diff --git a/.gitignore b/.gitignore
index 20fe29d..7233576 100644
--- a/.gitignore
+++ b/.gitignore
@@ -3,3 +3,4 @@
 *.jl.mem
 /Manifest.toml
 /docs/build/
+/test/Manifest.toml
diff --git a/src/utils.jl b/src/utils.jl
index c9837a9..2a34014 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -4,6 +4,14 @@ function (project::ProjectTo{CoherencyMatrix})(dx::AbstractMatrix)
     return CoherencyMatrix(dx, project.basis1, project.basis2)
 end
 
+function (project::ProjectTo{CoherencyMatrix})(dx::CoherencyMatrix{B1, B2}) where {B1, B2}
+    @assert B1() == project.basis1 "First basis does not match in $(typeof(dx)) and $(project.basis1)"
+    @assert B2() == project.basis2 "Second basis does not match in $(typeof(dx)) and $(project.basis2)"
+    @assert size(dx) == (2,2) "Issue in Coherency pullback the matrix is not 2x2"
+    return dx
+end
+
+
 
 # function ChainRulesCore.rrule(::Type{<:CoherencyMatrix}, e11, e21, e12, e22, basis::NTuple{2, <:PolBasis})
 #     c = CoherencyMatrix(e11, e21, e12, e22, basis)
diff --git a/test/Project.toml b/test/Project.toml
index c416f8b..41b37d0 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,3 +1,5 @@
 [deps]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 JET = "c3a54625-cd67-489e-a8e7-0a5a0ff4e31b"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/test/runtests.jl b/test/runtests.jl
index ed9dd26..a2e3b76 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,4 +1,6 @@
 using PolarizedTypes
+using StaticArrays
+using ChainRulesCore
 using JET
 using Test
 
@@ -190,4 +192,20 @@ using Test
         end
 
     end
+
+    @testset "ChainRules" begin
+        I = 2.0 + 0.5im
+        Q = rand(ComplexF64) - 0.5
+        U = rand(ComplexF64) - 0.5
+        V = rand(ComplexF64) - 0.5
+        s = StokesParams(I, Q, U, V)
+        c = CoherencyMatrix{CirBasis, LinBasis}(s)
+
+        cmat = SMatrix(c)
+        prc =  ChainRulesCore.ProjectTo(c)
+        @test prc(cmat) == c
+        @test prc(c) == c
+        @test_throws "First basis does" prc(CoherencyMatrix(cmat, LinBasis()))
+        @test_throws "Second basis does" prc(CoherencyMatrix(cmat, CirBasis()))
+    end
 end