for project “Comprehensive theory of noise in SC optical sources and out of interferometers driven by SC optical sources”
Part 1: Noise in supercontinuum sources
Noise from optical sources is one particular concern when designing an OCT imaging system. The commercial needs for resolution and sensitivity often come as a compromise to image quality. A low noise Ti:Sapphire source or SLD suits the primitive purpose of endoscopy and skin imaging.
However, the narrow bandwidth of these lasers provides limited imaging range to that of a broadband supercontinuum (SC) source. SC has in recent years show promising results in terms of ultra high axial resolution for clinical use. Proper characterisation of noise performance in existing SC sources is essential.
The fundamental in understanding noise in optical sources relies on a good understanding on different type of noise. Noise in an optical source can be broadly categorised into RIN, shot noise and excess photon noise. The contribution of these noise terms in SC sources can be characterised based on the power level required for broad spectrum generation.
We can evaluate shot noise and excess noise bandwidth using the following relations, where shot noise current equation (IDC), and shot noise threshold equation (Ith) are proportional to bandwidth of our optical source (Δλ). In narrowband sources like the superluminescent diodes (SLD), typical bandwidth is 50 nm to 100 nm. In ultra broadband supercontinuum sources, for example NKT SuperK Extreme or Fianium WhiteLase, the usable optical bandwidth for OCT application can be as wide as 2000 nm.
In the equations below, the parameters Δq denotes the quantum electron charge (per unit Coulomb), t is time (in seconds), v is the optical freqeuencies (in Hz) and c is the speed of light constant (3 × 108 m/s).
In a shot noise limited system, a further increase in optical power at the source will noise improve signal-to-noise performance of an imaging system. The two summing terms in equation (R<Idc²>) are shot noise and EPN respectively. For complete derivations, refer paper by C. Rosa and A. Podoleanu, titled “Limitation of the achievable signal-to-noise ratio in optical coherence tomography due to mismatch of the balanced receiver”
For the purpose of noise characterisation, a simple time domain interferometer was constructed. This is a typical Michelson interferometer. It consists of two single mode fibre couplers (DC1 and DC2), purchased from AFW technologies, Australia. The two couplers have different splitting / combining power ratios, DC1 at 80:20, while DC2 at 50:50. The use of unequal ratio allows better optimisation of SNR of the OCT system.
Figure 1 above illustrates the principle of operation for a time-domain interferometer system used for noise and signal-to-noise measurement. The legends used are FPR: fibre injector with achromatic lens; M: mirror; DC: directional coupler; PD: InGaAs photodiode module model PIN G10899 with a 0.8 or higher responsivity for wavelengths 800-1700 nm.
Part 2: Noise measurement
Two separate studies were performed to evaluate noise bandwidth effect to time-domain OCT system.
For that purpose, a dual output balance photodetector, consists of a rectified sum and difference output, was constructed. A rectified DC output VDC, was used to monitor the linear DC current to input voltage across a 2.2kΩ resistor. A parallel connection to an AC voltmeter were made to record small photocurrent fluctuation for frequencies up to 100 kHz. Relationship between AC and DC photocurrent shows contribution to shot noise and excess photon noise terms from different optical sources.
Total noise term <RI2> = <ΔI2rms>
Fig.2: Balance heterodyne photoreceiver module used for OCT noise characterisation
Noise power and OCT SNR measurement
Fig.3: (top) Measured noise power variation with respect to input power into system. (bottom) Measured SNR in time-domain OCT system in variation to reference arm power with four different optical sources of 35nm
Based on our measurement data, we have concluded that in order to achieve high SNR imaging with OCT system, a low-noise supercontinuum operating in the excess photon noise regime is needed. Even though the contribution of shot, quantum and excess photon noise are low in comparison to intensity noise in existing supercontinuum sources, a further improvement of 5 dB in SNR could be attained with a low noise broadband SC source (BW>150 nm)