An Estimator for the lensing potential from galaxy number counts

We derive an estimator for the lensing potential from galaxy number counts which contains a linear and a quadratic term. We show that this estimator has a much larger signal-to-noise ratio than the corresponding estimator from intensity mapping. We show that this is due to the additional lensing term in the number count angular power spectrum which is present already at linear order. We estimate the signal-to-noise ratio for future photometric surveys. We find that particularly at high redshifts, $z\gtrsim 1.5$, the signal to noise ratio can become of order 30. We therefore claim that number counts in photometric surveys are an excellent means to measure tomographic lensing spectra.