Spectral Domain OCT: Calibration

To convert a spectral domain signal to an OCT A-scan, the signal must be sampled evenly as a function of wavenumber and Fourier Transformed. Calibration is required in order to resample the measured signal to be evenly spaced with respect to wavenumber. Consider that the desired sample value, S(ks), occurs at circular wavenumber, ks, which is between two actually sampled circular wavenumbers, kn-1 and kn. The value S(ks) is assumed to line upon a line drawn between the values S(kn-1) and S(kn). The equation for this line is given below:



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From the perspective of the CCD pixel data, the circular wavenumbers k correspond to pixels p. The signal read from the pixel array is S(p). By rearranging equation above, the desired signal value, S(ps), can be described as a weighted sum of the actual sampled values S(pn-1) and S(pn), as shown below.



To resample the data, only three variables need be recorded for each desired sample location, ps: W1, W2, and n. To determine the desired sample values, S(ps), consider the simple case of a mirror in both the sample and reference arms at a nonzero optical path difference, opd. The phase of the spectral signal is phi = ko opd + phi(ko)[dispersion], where ko is the circular wavenumber in free space, ko = 2 π / λ. Without the system dispersion term, the phase, phi, should be linear with respect to circular wavenumber ko. To eliminate the system dispersion term, the spectra from the mirror at two different opds are collected, resulting in the phase terms phi[1] and phi[2].



Since the dispersion term is the same for both phi[1] and phi[2], subtracting the two results in the term Δphi which is free of system dispersion.



Linear interpolation between the maximum and minimum phase can be used to find the desired sample locations, ps. The locations ps must lie between actually sampled locations pn-1 and pn. The calibration algorithm using MATLAB is described below which identifies these indices pn and weighting coefficients W1 and W2.

After resampling phi[1] or phi[2], any nonlinearity must be due to the system dispersion term, phi[dispersion]. By fitting phi[1] or phi[2] to a line and subtracting the fitted line from the phi[1] or phi[2], the system dispersion term, phi[dispersion] is isolated. The same MATLAB code computes phi[dispersion] for every resampled pixel and saves it along with W1, W2, and n.

While the procedure described assumes a shift in air of the mirror location, a similar procedure can be used in which the shift is an a dispersive medium like water. In this case, the sample locations ps are found for sampling evenly with respect to the circular wavenumber in water, k[water]. This type of resampling is proposed by Marks, et al. and Tumlinson, et al. to eliminate sample dispersion. Sampling with respect to the circular wavenumber in water means that additional path differences of water, such as differences in the vitreous humor length in the eye, will not result in image degradation due to dispersion. The system user must beware, however, that additional path differences in air will become dispersive using this procedure.