function [x,delta]=SF_Spec_Calc(r0,lambda_r0,loss,lambda_loss,dia)
% SF_Spec_Calc.m
% Written by Stacie Manuel

% Version History:
% June 4, 2009 - Version 1

%% Overview

% This function calculates the polishing specification for a telescope,
% following the discussion by Hill in "Optical Design, Error Budget and
% Specifications for the Columbus Project Telescope" (Proc. SPIE 1236,
% 86-107 (1990)). This calculation assumes the telescope has tilt
% correction.

% Inputs
% 1) r0: the coherence length of the atmosphere, also known as Fried's
%    parameter, in units of cm 
% 2) lambda_ro: the wavelength for which r0 is given, in units of nm
% 3) loss: loss due to scattering normalized to 1
% 4) lambda_loss: the wavelength for which the loss is given, in units of nm
% 5) dia: the diameter of the telescope, in units of cm
% 
% Outputs
% 1) x: the separation values, in units of cm
% 2) delta: the rms wavefront difference between points separated by x, in
%    units of nm 

% The example script SF_Specification.m shows an example of how to call
% this function.

%% Calculations

r0=r0*(lambda_r0/500)^1.2; % adjust r0 so that it is given for lambda = 500nm

x = logspace(-3,0,100); % Separation distances to form the x axis of the graph (normalized to 1)
x = x*dia; % Separation distances to form the x axis of the graph (in units of cm)

% Contribution due to scattering:
SF_loss = 2*loss*(lambda_loss/(2*pi))^2;

% Contribution due to atmospheric turbulence:
SF_atm = ((lambda_r0/(2*pi))^2)*6.88*((x/r0).^(5/3)).*(1-0.975*(x/dia).^(1/3));

% Total structure function:
SF = SF_loss + SF_atm;

% rms wavefront difference between points separated by x given in the same
% units as the wavelengths (nm)
delta = sqrt(SF);