Chao's Blog

If you are interested in this paper Shot-noise limited, supercontinuum-based optical coherence tomography, please find it here.

# Main contribution

Current supercontinuum (SC) -based SD-OCT system cannot be operated in the shot-noise limited area because of its strong pulse-to-pulse relative intensity noise of the supercontinuum source. The authors propose an all-normal dispersion (ANDi) fiber based supercontinuum source, which is pumped by a femtosecond laser, to overcome this problem. The 90MHZ ANDi SC source show lower noise, better sensitivity, higher contrast, and improved penetration when compared with the state-of-the-art SC source at 80 and 320MHZ repetition rate.

# Limitation of SC source

The main disadvantage of SC laser sources in OCT is the strong pulse-to-pulse relative intensity fluctuations, which limits the sensitivity of OCT far from ideal shot-noise limit. One method to alleviate this problem is to use high (320MHZ) repetition rate SC sources to average out some of the intensity noise. The reason behind this common intensity noise problem of SC sources lies in the fact:

In most commercial SC sources, the broadband light is generated by launching a long [picosecond (ps) or nanosecond (ns)] light pulse through a nonlinear optical fiber. Complex interplay between linear and nonlinear effects create solitons and dispersive waves (DWs) that together constitute an ultrawide spectrum covering several octaves. In the regime of long pulses, the initial broadening of the SC is generated by nonlinear amplification of quantum noise, and the resulting spectra are thus particularly noisy and uncorrelated from pulse-to-pulse.

Even short pulse [femtosecond (fs)] regime for SC sources has its own restrictions, for example, polarization coupling, nonlinear effects and pump laser noise. All these together make fs-based SC sources less broadband and of lower power.

# New design of the SC source

The SD-OCT system is working around 1370nm with an axial resolution of 5.9\mu m. The customized SC laser source uses a fiber with weak all-normal dispersion pumped by a fs laser, in which the spectral broadening is dominated by the coherent process of self-phase modulation and optical wave-breaking. The weak normal dispersion and short pulse length ensure that some noise effects, such as parametric Raman noise and polarization mode instability, can be avoided.

# Results

\sigma _{r + d}^2 is the read out and dark noise from the spectrometer, which is independent of input power. \sigma _{shot}^2$ is the shot-noise, which obeys Poisson statistics and scales linearly with the power incident on the spectrometer. \sigma _{ex}^2 is the excess photon noise, in this case due to the pulse-to-pulse relative intensity noise (RIN) fluctuations of the SC source. \sigma _{ex}^2 scales with the square of the incident power. It can be seen from Fig.1 (a) and (b) that the high RIN of the 80 and 320 MHz SuperK extreme sources does not allow the OCT system to be operated in the shot-noise limited region (250 counts can be the optimum situation). On the other hand, the excess noise of the ANDi SC source never dominates within the dynamic range of the spectrometer, and for readings over 1000 counts the recorded variance remains shot-noise limited (Fig.1 (c)). Fig.1. The variance in counts versus the mean counts (over 1024 measurements) at 1432 nm for the 80 MHz SuperK extreme (a), 320 MHz SuperK extreme (b), and ANDi SC source with 90 MHz repetition rate (c) (From the original paper). After the optimum counts are chosen for each SC source, the A-scans are performed to evaluated the noise effect (the sample arm is blocked). It can be seen from Fig.1 (g) that the ANDi SC source provides a significant improvement in A-scan variance for all optical path differences (OPDs) of about 13 dB compared with the 80 MHz SuperK extreme source and 9 dB compared with the 320 MHz SuperK extreme source. This means that ANDi SC source can provide a darker background in SD-OCT imaging. Fig.1.(f) spectral counts across the spectrometer bandwidth for the three sources, when the counts at 1432 nm is fixed at the optimum value for imaging (250 counts for SuperK extreme sources and 1000 counts for the ANDi SC source); (g) Corresponding variance in A-scans over 1024 measurements. (From the original paper). ## Images For the B-scan of adhesive tape, the ANDi SC source gives the largest signal contrast of the reflections from the plastic to adhesive interfaces compared with 80MHZ and 320MHZ SuperK extreme source, as shown in Fig.2 (a), (b) and (c). In Fig.2 (d), the average is taken over 146$\mu m\$ wide (49 A-scans) dotted box in Fig. 2 (b). The plastic is scattering much than the adhesive, and thus the maxima in the A-scan represents the plastic, while the valley represents the adhesive. It can be seen that ANDi SC offers a contrast of 5.4dB for layer structure, compared with 2.9dB and 3.6dB from 80MHZ and 320MHZ SuperK extreme sources.

Fig.2 Single B-scans of tape layers (2 × 3 mm), obtained using the 80 MHz SuperK extreme (a), ANDi SC (b),and 320 MHz SuperK extreme (c) sources. Averaged A-scans within the 146 μm wide dotted box in (b) for the three sources offset by 5 dB (d).

The imaging performance of the ANDi SC source is also tested on a mouse retina, mainly focusing on the lower part of the retina around the optical nerve, as dash-boxed of the B-scan (averaged over 9 B-scans) in Fig.3 (c). Compared with 80MHZ and 320MHZ SuperK sources, the ANDi source provides a better contrast up to 5.3dB (Fig. 3 (d), (e), (f), (g)).

Fig.3 Ex vivo rat-eye imaging: Artistic image of a mouse eye (a) with a cross-sectional schematic shown in (b). Single B-scan OCT image in depth of a 1.95 × 2.62 mm section of a mouse retina obtained using the ANDi SC source (c). Averaged A-scans (averaged over 4 equally spaced A-scans) from the marked region in (f) for the three sources (d). Zooms of the retina and optic nerve in the area marked by a yellow box in (c) using the 80 MHz SuperK extreme (e), ANDi SC (f), and 320 MHz SuperK extreme (g) sources.

## Sensitivity

The sensitivity of OCT system is commonly expressed as the signal-noise-ratio for a perfect reflector:

where SNR_{\max } is the maximum of the detected point spread function of the reflector, and the sigmas are the respective noise contributions from spectrometer, shot noise and excess noise from the SC source.

From Fig. 4, we can see that the 80MHZ and 320MHZ SuperK extreme sources must be operated under a reference power (about 250 counts), at which the total noise level is dominated by the RIN of the source. It indeed limits the maximum sensitivity. For the ANDi source, on the contrary, the reference power can be increased very close to the shot-noise limit until the detector reaches its saturation. Considering the limitation of high read out and dark noise of the InGaAs detector used in the OCT system, the maximum reference power is reduced to about 1000 counts, leading to a maximum sensitivity of 96 dB. This is 7 dB above the maximum achievable sensitivity when using the 320 MHz SuperK extreme source, but still 6 dB below the maximum shot-noise limit.

Fig.4 Theoretical sensitivity as a function of reference power for the 80 MHz SuperK extreme, 320 MHz SuperK extreme, and ANDi SC sources. Stars represent the experimentally obtained sensitivities presented in the materials and methods section.