty hertz (i.e., a real-time image stream). In some embodiments, the electronic processing circuit  135  is configured to capture data, process the data, and display the data in real-time. 
     In the embodiment illustrated in  FIG. 1 , the FD-DOS device  100  is powered by the battery module  140 . The battery module  140  includes one or more batteries or battery packs. In some such embodiments, the components of the FD-DOS device  100  (for example, the radio frequency signal generator  110 , the driver  115 , the light source  120 , the silicon photomultiplier  125 , the analog to digital conversion circuit  130 , the electronic processing circuit  135 , and the battery module  140 ) are mounted in a housing that is sized to be handheld.  FIG. 3B  is an example embodiment of a handheld housing for the FD-DOS device  100 . The dimensions of the handheld housing illustrated in  FIG. 3A  are 3 inches by 4.5 inches by 1 inch. Alternatively, or in addition, the FD-DOS device  100  is powered by mains power having nominal line voltages between, for example, 100 volts and 240 volts AC and frequencies of approximately 50 hertz to 60 hertz. 
     The orientation sensors  145  are configured to generate orientation signals indicative of the orientation and/or position of the FD-DOS device  100 . The orientation sensors  145  include gyroscopes, accelerometers, magnetometers, optical tracking sensors, or a combination thereof. In some embodiments, the electronic processing circuit  135  is also configured to correlate the orientation signals to the image stream. 
     The communication module  150  sends and/or receives signals to and/or from one or more separate communication modules. Signals include, for example, information, data, serial data, data packets, concentration values, image streams, and orientation signals. The communication module  150  is coupled to one or more separate communication modules via wires, fiber, and/or wirelessly. Communication via wires and/or fiber can be any appropriate network topology known to those skilled in the art (for example, Ethernet). Wireless communication can be any appropriate wireless network topology known to those skilled in the art (for example, Wi-Fi and Bluetooth™). 
       FIG. 3C  illustrates an example embodiment of an FD-DOS system  300 . The FD-DOS system  300  illustrated in  FIG. 3C  includes the FD-DOS device  100  and a display device  305 . The display device  305  is configured to receive and display the image stream. The display device  305  includes, for example, a mobile phone, a tablet, a laptop, a desktop, or a server. The display device  305  communicates with the FD-DOS device  100  via wires, fiber, and/or wirelessly. 
     Table 1 illustrates a comparison of physical and electrical characteristics between the SensL MicroRB-10020 by ON Semiconductor (an example of a “SiPM”) and the S12060-10 by Hamamatsu (an example of an “APD”). 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 COMPARISON OF SIPM AND APD 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Photo- 
                   
                   
                   
                   
                   
                 Excess 
               
               
                 Optical 
                 sensitive 
                 Operating 
                 PDE at 
                 PDE at 
                   
                 Dark 
                 Noise 
               
               
                 Detector 
                 Area 
                 Voltage 
                 650 nm 
                 850 nm 
                 Gain 
                 Current 
                 Factor 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 SiPM 
                 0.63 
                 mm 2   
                 33 
                 volts 
                 27% 
                 12.5% 
                 1.5e6 
                 831 
                 nA 
                 1.19 
               
               
                 APD 
                 0.785 
                 mm 2   
                 250 
                 volts 
                 85% 
                     60% 
                 100 
                 10 
                 nA 
                 3.98 
               
               
                   
               
            
           
         
       
     
       FIG. 4A  is a graph of example signal to noise ratios (SNRs) of an APD and a SiPM as a function of input at a radio frequency modulation frequency of 50 megahertz. The signal to noise ratios illustrated in  FIG. 4A  were obtained by biasing a 660 nanometer edge-emitting laser diode with a direct current (DC) from a laser driver and radio frequency power from a vector network analyzer (VNA). The modulated light was collimated, passed through a variable optical density filter wheel, and fiber-coupled to the optical detector. The graph in  FIG. 4A  characterizes the signal to noise ratios of the S12060-10 and the SensL MicroRB-10020 listed above in Table 1 at a 50 megahertz radio frequency modulation frequency. No pre-amplification module was used and each type of optical detector was connected directly to a 50 ohm input of the VNA. As illustrated in  FIG. 4A , the signal to noise ratio of the SiPM is about 10 decibels to 30 decibels greater than the signal to noise ratio of the APD at 50 megahertz and depends upon the incident optical power. As also illustrated in  FIG. 4A , the SiPM&#39;s signal to noise ratio advantage increases with lower input powers and reaches zero at about 1.5 to 2 orders of magnitude lower input power than the APD. Further, the SiPM&#39;s photo response is non-linear. 
     The bandwidths of each type of optical detector was measured by recording optical detector radio frequency output amplitude as a function of frequency with the VNA.  FIG. 4B  shows an example of each type of optical detector&#39;s normalized (to the maximum signal) frequency response. Normalization is helpful because the same absolute optical power cannot be used simultaneously for both types of optical detectors across the entire frequency range. At low attenuations, the current limit of the SiPM&#39;s power supply is reached (about 2 milliamps), while the APD is not sensitive at the higher attenuations. From  FIG. 4B , it is observed that the APD has a better normalized frequency response than the SiPM. For example, the normalized frequency response of the SiPM in  FIG. 4B  decays at about 10 decibels at 500 megahertz. 
     In FD-DOS, diffuse RF-modulated light reaching the optical detector after propagation through tissue lags in phase and is diminished in amplitude. This phase lag and amplitude reduction is related to the optical properties of the sample via the radiative transport equation (RTE). A P1 semi-infinite approximation to the RTE can be used to fit the measured phase and amplitude and estimate the sample&#39;s optical properties. The fitting can be done, for example, using a Levenberg-Marquardt least squares minimization algorithm. 
     To more accurately fit the measured data, the amplitude reduction and phase lag should be attributed to the sample, and not the instrumentation (for example, frequency response/attenuation of the RF cables and electronic components). Current calibration methods require that the optical detector has a linear response with optical power. Current FD-DOS systems compensate for the linear response requirements of current calibration methods by limiting the range of frequencies scanned during a frequency sweep. For example, current FD-DOS system that use APDs limit the range of the optical powers scanned during a frequency sweep to optical powers in which the APDs have a linear response. Limiting the range of optical powers scanned during a frequency sweep limits the dynamic range of the optical detector. Further, since the amplitude response of a SiPM is non-linear, a more intricate calibration is needed. 
       FIG. 5  is an example of a method  500  for calibrating an optical detector (such as a SiPM) in a DOS device (such as FD-DOS  100 ). The method  500  enables any non-linear optical detector to be used in FD-DOS, so long as the response does not change. At block  505 , a filter (for example, a continuously variable intensity filter) (an example of a “first sample”) is measured with the optical detector to determine a measured power response. For example, the optical response of a variably attenuating filter is measured with a calibrated optical detector to determine the measured power response.  FIG. 6A  is an example of a measured power response of a continuously variable intensity filter. At block  510 , an inverse response is determined based on the measured power response and a predetermined power response of the filter. The inverse response represents the power response of attenuated signals through the filter. In some embodiments, the inverse response is determined by fitting the measured power response to the predetermined power response of the filter (using, for example, a polynomial fit).  FIG. 6B  is an example of a predetermined power response. At block  515 , a known and controlled phantom (an example of a “second sample”) is measured with the optical detector to determine a measured frequency response (an example of a “first frequency response”). At block  520 , the measured frequency response is adjusted based on the inverse response to determine an adjusted frequency (an example of a “second frequency response”). In some embodiments, only the relative amplitude dependence on frequency is corrected to eliminate nonlinearity measured at block  510 .  FIG. 6C  includes examples of a measured and an adjusted frequency response of a known and controlled phantom as a function of swept frequencies. At block  525 , a model frequency response (an example of a “third frequency response”) is determined based on predetermined absorption and scattering coefficients of the known and controller phantom.  FIG. 6D  includes examples of an adjusted and a model frequency response of a known and controlled phantom. The model frequency response in  FIG. 6D  is generated using a photon transport model based on predetermined phantom absorption and scattering coefficients. In some embodiments, the absolute amplitude and phase response is adjusted, for example, to account for power attenuations and phase delays in the system. At block  530 , a plurality of correction factors are determined based on the adjusted frequency response and the model frequency response. The plurality of correction factors represent corrections for non-linear amplitude changes at different signal levels. In some embodiments, the plurality of correction factors are determined by comparing the adjusted frequency response and the model frequency response. In some embodiments, a correction factor is determined for each wavelength in a frequency sweep. For example, if a frequency sweep includes 100 frequencies, 200 correction factors are determined (i.e., 100 correction factors for amplitude and 100 correction factors for phase). In some embodiments, the frequency responses described herein with respect to the method  500  illustrated in  FIG. 5  include amplitude data, phase data, or both. In some embodiments, the method  500  can be used for calibrating FD-DOS systems that include APDs or a PMTs as the optical detector. 
     With the inverse function and the plurality of correction factors, the FD-DOS device  100  calibrates measured frequency responses to account for non-linear amplitude changes at different signals levels.  FIG. 7  is an example of a method  700  for calibrating a measured frequency response of an optical detector (such as the SiPM) in a DOS device to account for non-linear amplitude changes at different signals levels. The method  700  can be an extension to method  500  to confirm the accuracy of the calibration. In addition, the method  700  can be used by the electronic processing circuit  135  for real-time calibration. At block  705 , an unknown phantom (for example, a tissue sample) (an example of a “third sample”) is measured with the optical detector to determine a measured frequency response (an example of a “fourth frequency response”). At block  710 , the measured frequency response is adjusted based on the inverse response to determine an adjusted frequency response (an example of a “fifth frequency response”).  FIG. 8A  includes examples of a measured and an adjusted frequency response of an unknown phantom. At block  715 , the adjusted frequency response is adjusted based on the plurality of correction factors to determine a corrected frequency response (an example of a “sixth frequency response”).  FIG. 8B  includes examples of an adjusted and a corrected frequency response of an unknown phantom. In some embodiments, the method  700  can be used for calibrating FD-DOS systems that include APDs or a PMTs as the optical detector. 
       FIG. 9  is an example of a process  900  for imaging a sample with FD-DOS. For ease of description, the process  900  is described below in relation to the FD-DOS system  300  illustrated in  FIG. 3 . At block  905 , the process  900  is started via user input. For example, a user initiates the process  900  by providing user input to the display device  305 . At block  910 , the imaging region is selected. For example, a user paints an image using the FD-DOS device  100 , in any direction, displayed in real-time on the display device  305  and tracked via the orientation sensors  145 . At block  915 , the FD-DOS device  100  emits modulated light at the sample (for example, at tissue  105 ). In some embodiments, the FD-DOS device  100  performs a frequency sweep in the 10 hertz to 400 megahertz range (with a user defined step size) and modulates each of the four laser diodes  205 A through  205 D in sequential order. At block  920 , the FD-DOS device  100  detects optical signals emanating from the sample in response to the emitted modulated light. In some embodiments, up to 65,556 samples are captured per frequency per wavelength. In some embodiments, the optical detector collects scattered light, which is captured at 250 megahertz by a dual channel analog to digital converter. In some embodiments, modulation frequencies above 125 megahertz are aliased (due to a 250 megahertz ADC capture rate), however since all modulation frequencies are known, aliased frequencies in overlapping Nyquist zones are removed. At block  925 , the FD-DOS device  100  determines image data based on the detected optical signals. An example of a process for determining the image data based on the detected optical signals is described below in relation to  FIG. 10 . At block  930 , the FD-DOS device  100  correlates orientation data from the orientation sensors  145  with the image data. At block  935 , the FD-DOS device transmits the image data (for example, to the display device  305 ). In some embodiments, the FD-DOS device  100  transmits chromophore values and orientation data to the display device  305  at about 5 to 10 megabits per second (i.e., via Bluetooth™) or at about 50 megabits per second (i.e., via Wi-Fi). At block  940 , the display device  305  displays the image data in real-time (for example, at a frame rate that is greater than 30 hertz). 
       FIG. 10  is an example of a process  1000  for determining image data based on optical signals detected by an optical detector. For ease of description, the process  1000  is described below as being performed by the FPGA  155  of the FD-DOS device  100  illustrated in  FIG. 1 . At block  1005 , the FPGA  155  captures digital sample data for the detected optical signals. At block  1010 , the FPGA  155  performs a Fourier transform (for example, a single frequency discrete Fourier transform (DFT), a full fast Fourier transform (FFT) and/or a Goertzel algorithm) on the digital sample data to determine measured amplitudes. At block  1015 , the FPGA  155  transforms the measured amplitudes based on a responsivity curve of the optical sensor. At block  1020 , the FPGA  155  transforms the measured amplitudes into input amplitudes based on a responsivity curve of the diode. At block  1025 , the FPGA  155  determines calibration coefficients based on calibration phantom measurements. For example, in some embodiments, prior to process  1000 , a calibration measurement on a phantom with known optical properties is taken using, for example, method  500  and transferred to a memory in the FPGA  155 . In some embodiments, the FPGA  155  determines the calibration coefficients in about 3 to 8 clock cycles. At block  1030 , the FPGA  155  determines corrected phase data and amplitude data based on calibrated measured data. At block  1035 , the FPGA  155  loads a forward modeled lookup table in a memory. For example, the FPGA  155  loads a forward modeled lookup table into a fast searchable hardware RAM included in the FPGA  155  or in the memory  160 . At block  1040 , the FPGA  155  determines calibrated scattering data and absorption data from the forward modeled lookup table. At block  1045 , the FPGA  155  determines chromophore concentrations (for example, deoxy/Oxy-hemoglobin (Hb, HHb), water, and lipid concentrations) based on the calibrated scattering data, the calibrated absorption data, and predetermined molar extinction coefficients. At block  1050 , the FPGA  155  determines a bi-cubic interpolated image based on the chromophore concentrations. In some embodiments, the FPGA  155  performs the process  1000  in less than one second. In some embodiments, each subsequent scan uses the calibration data to correct amplitude and phase accounting for system dependent response. In some embodiments, during sample capture, the residuals of measured phase and amplitude are determined in parallel in order to find the optical properties associated with the lowest residuals. 
     Instrument validation can be performed by comparing a reference system to a custom all-digital based DOS system. For example, validation can be performed by: 1) assessing signal to noise, linearity, and dynamic range to optical signals, and 2) comparing recovered optical properties of tissue-simulating phantoms. As illustrated in  FIG. 11A , the digital system response is within 3% of the reference system with a similar noise floor of −72 dBm. In one example, optical properties measured with the digital system were within 12% for absorption and 7% for scattering as compared to the reference, as illustrated in  FIG. 11B . 
     The optical properties of different silicone-based tissue simulating phantoms can be separately measured using the SiPM and the APD described above in Table 1. For example, the radiofrequency outputs of the photodetectors can be directly connected to an FD-DOS module which contains excitation wavelengths of 659 nanometers, 687 nanometers, 786 nanometers, and 829 nanometers. The SiPM can be biased at 33 volts for a gain of 1.5e6 and used without any form of amplification. On the other hand, the APD can be incorporated into a pre-amplification module (for example, a C5658 module with S12060-10 APD from Hamamatsu Photonics) and be biased for an intrinsic APD gain of 100. The APD module adds about another 40 decibels (RF power gain), for a total system gain of 10,000. Both photodetector can be placed directly on the phantom surface, requiring no fiber coupling. The optical property recoveries at a fixed source/detector separation of 28 millimeters can be compared in Bland-Altman format. For example,  FIGS. 12A and 12B  are graphs of an example Bland-Altman comparison of absorption coefficients and reduced scattering coefficients recovered with the SiPM and the APD for three different phantoms. The x&#39;s in  FIGS. 12A and 12B  represent data for a first phantom excited with a wavelength of 659 nanometers. The triangles in  FIGS. 12A and 12B  represent data for the first phantom excited with a wavelength of 687 nanometers. The filled diamonds in  FIGS. 12A and 12B  represent data for the first phantom excited with a wavelength of 786 nanometers. The filled squares in  FIGS. 12A and 12B  represent data for the first phantom excited with a wavelength of 829 nanometers. The filled circles in  FIGS. 12A and 12B  represent data for a second phantom excited with a wavelength of 659 nanometers. The non-filled squares in  FIGS. 12A and 12B  represent data for the second phantom excited with a wavelength of 687 nanometers. The non-filled circles in  FIGS. 12A and 12B  represent data for the second phantom excited with a wavelength of 786 nanometers. The filled triangles in  FIGS. 12A and 12B  represent data for the second phantom excited with a wavelength of 829 nanometers. The x|&#39;s in  FIGS. 12A and 12B  represent data for a third phantom excited with a wavelength of 659 nanometers. The plus signs in  FIGS. 12A and 12B  represent data for the third phantom excited with a wavelength of 687 nanometers. The minus signs in  FIGS. 12A and 12B  represent data for the third phantom excited with a wavelength of 786 nanometers. The diamonds in  FIGS. 12A and 12B  represent data for the third phantom excited with a wavelength of 829 nanometers. 
     The precision and stability of FD-DOS with an SiPM can be characterized by repeatedly measuring the optical properties of a tissue-simulating phantom a period of time. For example, the precision and stability of FD-DOS with an SiPM can be characterized by repeatedly measuring (every 15 seconds) the optical properties of a tissue-simulating phantom for one hour (see  FIGS. 13A and 13B ). As illustrated in  FIGS. 13A and 13B , a coefficient of variation is less than 1% in optical properties at all four wavelengths. The optical property recoveries illustrated in  FIGS. 13A and 13B  do show slowly varying drift, which is due to the temperature dependence of the SiPM gain. 
     The single-wavelength optical property recoveries of an SiPM-based system and an APD-based system can be compared on a silicon-based homogeneous tissue-simulating phantom while varying the source/detector separations. For example,  FIGS. 14A and 14B  are graphs of example absorption and reduced scattering optical property recoveries on a 50 millimeter thick silicone-based homogeneous tissue-simulating phantom at a wavelength of 659 nanometers with source/detectors separations of 28 millimeters, 35 millimeters, 42 millimeters, and 48 millimeters. As illustrated in  FIGS. 14A and 14B , the APD-based system recovers optical properties at 35 millimeters within 10% of the expected value at the shortest 28 millimeter source/detector separation. Also, as illustrated in  FIGS. 14A and 14B , the APD-based system optical property recoveries at longer source/detector separations diverge rapidly from the expected value with errors greatly exceeding 10%. As illustrated in  FIGS. 14A and 14B , the SiPM-based system recovers optical properties within 13% (10% for most optical properties) of the APD-based system&#39;s 28 millimeter source/detector values for all measured source/detector separations. Examples of the signal to noise ratio as a function of source/detector separation for both photodiodes on the phantom at excitation frequencies of 50 megahertz, 150 megahertz, and 250 megahertz are illustrated in  FIGS. 14C and 14D . As illustrated in  FIGS. 14C and 14D , the signal to noise ratio for the SiPM-based system is about 5 to 30 decibels higher than the APD-based system at all source/detector separations and at frequencies up to about 400 megahertz. 
     One or more embodiments are described and illustrated in the description and accompanying drawings. These embodiments are not limited to the specific details provided herein and may be modified in various ways. Furthermore, other embodiments may exist that are not described herein. Also, the functionality described herein as being performed by one component may be performed by multiple components in a distributed manner. Likewise, functionality performed by multiple components may be consolidated and performed by a single component. Similarly, a component described as performing particular functionality may also perform additional functionality not described herein. For example, a device or structure that is “configured” in a certain way is configured in at least that way, but may also be configured in ways that are not listed. Furthermore, some embodiments described herein may include one or more electronic processors configured to perform the described functionality by executing instructions stored in non-transitory, computer-readable medium. Similarly, embodiments described herein may be implemented as non-transitory, computer-readable medium storing instructions executable by one or more electronic processors to perform the described functionality. As used in the present application, “non-transitory computer-readable medium” comprises all computer-readable media but does not consist of a transitory, propagating signal. Accordingly, non-transitory computer-readable medium may include, for example, a hard disk, a CD-ROM, an optical storage device, a magnetic storage device, a ROM (Read Only Memory), a RAM (Random Access Memory), register memory, a processor cache, or any combination thereof. 
     In addition, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. For example, the use of “including,” “containing,” “comprising,” “having,” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. The terms “connected” and “coupled” are used broadly and encompass both direct and indirect connecting and coupling. Further, “connected” and “coupled” are not restricted to physical or mechanical connections or couplings and can include electrical connections or couplings, whether direct or indirect. In addition, electronic communications and notifications may be performed using wired connections, wireless connections, or a combination thereof and may be transmitted directly or through one or more intermediary devices over various types of networks, communication channels, and connections. Moreover, relational terms such as first and second, top and bottom, and the like may be used herein solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.