In this paper we presented a high speed complex SD-OCT system, based on a very fast electro optic phase modulator. An imaging speed of 10000 A-lines/s equivalent to 5000 complex full range A-lines was achieved. This is an improvement of more than one order of magnitude as compared to previously reported complex SD-OCT. A further advantage of using an electro optic phase modulator is that this device is not limited to sinusoidal phase shifts at high frequency (as mechanically moving mirrors are due to their inertia). Since the cutoff frequency of the phase modulator is 100 MHz, it is able to support all the higher harmonics necessary to generate smooth, high frequency rectangular waveforms which fulfill the requirements of the phase shifting method better than a sinusoidal wave form.
The modified two-frame technique presented in this paper solves a problem of the original version of the algorithm, the suppression of symmetric structure terms. Although the original version provides images that can be used to derive the shape of the different structures of the anterior chamber and to determine the boundaries of, e.g., iris and cornea with great accuracy (cf. ), the shadows observed at object structures symmetric to the zero position degrade the image quality and prevent a quantitative determination of signal intensities. These image artifacts are likely to be more critical in strongly scattering tissue. The new, enhanced algorithm solves this problem. The quantity ΔM(τ)
is used to determine the locations of symmetric structure terms. It should be pointed out that the measured value of ΔM(τ)
cannot be used directly as a measure of the signal magnitude of these symmetric terms. The reason is that the measured value of ΔM
deviates from the value provided by eq. (8)
by a factor that depends on the initial phase offset of the cosine terms of which I(ν)
consists (the phase offset was assumed to be zero in the derivation of eq.(8)
). This factor varies between 1 (zero phase offset) and 0 (45° phase offset). Therefore, ΔM(τ)
is just used to locate the positions of the symmetric structure terms; their values are obtained by gating signal S1(τ)
with the positions where ΔM(τ)
exceeds a threshold larger than noise. Only in rare cases, where the initial phase offset of a cosine term in the real-valued intensity signal I(ν)
will be close to 45°, the method might fail (because then ΔM
will be zero). However, given the random distribution of backscattering sites in scattering tissue, only a very small fraction of data points will be missed for this reason, and in a logarithmic intensity plot, as usual in OCT, this effect will probably be negligible.
Although the phase shift provided by the electro optic phase modulator has the required rectangular waveform, there are additional sources of phase instabilities that can degrade the results. Before we discuss the different sources of phase errors, we analyze their possible consequences.
Our derivations in section 2 were based on a phase shift Δ
= 90° between alternate A-lines. Only in this case, the separation of structure and mirror terms in signals S1(τ)
will be perfect. If Δ
deviates from 90°, signal S1(τ)
will contain residual mirror terms, and signal S2(τ)
will contain residual structure terms. However, these residual terms in S1
have no influence on the suppression of the mirror image in the actually displayed signal ΔS+(τ)
) (as long as the residual mirror term is not stronger than the real structure term). This can best be seen in an example where a large deviation from the ideal value of Δ
= 90° is introduced. shows such an example, where Δ
40° (sample: attenuated mirror). From , which shows signals S1
, it can be seen that the residual mirror term has ~ half of the amplitude of the real structure term. After calculating ΔS
(), the real structure term is reduced in height (by a factor of ~ 2), and a corresponding negative mirror term is observed. In a final step, ΔS+
is calculated (). The negative mirror term is eliminated by the step function, the reduced structure term remains. This example shows that phase errors have no influence on the effectiveness of the algorithm to eliminate mirror terms. Instead, the effect of phase errors is to reduce the signal magnitude of real structure terms (because the residual mirror terms are subtracted). The consequence is a reduction of SNR. Simulations have shown that a phase error of 30° causes a SNR drop by 3 dB. This indicates that our algorithm is rather immune to small phase errors. If, on the other hand, very large phase errors occur (> 90°), real image and mirror image are reversed (cf. ).
Fig. 4 Effect of phase error. A-lines obtained from single reflecting surface (cf. ). Abscissa: distance (mm), ordinate: signal amplitude (linear scale, arbitrary units, normalized to amplitude of structure peak of signal S1 in (a)). (a) Signals S1 (black) (more ...)
Fig. 5 Image of human anterior chamber showing motion artifacts. Size of imaged area: 5.9 mm (horizontal, optical distance) × 8 mm (vertical); each image consists of 800 A-lines. Logarithmic intensity scale. (a) Image obtained from inverse Fourier transform (more ...)
We now discuss possible sources of phase errors and the impact they might have on the results. One source of phase error can be interferometric jitter. However, since we use a very short integration time of 100 μs, this can easily be avoided. A second possible error source is polychromatic phase error. The phase shift introduced by the electro optic modulator depends on the wavelength. If a perfect 90° phase shift is introduced for the center wavelength λ0, the shift will deviate from 90° for the other wavelengths of the broadband source. With λ0 = 821 nm and δλ = 25 nm, as used in our setup, the polychromatic phase error within the FWHM bandwidth will not exceed 1.4°. This can be neglected in the light of the previous discussion.
Another source of error is a phase change due to the galvanometer scanner movement between the two A-scans necessary to compute the complex signal. This effect has to be divided into two different sources of phase error. The first phase change arises from the sample path length variation with varying scanner angle. The sample path length shows a quadratic dependence on the angle of the scanner [20
]. An additional phase change occurs, if the beam incident upon the scanning mirror does not fall on its axis of rotation [21
]. This path length change depends on the off pivot point distance and on the angle of the scanner. The corresponding phase instabilities can be quite large. The example shown in was taken from an experiment where the incident beam position on the scanner was not exactly the pivot point of the scanner.
To avoid SNR degradation, the incident beam onto the scanners has to be carefully adjusted, ensuring pivot point illumination. It is clear that the effect of scanner movement strongly depends on the scanner velocity and the integration time. Therefore measurements might be difficult to realize, where a fast scanner velocity is necessary (e. g. 3D measurements). Further quantitative investigations are necessary to look into this problem in more detail. One solution would be to drive the scanner with a stepwise waveform. However, up to now no scanners with an appropriate response time (due to the very short integration time used in modern SD-OCT systems) are available.
A further source of phase errors are involuntary movements of the subject. In case of large movements, signals similar to those in can be observed. The flip of the image approximately at its middle position occurred due to an involuntary movement of the subject which caused a phase error larger than 90°. In this case, signals S1
are switched, which, after calculation of ΔS+
, results in a flip of the image. This motion induced artifact must not be confused with the so called phase washout. A detailed description of this phenomenon can be found in [22
The previous discussion has shown that some phase instabilities can be a problem with our technique. A possible solution to this problem will be to further decrease the integration time for one A-scan. Our camera allows integration times down to 35 μs. This should be possible without decreasing the signal to noise ratio, if the light power is increased. In our application, the light is focused on the cornea and divergent on the retina (divergence angle
19 mrad). This corresponds to viewing of an extended light source, for which the ANSI standards [23
] allow an illuminating power of
7.6 mW for illumination times > 15 s in the case of the parameters (λ, α) used in our setup.
In conclusion we presented a high speed experimental setup of a full range complex SD-OCT system using a 2 frame technique with the capability to measure 10000 A-scans per second. This is more than 20 times faster than previously published results [13
]. A modified two-frame algorithm prevents cancellation of symmetric structure signals. To demonstrate the possibility of in vivo measurements with this method, we presented images of the anterior chamber of a human eye in vivo with a recording time of 160 ms per image. The short imaging time allows to record images from the anterior segment without motion induced distortions. Nevertheless, decrease of sensitivity with depth is still a major problem of SD-OCT, especially when measuring thick tissue (e. g. anterior chamber). Future work will concentrate on possibilities to overcome this sensitivity decrease.