**AAS 197, January 2001**

*Session 14. New Space Missions and Instrumentation*

Display, Monday, January 8, 2001, 9:30am-7:00pm, Exhibit Hall
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## [14.06] White light fringe modeling for the SIM CCD detector.

*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} V_{0\ell}\cos
{\phi}_{\ell} &=&1/{\cal D}_\ell\sum^{N}_{j=1}~K_{\ell
j}~ {\cal A}_{\ell j}, \nonumber\\[6pt] Y_{\}ell\equiv{\cal
P}_{0\ell} V_{0\ell}\sin {\phi}_{\ell} &=& 1/{\cal
D}_\ell \sum^{N}_{j=1}~K_{\ell j}~ {\cal B}_{\ell j},
\nonumber\\[6pt] {\cal P}_{0\ell}&=&1/{\cal
D}_\ell\sum^{N}_{j=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.

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