Sensitivity and dynamic range

In this chapter, several important characteristic parameters for OCT imaging are defined and corresponding measurements determining these parameters are introduced. Since within the research work presented in this thesis all OCT imaging was based on the swept source approach, the following analysis is restricted to SS-OCT. However, the principle easily can be transferred to other OCT techniques.

2.1.4.1 Sensitivity

The sensitivity in an OCT system is defined as the ratio of incident power on the sample to the minimum detectable power that is backscattered from a certain depth corresponding to a path length difference . Sensitivity is given in a logarithmic rep-resentation:

2.17 The sensitivity can also be defined as the ratio of peak detector current signal in the Fourier transform (equation 2.10) to the corresponding value of the minimum detectable power . Note that the additional factor 2 stems from the fact that . Moreover, the sensitivity is directly linked to the smallest possi-ble power reflectivity that enables detection of backscattered light. One straight-forward approach to measure sensitivity is to use a mirror in the sample arm , determine the PSF and attenuate the light in the sample until the signal in the Fourier transform cannot be detected any more. However, the transition between the condition that a signal can be detected and that it vanishes in the noise background is smooth.

Therefore, a definition has been introduced, most commonly accepted in the OCT community, that states that this transition occurs when the signal to noise ratio is equal to 1. The is defined in terms of electrical power and reads as follows:

2.18

Here, is the mean-square peak signal power and is the variance of the noise background in a small window centered at . With , the minimum peak detector current signal reads:

2.19

A typical measurement of sensitivity at , as done during research work presented in this thesis, is performed as follows: Firstly, a mirror is placed in the sample arm yielding a path length difference . Since a direct measurement of the PSF aiming to determine would saturate the detector, a neutral density filter of optical density OD is introduced in the sample arm (attenuation of ( ) dB) and the peak value of the PSF (after resampling) is determined. Secondly, the sample arm is blocked and the standard deviation of the noise floor in the Fourier transform in a window centered at is calculated. Blocking of the sample arm and performing both measurements separately is essential since an additional signal increases the noise floor over the whole z-domain. Using equation 2.17 and 2.19, the sensitivity is then given by:

2.20 Since the sensitivity depends on the reflected optical reference arm power (optical pow-er of light returning from the refpow-erence arm; see chaptpow-er 2.1.5.6), the measurement is repeated for different power reflectivities changing the attenuation in the reference arm. In this way, the optimum reflected reference arm power can be determined. Note that, understandably, the power incident on the sample is limited to avoid potential thermal damages to the tissue. These limits depend on the medical application and were determined by the American national standards institute (ANSI) [80]. Since the power reflectivities from interesting layers in biological tissue can be very small and due to the limitation of optical power on the sample, sensitivity is a very important parameter for OCT imaging. Depending on the OCT application, sensitivities of at least 90 dB or, in many cases, even higher than 100 dB are required to ensure high OCT image quality.

Assuming an incident average power of 1 mW, a sensitivity of 100 dB translates to a minimum detectable power of only 100 fW. In chapter 2.1.5, the theoretically achiev-able maximum sensitivity as a function of incident power and A-scan time is derived.

2.1.4.2 Sensitivity roll-off with increasing depth

As already mentioned in chapter 2.1.4.2, an intrinsic characteristic of FD-OCT is the depth dependent sensitivity roll-off, which, in SS-OCT, is due to the finite instantaneous linewidth of the wavelength-swept light source. Typically, the experimental deter-mination of this effect is simply carried out by measuring the PSFs corresponding to different imaging depths . This is realized by recording the fringe signal for different reference mirror positions. The same numerical resampling is applied to all fringe signal traces and the resulting Fourier transformed signals (single sided) are plotted, as shown in Figure 2.6, representing a typical sensitivity roll-off measurement. The sensi-tivity drop over imaging depth can then directly be derived from the decay of the peaks of the PSFs. Note that the y-axis is representing the sensitivity that was determined a single time for a small as described above (see equation 2.20). Generally, in SS-OCT, a logarithmic representation is preferred using a ) representa-tion due to the fact that is proportional to . Optionally, the decay of the cor-responding fringe visibilities can be plotted. The fringe visibility is defined as the time averaged amplitude of the interferometric fringe signal envelope (see equation 2.8).

A discrepancy between fringe visibility decay and the decay of the PSF peaks, which typically increases for larger , can be caused by non-perfect numerical resampling or/and can be due to phase noise in the fringe signal. The sensitivity roll-off is often specified in different ways in literature. A common way is to name the 6 dB roll-off point which corresponds to halving of . Other descriptions, considering a larger imaging range, define the R-number [14] which is given by the slope of a linear fit to the peak maxima of the PSFs (logarithmic representation). There are several applica-tions in OCT that require a large imaging range making an optimum roll-off perfor-mance highly desirable like OCT imaging of the anterior segment of the human eye [81]. However, for many applications using FD-OCT, the achievable imaging range is less determined by the sensitivity roll-off than by the penetration depth of the light in the biological tissue (~2-3 mm).

Figure 2.6: Typical sensitivity roll-off measurement, extracted from [11]. The picture shows sev-eral PSFs corresponding to different OCT ranging depths . The peaks of the PSFs represent the decay in sensitivity. The red circles are the corresponding fringe visibilities.

0 1 2 3 4 5 6 7 8 9 10

60 70 80 90 100 110 120

OCT ranging depth [mm]

sensitivity [dB] 20*log(amplitude) + const

2.1.4.3 Dynamic range

The dynamic range in an OCT system is defined as the ratio of maximum to minimum reflected power that can be detected simultaneously. The measurement of dynamic range is performed similarly to a sensitivity measurement. A mirror is placed in the sample arm and the PSF is determined corresponding to a certain path length difference in the interferometer arms. If necessary, a neutral density filter can be used to attenuate the light in the sample arm. The maximum detected signal then corre-sponds to the peak value of the PSF . As already mentioned, the minimum de-tectable signal is equal to the standard deviation of the noise floor . However, the main difference to the determination of sensitivity is the fact that here both measurements have to be done simultaneously and not separately. The standard deviation of the noise floor typically is determined in a window close to the peak at where the coherence function is negligible small. Therefore, the dynamic range in logarithmic representation at reads as follows:

2.21

In OCT, the dynamic range is typically several orders of magnitude smaller than the sensitivity. OCT imaging quality and imaging range can be affected if the dynamic range is not sufficiently high to enable simultaneous detection of the weakest and strongest reflections from biological tissue. However, in OCT, the limiting factor is of-ten not dynamic range but rather insufficient sensitivity and the multiple scattering of photons in optical dense tissue.