update

.ipynb_checkpoints/Project-checkpoint.toml

@@ -12,9 +12,9 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [compat]
 Healpix = "3.0.0"
-ProgressMeter = "1.7.1"
 ReferenceFrameRotations = "1.0"
-StaticArrays = "1.2.9"
+StaticArrays = "1.2"
+ProgressMeter = "1.6.2"
 julia = "1.6"
 
 [extras]

Project.toml

@@ -11,7 +11,7 @@ ReferenceFrameRotations = "74f56ac7-18b3-5285-802d-d4bd4f104033"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [compat]
-Healpix = "2.3.0, 3.0.0"
+Healpix = "3.0.0"
 ReferenceFrameRotations = "1.0"
 StaticArrays = "1.2"
 ProgressMeter = "1.6.2"

docs/src/.ipynb_checkpoints/Mapmake-checkpoint.md

@@ -22,14 +22,20 @@ outmap[3]: Crosslink map (n=2)
 outmap[4]: Crosslink map (n=3)
 outmap[5]: Crosslink map (n=4)
 ```
-The crosslink is represented by the following equation
+The crosslink $X_n$ is represented by the following equation
+
+$$
+X_n = \left[ \left(\frac{\sum^{N_{hits}}_i{\sin{(n\psi_i)}}}{N_{hits}} \right)^2 + \left( \frac{\sum^{N_{hits}}_i{\cos{(n\psi_i)}}}{N_{hits}}\right)^2 \right]
+    = \langle \sin(n\psi_i) \rangle^2 + \langle \cos(n\psi_i) \rangle^2
+$$
 
-$Crosslink(n)=<\sin(n\psi_i)>^2+<\cos(n\psi_i)>^2$.
 The subscript $i$ indicates that this is the $i$-th time series data within a certain pixel, and $< >$ indicates that the average should be taken.
 
 The $n$ is the spin, a measure to define the scan-derived systematic effect. It is described in detail in this [paper](https://arxiv.org/abs/2008.00011).
 
 ## Crosslink with half-wave plate
 The next generation of CMB polarimetry satellites, such as LiteBIRD, will be equipped with a half-wave plate(HWP). Falcons is also possible to create a crosslink map that takes into account the optical axis of the HWP.
 The crosslink with HWP is calculated by the following equation
-$Crosslink_{hwp}(n)=<\sin(4\rho-n\psi)>^2+<\cos(4\rho-n\psi)>^2$.
+$$
+X_n^{w/ HWP}=<\sin(4\rho-n\psi)>^2+<\cos(4\rho-n\psi)>^2 .
+$$

docs/src/Mapmake.md

@@ -22,14 +22,20 @@ outmap[3]: Crosslink map (n=2)
 outmap[4]: Crosslink map (n=3)
 outmap[5]: Crosslink map (n=4)
 ```
-The crosslink is represented by the following equation
+The crosslink $X_n$ is represented by the following equation
+
+$$
+X_n = \left[ \left(\frac{\sum^{N_{hits}}_i{\sin{(n\psi_i)}}}{N_{hits}} \right)^2 + \left( \frac{\sum^{N_{hits}}_i{\cos{(n\psi_i)}}}{N_{hits}}\right)^2 \right]
+    = \langle \sin(n\psi_i) \rangle^2 + \langle \cos(n\psi_i) \rangle^2
+$$
 
-$Crosslink(n)=<\sin(n\psi_i)>^2+<\cos(n\psi_i)>^2$.
 The subscript $i$ indicates that this is the $i$-th time series data within a certain pixel, and $< >$ indicates that the average should be taken.
 
 The $n$ is the spin, a measure to define the scan-derived systematic effect. It is described in detail in this [paper](https://arxiv.org/abs/2008.00011).
 
 ## Crosslink with half-wave plate
 The next generation of CMB polarimetry satellites, such as LiteBIRD, will be equipped with a half-wave plate(HWP). Falcons is also possible to create a crosslink map that takes into account the optical axis of the HWP.
 The crosslink with HWP is calculated by the following equation
-$Crosslink_{hwp}(n)=<\sin(4\rho-n\psi)>^2+<\cos(4\rho-n\psi)>^2$.
+$$
+X_n^{w/ HWP}=<\sin(4\rho-n\psi)>^2+<\cos(4\rho-n\psi)>^2 .
+$$