Theoretical sensitivity calculation

Leitgeb’s paper1

% Sensitivity from [Performance of FD vs TD]
N = 2048;
rho = 0.4;                                                                % spectrometer efficiency rho
eta = 0.8;                                                                 % detector quantum efficiency
tau = 14.2 * 10^(-6);                                                             % exposure time / s 
h = 6.63 * 10^(-34);                                                       % planck constant / J * s
P_0 = 3 * 10^(-3);                                                      % power at the sample / Watt 
gamma_s = 1;                                                            % part of input power on sample arm 
gamma_r = 1;                                                            % part of input power on ref arm 
c = 2.99 * 10^(8);                                                          % light speed m/s
lambda_0 = 820 * 10^(-9);                                                  % center-wavelengt / m
delta_lambda = 120 * 10^(-9);                                               % FWHM bandwidth / m
nu_0 =  c / lambda_0;                                                      % center-frequency / hz
e = h * nu_0;                                                              % electron charge
delta_nu = (pi / (2 * log(2)))^(1/2) * c * delta_lambda /[(lambda_0)^(2)]; % effective line width
R_r = 1;                                                                   % reference arm reflectivity

% Sensitivity
a = 1/N * (rho*eta*tau*P_0/e)^2 * gamma_s * gamma_r * R_r;
b = (1/N*rho*eta*tau*P_0*gamma_r*R_r/e)*[1+1/2*(rho*eta/e)*(P_0/N)*gamma_r*R_r*(N/delta_nu)]+250*e;
sensitivity = 10*log10(a/b)
  • For parameters in paper, it’s 94.5020 dB
  • For our system, it’s 93.4097 dB

Choma’s paper2

%% Sensitivity from [Choma paper]
N = 2048;
rho = 0.6;                                                                % spectrometer efficiency rho
eta = 0.8;                                                                 % detector quantum efficiency
tau = 14.2* 10 ^(-6);                                                             % exposure time / s 
h = 6.63 * 10^(-34);                                                       % planck constant / J * s
P_0 = 3 * 10^(-3);                                                      % power at the sample / Watt 
c = 2.99 * 10^(8);                                                          % light speed m/s
lambda_0 = 820 * 10^(-9);                                                  % center-wavelengt / m
delta_lambda = 120 * 10^(-9);                                               % FWHM bandwidth / m
nu_0 =  c / lambda_0;                                                      % center-frequency / hz
e = h * nu_0;                                                              % electron charge
%% Sensitivity
a = rho * eta * P_0 * tau;
b = 2*e;
sensitivity = 10*log10(a/b)

  • For parameters in paper, it’s 120.1337 dB
  • For our system, it’s 106.2625 dB
  1. Leitgeb, R., Hitzenberger, C. & Fercher, A. F. Performance of fourier domain vs. time domain optical coherence tomography. Opt. Express 11, 889-894 (2003).
  2. Choma, M. A., Sarunic, M. V., Yang, C. & Izatt, J. A. Sensitivity advantage of swept source and Fourier domain optical coherence tomography. Opt. Express 11, 2183-2189, doi:10.1364/OE.11.002183 (2003).
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