A frame
(
x
j
)
j
∈
J
(x_j)_{j\in J}
for a Hilbert space
H
H
is said to do phase retrieval if for all distinct vectors
x
,
y
∈
H
x,y\in H
the magnitudes of the frame coefficients
(
|
⟨
x
,
x
j
⟩
|
)
j
∈
J
(|\langle x, x_j\rangle |)_{j\in J}
and
(
|
⟨
y
,
x
j
⟩
|
)
j
∈
J
(|\langle y, x_j\rangle |)_{j\in J}
distinguish
x
x
from
y
y
(up to a unimodular scalar). A frame which does phase retrieval is said to do
C
C
-stable phase retrieval if the recovery of any vector
x
∈
H
x\in H
from the magnitude of the frame coefficients is
C
C
-Lipschitz. It is known that if a frame does stable phase retrieval then any sufficiently small perturbation of the frame vectors will do stable phase retrieval, though with a slightly worse stability constant. We provide new quantitative bounds on how the stability constant for phase retrieval is affected by a small perturbation of the frame vectors. These bounds are significant in that they are independent of the dimension of the Hilbert space and the number of vectors in the frame.