We propose an extension of the Spline based ABerration Reconstruction (SABRE) method to Shack-Hartmann (SH) intensity measurements, through small aberration approximations of the focal spot models. The original SABRE for SH slope measurements is restricted to the use of linear spline polynomials, due to the limited amount of data, and the resolution of its reconstruction is determined by the number of lenslets. In this work, a fast algorithm is presented that directly processes the pixel information of the focal spots, allowing the employment of nonlinear polynomials for high accuracy reconstruction. In order to guarantee the validity of the small aberration approximations, the method is applied in two correction steps, with a first compensation of large, low-order aberrations through the gradient-based linear SABRE followed by compensation of the remaining high-order aberrations with the intensity-based nonlinear SABRE.