/
supergaussian.jl
68 lines (59 loc) · 2.52 KB
/
supergaussian.jl
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"""
Code for a super-Gaussian mask shape for use with CCF
Author: Eric Ford
Created: September 2020
"""
using QuadGK
""" SuperGaussianCCFMask
A truncated Gaussian mask with two parameters, its standard deviation and where to truncate it, both as a velocity in m/s.
Mask weights are stored separately in a line list.
TODO: Replace Gaussian with super-Gaussian
Warning: Not implemented/tested yet.
"""
struct SuperGaussianCCFMask <: AbstractCCFMaskShape
σ_sqrt2::Float64
power::Float64
half_width_truncation::Float64
normalization::Float64
""" `SuperGaussianCCFMask( σ ; half_truncation_width_in_σ=2 )` """
function SuperGaussianCCFMask(σ::Real, p::Real, w::Real=2 )
@assert 0 < σ <= 300000 # 300km/s is arbitrary choice for an upper limit
@assert 1 <= p <= 2
@assert 0 < w <= 4
function integrand(x)
exp(-(0.5*(x/σ)^2)^p)
end
integral = quadgk(integrand, -w*σ, w*σ)[1]
norm = 1.0/integral
new(σ*sqrt(2.0),p,σ*w,norm)
end
end
""" `SuperGaussianCCFMask( inst ; scale_factor )` """
function SuperGaussianCCFMask(inst::InstT; power::Real = default_supergaussian_ccf_exponent, fwhm::Real = default_supergaussian_ccf_fwhm,
σ_scale_factor::Real = 1, truncation_scale_factor::Real = default_supergaussian_ccf_truncation_scale_factor ) where { InstT<:AbstractInstrument }
# TODO: Update default values
σ = σ_scale_factor * fwhm/sqrt(8 * log(2)^(1/power)) # From Ryan Petersburg email 9/11/2020
w = truncation_scale_factor
SuperGaussianCCFMask(σ,power,w/2)
end
λ_min(m::SuperGaussianCCFMask,λ::Real) = λ/calc_doppler_factor(m.half_width_truncation)
λ_max(m::SuperGaussianCCFMask,λ::Real) = λ*calc_doppler_factor(m.half_width_truncation)
function integrate(m::SuperGaussianCCFMask, v_lo::Real,v_hi::Real)
quadgk(m, v_lo, v_hi, atol=1e-4)[1]
end
""" Functor for returning PSF for Δv <= half_width. """
function (m::SuperGaussianCCFMask)(Δv::Real)
if abs2(Δv) > abs2(m.half_width_truncation)
return zero(Δv)
else
return m.normalization*exp(-((Δv/m.σ_sqrt2)^2)^m.power)
end
end
function mask_with_increased_fwhm(m::SuperGaussianCCFMask, Δfwhm::Real )
# WARNING: Haven't checked how good of an approximation this is
σ = m.σ_sqrt2/sqrt(2)
fwhm_orig = σ * sqrt(8 * log(2)^(1/m.power))
fwhm_new = sqrt(fwhm_orig^2 + Δfwhm^2)
σ_new = fwhm_new/sqrt(8 * log(2)^(1/m.power))
return SuperGaussianCCFMask(σ_new, m.power, m.half_width_truncation * (σ_new /σ) )
end