double_edge_integrand.m

计算大气后向散射的Rayleigh光谱宽度

function y = double_edge_integrand(frequency,frequency_shift,etalon_position,etalon_fwhm)
%the integrand of doble edge method,from applied optics v38,n3,p434
laser_frequency = 8.458E14; %frequency of 354.7nm laser
etalon_central_frequency = laser_frequency + etalon_position; %position of the etalon channel
%backscattered_FWHM = 1.241E-10*transmitted_FWHM.^2 + 0.00337*transmitted_FWHM + 3.851E9; %20 centigrade, backscattered FWHM,simulated by mento carlo
%backscattered_FWHM = 4.787E-11*transmitted_FWHM.^2 + 0.6655*transmitted_FWHM + 3.884E9; %25 centigrade, backscattered FWHM,simulated by mento carlo
%backscattered_fwhm = 4.97E-11*transmitted_fwhm.^2 + 0.6679*transmitted_fwhm - 1.5E-5*temperature*transmitted_fwhm  + 6.681E6*temperature + 1.8867E9;
backscattered_fwhm = 3.884E9; %25 centigrade, backscattered FWHM,simulated by mento carlo
backscattered_sigma_square = backscattered_fwhm.^2/(8*log(2));

etalon_transmission = 1./(1+(2*(frequency - etalon_central_frequency)/etalon_fwhm).^2); %transmission of etalon,from Applied Optics v38,n3,p433
backscattered_spectrum = 1./sqrt(2*pi*backscattered_sigma_square).*exp(-(frequency-(laser_frequency+frequency_shift)).^2./(2*backscattered_sigma_square)); %since it is normal distributed
y = etalon_transmission.*backscattered_spectrum;