[Previous] | [Session 14] | [Next]
Slava G. Turyshev (JPL)
This paper addresses the issue of the white light fringe modeling as needed for the phase information extraction with the Space Interferometry Mission (SIM) CCD detector. We developed a set of analytic expressions for the white light fringe estimation using the complex visibility phasors. The obtained expressions are valid for an arbitrary number of detector spectral channels and for an arbitrary number and sizes of the PZT dither steps. In particular, the expressions may be used to obtain estimators of the real, X\ell, and imaginary, Y\ell, phasors, as well as for the total intensity of light in the \ell-th spectral channel {\cal P}0\ell that are given as: \small \begin{eqnarray} X\ell\equiv{\cal P}0\ell V0\ell\cos {\phi}\ell &=&1/{\cal D}_\ell\sumNj=1~K\ell j~ {\cal A}\ell j, \nonumber\\[6pt] Y\ell\equiv{\cal P}0\ell V0\ell\sin {\phi}\ell &=& 1/{\cal D}_\ell \sumNj=1~K\ell j~ {\cal B}\ell j, \nonumber\\[6pt] {\cal P}0\ell&=&1/{\cal D}_\ell\sumNj=1~ K\ell j~{\cal C}\ell j, \nonumber \end{eqnarray} \normalsize \noindent where K\ell j being the flux registered by CCD detector at \ell-th channel at the j-th PZT dither step. Coefficients {\cal A}\ell j, {\cal B}\ell j, {\cal C}\ell j and {\cal D}\ell that depend only on the sizes of individual PZT steps, the width of a particular spectral channel \Delta k\ell with the mean wavenumber k\ell and corresponding wavelength \lambda\ell, and on the photon statistics for a particular temporal bin. Index j is a summation index that defines a particular temporal bin; index \ell is used to define a particular spectral channel. We discuss implementation of this formalism for the SIM detector in light of our simulations of the residual group delay estimation and suggest directions for further research on this problem.
This work was performed by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.