Depth resolved measurements of absorption profiles in the wavelength range of 800 nm with a bandwidth of 120 nm are demonstrated using high speed spectroscopic frequency domain OCT (SOCT) and a full range reconstruction algorithm (dispersion encoded full range, DEFR). The feasibility of the algorithm for SOCT is tested in simulation and experiment. With proper calibration, SOCT with DEFR is able to extract absolute, depth resolved absorption profiles over the whole wavelength range at once without the need of tuning and performing measurements at single wavelengths sequentially. The superior acquisition speed and better phase stability in frequency domain as compared to time domain results in a better reproducibility and practicability for spectroscopic measurements. In addition, high acquisition speed in excess of 20 kHz allows to measure absorption dynamics with 50 µs time resolution, which might be useful for the investigation of pharmacokinetics or pharmacodynamics. SOCT of ~600 µm thick single- and multilayered, non–scattering phantoms with varying absorption in the range of 5–80 cm-1, equivalent to blood absorption in capillaries, is presented. SOCT measurements are compared with those using a spectrometer in transmission mode. For Indocyanine Green (ICG), dynamic absorption measurements are demonstrated.
© 2009 Optical Society of America
Optical coherence tomography  (OCT) is an established modality for morphological imaging with micrometer-scale resolution in a variety of medical fields. It is mainly applied in ophthalmology [2, 3, 4, 5] and endoscopy [6, 7, 8].
Extensions of OCT that provide non-invasive depth resolved functional imaging of the investigated tissue should not only improve image contrast, but should also enable the differentiation and early detection of pathologies via localized spectroscopic properties or functional state. This includes the extraction of spectroscopic tissue information, e.g. metabolic information via absorption, which is related to functional parameters, like blood oxygenation levels [9, 10]. The principle of spectroscopic OCT (SOCT) was shown for non–scattering media in time–domain [11, 12] and frequency–domain (FD-) OCT . Xu et al. demonstrated a least square algorithm to separate scattering and absorption profiles for TD-OCT data  and described OCT with wavelength-dependent scattering . In  the performance of different time-frequency distributions are compared. The sensitivity and error estimation for a given time-domain set-up has been described . Recently Yi et al. have shown the recovery of absorption and scattering profiles for microspheres .
In SOCT the useful depth range is limited and usually smaller than the depth range for morphological measurements. This fact has multiple reasons. First, the roll-off  reduces signals which are farther away from the zero delay. Second, typical absorption in biological tissue leads only to small alterations of the spectrum of the light source. The way the absorption is then calculated, namely as logarithm of the ratio of two (nearly similar) spectra, enhances small errors in the spectrum. For larger samples it is therefore beneficial to utilize the full range.
In this paper we investigate the quantitative extraction of absorption coefficients in non–scattering phantoms using frequency domain OCT in combination with a full range technique, dispersion encoded full range (DEFR) . DEFR iteratively removes the complex conjugate image with a suppression of 50–60 dB, allowing to use both the positive and negative range around the zero delay.
We first evaluate in a simulation that the DEFR algorithm is suitable for extracting spectroscopic signals. The result of the simulation is then experimentally tested in single- and multilayered phantoms. In addition, dynamic changes in absorption profiles for indocyanine green dye (ICG) are being demonstrated.
The experimental set-up consists of a free-space interferometer (cf. Fig. 1) with a spectrometer at its exit. A Ti:Sapph laser with 120 nm bandwidth centered at 800 nm was used as light source. An achromat (f=50 mm) was utilized to focus into the samples. A variable neutral density (ND) filter was used to adjust the power incident at the sample between 0.5 and 2 mW. Detection was realized with a 27 kHz, 2048 pixel camera (Atmel Aviiva) and a reflective grating. The inherent depth-dependent signal loss if the spectrometer is shown in Fig. 2.
The sensitivity at zero delay was 96 dB [cf. Fig. (2)]. A reflection from a mirror, attenuated by a neutral density filter (ND=1.03) was measured at different zero delay positions (colored peaks). The black curve shows a second order polynomial fit of the individual SNR values (red diamonds). Maximum sensitivity for positions close to zero delay is smaller compared to Wojtkowski et al.  since the spectrometer used in our system is optimized for minimal sensitivity decay. The remaining sensitivity decay of 9 dB at 800 µm originates from small spectral overlap between adjacent CCD pixels. The DEFR processing causes no additional reduction of the sensitivity.
This section describes how the absorption is extracted from the measured spectra. First the frequency dependent components which contribute to the overall spectral change are identified. Reflectivities are noted as field reflectivities r, which is equal to the square root of the amplitude, or power reflectivity R: r=√R .
A large contribution to the overall spectral change is given by the chromatic aberration of the microscope lens. Figure 3 shows the dependence of the reflected spectrum on the displacement z between focus and zero delay. At zero-delay position the intensity is at its maximum, with a decrease for increasing displacement, which also includes the depth-dependent signal loss. In addition to the intensity, also the spectral shape changes with displacement.
In Fig. 4 the incident electrical field E 0 passes at depth z0 through the glass-medium interface with transmission coefficient (1-r 2 0(ω))1/2, reflected at depth z 1 with reflection coefficient r 1(ω). Absorption is usually described by Beer-Lambert’s law with an exponential decay of the intensities I=I 0 exp(-µd), with thickness d=z 1-z 0 and absorption coefficient m. The effect on the electrical field is than described by an exponential decay , with the exponential factor of originating from E∝√I.
The electric field ES, reflected from behind the absorbing medium can be described as
In the interferometer the two waves from sample and reference arm are recombined, and the detected intensity is described by
The spectroscopic information is contained in the envelope S̃ of the spectrum. The DC term is canceled by background subtraction, and the envelope S̃ is obtained by low pass filtering. The ratio of signals from two different surfaces S̃0(z 0) and S̃1(z 1) results with (1) and (2) in
with field reflectivities r, thickness d=z 1-z 0, and chromatic transfer function h(z) as defined above (cf. Fig. 3). The absorption coefficient originates from the medium between the reflective surfaces and includes also spectral backscattering, which is the main contribution to spectroscopic changes in biological tissue . To extract the absorption coefficient we propose a water normalization method. If we assume identical refractive indices for both water and sample, the reflectivities at the interfaces under investigation are equal as well. With the measured signal from a glass-water interface the normalization leads (3) to
which allows easy extraction of the absorption coefficient.
The DEFR algorithm and the simulation require manipulation of the dispersion. From (1) the phase factor can be written as Taylor expansion series :
with ai the dispersion coefficient of order i. It is usually sufficient to correct dispersion up to third order.
2.3. Signal Processing
In frequency domain OCT the time-domain signal is basically generated by inverse Fourier transform of the measured spectrum. The processing algorithm (Fig. 5), realized in labview, starts with a resampling of the spectrum from wavelength λ to frequency ω, followed by background subtraction and the DEFR algorithm. This algorithm works on the principle, that the dispersion mismatch of the OCT system can be compensated during post-processing by phase manipulation of the frequency domain signals. If the phase ϕ compensates the dispersion for a non-dispersion balanced system, the mirror terms are broadened. When the negative phase -ϕ is applied, these mirror terms appear sharp, which allows to remove them from the data. The suppression of the complex conjugate terms is 50–60 dB. A detailed description of the algorithm can be found in .
In the next step reflections from the desired surfaces are filtered in spatial domain: The spectrum is transformed into the spatial (or time) domain by inverse Fourier transform, spatially filtered, and transformed back into frequency domain. After this step the spectra are connected to a given depth, as chosen by the spatial filter. The envelopes of the spectra S̃ are then extracted by low pass filtering. Water normalization is applied before in the final step the absorption is calculated.
In order to evaluate DEFR for spectroscopic OCT measurements a simulated signal was fed into the full range reconstruction algorithm (dispersion encoded full range, DEFR). The output was then evaluated against the input and error measures were calculated. Resampling was not necessary, as the spectra are already equidistant in frequency. The simulation was implemented in Matlab.
First a sample was defined, given by a set of individual time domain interface signals. Absorption and dispersion values between the surfaces as well as global dispersion were added in the frequency domain. The spectral shape of the light source was Gaussian with a full-width-half-maximumof 1024, corresponding to half the number of pixels. The shape of the absorption spectrum was following the shape of the light spectrum. Figure 6 (left) shows an example for two surfaces situated at -100 and 120 µm around the zero delay. The dashed line (left, top) showing the originally defined positions, the black line showing the absolute part of the time domain signal after adding absorption, dispersion (a 2=3.6×10-5), and noise to the frequency domain signal. This complex ambiguity-free signal was used for baseline calculation of the absorption without compensating for dispersion. Windowed Fourier transform (cosine tapered window, 128 pixel) was applied to extract the spectra. The center position of the windows was automatically adjusted to the centre of the corresponding peak. This was necessary because peak broadening caused by dispersion is not symmetric around the original peak positions, although the peak shape itself stays symmetric for second order dispersion (cf. Fig. 6, left).
In the next step the real part of the complex spectrum was used as input for the DEFR-algorithm. Figure 6 (left, bottom) shows the time-domain signal output from the algorithm (solid blue line). Residuals from the complex conjugates are visible neighbored to the main peaks. The suppression is >60 dB. As comparison the time domain signal, calculated in the standard way using the inverse Fourier transform, is shown (dashed line, dispersion not compensated). Note that this signal also shows the well known ambiguity.
As mentioned above, noise was added to the spectrum in the frequency domain, simulating a certain signal–to–noise–ratio (SNR). For SNRFD=0, the corresponding SNR in time-domain (SNRTD) is still ≈5dB. Because noise in frequency domain is distributed over all frequencies [19, 23], after Fourier transform the peaks corresponding to spatial frequencies are still visible above the noise (cf. Fig. 6 right, top). Figure 6 right, bottom shows the nearly linear correspondence between SNRFD and SNRTD (average of 4).
The time domain signal from the DEFR output was spatially filtered with a cosine tapered window (128 pixel) at the peak positions, and the individual spectra were calculated using the Fourier transform. The absorption was then calculated as the decadic logarithm of the ratio of the individual spectra, divided by the distance between the peaks. As error measures the mean absolute error (MAE) and the root-mean-square (RMS) were used:
with µ 0 the input, and µ the output absorption values. The errors are evaluated only for values with index i, where µ (i) 0≥0.1 max(m0). The MAE is a measure for the mean deviation from the input signal, whereas the RMS indicates the distribution of the error. The MAE equals one, when the absolute error is one for each measurement point. A larger RMS indicates that the error is less evenly distributed.
2.5. Experiment and Sample Preparation
Two different kinds of experiments were performed, measuring static and dynamic absorption. For both experiments the measurement beam was blocked until start of the measurement in order to prevent bleaching of the samples. Static absorption measurements were recorded over a short time (<50 ms). Within this time frame no changes in absorption due to photobleaching were observed. From six different positions 50 absorption profiles were averaged, resulting in a total of 300 averaged spectra. Within one position the error was negligible.
For dynamic measurements the reflected intensity was recorded over ~15 s, allowing to measure absorption changes.
Single and double-layered phantoms consisted of drops of absorbing medium (ICG and IR 820 dye solved in water) between glass slides (Fig. 1 a and b) with varying absorption.
An initial concentration S0 of ~8 g/l of IR820 was prepared. For the final concentrations S0 was then diluted with destilled water between 1:2 and 1:12 (S0 : H2O). A 5 ml drop was placed on a microscope glass slide between two cover glasses (~200 µm), and then covered with a cover glass. For double layered samples, on top of this cover glass a slightly smaller (3 µl) second drop of different concentration was placed. This drop was again covered with a cover glass slide. The different size of the drops was necessary in order to equalize capillary forces and prevent displacement of the central cover glass.
3. Results and Discussion
First the behavior of the DEFR algorithm was investigated for second order dispersion coefficients without adding noise. Figure 7 shows as an example the extracted absorption profiles for baseline (solid black line), DEFR (solid red line), and the input profile (dotted blue line) for three different global 2nd order dispersion coefficients.
Baseline and input absorption differ only on a very small scale (10-4) and appear therefore on top of each other. Absorption extracted from DEFR algorithm is strongly modulated for lower dispersion, resulting from residuals. They are responsible for higherMAE and RMS values [cf. Eq. (5)], as shown in table 1. Filtering of the extracted absorption would reduce the modulations and decrease the error, but was not implemented in the simulation. With increasing dispersion, both MAE and RMS decrease.
The error distribution for a range of global 2nd order dispersion is shown in Fig. 8, left, for baseline (black) and DEFR (red). Error measures are defined in Eq. (5). The RMS value is close to the MAE, indicating an evenly distributed error. With increasing global 2nd order dispersion the residuals and therefore the error of the DEFR algorithm decreases. For a 2>10-5 the error becomes negligible (<10-1 cm-1), but is still two orders of magnitude above the baseline. The rise in the baseline error for higher dispersion can be explained by broadening of the peaks in the time domain. During data processing the applied windowed Fourier transform is clipping parts of the the data. Third order dispersion did show only an effect when the second order dispersion was set to zero (not shown).
The influence of the system’s SNR is shown in Fig. 8 (right). As expected, errors for baseline and DEFR decrease with increasing SNR, with both following the same characteristic. Below 20 dB the error is 100% (relative to the maximum absorption of 10 cm-1), decreasing to ~10% at 40 dB SNR. The DEFR error appears close to baseline, saturating at ~70 dB and 4×10-2 cm-1. In the interval from 10 to 70 dB their behavior can be modelled with
indicated by dashed lines. The DEFR algorithm shows good performance for SOCT. The SNR should be at least 40 dB in order to achieve errors below 10%.
For the experiment the dispersion of the focusing lens in the sample arm was not compensated and was responsible for a peak broadening similar to the one shown in Fig. 6, corresponding to a second order dispersion of ~4×10-5. Global dispersion was sufficient to assure good performance of the DEFR algorithm.
Static absorption The wavelength calibration was tested by measuring two absorptive bandpass filters (780 and 850 nm, 10 nm bandwidth). The result obtained with OCT was then compared to a measurement with an independent spectrometer (Ocean Optics). Figure 9 shows that both measurements are in good agreement. The slight shift for 780 nm is caused by tilting of the filter.
Figure 10 shows the result for a single layered phantom of 600 µm thickness, averaging 50 profiles from 6 positions (Fig 10, solid red line); dotted lines showing the standard deviation. The measured absorption profile is in good agreement with the reference measurement (black line). IR 820 dye solved in water was used as absorptive media. The absorption coefficient was between 4 and 8 cm-1, comparable to the absorption of blood. As control the absorption of water was also measured (Fig. 10, solid blue line). The resulting exponent in Eq. (4) after water normalization leads to the difference of the absorption coefficients from the sample under investigation, and water. Both are identical for a water sample. Therefore the extracted absorption should be zero, which is not the case. The deviation of the extracted water absorption from zero gives an error estimate for repeatability and indicates that the procedure is as accurate as ~±2 cm-1.
Figure 11 shows the results for two double layered phantoms of weaker (10 to 25 cm-1, left) and stronger absorption (20 to 90 cm-1, right), with the weaker layer C1 in both cases situated below the stronger layer C2. Thickness of the absorptive layers was ~200 µm, separated by a microscope cover glass plate of the same thickness. Apart from modulations the extracted absorptions show general agreementwith independentlymeasured referencemeasurements (black lines).
The generally modulated appearance of the absorption spectra has different possible explanations. The modulations could be caused by the residual of the DEFR algorithm, but this is not supported by the simulation results. Interestingly also the standard deviation varies with wavelength. At some wavelengths the different measurements used for averaging show better agreement, which could indicate polarization changes. Also, the modulations in the reflectivity curves do not appear as pronounced as in the absorption profiles. The logarithm in the calculation process has the tendency to enhance errors.
The strongest layer (cf. Fig. 11, right, red line) has a larger deviation from the reference at shorter wavelengths, indicating that the OCT signals are getting too small for reliable quantitative measurements. The upper absorption limit for a 600 µm thick sample is therefore around 80 cm-1.
Dynamic absorption The high measurement speed of the camera of 20 kHz, corresponding to 50 µs per spectrum, allows to measure absorption dynamics. Figure 12 shows the time course of the total reflected power from a glass surface behind an ICG sample for two different power levels of 0.43 mW and 0.97 mW incident on the sample. The reflected power is showing an increase over time, indicating a decreasing absorption with time. After ~15 s the reflectivity was reaching a saturation plateau.
In addition the spectral characteristic of the absorption change over time can be extracted. Figure 13 shows the time evolution of the spectral absorption profile in the range of 5 s. It reveals that not only the total absorption changes over time as shown in Fig. (12), but also the spectral characteristic of the absorption. In the beginning the absorption for longer wavelengths is stronger than for shorter wavelengths, after ~300 ms absorption for shorter wavelengths becomes more pronounced.
4. Conclusion and Outlook
We showed that the dispersion encoded full range algorithm (DEFR) is suitable for spectroscopic OCT in simulation and experiment. We showed that quantitative spectroscopicmeasurements using OCT need a proper calibration to account for chromatic aberrations. Spectroscopic measurements in single- and double-layered phantoms, demonstrating the ability to obtain depth-resolved spectra from non–scattering media, were presented. Dynamic measurements with a time resolution of 50 µs have been demonstrated, showing the time course of the bleaching effect in an ICG dye sample.
In the next step we would like to include scattering in phantoms and move towards biological samples. Xu et al.  have proposed a method to separate scattering and absorption. The DEFR algorithm was shown to work for retinal tissue without obscuring the morphology . How the combination of SOCT end DEFR will work in the presence of chromophores needs to be investigated.
Time- and depth-resolved spectroscopic measurements could be of interest for measuring pharmacokinetics and pharmacodynamics. To extend the sensitivity range or to monitor concentrations of molecules, exogenous contrast agents, e.g. nanoshells could be applied.
We acknowledge technical support by B. Považay and financial support by Cardiff University; BBSRC; EU STREPT FP6-IST-NMP-2 (017128); EU STREPT (Nano UB-Sources); EU FUN OCT (FP7 HEALTH, contract no. 201880); Christian Doppler Society, Austria; Femtolasers Produktions GmbH, Austria.
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