GP-B Post-Flight Analysis—Final Report - Gravity Probe B - Stanford ...

s N+w i= sign+w i++−+−w i−w i−−Equation 11-1Note that the X-axis uses the detector currents designated by Y, and the Y-axis uses the detector currentsdesignated by X, which is the result of the detector axes being designated by their spatial location and thepointing angles by the X and Y rotation axes.The pointing signal s P in units of marcsec is found with a scale factor, which is approximately 3.3 × 10 3marcsec/normalized pointing signal for both axes.Equation 11-2The weighting factors that are used to determine the ATC pointing signal on orbit are listed in Table 11-4.Normally the same weighting factors are also used to calculate the science normalized pointing signal, althoughdifferent weighting factors can be used in principle for science since the processing of the science slope datatakes place on the ground.Table 11-4. Weighting factors used for processing dataElectronic Side A-Side B-SideDetector Designation \ Polarity + - + -X 0.9931 1.0070 1.0005 0.9995Y 0.9421 1.0655 0.9245 1.089011.4.3 Telescope Scale FactorFrom ground measurements, the scale factor, which converts the normalized pointing signal to pointing angle,as estimated in S0619 (J.P. Turneaure, M. Heifetz, “Flight telescope/window system analysis of wavelengthdependent properties”, GP-B S-Doc S0619 Rev. -, 3-Mar-02), was measured to be about 2.0 arcsec pernormalized pointing signal. This estimate was based on measurements of the telescope in its Payloadconfiguration (flight telescope at liquid helium temperature and with the 4 flight windows at temperatures closeto those of flight) made with Artificial Star #3, see S0570 (R. Bernier, T. Acworth, J.P. Turneaure, D. DeBra,“Flight telescope/window system verification”, GP-B S-Doc S0570 Rev. -, 20-November-01).Room temperature and low-temperature measurements of the telescope indicated that the bare telescope wasvery close to focus with little wavefront error. However after the telescope was integrated into the payload,which included the four windows, the telescope/window system was found to be out-of-focus. When ArtificialStar #3 was adjusted to compensate for the telescope/window system defocus, which amounted to a focalposition shift of 5.2 mm, a good quality focus occurred with very little astigmatism. The knowledge in thequality of the focus was limited by the uncertainty in the wavefront error introduced by Artificial Star #3, whichhad an estimated Strehl ratio of 65%. Flight data shows that both telescope pointing axes have a scale factor ofabout 3.3 arcsec per telescope normalized pointing signal, which is consistent within error to the defocusmeasured on the ground.The lack of focus has an advantage: namely that the linear range of the telescope is larger and thus larger RMSpointing errors are acceptable in the data analysis. The non-linearity of the telescope has been exploredanalytically using optical theory and experimental data. Initial analysis indicates the telescope is 0.17 inches (4.3mm) out of focus, which within error agrees with the value measured on the ground when considering320 March 2007 Chapter 11 — Telescope Readout Subsystem (TRE) Analysis