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We present a method to speed up the acquisition of multispectral photoacoustic data sets by using unipolar orthogonal Golay codes as excitation sequences for the irradiation system. Multispectral photoacoustic coded excitation (MS-PACE) allows acquiring photoacoustic data sets for two irradiation wavelengths simultaneously and separating them afterwards, thus improving the SNR or speeding up the measurement. We derive an analytical estimation of the SNR improvement using MS-PACE compared to time equivalent averaging. We demonstrate the feasibility of the method by successfully imaging a phantom composed of two dyes using unipolar orthogonal Golay codes as excitation sequence for two high power laser diodes operating at two different wavelengths. The experimental results show very good agreement with the theoretical predictions.
©2010 Optical Society of America
1. Introduction
The photoacoustic effect is based on the generation of acoustic waves in matter due to electro-magnetic irradiation. The effect has found many different bio-medical applications in recent years [1]. Methods like Photoacoustic Tomography (PAT) or Photoacoustic Microscopy (PAM) allow imaging the spatial distribution of optical absorption in biological tissue by irradiating tissue with laser pulses and receiving the generated ultrasound waves. For instance, PAT can be used to image the morphology of vasculature in vivo [2]. Since the optical absorption spectrum of tissue depends on underlying biological processes, measuring the photoacoustic response to multispectral laser irradiation provides additional functional information on the tissue under investigation. For example, blood changes its optical properties depending on the oxygen saturation of hemoglobin. This feature has already been exploited for photoacoustic imaging of cerebral blood oxygenation [3, 4]. Additionally, multispectral photoacoustic imaging allows to sensitively detect exogenous photoacoustic contrast agents, like nanoparticles [5–7] or fluorochromes [8].
Multispectral imaging modes require a consecutive irradiation of the object under investigation with different wavelengths and a consecutive acquisition of the ultrasonic responses to each irradiation. Consequently, the frame rate of multispectral photoacoustic imaging is reduced compared to monospectral procedures. We propose multispectral photoacoustic coded excitation (MS-PACE) as a remedy [9, 10]. This concept allows irradiating the object at two wavelengths simultaneously and separating the superimposed ultrasonic responses to both irradiation wavelengths after the data acquisition. The separation is achieved by employing unipolar orthogonal Golay codes (UOGC) as excitation sequences for two light sources and decoding the received ultrasonic responses. This concept is a multispectral extension of our previous work on photoacoustic coded excitation using unipolar Golay codes [9]. Our experimental realization is based on two high power pulsed laser diodes as multispectral irradiation source, whereas usually an Nd:YAG laser in combination with an optical parametric oscillator (OPO) is used for multispectral photoacoustic imaging. Pulsed laser diodes typically exhibit much lower pulse energy than OPO systems. However, due to their higher pulse repetition frequency (PRF), their low per pulse signal-to-noise ratio (SNR) can be increased by averaging [11, 12]. Laser diodes have already been successfully used for in vivo photoacoustic imaging [12].
Within the scope of this paper, first we present the concept of MS-PACE. As a next step, we derive an analytical estimation of the SNR improvement due to MS-PACE. Then, the experimental setup is described. Two high power pulsed laser diodes (irradiation wavelengths: 652nm and 808nm, respectively) are employed as excitation sources and a modified clinical ultrasound scanner is used for ultrasound data acquisition. A phantom composed of two dyes is used as multispectral absorber. Subsequently, we demonstrate the feasibility of MS-PACE imaging and compare the experimental results to the analytically derived SNR estimations.
2. Theory
2.1 Unipolar orthogonal Golay codes
In pulse-echo ultrasonic imaging, coded excitation is a well-known method to increase the SNR [13]. The basic idea is to transmit a coded signal distributing the pulse energy over time while keeping the signal bandwidth to achieve high resolution pulse-echo imaging. Correlating the received signal from a point scatterer with the code leads to a pulse-like correlation function, i.e. the distributed signal energy is again concentrated in a short time interval by correlation. However, correlation sidelobes occur before and behind the position of the point scatterer and limit the dynamic range of the resulting images. A solution to the problem of correlation sidelobes are Golay codes: they consist of a code pair with code A and B and two transmit/receive experiments lead to two signals with correlation sidelobes. By design, the mainlobes at the point scatterer position add up while the sidelobes of the A and B code cancel. For this reason, conventional Golay codes are widely used in medical ultrasound imaging [13]. These concepts can be transferred to photoacoustic imaging, as will be shown in this section.
Instead of using coded excitation, repeated experiments could be performed and averaged to increase the SNR. However, the maximum PRF of transmission is limited by the acoustic round-trip propagation time, i.e. the system has to wait for all echoes to return to the receiver limiting the average transmitted power. Consequently, starting from a certain depth, more energy per time unit can be emitted using coded excitation compared to a simple averaging procedure. This leads to a higher SNR gain per time unit. Additionally, orthogonal codes can be employed in order to emit two independent data sets simultaneously and to separate the received data afterwards.
Golay codes consist of two sequences commonly termed A and B with the code length N=2L, :
where , being the Kronecker delta, k being the discrete time, and T being a discrete-time delay. A characteristic of Golay codes is that the sum of the autocorrelation of sequence A and the autocorrelation of sequence B is zero for all time delays of the autocorrelations except for the zero time delay. This property of the Golay codes is called complementarity and can be expressed mathematically aswith * denoting the discrete-time convolution. These codes can be extended to orthogonal Golay codes, which satisfy the identities:The Golay code {A 1,B 1} is orthogonal to the Golay code {A 2, B 2}. This allows simultaneously emitting the sequences A 1 and A 2 as well as the sequences B 1 and B 2 and separating the responses to each sequence. In order to employ orthogonal Golay codes in photoacoustic imaging, the bipolar codes must be converted into unipolar sequences since it is not possible to emit negative light intensities. Consequently, the four sequences are split into eight sequences according to Eq. (4), with :These eight sequences constitute the unipolar orthogonal Golay code (UOGC). A similar concept was used for optical time domain reflectometry [14], employing monospectral unipolar Golay codes.2.2 Estimation of SNR improvement due to OUGC
The improvement of SNR due to multispectral coded excitation can be estimated based on the complementarity and orthogonality of the UOGC. These calculations rely on the following assumptions and definitions:
- • Two light sources repetitively emit short light pulses at the wavelengths λ 1 and λ 2, respectively. The minimum time interval between two light shots for repetitive irradiation is termed τL. It is equal for both light sources.
- • The maximum distance between the ultrasound transducer and the photoacoustic sources is given by za; the speed of sound of the surrounding medium is assumed as c 0 = 1490 m/s. The time interval between a light shot and the arrival of the latest photoacoustic signal at the ultrasound detector defines the acoustical time-of-flight τE. It is given by τE = za / c 0.
- • The measurement process of the photoacoustic response can be modeled as a linear system [15]. Consequently, the received responses of the whole experimental setup to light shots at the wavelengths λ 1 and λ 2 are modeled as discrete-time impulse responses hPA ,1 and hPA ,2, respectively.
Based on these assumptions, the concept of MS-PACE using UOGC is introduced by describing the timing diagram for the excitation of both light sources. In Fig. 1 , the coding process is exemplified for the code length N=4. Multiple codes exist for each length, exhibiting equivalent correlation properties. The two light sources irradiate the object under investigation simultaneously, however the sequences Ap,W, An,W, Bp,W, as well as Bn,W must be emitted consecutively. The time interval between two consecutive emissions within each sequence is determined by τL, i.e. by the maximum PRF of the light source. Between two sequences a waiting time τE is required in order to prevent range ambiguities. This leads to a total time
needed for sending the code.
Fig. 1 Timing diagram for the excitation of both light sources. The code length is set to N = 4 for this example.
The signal processing chain, which is necessary for coding and decoding, is displayed in Fig. 2 . It exemplifies the decoding process of the light source emitting at the wavelength λ 1, i.e. W = 1. The response to each coding sequence is modeled by a convolution of the sequence with the appropriate impulse response. We further assume that each of the four received responses is superimposed by stochastically independent, additive, white noise contributions n 1,…,n 4, each having a variance σ 2. Considering Eq. (3) the decoded signal y 1 for W = 1 is given by
with R being the noise induced error. An imperfect coding/decoding process induces additional errors. A potentially important source of error is the fluctuation of the laser pulse energy. This effect leads to a fluctuation of the amplitude during the emission of a coding sequence. Since this effect does not change the photoacoustic impulse response, the whole system still remains linear and time-invariant. If the coding and decoding sequences do not match perfectly, correlation sidelobes are induced and the amplitude of the main lobe is reduced. Consequently, a fluctuation of the laser pulse energy potentially leads to well known coding artifacts and reduces the SNR gain achieved by coding. This phenomenon will be further discussed in Section 4.The mean squared error (MSE) of the decoded signal for each light source is
with E being the mathematical expectation operator.The performance of the proposed coding procedure can be evaluated by comparing the MSE of MS-PACE using UOGC with the MSE of an averaging procedure, which takes the same amount of time as the coding procedure. Consequently, the number of possible acquisitions for averaging is
The maximum PRF for averaging must be lower than the inverse of the acoustic time-of-flight (τE) in order to prevent range ambiguities. Since data for two wavelengths are acquired in parallel using MS-PACE, the total number of acquisitions for averaging must be split evenly between the two wavelengths. Thus, the MSE of a time equivalent averaging procedure for one wavelength is given byBased on Eq. (7) and Eq. (9) the coding gain of UOGC can be defined as the reduction of the noise induced error in dBThe coding gain indicates the SNR gain due to coding compared to time equivalent averaging. If only one laser source is used for coding, i.e. only the code {A 1,B 1} is emitted, the coding gain is decreased by 3 dB [9] compared to MS-PACE using two laser sources. This means that the coding procedure becomes more advantageous compared to averaging for an increased number of wavelengths.2.3. Experimental setup
In order to validate the theoretical estimation of the coding gain and to show the feasibility of MS-PACE we employed the experimental setup displayed in Fig. 3 .
We used two different laser diodes as light sources. Diode 1 is a custom-made high power quasi-continuous laser diode bar, which emits light at a wavelength of 652 nm with a maximum optical power of 100 W at a maximum duty cycle of 2%. As Diode 2 we employ a laser diode bar, which emits light at a wavelength of 808 nm with a maximum optical power of 225 W at a maximum duty cycle of 10%. Current pulses lasting 30 ns drive both laser diodes. We used PRFs of 125 kHz, 250 kHz, and 500 kHz for the MS-PACE experiments. Under these conditions, Diode 1 and Diode 2 emit pulse energies of 1.53 µJ and 1.56 µJ, respectively. The laser diodes were operated well below their power limit due to limitations of the laser diode drivers. Both laser diodes were coupled into a glass fiber bundle and irradiated two dye phantoms placed in a water tank. Each dye phantom consisted of a PVC slab, which exhibits a centered cylindrical hole. The hole was sealed by optically and acoustically transparent polypropylene foils. It was filled with a dye via a drill hole. We used a phantom filled with a green dye (4001/301044, Pelikan AG, Schindellegi, Swiss) as the first absorbing target in the optical path. It primarily absorbs the light emitted by Diode 1 and transmits the light emitted by Diode 2. The second phantom was positioned approximately 1 cm behind the first phantom. It was filled with a black dye (4001/301218, Pelikan AG, Schindellegi, Swiss), which absorbs both wavelengths. Since the light emitted by Diode 1 is mostly absorbed by the first phantom, the ultrasound generated in the second phantom is primarily associated with the light emitted by Diode 2. An ultrasound transducer array (L14-5/38, Ultrasonix, Richmond, BC, Canada: 128 elements, −20 dB receive bandwidth: 1-14 MHz, array width of 38 mm, element spacing of 0.3 mm) was placed in the water tank, receiving the thermo-elastically generated ultrasound. The array was connected to a modified clinical ultrasound scanner (Sonix RP, Ultrasonix). It acquired single channel data synchronized with trigger 3 (cf. Fig. 3) during MS-PACE experiments. This trigger indicates the beginning of a coding sequence, whereas trigger 1 and trigger 2 indicate the emission of single light pulses within the coding sequence to the laser diode modules. Due to hardware restrictions of this particular ultrasound system, only data originating from one single element of the array were acquired for one trigger 3 event. Consequently, 128 emissions of the coding sequence were necessary for a complete data set comprising all channels. An alternative hardware implementation would allow parallel data acquisition. These data sets were transferred to a PC, decoded according to the signal processing scheme displayed in Fig. 2, reconstructed using a standard delay-and-sum beamforming algorithm, and demodulated for display purposes.
In order to verify the MS-PACE concept we also performed experiments without coded excitation. For these experiments, two separate data sets for both laser diodes were acquired. The PRF of the laser diodes was reduced to the inverse of the acoustical time-of-flight, which is determined by the distance between the ultrasound transducer and the farthest source of thermo-elastically generated ultrasound. Trigger 3 was synchronized with trigger 1 and trigger 2, respectively, for these experiments. Again, 128 acquisitions were need for one full frame. These data sets were reconstructed using the same delay-and-sum algorithm as used for the MS-PACE data sets.
3. Results
The feasibility of MS-PACE using UOGC was evaluated by imaging the phantoms described in Section 2.3 and by comparing the results to images obtained by time equivalent averaging. The results are displayed in Fig. 4 .
Fig. 4 Comparison of MS-PACE and time equivalent averaging for both excitation wavelengths. (a) photoacoustic image for averaging as many acquisitions as possible during the coding procedure for W=1, termed time-equivalent averaging. (b) photoacoustic image using MS-PACE for W=1. (c) photoacoustic image using time-equivalent averaging for W=2. (d) photoacoustic image using MS-PACE for W=2.
All images were normalized to their respective maximum and displayed in a dB-scale. The dynamic range for W=2 (cf. Fig. 4(c) and (d)) is 9 dB lower than the dynamic range for W=1 (cf. Fig. 4(a) and (b)) since the generated photoacoustic signal for W=2 is also lower. Fig. 4(b) shows the results of the decoding process using the code set {A 1,B 1}, Fig. 4(d) shows the results for {A 2,B 2}. One single area of high signal energy can be perceived in the images, indicating the position where the laser beam interacts with the dyes. As can be seen in Fig. 4(b) the maximum distance between the ultrasound transducer and a photoacoustic source za was 5 cm. For these exemplary MS-PACE experiments, a code length of 512 bit and a PRF of 500 kHz was employed. Consequently, the total time needed for sending the code was T UOGC=4.2 ms. During this time it is possible to acquire 126 waveforms for averaging without range ambiguities, i.e. 63 waveforms per wavelength. Based on these calculations, Fig. 4(a) and Fig. 4(c) show the results of 63-fold averaging for each wavelength. The averaging and MS-PACE images feature a similar spatial distribution of the photoacoustic signal.
Furthermore, we compared the noise characteristics of MS-PACE with the noise characteristics of time equivalent averaging. The noise floor of the averaging procedure is approx. 9 dB higher than the noise floor of the MS-PACE procedure for each wavelength. This value is in good agreement with the prediction of a coding gain of 9.12 dB (cf. Eq. (10)). Moreover, no crosstalk between the wavelengths or correlation sidelobes can be perceived in the photoacoustic images based on MS-PACE.
We evaluated additional experimental results by comparing them to the analytically derived coding gain for different parameter sets: we varied the code length from 24 bit to 29 bit and the PRF between 125 kHz and 500 kHz, as mentioned in Section 2.3. The maximum code length is limited by the maximum acquisition duration of the ultrasound system. Consequently, the maximum code length is shorter for a lower PRF. For each set of parameters, we computed four images similar to Fig. 4. Then, we calculated the SNR for all four cases as follows: we divided the mean signal energy within a region of interest (ROI) centered at the photoacoustically generated signal by the mean signal energy within a ROI containing solely noise. Additionally, the mean photoacoustic energy was normalized to the mean per pulse photoacoustic signal energy prior to decoding and beamforming in order to reduce the influence of light energy fluctuations and temperature effects.
The coding gain was computed for each wavelength by dividing the SNR of MS-PACE by the SNR of the time equivalent averaging procedure. The computation was performed for 50 independent data sets and the average results are displayed in Fig. 5 . For the highest PRF, the experimental values are consistently lower than the theoretical values, e.g. in average 0.63 dB for W=1. This could be explained by trigger jitter, which reduces the photoacoustic signal energy after the decoding process. Additionally, the electro-magnetic crosstalk induced by switching the laser diode drivers during the coding process potentially increases the noise for MS-PACE. For PRFs of 250 kHz and 125 kHz the experimental coding gain is sometimes higher than the theoretical coding gain. This could be attributed to light energy fluctuations or deterministic noise sources present during the averaging procedure. The total root mean squared difference between the experimental results and the theoretical results for all code lengths and all PRFs is 0.52 dB for W=1 and 0.62 dB for W=2. In general, a high PRF and a long code length increase the coding gain. Assuming a code length of 512 bit and a distance of the photoacoustic source to the ultrasound receiver of 5 cm, a minimum PRF of 59.71 kHz is theoretically needed for a positive coding gain.
Fig. 5 The coding gain for MS-PACE using UOGC is shown as a function of the code length and the PRF of the laser diodes. ‘T’ denotes the theoretical prediction based on Eq. (10), ‘E’ denotes the experimental results. The PRF of the laser diodes was varied between 125 kHz and 500 kHz for MS-PACE. The number of averages was adjusted for each parameter set according to Eq. (8). The maximum code length was limited by the maximum acquisition duration of the ultrasound system.
As next step, we varied the distance between the ultrasound receiver and the farthest photoacoustic source (za) by repositioning the ultrasound transducer with respect to the dye phantoms. The comparison between the experimental results and the theory is shown in Fig. 6 . The processing steps for this SNR analysis were equivalent to the processing steps used to generate Fig. 5. The root mean squared difference between the experimental results and the theoretical results is 0.32 dB for W=1 and 0.18 dB for W=2, respectively. The coding gain is reduced by shortening the distance za , assuming a fixed code length and a fixed PRF of the laser diodes for MS-PACE. Due to a lower distance za , the time-of-flight is reduced, thus the PRF for averaging can be increased compared to a high za without causing any range ambiguities. Assuming a code length of 512 bit and a PRF of 500 kHz a positive coding gain can only be achieved for a distance za longer than 6 mm.
Fig. 6 The coding gain is displayed as a function of the distance between the ultrasound receiver and the farthest photoacoustic source. For each distance the number of acquisitions for averaging was adjusted based on Eq. (8). ‘T’ denotes theoretical estimations, cf. Eq. (10), ‘E’ denotes experimental results. The PRF and the code length for MS-PACE were set to 500 kHz and 512 bit, respectively.
4. Discussion and conclusion
The results of our study demonstrate the feasibility of MS-PACE using UOGC. We irradiated dye phantoms by two coding sequences emitted at two different wavelengths simultaneously. We successfully separated the photoacoustic responses to both wavelengths. The photoacoustic signal components obtained by MS-PACE are equivalent to the photoacoustic signal components obtained by averaging multiple monospectral acquisitions. This verifies that the decoding process is executed correctly. No coding artifacts like correlation sidelobes are visible within the used dynamic range of 42 dB. However, the fluctuation of the laser pulse energy can potentially cause coding artifacts that might be visible within the resulting images. The pulse energy variance of the used experimental setup is below 5%. The influence of this error can be simulated by using a modified version of the signal processing chain displayed in Fig. 2. For this simulation, the emitted coding sequence is changed by adding a noise process, which exhibits a zero-mean normal distribution with a variance of 5%. For a code length of 512 bit, a mean main lobe to correlation sidelobe ratio of approx. 62 dB is obtained. These results suggest that the coding artifacts induced by the fluctuation of the laser pulse energy will reduce the dynamic range of MS-PACE to 62 dB for the assumed simulation parameters. Since the dynamic range for photoacoustic imaging is typically lower, e.g. 45 dB [16], these artifacts should not significantly decrease the image quality obtained by MS-PACE.
We experimentally determined the coding gain for different parameter sets: we varied the code length, the PRF of the laser diodes for MS-PACE, as well as the distance between the ultrasound transducer and the photoacoustic source za. We showed that the experimental results are in very good agreement with the theoretical predictions. Our experiments indicate that the PRF of the laser diodes and the distance of the photoacoustic source from the transducer (za) are crucial parameters, which determine the coding gain. The theoretical coding gain is displayed as a function of these two parameters in Fig. 7 . The results show that for a high PRF and a long source distance za the coding gain is positive, i.e. the SNR improvement due to MS-PACE is higher than the SNR improvement due to a time equivalent averaging procedure for these parameter sets. If the irradiation sources and imaging geometry fulfill these requirements, which are strictly formulated in Eq. (10), it is advantageous to employ MS-PACE instead of sequentially acquiring data sets for two different wavelengths. Under these conditions, MS-PACE can be used to increase the frame rate compared to a sequential data acquisition at two wavelengths, while maintaining a constant SNR for MS-PACE and sequential data acquisition. Alternatively, MS-PACE can be used to increase the SNR of the photoacoustic measurements compared to a time equivalent sequential averaging procedure. Consequently, MS-PACE using UOGC will not increase the SNR gain per time unit compared to simple averaging for a low PRF bispectral laser system, such as a combination of a q-switched Nd:YAG and a q-switched Alexandrite laser system, each running at a PRF of 10 Hz. The application of MS-PACE is beneficial for high PRF laser systems, such as laser diode based systems. The bispectral laser diode system presented in Section 2.3 can be operated at a maximum PRF of 500 kHz. For this PRF, a positive coding gain can be achieved for a distance between the photoacoustic source and the ultrasound receiver longer than 6 mm. Concerning biomedical applications of laser diode systems, it has been previously shown that such systems already have achieved a penetration depth of up to 9 mm in tissue mimicking phantoms [11]. Thus, multispectral laser diode systems using MS-PACE can be beneficial for applications like small animal photoacoustic imaging. In general, a positive coding gain can be achieved for an even lower penetration depth, if the PRF is further increased. The minimum distance for a positive coding gain scales proportionally with the PRF, i.e. for a PRF of 3 MHz the minimum distance is 1 mm.
Fig. 7 The theoretical coding gain is shown as a function of the PRF of the laser diodes for MS-PACE using UOGC and distance za. A constant code length of 512 bit is assumed for all calculations. The dashed line (–) indicates the 0 dB coding gain isoline.
The unipolar orthogonal Golay codes used for MS-PACE can be extended to complementary sets of sequences [16]. These codes allow emitting more than two wavelengths in parallel. Since the coding gain scales proportionally to the number of used wavelengths, an increase in the number of simultaneously emitted wavelengths significantly boosts the coding gain. This phenomenon was already observed in Section 2.2 by comparing the coding gain of MS-PACE using two wavelengths to the coding gain of PACE using one wavelength.
Laser safety issues might potentially limit the biomedical applications of MS-PACE. It has been previously shown that the maximum permitted exposure (MPE) for skin decreases when the PRF of the laser source is increased [12]. Since a high PRF is mandatory for a high coding gain using MS-PACE, the SNR improvement achieved by MS-PACE might be limited by the MPE. However, these laser safety regulations do not apply to patients [12]. Potential thermal damage can be efficiently reduced by cooling the irradiated skin surface. Additional studies are needed to assess the benefits and risks of high PRF biomedical photoacoustic imaging. Nevertheless, a laser diode systems using MS-PACE could be directly used as a cost efficient tool for preclinical small animal imaging and non-destructive testing.
Acknowledgments
This project is funded by the German Federal Ministry of Education and Research (bmb+f grant no. 01 EZ 0707).
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