Linearization of Spitzer IRS Data Via Minimization of χ With Correlated Errors

Abstract. The Spitzer Infrared Spectrograph (IRS) data are taken via readwithout-reset measurements to obtain multiple samples forming a photometric “ramp” for each pixel in an echellogram. Each ramp is linearized via a quadratic model. After linearization, a quality-assurance test is performed to determine how linear each pixel’s ramp has become. This is accomplished by fitting a straight line to the ramp via χ minimization. The goodness of fit is of primary importance, since this determines whether the inevitable deviations from linearity are statistically significant given the estimated photometric noise. Because the latter is dominated by photon noise which is summed up the ramp, the χ parameter used to measure goodness of fit must include the effects of correlated errors. This paper describes the construction of the full error covariance matrix and its use in the χ minimization.