- Abstract
- Sectionintroduction
- In recent years both
- External convergence
- This widelyused appr
- A second complementa
- Which perturbing galaxies are the
- In section ref sec 3dmassmodels
- Throughout this paper we assume
- Section gravitational lensing using 3
- Subsection building 3 d mass
- The first step of building
- Subsection multi plane lensing
- In practice there ca
- Our framework can be used
- Begin eqnarray x i b i 1
- Begin equation tau i j
- Begin eqnarray b j i sum
- Beginequation beta i
- We note that if we
- Begin equation b j c 0
- Begin equation f j g
- For a single main lens
- Begin equation x s b s x 1
- Subsection including a smooth mass
- There are a variety of 1
- We can consider empty space 1
- Where the critical surface density
- Converting to comoving distances x
- In our models we can
- Begin equation rho p f z
- Begin equation bar rho z
- Begin equation rho rm c
- Now we turn to our 1
- If there is only mean
- Now if plane j is
- Next we consider j 1
- This generalizes to begin equation
- Now that the discrete sum
- This form of the integral
- Now we take a derivative
- Next we take another derivative
- Now we combine equations ref
- The terms in the square
- This is a second order
- We can follow a similar
- The continuous limit is then
- We now take a derivative
- This is a first order
- Following a similar argument to
- These updates to the c
- Subsection simulation setup label sec
- Typical lens beams can have
- We model the main lens
- We choose source pos
- Throughout this anal
- It is important to
- Beginitemize item 2t
- Beginitemize item 4t
- Each of the models
- Beginitemize item so
- Double image configu
- Because the shear mo
- For the recovered le
- We assume a gaussian
- Begintable begintabu
- The final ingredient we need
- Mass completeness
- With this we now have
- Sectionanalytic back
- There are broadly two classes
- Subsection galaxies projected near the
- We first illustrate
- Beginequation al equ
- If the perturbing ga
- Beginequation phi p
- Beginequation phi p 1
- Beginequation phi p 2
- This expansion of th
- Beginequation phi p
- Beginequation gammai
- Beginequation sfijk
- To test these expectations based
- Toymass compare
- In all of these
- The next parameter o
- Subsection foreground pertubers are more
- We now turn our attention
- We begin by deriving
- Beginequation x jx 1
- For a single perturb
- Beginequation x 2 x
- Beginequation x s x
- Beginequation x s x1
- We now need to
- Subsectionbackground
- Beginequation x s x2
- Begin eqnarray x i s x
- Beginequation x s i
- Beginequation bu rm
- We now turn our
- Begin equation al g r e rhat
- From above for the
- Begin eqnarray label eqn backgroundorder2
- Begin equation x s x 1
- Beginequation vx s v
- Subtracting refeqsba
- Beginequation delta
- Beginequation delta 1
- Delta 3 x has the
- Subsectionforeground
- Beginequation x s x
- Begineqnarray xi s 1
- Beginequation x s i1
- To test this we simulate
- Frontback
- We now consider a
- Begin equation x s x 1 r e
- Begin equation x s x 1 1
- Beginequation delta 2
- Beginequation delta 3
- The last characteris
- Toyh
- In section refsecrea
- Real lens galaxies h
- Figure reffieldrz il
- Rxj1131 fieldrz
- A histogram of delta 3 x
- Rxj1131 dx3 hist
- This discussion about which galaxies
- Section external shear vs 3
- We begin by treating all
- All los 1e-2
- The lens shear models are
- All shear 1e-2
- The correlation between the power
- The angular part of equation
- Thus we can approximate the
- Los scaled h
- Our goal is to
- All models do poorly
- New rxj1131 reallos
- One key point is
- The total mass of
- Once we include a large
- Sectionrealistic
- Subsectiondifferent
- One of the simplest
- New b0712 reallos
- Figure refallfields
- Allfields
- While the external convergence does
- Suyu kappa
- Subsectionvarying th
- We next explore how
- As with the hubble
- Ecompare
- A second key paramet
- Recompare
- Lsst will find an
- Now that we have established
- In figure ref fig srcpos
- H src pos
- Sectionconclusions a
- We have defined the
- When accounting for
- For either methodolo
- We find that the importance
- We show that the all
- One possible approac
- Our main goal for

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