1. Introduction

Optical coherence tomography enables non-invasive, high resolution in vivo imaging in transparent and non-transparent tissue [1–3]. The possibility of extracting spatially resolved spectroscopic information simultaneously with the generation of high resolution images can significantly extend the range of biomedical applications of OCT. The first qualitative, proof-of-principle spectroscopic OCT studies were conducted using narrow bandwidth (~50 nm) light sources centered at 1300 nm [4] (time - domain OCT) and 830 nm [5] (frequency-domain). In other studies a combination of two narrow band sources centered at 1.3 µm and 1.5 µm, and a differential absorption method were used to quantify water content in phantoms at a single wavelength [6,7]. Utilization of a single broadband light source for quantitative, depth-resolved SOCT offers many advantages: it permits better spatial localization of the absorbing object, reduces the complexity of the instrument as well as the data acquisition and processing algorithm, eliminates the additional noise associated with the use of multiple narrow bandwidth, mutually incoherent light sources, and most importantly, permits extraction of absorption profiles µ_a(λ) over a broad wavelength range with a single measurement. Commercially available femtosecond Ti:Al₂O₃ lasers can generate a spectrum centered around 800 nm with a bandwidth larger than 100 nm at FWHM (full width at half maximum) [8], which overlaps with the so-called therapeutic window, covering the absorption profiles of several biological chromophores, such as melanin, oxy- and deoxyhemoglobin [9]. It was demonstrated in the past that qualitative spectroscopic information acquired with ultrahigh resolution SOCT in biological tissue can be used as a type of “spectroscopic staining,” in analogy to histological staining, thus enhancing the OCT image contrast [10]. In addition, it was lately shown that spectroscopic low coherence interferometry can aid measurements of dye diffusion constants in gels [11]. Recently, an in vitro quantitative SOCT measurement of blood oxygenation by use of a broad bandwith (Δλ=125 nm) Ti:Al₂O₃ laser has been published [12]. So far only preliminary results have been reported on the precision of the SOCT method utilizing a single broad bandwidth source for quantitative measurement of chromophores imbedded in weakly scattering media [13]. In this paper we present a thorough theoretical and experimental evaluation of the effect of various factors related to the performance of the TD-OCT (time-domain) instrument, the measurement procedure or the data processing algorithm on the precision of SOCT for extracting absorption profiles µ_a(λ) from weakly scattering phantoms.

2. Theory

As described in detail in [6] and [12], the signal detected with an OCT system is proportional to the cross-correlation between the electrical fields backscattered from the imaged object and the reference mirror. Assuming that the mirror reflectivity is spectrally flat over the emission bandwidth of the light source, the reference field can be represented as a Doppler shifted version of the light source field. However, the field backreflected from the imaged object is a convolution of the incident source field and the depth-dependent spectral reflectivity profile of the imaged object. In the frequency domain the convolution can be expressed as a product of the light source spectrum S(ω) and the spectral reflectivity of the object H(ω):

where I(ω) is the amplitude spectrum measured at the detector of the TD-OCT system. The magnitude of the spectral reflectivity H(ω) is a measure of the frequency (wavelength) dependent attenuation, µ(z,λ)=µ_a(z,λ)+µ_s(z,λ), of light in the imaged object resulting from scattering (µ_s) and absorption (µ_a) and is depends in general on the depth z. The magnitude of H(ω) can be obtained from the OCT fringe pattern by applying a frequency analysis to it such as Fourier- (FT) or wavelet transform (WT). Assuming that the sample has spatially and temporally homogeneous attenuation properties, µ(z,λ)≡µ(λ), that comply with Beer-Lambert law, the magnitude of H(ω) expressed in wavelength units can be written as a function of the depth z in the sample:

Here µ(λ) is the wavelength dependent attenuation coefficient of the imaged object. In very weakly scattering media where the attenuation of light is dominated by absorption, the attenuation coefficient can be substituted, within certain precision limits, with the corresponding absorption coefficient µ_a(λ). In SOCT µ_a(λ) can be obtained by extracting the amplitude spectra I ₀ and I ₁ at two depths within a weakly or non-scattering sample separated by distance d:

The factor of 2 in the denominator of Eq. (2) designates a bidirectional pass of the optical beam through an absorbing region in the sample with thickness d, since OCT detects backreflected light. In addition, Eq. (2) can be used to evaluate the expected error in measuring µ_a(λ) with SOCT:

Here Δd/d, ΔI ₀/I ₀ and ΔI/I are the statistical errors in measuring the sample thickness d and the amplitude spectra I ₀ and I obtained at the front and rear interface of the absorbing sample, while δ I ₀/I ₀ :=1-I/I ₀ is the differential change in the incident amplitude spectrum I ₀ resulting, in an ideal case, only from light absorption in a phantom with thickness d and absorption coefficient µ_a.

Since SOCT was developed with the intention to be used for quantitative measurement of absorption profiles µ_a(λ) of various biological chromophores, it may be useful to provide an initial theoretical estimate of the sensitivity of the method to weak and small size absorbers.

 

Fig. 1. Differential changes in the incident amplitude spectrum δI ₀/I ₀ as a function of the sample thickness d calculated for different absorption coefficients; (µ_a=0.4 mm^-1 is equal to the absorption coefficient of whole blood at the isosbestic point, λ=800 nm).

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For example, the absorption coefficient of blood ranges from 0.2 mm^-1 to 2 mm^-1 in the wavelength range of 650 nm to 950 nm depending on various physiological conditions such as blood oxygenation level, hematocrit content and osmolarity, and is ~0.4 mm^-1 at the isosbestic point (λ=800 nm) [14]. The size of blood vessels varies significantly in the human body. However, in the retina the largest arteries rarely exceed 300 µm in diameter. Figure 1 shows the expected effect of blood absorption with µ_a=0.2, 0.4, 0.6 and 0.8 mm^-1 on the differential change δI ₀/I ₀ as a function of the size of the blood vessel. The graph clearly shows that at the isosbestic point where µ_a~0.4mm^-1, light absorption in arterioles ~50 µm in diameter would result only in ~4% differential change in the attenuated amplitude spectrum, while absorption of light in vessels the size of 300 µm could produce a change δ I ₀/I ₀~20%.

Figure 2 is a graphical representation of Eq. (3) and demonstrates that the relative error Δµ_a/µ_a is very sensitive to the magnitude of the differential change in the incident amplitude spectrum δI ₀/I ₀ produced by the presence of an absorber, i.e. the weaker and smaller the absorber, the larger the error in the extracted µ_a. It also shows that Δµ_a/µ_a is strongly dependent on the relative errors in the amplitude spectra, ΔI ₀/I ₀ and ΔI/I, measured at the boundaries of the absorbing sample. For the case of an absorber with µ_a=0.4 mm^-1 (close to absorption of whole blood at λ=800 nm) and thickness d=50 µm, and assuming that the δI ₀/I ₀ is solely due to absorption in the object, that Δd/d=2% and that ΔI ₀/I ₀=ΔI/I=2% (spectrally flat over the examined wavelength region), the expected Δµ_a/µ_a~70%. If the size of the absorbing object increases to 300 µm, the relative error in extracted µ_a is reduced to ~12%.

The theoretical evaluation presented above shows that if SOCT is used for quantitative evaluation of blood oxygenation, care has to be taken about the experimental errors, since the overall error Δµ_a/µ_a is very sensitive on them. In an SOCT measurement, the errors ΔI ₀/I ₀ and ΔI/I are sensitive to both the intensity noise and spectral noise of the light source. In addition, the differential change δI ₀/I ₀ may be influenced by presence of chromatic aberrations, dispersion mismatch, angle and wavelength dependent specular and/or diffuse reflections, as well as artifacts in the extracted spectra, generated by the processing algorithm (dependent on parameters such as the size and shape of the window in the windowed FT), the effects of which on δ I ₀/I ₀ may be falsely interpreted as induced by presence of absorbers within the imaged object. The following sections of the paper will discuss the experimental evaluation of various factors that primarily affect the precision of SOCT for extraction of absorption profiles, as well as different strategies that can be applied to minimize the experimental errors.

 

Fig. 2. Relative error in the extracted absorption coefficient, Δµ_a/µ_a, as a function of the differential changes in the incident amplitude spectrum δ I ₀/I ₀.

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3. Experiments

For the purpose the this study an ultra-broad bandwidth, state-of-the-art Ti:Al₂O₃ laser [15] (Femtolasers GmbH, λ_c=800, Δλ=260 nm, P_out=120 mW ex-fiber, see Fig. 3, black line) was interfaced to a free-space OCT system, described in detail in [16], and modified in this case for optimal performance in the 600–1000 nm wavelength range. The system’s optical components were selected to support propagation of broadband light and to compensate for any polarization and dispersion mismatch between the two arms of the interferometer. Custom designed achromat lenses (D=5 mm, f=10 mm) were used in the sample and reference arms of the interferometer to minimize the effect of chromatic aberrations and dispersion mismatch on the precision of the measurement. The system utilized dynamic focus tracking to closely match the position of the coherence gate with the focal plane of the imaging lens within the samples. Nonlinearities in the voice coil (VC) scanning rate were accounted for by acquiring a reference fringe pattern from an additional interferometer powered by a He-Ne laser, simultaneously with the actual data acquisition and subsequently applying a data correction algorithm. The OCT system provided 1.3 µm axial and 3 µm lateral resolution in air with 107 dB sensitivity of for 5 mW incident power.

All phantoms used in the SOCT measurements were prepared by bounding single or multiple gel layers (4 g/l agar in distilled water) doped with ICG (Indocyanine Green dye, initial concentration of 50 µM/l solution in distilled water) between thin (~150 µm) glass coverslips. One of the reasons for using ICG dye as an absorbing agent in this SOCT study was the fact that its absorption profile overlaps partially with the emission spectrum of the Ti:Al₂O₃ laser (see Fig. 3), which facilitated data normalization. The ICG dye was mixed very well with the gel to produce homogeneous mixture and the ICG:gel ratio was varied to result in absorption profiles µ_a(λ) with various shapes and peak absorption magnitude. As a base-line reference, the attenuation properties of pure (undoped with ICG) gel were measured with a spectrometer (Ocean Optics, USB2000). The attenuation coefficient µ(λ) of pure gel appeared almost flat over the wavelength range of 550–950 nm, with magnitude ~2 orders smaller than the absorption peak of the smallest concentration of ICG used in experiments described here.

 

Fig. 3. Emission spectrum of the Ti:Al₂O₃ laser (black line) as measured with SOCT from a mirror reflection. Absorption profiles measured with a spectrometer from two gel samples with different concentration of ICG (green and red lines).

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To evaluate the sensitivity of SOCT to the size of the absorbing object, phantoms with various thickness of the ICG-gel layer were prepared. Since the absorption profile of the ICG dye is dependent on time, chromophore concentration and light illumination [17], the absorption spectrum of each phantom was measured with the spectrometer immediately before and after an SOCT measurement in order to account for any time or exposure to Ti:Al₂O₃ light related changes in the spectrum. Furthermore, to minimize the effect of high power radiation on the ICG spectrum, all samples were imaged with incident power lower than 1 mW.

For each phantom 50 A-scans were acquired at a single position. Prior to the data acquisition the OCT system was aligned so that the imaging beam was focused on the first glass-gel interface and the reference arm coherence gate overlapped with the focal plane. Similar measurements were performed in pure undoped gel samples to be used as reference and correction factors. The dispersion in the system was matched at the first glass-gel interface. The OCT fringe data was digitized with a 16 bit, 10 Ms/s A/D converter and filtered with a band-pass filter centered at 195 kHz (corresponding to VC velocity of ~38 mm/s). Windowed Fourier transform (WFT) was used to extract power density spectra from the fringe patterns corresponding to reflections from the glass-gel and gel-glass interfaces in a sample.

The size of the window is a critical parameter: a small window leads to a good spatial localization with poor spectral information, i.e. the density of points on the wavelength scale of the extracted spectra. A large window leads to a good spectral resolution at the expense of the spatial resolution, since the spectroscopic information is averaged over the window size. However, in tissue samples a time-frequency-decomposition, i.e. sliding WFT or wavelet transform, can lead to a better spatial localization. In this experiment a super-gaussian window with a width of 8×FWHM (FWHM is the full width at half maximum of the fringe envelope) was found to provide spectra which were in in very good agreement with spectrometer measurements. Since the FWHM changes with depth due to dispersion, but the same wavelength scale for spectra abtained from different depth is needed for the calculation of the absorption, each data set was expanded to the size of 1024 points by zero-padding. The extracted spectra were averaged over the 50 scans and the mean spectra corresponding to the front and the back surface of the examined gel layer were used to calculate the absorption coefficient µ_a(λ) of ICG using Beer-Lambert’s law (2). The standard deviation for the averaging of the 50 scans is a measure for the repeatabilty of the obtained spectra, and does not include systematic errors.

4. Results and discussion

To evaluate the overall performance of the SOCT system, a reflection from a mirror was repeatedly measured (50 A-scans acquired at one location) and the corresponding spectra were extracted by using the windowed FT algorithm described above. Care was taken to precisely match the dispersion of the two arms of the interferometer before the measurements. The acquired data was statistically averaged and the standard deviation for the series of measurements was evaluated to be below 3% for a wavelength range corresponding to the FWHM of the Ti:Al₂O₃ laser emission spectrum (Δλ=260 nm). The spectral fluctuations of the light source alone, which constitute a part of the total SOCT measurement error, were measured separately and were determined to be below 2% for the same wavelength range.

Since in this study we used a spectrometer as a ‘golden standard’ to evaluate the performance of the SOCT method, the precision of the spectrometer was also tested by measuring the absorption profile of a neutral density (ND) filter. The uncertainty in this case was evaluated to be ~2% for the wavelength range 550–950 nm for a series of 10 measurements.

To examine the reproducibility of OCT for measuring distances, the thickness of a glass coverslip was measured multiple times at different locations. The experimental error was found to be less than 1.5%.

To evaluate the effect of dispersion mismatch on the precision of SOCT, power spectra were extracted from the front and back boundaries of a 160 µm thick glass coverslip and a 1050 µm thick microscope glass slide. In both cases comparison of the two spectra (corresponding to the front and back air-glass interfaces) showed that they matched within 3% of each other for the entire wavelength range corresponding to the FWHM of the Ti:Al₂O₃ emission spectrum, signifying that dispersion mismatch has a negligible effect on the precision of SOCT.

The use of a broad bandwidth light source in an OCT system that utilizes refractive optics is inevitably accompanied by chromatic aberrations. In this experiment custom designed achromat doublets were used to provide optimal correction in the wavelength range 600–1000 nm. The chromatic focal length aberrations were evaluated to be less than 0.25% of the focal length of the lens (f=10 mm), corresponding to ~25 µm spectral spread in air which is comparable to the depth of focus of the lenses (~50 µm in air).

The use of a Ti:Al₂O₃ laser with a spectral width Δλ=260 nm resulted in ~1.3 µm coherence gate length in air. Translation of the coherence gate along the optical axis within the depth of focus will change the power spectral density of the OCT-signal. Since in this study the spectral spread in the focal region was ~25 times larger than the coherence gate width, variations in the shape and magnitude of the spectra extracted at various positions of the 1.3 µm wide coherence gate within the beam depth of focus were expected. This fact was confirmed experimentally by focusing the imaging beam onto a mirror and translating the coherence gate within the depth of focus of the beam. The spectra measured at different locations of the coherence gate thereby exhibited significant variations in shape and magnitude. This experiment demonstrates that changes in the overlap during scanning between the focal volume of the imaging beam and the coherence gate within the sample is by far the largest source of error in extraction of absorption profiles from weakly scattering, absorbing media.

Currently, OCT system designs utilize either static focusing (the imaging beam is focused at one location and the coherence gate is swept through it), or dynamic focusing, where in theory the coherence gate can be centered in the focal region and its position relative to the focal plane is kept the same as the imaging beam is focused deeper into the sample. Dynamic focus tracking techniques that utilize a retroreflector and a scanner to expand simultaneously the beam paths in the sample and reference arms of the interferometer [6] (similar to the voice coil used in the SOCT system for the experiments described in this paper) operate perfectly only in sample media with refractive index n=√2. In a medium with a different refractive index there is an immanent mismatch between the positions of the focal plane and the coherence gate. As a result, the detected interferometric signal will correspond to an intensity distribution located in front or behind the focal plane of the imaging lens, depending on whether the refractive index is larger or smaller than √2. The mismatch, ΔL, between the coherence gate and the focal plane increases with the depth within the sample: ΔL=L_R-L_S=(2-n ²)×d, where L_R is the pathlength in the reference arm, and L_S the sample arm length, and d is the change of L_S in air.

 

Fig. 4. Absorption profiles measured from 450 µm thick (A) and 180 µm thick (B) single layered gel:ICG phantoms with SOCT (red line) and with the spectrometer (black line). The insets show schematics of the sample; light is incident from the top.

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For the case of gel phantoms (n=1.34) the mismatch constituted ~20% of the distance d, and in combination with the present chromatic aberrations caused changes in the incident spectrum larger than the changes expected purely from absorption.

To compensate for the combined effect of chromatic aberrations and the focal plane - coherence gate mismatch, we have developed a data correction procedure: reference measurements were performed in phantoms containing pure (without ICG-doping) gel with approximately the same layer thickness as the phantoms with the ICG doped gel layers. In all cases the coherence gate was overlapped with the focal plane of the imaging lens, which in turn was positioned at the first glass-gel interface in the phantoms. The spectra extracted at the different gel-glass interfaces in the pure gel phantoms were used as correction factors for the spectra obtained at the corresponding glass-gel interfaces in the ICG doped gel phantoms. Not using this correction would result in a systematic error in the order of 100%–200% at the edges of the wavelength range.

Figure 3 shows the spectrum extracted with SOCT from a mirror reflection (black line), and the absorption profiles of ICG doped gels for two different dye concentrations (red and green lines) as measured with the spectrometer. Due to the partial overlap between the ICG absorption spectra and the light source emission spectrum, the relative error Δµ_a/µ_a was expected to be minimal in the wavelength region of 675 nm–840 nm.

Figure 4(a) shows the mean ICG absorption profile µ_a(λ) extracted from a 450 µm thick sample (red line) and the standard deviation of 4 measurements (50 scans each). Comparison with a reference ICG spectrum measured with the spectrometer from the same phantom (black line) demonstrates excellent agreement to within 2% in the central region and 8% at the edges of the 690 nm–810 nm wavelength range. Note that the statistical error quickly becomes larger for wavelengths shorter than 690 nm and longer than 810 nm. Similar measurements were obtained from an 180 µm thick phantom with the same ICG:gel ratio in the doped gel layer (see Fig. 4(b)). As expected, the measurement error in this case was higher - the agreement between the absorption profiles measured with OCT and the spectrometer was within 10% in the central region and larger than 50% at the edges of the examined wavelength range.

To evaluate the ability of SOCT to discriminate between regions in the sample with different absorption properties, measurements were performed in multilayered phantoms. Figure 5 shows absorption spectra extracted from two-layered samples using SOCT (red and green lines) and the spectrometer (black line). The insets in Figs. 5(a) and 5(b) show schematics of the multilayered gel-glass samples. In Fig. 5(a) a low absorptive layer (~490 µm) is positioned on top of a high absorptive layer (~530 µm). The SOCT precision in the wavelength range 690 nm–810 nm for the µ_a(λ) extracted from the top layer (average over 4 measurements, 50 scans each) appears similar to the precision achieved in single layered samples. Although the magnitude of the absorption profile of the bottom layer was ~1.5 to 2 times larger than the absorption of the top layer, the precision in this case was worse. In the reverse situation, shown in Fig. 5(b), when the low absorption layer (~510 µm) was below the high absorptive layer (~560 µm), the statistical error in the extracted absorption profile was greater than 80% at the edges of the examined wavelength range. The larger errors in Fig. 5(b) compared to Fig. 5(a) might be due to a different focal position within the samples. In Fig. 5(b) the larger systematic errors below 740 nm show that the correction procedure in this case was not optimized, because the pure gel phantom used for correction did not match the thickness.

The results obtained after correction from both the single and double layered gel samples (presented in Fig. 4 and Fig. 5) still exhibited significant variations in the extracted absorption profiles, larger at the edges and smaller in the central part of the wavelength region 690–850 nm. To investigate the error’s dependence on the wavelength, we calculated the expected error Δµ_a/µ_a by assuming a perfectly matched coherence gate, lack of chromatic aberrations and total differential change δ I ₀/I ₀ due to absorption 2dµ_a. This was accomplished by substituting in Eq. (3) the experimentally determined errors Δd=0.7 µm, ΔI ₀/I ₀(λ), ΔI/I(λ) and the absorption profile µ_a(λ) as measured with the spectrometer. The expected errors calculated for the top and bottom layers of a double layered sample and compared with the corresponding measurement errors (red line) are shown in Figs. 6(a) and 6(b). The figures show that the expected error is always smaller than the measurement error at the edges of the selected wavelength region. This result is most probably due to imperfect data correction procedure related to possible discrepancies between the thickness of the undoped and ICG-doped gel phantoms, as well as local absorption density variations. The increase in the error at wavelengths longer than 810 nm can be partially explained with the expected rise in imprecision resulting from the decreasing ICG absorption.

 

Fig. 5. Absorption profiles measured from double layered gel:ICG samples with SOCT (red and green lines) and with the spectrometer (black line). The insets shows schematics of the phantoms, light is incident from the top. (A) Low absorption layer on top (~490µm), high absorption layer below (~530µm). (B) High absorption layer (~560µm) on top of a low absorption layer (~510µm).

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The results presented so far demonstrate that with proper optimization of the data acquisition and processing procedures SOCT is capable of extracting absorption profiles of weak and small absorbers imbedded in very weakly scattering media with fairly high precision. Development of better focus tracking techniques along with methods for better compensation of chromatic aberrations can significantly improve the precision of the method in weakly or non-scattering media. However in turbid media such as biological tissue where scattering of light can be orders of magnitude larger than absorption and where spatial variations in the refractive index can be significant on a micrometer scale, precise alignment between the focal plane and the coherence gate may be challenging. Therefore extraction of absorption spectra from biological samples will necessitate development of novel data processing algorithms that are able to separately estimate the absorption and scattering properties of tissue.

 

Fig. 6. Comparison between the due to Eq. (3) expected error (black line) and the statistical error (red line) Δµ_a/µ_a(λ) (average of 4 profiles, 50 A-scans each) determined for a double layered phantom corresponding to Fig. 5(a). Absorption profiles measured from the top (A) and the bottom (B) layer of the phantom (green line).

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5. Conclusion

The results presented in this study demonstrate the feasibility of SOCT to extract spatially resolved, quantitive absorption profiles of weak and small absorbers imbedded in weakly scattering media with fairly high precision over a wavelength region equivalent to the FWHM of the light source. This result is very promising, considering the fact that the Ti:Al₂O₃ spectrum covers the absorption peak of deoxy-hemoglobin at 760 nm as well as the hemoglobin isosbestic point at around 800 nm providing an opportunity for evaluation of blood oxygenation. However, development of better focus tracking techniques and data processing algorithms that can overcome the limitations of the currently existing methods will be essential for the achievement of high precision µ_a(λ) measurements with SOCT. In addition, since light scattering in biological tissues is orders of magnitude larger than the absorption of blood, development of strategies how to differentiate absorption from scattering in highly scattering media will be necessary.