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In the comment to our paper [1], Kraszewski et al argue that estimation of hemoglobin oxygen saturation (SO₂) from Spectroscopic Optical Coherence Tomography (SOCT) can be obtained with <1% accuracy by optimizing the shape of the window function used in the spectral anlysis. Specifically, more accurate recovery of the absorption spectrum of hemoblobin from SOCT simulations was found using a rounded rectangular window as compared to the ‘standard’ Gaussian window function of comparible width. This is clinically important because an accuracy of ~2% in SO₂ determination; ~0.5 g/L in total hemoglobin concentration and consequently ~0.1 mm⁻¹ in absorption coefficient is desired.

The use of a Gaussian window is beneficial because it minimizes the product of window duration (in one domain) and bandwidth (in the other domain). Morover, the shape of the window is the same in both domains. Consequently, the Gaussian window function is indifferent to which domain the data is acquired; application to time-domain OCT and spectral domain OCT yields identical time-frequency distributions (TFDs).

To illustrate, we repeated our earlier simulations [1] of a blood layer of 25 μm thickness, total hemoglobin concentration 150 g/l, hemoglobin oxygen saturation SO₂ = 85% (Case 1 in our paper). Figure 1 shows obtained TFDs (or depth-wavenumber distributions) using a smoothed rectangular window as defined by Kraszewski et al (left pane) and our previously used Gaussian window of 22 μm duration in the spatial domain (linear amplitude scale). The duration of the smoothed rectangular window is chosen at 13 μm, ensuring that both windows have the same −3dB width in the spatial domain.

 

Fig. 1 Time-frequency distributions of the simulated OCT signal from a 25 μm thin blood layer. Left pane: using a smoothed rectangular window function of 13 μm duration in the spatial domain; right pane: using a Gaussian window of 22 μm duration in the spatial domain. Both window functions have equal −3dB width; amplitudes are represented on a linear scale.

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From these TFDs, the A-scan at the center wavenumber (12 μm⁻¹) can be extracted as a representation of the spatial resolution at which spectra can be obtained. Spectra of the front and back surface of the blood layer are found from the spectra at the respective depth coordinates (220 and 245 μm, respectively) from which the absorption spectrum can be estimated using Beer’s law. The results are shown in Fig. 2.

 

Fig. 2 Left pane: OCT signal amplitude vs depth at center wavenumber k₀ = 12 μm⁻¹. Right pane: retreived absorption spectra from the front and backsurface reflection of the blood layer. Red curves are based on time-frequency analysis using a smoothed rectangular window as proposed by Kraszewski et al; blue curves use a Gaussian window as in our previous work [1].

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The hemoglobin oxygen saturation obtained from these simulations are SO₂ = 80% (smoothed rectangular window) and SO₂ = 70% (Gaussian window), consistent with the results of Kraszewski and our previous simulations [1]. We also tested the robustness to noise by decreasing the SNR from 100 dB downto 50 dB. The smoothed rectangular window consistantly yields values closer to the actual value of SO₂ = 85%.

Kraszewski finds a smoothed rectangular window as the optimal window shape in the spatial domain (i.e.. z → k transormation). Wheter this window shape is optimal when applied to data acquired in the spectral domain (i.e. k → z transformation) remains to be investigated. Such simulations are beyond the scope of this Reply.

We conclude that our simulations show good qualitative agreement with the results of Kraszewski. We therefore support their conclusion that SOCT optimization should include window shape, next to choice of window size and analysis algorithm.