Photoacoustic remote sensing microscopy (PARS) represents a new paradigm within the optical imaging community by providing high sensitivity (>50 dB in vivo) non-contact optical absorption contrast in scattering media with a reflection-mode configuration. Unlike contact-based photoacoustic modalities which can acquire complete A-scans with a single excitation pulse due to slow acoustic propagation facilitating the use of time-gated collection of returning acoustic signals, PARS provides depth resolution only through optical sectioning. Here we introduce a new approach for providing coherence-gated depth-resolved PARS imaging using a difference between pulsed-interrogation optical coherence tomography scan-lines with and without excitation pulses. Proposed methods are validated using simulations which account for pulsed-laser induced initial-pressures and accompanying refractive index changes. The changes in refractive index are shown to be proportional to optical absorption. It is demonstrated that to achieve optimal image quality, several key parameters must be selected including interrogation pulse duration and delay. The proposed approach offers the promise of non-contact depth-resolved optical absorption contrast at optical-resolution scales and may complement the scattering contrast offered by optical coherence tomography.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
All-optical imaging modalities represent a powerful tool-set in clinical and preclinical settings which necessitate micron scale resolution and non-contact operation. Optical coherence tomography (OCT) in particular has seen clinical adoption and provides depth-resolved optical scattering contrast. However, high-quality imaging with optical absorption contrast has proved more challenging. Photoacoustic modalities provide optical absorption contrast, however, most photoacoustic methods are not all-optical and require contact or acoustic coupling. The requirement for acoustic coupling to the sample limits potential applications of photoacoustic microscopy such as monitoring of wound-healing , monitoring of neonatal vital signs [2,3], surgical imaging , and monitoring of burn recover 
There has been a great deal of work within the literature aimed at creating a non-contact photoacoustic modality. Air-coupled transducers have been developed for this purpose but commonly suffer from poor sensitivity . As well, several groups have attempted interferometric detection of surface oscillations using a secondary probe beam [7–9]. Although these approaches have proven capable in phantom experiments they still tend to suffer from poor signal-to-noise and have not yet demonstrated effective in vivo visualization.
A recently reported photoacoustic modality known as photoacoustic remote sensing (PARS) microscopy [10,11] presents a non-contact optical-resolution photoacoustic approach. Here, the large photoacoustic initial pressures can be observed as small modulations in the back-reflected intensity of a continuous-wave probe beam co-focused to the excitation spot. PARS has already demonstrated comparable sensitivity to Optical-Resolution Photoacoustic Microscopy (OR-PAM) while offering comparable signal-to-noise and improved imaging depths in scattering tissues. Since optical focusing can be provided by either the excitation beam or the interrogation beam, lateral-resolution can be maintained to significant depths by appropriate selection of a deep penetrating interrogation wavelength.
Since detection is performed at the source of the acoustic pressures, the same time-gating approach used by other photoacoustic modalities to discern depth information does not apply with PARS. This in turn provides no depth information beyond that provided by optical sectioning necessitating depth-scanning. Despite this limitation, rapid acquisition (>10MHz point rate) is possible since the technique is primarily stress-confinement limited . The modality is commonly operated at a high numerical aperture to provide tight lateral resolution, in which case the expected axial resolution is also potentially good at superficial depths. However, beyond superficial imaging depths degradation to the axial resolution will occur due to multiple scattering. These issues in part inspired the current investigation.
The purpose of this paper is to introduce a PARS-based method for achieving depth-resolved images with optical absorption contrast. To accomplish this, we propose imaging depth-resolved changes in the refractive index immediately after an excitation pulse induces large initial pressures associated with light absorption. This could be accomplished through the use of an OCT A-scan which is sensitive to local scattering and infers a refractive index distribution. By forming the difference between OCT A-scan envelope signals with and without excitation pulses, depth-resolved images with optical absorption contrast are generated. To demonstrate the proof of principle of this method we perform simulations which build on our previously validated models of the PARS detection mechanism [13,14].
The proposed approach is not to be confused with previous OCT-based photoacoustic detection methods which aimed to detect outward propagating acoustic waves manifesting themselves as subtle oscillations at the sample outer surface [15–18]. Instead our approach locally detects optical-absorption-induced initial pressures directly at their sub-surface origins. These effects have been demonstrated in modeling and experiments to be substantial. For example, in  red-blood-cell scattering cross sections were observed to change by greater than 5% when illuminated with pulses of mere nJ energies. We propose using a pulsed low-coherence source spectral-domain optical coherence tomography (SD-OCT) method, which enables full A-scan acquisitions without mechanical depth-scanning, reference-beam scanning or swept-source wavelength-scanning. This approach also offers high signal-to-noise . Our proposed method which we call coherence-gated photoacoustic remote sensing microscopy (CG-PARS) would involve replacing the standard PARS detection pathway with a pulsed low-coherence interrogation beam, low-coherence interferometer and a spectrometer to capture the nanosecond-scale absorption-induced changes in refractive index. The presented results demonstrate the potential of the proposed method and illustrate the importance of key design parameters.
2.1. Coherence-gated PARS detection
The proposed detection process behind CG-PARS is effectively similar to the process used for SD-OCT. The primary difference is that ns-scale time-dependent effects must now be captured. The recovery of a SD-OCT reflectivity envelope in depth rs(ℓs, t), where ℓs and t are the scattering depth and time respectively, is well known  and can be related to the reflectivity spectrum I(ν, t), where ν is the optical frequency, captured on a spectrometer through a Fourier transform. One way to form a CG-PARS image is to capture the modulation ΔI(ν, t) due to an excitation pulse, then relate this to a time-sequence of OCT A-scans. This could be accomplished using a photodiode array in the spectrometer rather than a CCD-based spectrometer although it would require a multi-channel data acquisition system and dense photodiode array. CCD cameras themselves do not typically have the temporal bandwidth to capture required modulations. Even rapid SD-OCT systems with low MHz-range A-scan rates  yield total integration times which are substantially longer than the 10ns to 50ns time-domain behavior experimentally observed with the PARS mechanism. To overcome this issue a pulsed detection scheme is proposed, and is the focus of this manuscript.
By appropriate timing of the interrogation pulses a relatively slow detection array can be forced into capturing brief reflectivity perturbations within the sample. Specifically an acquisition is made with the unperturbed sample and then again directly after an excitation event (Fig. 1). Each of these i intensity spectra then relate to a given estimate of the stationary reflectivity distribution r̂s,i(ℓs), which individually represent SD-OCT A-scan acquisitions after taking their envelopes. Subtracting two appropriate envelopes may then highlight modulation in the local scattering distribution, which is primarily attributed to PARS modulation and therefore implies optical absorption proportionality in the A-scan envelope-detected difference signal b(z), represented as
Here |ℋ| represents the the magnitude of the Hilbert transform, an envelope-detection operation.
The expected behavior for this process is highlighted in Fig. 2. Objects which have optical scattering contrast will be visualized through the individual OCT acquisitions. Objects which have optical absorption contrast may then be recovered through the difference between a perturbed scattering profile and one which has not yet undergone photoacoustic excitation.
One key aspect of CG-PARS over conventional PARS microscopy involves the acquisition time needed to acquire full B-scans and volumetric C-scans (Fig. 3). Within two laser pulse events CG-PARS can provide full depth-encoded A-scans and it does not necessitate depth scanning, whereas PARS only yields a small region defined by the optical section for a given acquisition event. This requires depth scanning with conventional PARS yielding significantly higher acquisition times.
2.2. 1D simulation
The first proposed approach for modeling these effects involves an effective 1D simulation. Much of this work follows closely from previous efforts on modeling the time-evolution of PARS signals due to pulsed absorption-based reflectivity changes and scattering cross section modulations of planar and spherical scatterers, respectively [13,14]. First, for a spacial coordinate x = (x, y, z) we consider a sample with a spatially-varying refractive index profile n0(x), optical absorption at the excitation wavelength μa(x), and constant acoustic propagation velocity ca. This region is then illuminated with a Gaussian beam having an intensity distribution Iex(x, t). We then assume a thermal confinement condition such that the local heating within the region can be approximated as H(x, t) ≈ μa(x)Iex(x, t) for unity Gruneisen parameter. This is used as a source term within the inviscid photoacoustic equation to find the pressure field p(x, t) following where ∇2 is the Laplacian, β is the thermal coefficient of volume expansion, and Cp is the specific heat capacity at constant pressure . Here a subscript t denotes a temporal derivative, and two such subscripts denote the second derivative in time.
Simulation of this problem is performed through explicit finite-difference numerical methods which are well summarized in many other works [22,23]. In brief, we discretized the photoacoustic equation components as
Apart from conventional stability condition where , consideration here must also be given to the desired pulse-width of the excitation laser such that at minimum the Nyquist sampling criteria is satisfied.
The photoacoustic pressure may be significantly large to generate non-trivial modulations in the refractive index profile such that optical scattering changes from the excited region are detectable. This process follows the elasto-optic relation 25,26]) and ρm is the mass density. As mentioned in the previous section, rather than simulating a continuous-wave interrogation beam, a pulsed detection scheme is used. Since it will be of interest to track phase fronts for coherence considerations, the full electric field of the interrogation beam is considered within the region. As with the excitation beam, an ideal Gaussian is used to represent the interrogation pulse intensity profile. This approximation is of course not valid in general (particularly at depth) so we limit consideration to within the minimum transport mean free path of both wavelengths. Since it would require substantial computational power to now simulate the full three-dimensional electromagnetic field of the interrogation interaction with the sample, the dimensionality of the problem is reduced to one by taking a weighted sum across regions of equal phase such that the resulting equivalent linear refractive index profile n̄*(z, t) is given by 13].
The back-reflected interrogation light from the sample is compared with a reference path with a low-coherence interferometer. The electric field which is back-reflected from the sample Es(ν, t) is compared with that of the reference arm Er(ν, t), represented as
2.3. Shift-variant linear system models
The previous approach is an approximate method for reducing the OCT and CG-PARS modeling problem to 1D. It allows investigation of the temporal evolution of the PARS signals and is most accurate for planar structures. An alternate approach for more general geometries and used for validation is to consider a linear shift-variant (LSV) point-spread function (PSF) model, which will then be further simplified to a convolution-based shift invariant approximation.
In the absence of noise, the complex OCT signal as a function of image space coordinate x = (x, y, z) can be written as [27–29]
The displayed signal is usually the envelope or complex magnitude, |SOCT|. Here r is the amplitude reflectivity distribution.
For a planar interface r(x) can be represented as a Fresnel reflectivity. For an isotropic-scattering point target, r(x) = r0δ(x − x0), where r0 relates to the scattering cross-section . In general a more complex target can be considered a superposition of such point targets.
When the interrogation source is focused on illumination and detection, the point-spread function can be modeled as
Here hE,int is the shifted normalized electric field of a focused beam, ER is the amplitude of the reflected the electric field along the reference arm, and ES0 is the incident electric field amplitude on sample. hE,int is squared in the above expression to denote focusing on illumination and detection. Rzz is the axial autocorrelation function that represents coherence-based depth-gating.
When the interrogation source is a focused Gaussian beam in a minimally-scattering medium or at a depth where ballistic light transport dominates, hE,int can be modeled as:30].
When the interrogation source has a Gaussian power-spectral density, the autocorrelation function is a Gaussian modulated sinusoid as given by Eq. 9.38 of . For frequency-domain systems, signals are recorded in the spectral domain and inverse-transformed to the spatial domain, with filtering to remove the modulations. In this case, a model for the effective autocorrelation function is simply
If within the depth of focus, we take w(z), R(z) and ψ(z) as roughly constant so that SOCT can be approximated as a linear shift-invariant (LSI) model of the form
The shift-variant approach offers the power to study highly focused beams whereas the shift-invariant model is more suitable for looser focusing and offers intuition and fast simulation performance.
When performing speckle simulations, statistically-independent normally-distributed random fields may be chosen for the real and imaginary parts of r, in which case the resulting speckle statistics for |S| are Rayleigh distributed  for both the LSV and the LSI models as expected for fully-developed OCT speckle.
To model PARS as a linear system, we express the PARS signal as10,13] that the intensity reflectivity is proportional to the perturbation of the refractive index (ΔrI ∝ rδn), and that the perturbation relates to the optical absorption and the optical fluence distributions such that
However, since the focal depth is scanned throughout the target such that f = z′, if we assume local shift invariance, we can write an LSI expression as
The CG-PARS signal distribution will be considered the difference between a perturbed SOCT envelope signal with an unperturbed one such that
For primarily real positive signals, this expression becomes
This illustrates that CG-PARS detects optical absorption by measuring changes in OCT signal induced by a pulsed excitation beam.
If the LSI approximation can additionally be used, the expression can be further reduced as
3. Simulations and results
3.1. Temporal evolution of PARS modulations
First the 1D model is used to examine the temporal effects discussed in section 2.1 by simulating a single OCT A-scan repeated at multiple time-delays following a photoacoustic excitation event (Fig. 4(a)). We refer to this as an M-mode OCT acquisition. Here a 4 μm diameter tube with optical absorption of μa = 250 cm−1 and a mean refractive index n = 1.41 (to provide a blood-like target) is simulated within a homogeneous non-absorbing medium (n = 1.33). The simulation is performed assuming an interrogation beam with central wavelength λ = 1310 nm, and spectral bandwidth Δλ = 85 nm which gives a free-space full-width at half maximum (FWHM) coherence length of 8.9 μm. Figure 4(a) shows the reflectivity signals in time where the out-propagating acoustic waves are clearly visible for an excitation event at time t = 0. Then, if all subsequent time points (t > 0) are subtracted from the unperturbed profile (t = 0) (Fig. 4(b)) the change to the reflectivity profile (ΔR) is highlighted. It can be seen that following the excitation event the targets are perturbed to a significant degree, but the acoustic propagation has not yet distorted the original object. This is the aspect which CG-PARS is attempting to capture. However, the timescales necessary (∼ns) are currently not obtainable by modern OCT devices. This then motivates the use of a short pulse for interrogation. This implementation should allow for precise timing and duration of the acquisition events. As well, using a pulsed interrogation allows for higher peak intensities and previous work has demonstrated large signal-to-noise ratios (∼ 100dB) . This dynamic range may be necessary for weak modulation signals.
These results also highlight the importance and potential impact when selecting the relative delay and duration of the secondary interrogation pulse which directly follows the excitation event. To examine the effects of these parameters, a study is performed observing a single A-scan for a homogeneous absorbing region (Fig. 5). Here, it is quite obvious that if the interrogation is made too early then a yet unperturbed profile may be examined (Fig. 5(a)). If the interrogation is made too late then undesirable non-localized signal artifacts may be recovered resulting from the out-propagating acoustic waves (Fig. 5(c), 5(d)). This could result in artificial broadening of the target and reduce CG-PARS signal contrast. The duration of the interrogation should be sufficiently long to provide adequate sensitivity, but not so long as to also capture out-propagating acoustic waves. Despite our efforts here, the precise values of these will likely require tuning for a given experiment.
3.2. Effects of receive SNR and discretization error
Perhaps one of the most critical components to investigate here in terms of the potential feasibility of the proposed device involves a study of the required detector sensitivity compared to their noise vs. what might be expected from the recovered image (Fig. 6). Although there will be a significant number of possible noise sources throughout the system, two large components are likely to be the receive sensitivity of the detector array elements, and additional errors brought on through analog-to-digital readout of these elements. Studies were performed by imaging a single homogeneous 10μm thick absorbing layer for various receive bit discretization (from 8-bit to 14-bit) and for various receive element SNR values (1 dB to 100 dB). The results of these are summarized in graphs (Fig. 6(a), Fig. 6(b)) where the recovered scattering SNR (OCT) is included for comparison. For these particular values (where the mean absorption of the region is taken as 250 cm−1, the 532 nm excitation pulse energy is 25 nJ), the maximum recovered scattering SNR is near ∼ 90 dB which is consistent from reported values for pulsed-detection OCT systems . The recovered absorption SNR by comparison seems to have taken values roughly ∼ 20 – 30 dB lower. However, this limitation may not be problematic given available hardware. For example in  an OCT device was constructed with an OCT spectrometer with available pixel sensitivity of 66 dB and a 12-bit ADC. This would yield a predicted recovery of around 34 dB for CG-PARS. CG-PARS will require some minimum level of sensitivity in the OCT detection to achieve practical signal-to-noise which may limit its performance at depth in scattering media.
3.3. Contrast mechanism
PARS contrast is already discussed in our previous papers, but has previously not been investigated for CG-PARS. Contrast behavior is highlighted in Fig. 2. Three different types of targets are situated within a scattering phantom, and their responses are simulated using the LSV method described in section 2.3. Targets with optical absorption (i–ii) are detected with CG-PARS whereas those with optical scattering (ii–iii) can be recovered using the OCT acquisition which is also provided by the technique. Targets are 80 μm cylindrical regions within a discreet random media background with optical reflectivity variance of 2 × 10−4 and no optical absorption. Methods for calculating more precise values for the scattering variance distributions have been discussed  but are not used here. The targets themselves have amplitude reflectivity variances of , and , and mean optical absorption μa,i = 250 cm−1, μa,ii = 50 cm−1, and μa,iii = 0 cm−1 respectively. The region is again simulated using an interrogation beam with central wavelength λ0 = 1310 nm, and spectral bandwidth Δλ = 85 nm, and Gaussian waist with NA = 0.02. Since CG-PARS has sensitivity to the inherent reflectivity profile of the region, the absorption of target (i) needs to be significantly higher than that of target (ii) to provide similar CG-PARS signal. This is a preexisting trait of the PARS mechanism. However, biological tissues tend to be highly heterogeneous in their microscale optical properties, and thus are likely to provide a large degree of optical scattering. Indeed this limitation has not been problematic for conventional PARS microscopy. This is not to be interpreted as a requirement for speckle contrast such as that required by OCT. Rather, the CG-PARS approach only requires optical absorption contrast and some degree of inherent scattering from the material. For example, a blood vessel may be indistinguishable by conventional OCT providing similar speckle characteristics to the surrounding tissue. CG-PARS may then overcome this issue through visualization of the optical absorption contrast.
3.4. PARS experimental comparison
Prior to demonstrating the potential advantages of CG-PARS over PARS, B-scan point-spread functions from PARS systems are compared with PSF models. The PARS LSV model (Sec. 2.3.3) is compared against experimental B-scans results (Fig. 7). The experimental system used is similar to that provided in . In brief, a 532-nm ns-pulsed excitation is co-focused with a 1310-nm continuous-wave super luminescent diode (SLD) with spectral bandwidth of Δλ = 45 nm. Focusing is provided by a NA = 0.4 objective lens which is assumed to provide NA ≈ 0.2 when considering the effective focal length f = 10 mm, and input beam diameter d ≈ 4 mm. Experimental results are acquired by performing several sequential C-scan maximum amplitude projections (MAP) at 22 progressive depths (with a 25 μm step-size) using a translation stage. The phantom used consisted of a network of 7 μm carbon fibers suspended in clear gelatin at various depths. If we compare with the ideal performance for such a structure (Fig. 7(c)) simulated using the LSV PARS model (Sec. 2.3.2) there exists some discrepancy likely attributed to misalignment between the excitation and interrogation focii and potentially heterogeneity within the medium. These problems further highlight the need for coherence gating to improve depth-resolution.
3.5. Point spread functions
The point-spread functions (PSFs) for the 1D CG-PARS simulation and LSV model are shown in Figs. 8(a) and 8(b). Here a low numerical aperture is used similar to that seen in OCT providing reduced lateral performance but greater depth-of-focus. The detection source stimulated again has a λ0 = 1310 nm central wavelength with a Δλ = 85 nm spectral bandwidth. Both models agreed reasonably with each other in particular with predicted axial performance. As a final comparison, a conventional PARS visualization is simulated using the LSV model on the same target (Fig. 8(c)). If the same numerical aperture (NA = 0.02) is used, the points are not well recovered as conventional PARS microscopy relies on optical sectioning for axial resolution. Here a substantially larger numerical aperture is necessary to provide the same axial performance (Fig. 8(d)), however experimental results thus far suggest that this represents a highly idealized situation which is unlikely to occur deep within scattering phantoms and in vivo. It is also important to note that conventional PARS necessitates depth scanning and thus may require a significantly higher acquisition times. For example, if scanning a 1mm deep and 2mm wide region with respective step sizes of 4 μm and 2 μm yields B-scan frame rates of 1 fps for conventional PARS and 250 fps for CG-PARS assuming a 500kHz laser pulse rate.
3.6. Scattering phantom simulations
Next, a more complex phantom is simulated using the LSV model (Fig. 9). Several blood-vessel-like structures are placed within a scattering phantom with two different scattering layers. Despite the subtle contrast which can be seen in the ground-truth phantom (Fig. 9(a)) the structures are not significantly recovered through simple OCT methods. It is worth noting that other OCT methods such as OCT angiography and visible OCT would likely perform better here at recovering the vessel structures. CG-PARS offers improved recovery of these structures relative to OCT due to the optical absorption contrast available. Within highly scattering targets such as skin or brain tissue CG-PARS may offer structural visualization complimenting that provided by OCT.
The proposed coherence-gated photoacoustic remote sensing (CG-PARS) modality offers potential benefits over conventional PARS microscopy in terms of improved axial performance and acquisitions speeds. It also offers complementary absorption contrast to the scattering contrast offered by coherence-gated methods such as OCT. By enabling full depth-resolved acquisitions CG-PARS may be the path forward towards creating a fully functional non-contact optical resolution photoacoustic modality which may offer competitive functionality to conventional OR-PAM. The predicted linear behavior of the recovered signal to the optical absorption may enable spectral unmixing capabilities for measurement of blood oxygen saturation and molecular reporters. Future work should include the design and construction of an experimental apparatus to realize these predictions. Such systems will require careful attention to interrogation pulse duration and timing relative to excitation pulses. Adequate sensitivity and dynamic range will also prove critical.
The present work represents a first investigation of coherence-gating for photoacoustic remote sensing and may provide a simulation platform for achieving optimal experimental design. This paper also introduces important point-spread function representations which will be beneficial for system modeling and for guiding design.
Preliminary work regarding a new non-contact photoacoustic modality called CG-PARS was presented. Here, CG-PARS interactions were simulated with several approaches. This method offers the promise of overcoming many limitations with current competing techniques such as conventional PARS microscopy, OR-PAM, OCT, and visible-OCT. The ability to perform complete A-scan acquisitions offers significant speed benefits over voxel-based scanning provided by conventional PARS. Like conventional PARS, there exists the ability to select appropriate wavelengths for both excitations and detection which could provide greater penetration depths than those available to OR-PAM. Since CG-PARS contrast is proportional to optical absorption, future work may realize functional imaging of oxygen saturation and molecular imaging of reporters to provide information complementary to optical coherence tomography. CG-PARS presents exciting possibilities for the future of optical absorption microscopy.
NSERC (RGPIN 355544 and STPGP 494293-16) and CIHR (PS 153067).
We gratefully acknowledge funding from NSERC and CIHR. KB acknowledges scholarship support from NSERC and Alberta Innovates.
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