Added Unit Wisp Geometrical Model

[dominic-chang]

Added model for a Unit Wisp. I hope the area scaling is correct

[ptiede]

I took a look at the implementation today and I think there is a small bug somewhere. The visibility should be equal to the intensity at the origin however I am not getting a unit flux. Instead, I get something ~1.35. I am guessing there is a small missing factor.

edit: I just looked into this and the normalization is off by a factor of arclength/4. If you take the limit as (u,v)->0 I get the visibility is equal to 4/l. So if I change

[dominic-chang]

For the wisp or the parabolic segment? Or both?

[ptiede]

For the wisp or the parabolic segment? Or both?

This is for both. I think the length should drop out here for the Fourier transform so the function should be

function visibility_point(::ParabolicSegment{T}, u, v) where {T}
    ϵ = eps(T)
    vϵ = v + ϵ + 0im
    phase = exp(1im*π*(3/4 + 2*vϵ + u^2/(2vϵ)))
    #length = (√5 + asinh(2)/2)
    Δ1 = erf(√(π/(2vϵ))*exp(π*im/4)*(u-2vϵ))
    Δ2 = erf(√(π/(2vϵ))*exp(π*im/4)*(u+2vϵ))
    return phase/(√(2vϵ))*(Δ1-Δ2)/4
end

This also fixes the confusion about the normalization. There is no sinh issue so the ParabolicSegment and the Wisp should be equal.

edit ignore the prinln

[dominic-chang]

I think the length should drop out here for the Fourier transform so the function should be

Yep, your totally right. The normalization factor is actually proportional to "a" and not the length. I made the fallacious assumption that the integral of a delta of a function that describes a level curve is the area of that curve. I just checked it for this wisp and it in fact just "a"

[ptiede]

Alright, I did a rebase off main and fixed the normalization. Given that the Parabolic segment should equal the Wisp I decided to just ax it. Let me know if you object to it!

[codecov-commenter]

Codecov Report

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[ptiede]

Merged! Great job Dominic.