Born approximation in cosmological lensing ($\Psi (\eta ,\mathbf{x})\simeq \Psi (\eta ,{\mathbf{x}}_{\mathrm{background}})$)

In a first-order light-deflection calculation, evaluate the Weyl lensing potential and its gradients on the unperturbed null geodesic. The position correction is first order, so inserting it into an already first-order potential produces a second-order correction. This approximation omits repeated deflection and lens-lens coupling.