  We address the phase retrieval problem with errors in the sensing vectors. A
number of recent methods for phase retrieval are based on least squares (LS)
formulations which assume errors in the quadratic measurements. We extend this
approach to handle errors in the sensing vectors by adopting the total least
squares (TLS) framework that is used in linear inverse problems with operator
errors. We show how gradient descent and the specific geometry of the phase
retrieval problem can be used to obtain a simple and efficient TLS solution.
Additionally, we derive the gradients of the TLS and LS solutions with respect
to the sensing vectors and measurements which enables us to calculate the
solution errors. By analyzing these error expressions we determine conditions
under which each method should outperform the other. We run simulations to
demonstrate that our method can lead to more accurate solutions. We further
demonstrate the effectiveness of our approach by performing phase retrieval
experiments on real optical hardware which naturally contains both sensing
vector and measurement errors.
