[en] The ever-increasing demand for better performance from circular accelerators requires improved methods to calibrate the optics model. We present a linear perturbation approach to the calibration problem in which the modeled BPM-to-corrector response matrix is expanded to first order in quadrupole strengths. The result is numerically fit to the measured response matrix yielding quadrupole strength errors, corrector strength errors, and BPM linearity factors. The large number of degrees of freedom in the fit allows a comprehensive error analysis, including the determination of BPM resolutions. In this way, a self-consistent first order optics model of SPEAR was generated which reproduces the measured tunes