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%
% I use the very useful ASTRON.STY, renamed for this paper
% This is ASTRON.STY, a LaTeX style for use with the BibTeX style ASTRON.BST.
%\usepackage{P6-11}

\begin{document}

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%%%% ID=P6-11

%-----------------------------------------------------------------------
%		            Paper Title 
%-----------------------------------------------------------------------
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\title{Non-linear transient models and transient corrections methods
for IR low-background photo-detectors}
\titlemark{Non-linear transient models for IR photo-detectors}

%-----------------------------------------------------------------------
%		          Authors of Paper
%-----------------------------------------------------------------------
% Enter the authors followed by their affiliations.  The \author and
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%                  R.\ M.\ Crutcher\altaffilmark{1}}
%          \affil{National Center for Supercomputing Applications, 
%                 University of Illinois Urbana-Champaign, Urbana, IL
%                 61801}
%          \author{Tom Troland}
%          \affil{University of Kentucky}
%
%          \altaffiltext{1}{Astronomy Department, UIUC}
%
% In this example, the first three authors, "Plante", "Roberts", and
% "Crutcher" are affiliated with "NCSA".  "Crutcher" has an alternate 
% affiliation with the "Astronomy Department".  The fourth author,
% "Troland", is affiliated with "University of Kentucky"

\iffalse	% --- Long list
\author{A. Coulais}
\affil{LERMA, Observatoire de Paris-Meudon, 75014 Paris, France}

\author{J. Malaiz\'e, J.-F. Giovannelli, T. Rodet}
\affil{LSS (CNRS-Sup\'elec-UPS), Plateau de Moulon, 91 Gif/Yvette, France}

\author{A. Abergel, B. Wells}
\affil{IAS, Universit\'e Paris XI, 91 Orsay, France}

\author{M. Patrashin, H. Kaneda}
\affil{ISAS/JAXA, Sagamihara, Japan}

\author{B. Fouks}
\affil{IRE, Moscow, Russia}
\else

\author{A. Coulais\altaffilmark{1}, 
        J. Malaiz\'e\altaffilmark{2}, J.-F. Giovannelli\altaffilmark{2}, 
	T. Rodet\altaffilmark{2},
     A. Abergel\altaffilmark{3}, B. Wells\altaffilmark{3},
     M. Patrashin\altaffilmark{4}, H. Kaneda\altaffilmark{4},
     B. Fouks\altaffilmark{5}
}
\vspace*{2ex}   % Corrected style FO
\altaffilmark{1}\affil{
   LERMA, Observatoire de Paris-Meudon, 75014 Paris, France}
\altaffilmark{2}\affil{
       LSS (CNRS-Sup\'elec-UPS), Plateau de Moulon, 91 Gif/Yvette, France}
\altaffilmark{3}\affil{
       IAS, Universit\'e Paris XI, 91 Orsay, France}
\altaffilmark{4}\affil{
       ISAS/JAXA, Sagamihara, Japan}
\altaffilmark{5}\affil{
       IRE, Moscow, Russia}
\fi

%\altaffiltext{1}{IAS}

%-----------------------------------------------------------------------
%			 Contact Information
%-----------------------------------------------------------------------
% This information will not appear in the paper but will be used by
% the editors in case you need to be contacted concerning your
% submission.  Enter your name as the contact along with your email
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%           \email{crabtree@cfht.hawaii.edu}
%


\contact{Alain Coulais}
\email{alain.coulais@obspm.fr}

%-----------------------------------------------------------------------
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% Specify how each author name should appear in the author index.  The 
% \paindex{ } should be used to indicate the primary author, and the
% \aindex for all other co-authors.  You MUST use the following
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\paindex{Coulais, A.}
\aindex{Malaiz\'e, J.}
\aindex{Giovannelli, J.-F.}
\aindex{Rodet, T.}
\aindex{Abergel, A.}
\aindex{Wells, B.}
\aindex{Patrashin, M.}
\aindex{Kaneda, H.}
\aindex{Fouks, B.}

%-----------------------------------------------------------------------
%		      Author list for page header	
%-----------------------------------------------------------------------
% Please supply a list of author last names for the page header. in
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%
% Use the "et al." form in the case of seven or more authors, or if
% the preferred form is too long to fit in the header.

\authormark{Coulais et al.}

%-----------------------------------------------------------------------
%			Subject Index keywords
%-----------------------------------------------------------------------
% Enter a comma separated list of up to 6 keywords describing your
% paper.  These will NOT be printed as part of your paper; however,
% they will be used to generate the subject index for the proceedings.
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% In this example, the author noticed that "radio astronomy" appeared
% in the ADASS VII Index as "astronomy" being the major keyword and
% "radio" as the minor keyword.  The colon is used to introduce another
% level into the index.

\keywords{ Infrared Space Observatory (ISO), CAM, LWS, SWS, PHT: SIRTF MIPS, Si::Ga, Ge::Ga,
physical model, transient, non linear models }

%-----------------------------------------------------------------------
%			       Abstract
%-----------------------------------------------------------------------
% Type abstract in the space below.  Consult the User Guide and Latex
% Information file for a list of supported macros (e.g. for typesetting 
% special symbols). Do not leave a blank line between \begin{abstract} 
% and the start of your text.

\begin{abstract}
%
%Physical models are used to reproduce and correct the transient
%effects of infrared (IR) photo-detectors observed in time series after
%a change of incoming illumination level. 
%
Physical models are used to reproduce and correct transient
effects of infrared (IR) photo-detectors in time series after
incoming illumination changes. Such photo-detectors,
working at low background for IR astronomy in space,
cover the ranges 6-15 $\mu$m (Si:Ga), 40-110 $\mu$m (unstressed Ge:GA)
and 120-210 $\mu$m (stressed Ge:Ga) and are working at low temperature. 
We discuss detectors models (direct models) and
transients corrections (inversion methods).
Some have been successfully applied to ISO data,
others are in preparation for SIRTF (MIPS) -- launched in August 2003 --
and ASTRO-F (FIS) -- to be launched in 2005.
New results for MIPS 160 $\mu$m and the FTS of ASTRO-F/FIS
are evidenced.

\end{abstract}

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\section{Introduction}

Most of the photo-detectors used for low background IR astronomy
are working at low temperature (around 1.7 K (Ge:Ga) and 3 K (Si:Ga))
and therefore are affected by memory/transient effects
due to the time needed by the detector to reach a new stable 
state after a change of incoming flux.
%These effects reflect the time needed by the detector to reach a new stable
%state after a change of incoming flux. 
%
Depending on the detector
but also on the IR level, the time constant can be as long as seconds to hours.
Such transient responses are non-linear.
Without correcting from this transient effect,
the observations can be systematically biased.

In this paper we show that an approach combining
analytical models and inversion methods can correct these effects.
First we remain the results for Si:Ga detectors,
then we discuss the work actually in progress for Ge:Ga ones.

%In any case we have to be sure that what we measure reflects
%what we are looking for \cite{LC_Coulais_GBT}.

%Section \ref{P6-11:SAC:direct} focuses on models which are used,
%Section \ref{P6-11:SAC:inverse} on inversion method we have developed.
%For both section, we separate the well established Si:Ga case
%and the more work-in-progress Ge:Ga case.
%\section{The directs models}\label{P6-11:SAC:direct}
%\subsection{Si:Ga photo detectors}

\section{Si:Ga photo-detectors}

Concerning Si:Ga detectors,
several results have been achieved since ISO launch.
It has been confirmed on three different detectors
(ISO-CAM LW, ISO-SWS b2 and ISO PHOT S\&P) that a physical model
%\cite{VinoFouks91,FouksSchu95} 
(Vinokurov and Fouks, 1991; Fouks and {Schubert, 1995}) 
can describe at percent level
the transient response of such detectors on uniform illumination.
This analytical direct model is strongly non-linear, non-symmetrical
and includes the long term memory effect.
This model is based only on two parameters:
the instantaneous jump $\beta$ and a time constant $\lambda$.
For all Si:Ga detectors of ISO it was shown that ($\beta$,$\lambda$)
are constant for a given pixel.
%
%A correction method can invert such model at
%readout\footnote{a readout is the output after processing a ramp.} level
%(without taking into account block information) \cite{ACAA2000}.
%
A readout by readout inversion method achieves accurate correction
of these effects ({Coulais} and {Abergel, 2000}). %\cite{ACAA2000}.
Limitations are detailed in Coulais \& Abergel (2003a). %\cite*{ACAA2002Sig}.
This inversion method can be applied to any analytical model:
e.g. SWS b2 ({{Kester} et~al., 2003}) %\cite{LC_Kester} 
where variations of the dark current
was included and for Ge:Ga detectors where main problem was coming
from memory effect ({{Caux}, 2003}). %\cite{LC_Caux}.
%Similar approaches have been used when problems coming from detector stability
%(variation of the dark current, ...) (SWS : Kessler et al.) or
%small modification of the model for Ge:Ga (LWS : Caux).
%Since it has been checked and confirmed that the two parameters
%of the model are fixed the correction method is only looking for
%unknown incoming flux, not for the parameters of the model ...

The Si:Ga model mentioned here does not describe
the transients response for non uniform illumination.
A new numerical 3D model was derived, based on same physics 
({{Fouks} et~al., 2003}) %\cite{FCN2002Sig}
and a more classical fitting approach
was developed to recover the parameters of the observed source.

\section{Ge:Ga photo-detectors}

While Ge:Ga detectors do not exhibit strong non-linear transient effects
as the Si:Ga ones, their models are up to now less accurate.
Because polarization voltage is lower for the Ge:Ga ones than
for the Si:Ga ones, equations are more complex, then approximations
are needed to derived analytical models 
({Fouks, 1997}; Haegel et~al., 1999). %\cite{Fouks97,Haegel99}.

The direct models used for Ge:Ga detectors on-board ISO 
have been reviewed in Coulais et al. (2002). %\cite*{CAF2002Mont}.
It was also pointed out that results suffer from limited accuracy of ramp
processing (Coulais et~al., 2003) %\cite{LC_Coulais_PHT} 
and limited numbers of dedicated tests
({{Coulais} and {Abergel}, 2003b}). %\cite{LC_Coulais_GBT}.

A new very interesting case appears with the MIPS 70 $\mu$m array
({{Young} et~al., 2003}) %\cite{Young03}. 
This thin detector is affected
by a strong continuous drift and a StimFlash is applied every $\sim$2 minutes
to continuously calibrate this drift.
Unfortunately, the accuracy of this system is limited to a few percents,
it adds noise in the data, and transients at small time scales
remain uncorrected.  Up to now, no simple analytical model can
described the complex transients of this detector.
Numerical approach was also used for these data 
({{Haegel} et~al., 2001}) %\cite{Haegel01}
but without any quantitative results yet published.
Furthermore, it is difficult to build an efficient correction method
from such numerical direct model.
From our study of the ground based test (GBT) data,
the key points in the error and bias grand total appear to be:
(1) the sensitivity of the array
to glitches (impact of high energetic particles)
(2) the accuracy of the latents correction (transients after StimFlash)
(3) the accuracy of the calibration based on StimFlash
(4) the transients them-selves.
As a result, transient modeling and correction for the MIPS 70 $\mu$m detector
is not the most urgent point.

%It is claimed in \cite{Haegel01} that the hook response
%observed in particular cases can be reproduce by a numerical model.
%We hope a comparison with results presented in \cite{VinoFouks91}
%will occurs soon.

For the MIPS 160 $\mu$m detector, the situation is much more conventional.
On the one hand, a first order model based on physics 
({Fouks, 1992}) %\cite{Fouks92ESA}
accurately reproduces upward steps. Moreover, from dedicated GBT,
we have shown that the two model parameters are constant for a given pixel.
On the other hand, the downward steps are quasi instantaneous.
A promising inversion method has been developed 
(Malaiz\'e, 2003, see Fig.~\ref{P6-11:AC:Fig:MIPS}). 
%\cite{Malaize2003} (see Fig. \ref{P6-11:AC:Fig:MIPS}). 
It is founded on a least square estimate
accounting for first order upward + instantaneous downward models as well
as piece-wise constant incoming flux.
Obviously the longer the blocks, the more efficient the correction.

\begin{figure}
%\begin{center}
%\setlength{\unitlength}{1.cm}
%\includegraphics[width=12cm]{Poster/MipsReel.eps}
%\plotone{P6-11_1.eps}
%\plotfiddle{P6-11_1.eps}{7cm}{270}{75}{50}{-240}{-100}
\plotfiddle{P6-11_f1.eps}{5.5cm}{270}{50}{60}{-240}{190}
%\end{center}
\caption{SIRTF MIPS 160 $\mu$m data from dedicated GBT~:
observed data, estimated incoming flux and model output.
A series of steps was requested in order to characterize
the transient response (to distinguish between different models
and to explore a large range of incoming flux).}
\label{P6-11:AC:Fig:MIPS}
\end{figure}

ASTRO-F carries two types of focal-plane instruments, one of which is 
the Far-Infrared Surveyor (FIS) 
({Takahashi} et~al., 2000). %\cite{Takahashi00}.   
The FIS adopts a stressed Ge:Ga array 
({{Doi} et~al., 2002}) %\cite{Doy02}
of $5\times 15$ and monolithic
arrays (Matsuura et~al., 2002; Fujiwara et~al., 2003) %\cite{SW1,SW2} 
of $3\times 20$ and $2\times 20$ pixels to
continuously cover 50 to 200 $\mu$m in wavelength. The FIS is designed
primarily to perform an all-sky survey and additionally to have spectroscopic
capability with a Fourier transform spectrometer (FTS) 
({Takahashi} et~al., 2003) %\cite{Takahashi03}
-- using the same detectors than FIS.

Up to now, no one of the models previously used
can fit the experimental transient responses.
GBT for transient characterization
is still an on-going work 
({{Kaneda} et~al., 2002}) %\cite{Kaneda02}.
Since (1) we know that the Ge:Ga detectors are significantly affected
by transient effects and (2) we do not have any direct model,
we have studied with two extreme models which
effects may be dominant for the FTS mode.
One model was the Fouks model for the Si:Ga detectors.
This model does not reproduce well the main transient effect
for the ASTRO-F detectors, but it is interesting since it is
very efficient to introduce strong long term memory effect.
The second model was derived by Patrashin (Priv. Com.)
from another model ({Fouks, 1992}). %\cite{Fouks92ESA}.
In such a case, the long term memory effect is not strong.
We have used a readout per readout correction method in both cases
since we have full analytical models.
This end-to-end simulator allows us to check the acceptable ranges
for scanning speed, noise and also the hint level for glitches.

\section{Conclusion}

Significant progress has been made during last years in order to correct
transient effects of IR photodetectors.
Models coming from the physics give high accuracy prediction
for the transient response.
Models can be used to check problems within systems
(detector and associated devices)
and also to improve and optimize future detectors.
Several methods have been developed to remove
the transients effects in scientific data.

The obvious success of such approach for most of the ISO detectors
is very useful for present and future space missions,
especially SIRTF, ASTRO-F, Herschel and MIRI on-board the NGST.
First results for MIPS 160 $\mu$m and ASTRO-F are encouraging.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\acknowledgements
%
AC would like to thank all the people he has collaborated with,
at IAS, LSS, Tucson and Sagamihara.
Thanks to the MIPS team of Arizona University at Tucson (USA)
for access to the data from GBT of SIRTF MIPS arrays at
70 and 160 $\mu$m.
Thanks to the ASTRO-F/FIS team at ISAS/JAXA (Japan)
for access to the data from GBT.

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%			      References
%-----------------------------------------------------------------------
% List your references below within the reference environment
% (i.e. between the \begin{references} and \end{references} tags).
% Each new reference should begin with a \reference command which sets
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% the User Guide listing "macro-ized" journals.   
%
% EXAMPLE:  \reference Hagiwara, K., \& Zeppenfeld, D.\  1986, 
%                Nucl.Phys., 274, 1
%           \reference H\'enon, M.\  1961, Ann.d'Ap., 24, 369
%           \reference King, I.\ R.\  1966, \aj, 71, 276
%           \reference King, I.\ R.\  1975, in Dynamics of Stellar 
%                Systems, ed.\ A.\ Hayli (Dordrecht: Reidel), 99
%           \reference Tody, D.\  1998, \adassvii, 146
%           \reference Zacharias, N.\ \& Zacharias, M.\ 2003,
%                \adassxii, \paperref{P7.6}
% 
% Note the following tricks used in the example above:
%
%   o  \& is used to format an ampersand symbol (&).
%   o  \'e puts an accent agu over the letter e.  See the User Guide
%      and the sample files for details on formatting special
%      characters.  
%   o  "\ " after a period prevents LaTeX from interpreting the period 
%      as an end of a sentence.
%   o  \aj is a macro that expands to "Astron. J."  See the User Guide
%      for a full list of journal macros
%   o  \adassvii is a macro that expands to the full title, editor,
%      and publishing information for the ADASS VII conference
%      proceedings.  Such macros are defined for ADASS conferences I
%      through XI.
%   o  When referencing a paper in the current volume, use the
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%      the paper ID code for the paper you are referencing.  See the 
%      note in the "Paper ID Code" section above for details on how to 
%      determine the paper ID code for the paper you reference.  
%
%\begin{references}

\begin{references}	%\begin{thebibliography}{}

\reference %\bibitem[\protect\astroncite{{Caux}}{2003}]{LC_Caux}
{Caux}, E. 2003, in {\em ESA SP-481}

\reference % \bibitem[\protect\astroncite{{Coulais} and {Abergel}}{2000}]{ACAA2000}
{Coulais}, A. and {Abergel}, A. 2000,
\aaps\  141, 533 %\newblock {\em Astron. Astrophys. Suppl. Ser.} {\bf 141}, 533

\reference % \bibitem[\protect\astroncite{{Coulais} and {Abergel}}{2003a}]{ACAA2002Sig}
{Coulais}, A. and {Abergel}, A. 2003a, in {\em ESA SP-511}

\reference % \bibitem[\protect\astroncite{{Coulais} and {Abergel}}{2003b}]{LC_Coulais_GBT}
{Coulais}, A. and {Abergel}, A. 2003b, in {\em ESA SP-481}

\reference % \bibitem[\protect\astroncite{{Coulais} et~al.}{2002}]{CAF2002Mont}
{Coulais}, A., {Abergel}, A., and {Fouks}, B.~I. 2002, in {\em NASA/CP-211408}

\reference % \bibitem[\protect\astroncite{{Coulais} et~al.}{2003}]{LC_Coulais_PHT}
{Coulais}, A., et~al. 2003, in {\em ESA SP-481}

\reference % \bibitem[\protect\astroncite{{Doi} et~al.}{2002}]{Doy02}
Doi, Y., et al. 2002,
%\newblock {\em Adv. in Space Res.} {\bf 30} (9), 2099
{\em Adv. in Space Res.} {\bf 30} (9), 2099

\reference % \bibitem[\protect\astroncite{{Fouks} et~al.}{2003}]{FCN2002Sig}
{Fouks}, B.~I., {Coulais}, A., and {Normand}, J. 2003, in  {\em ESA SP -511}

\reference % \bibitem[\protect\astroncite{Fouks}{1992}]{Fouks92ESA}
Fouks, B.~I. 1992, in {\em ESA SP-356}

\reference % \bibitem[\protect\astroncite{Fouks}{1997}]{Fouks97}
Fouks, B.~I. 1997,
%\newblock {\em Proc. of SPIE} {\bf 3122}, 441
{\em Proc. of SPIE} {\bf 3122}, 441

\reference % \bibitem[\protect\astroncite{Fouks and {Schubert}}{1995}]{FouksSchu95}
Fouks, B.~I. and {Schubert}, J. 1995,
%\newblock {\em Proc. of SPIE} {\bf 2475}, 487
{\em Proc. of SPIE} {\bf 2475}, 487

\reference % \bibitem[\protect\astroncite{{Fujiwara} et~al.}{2003}]{SW2}
Fujiwara, M., et~al. 2003,
%\newblock {\em Applied Optics} {\bf 42} (12), 2166
{\em Applied Optics} {\bf 42} (12), 2166

\reference % \bibitem[\protect\astroncite{{Haegel} et~al.}{2001}]{Haegel01}
{Haegel}, N.~M., et~al. 2001,
%\newblock {\em Applied Optics} {\bf 40} (31), 5748
{\em Applied Optics} {\bf 40} (31), 5748

\reference % \bibitem[\protect\astroncite{Haegel et~al.}{1999}]{Haegel99}
Haegel, N.~M., et al. 1999,
%\newblock {\em Applied Optics} {\bf 38} (10), 1910
{\em Applied Optics} {\bf 38} (10), 1910

\reference % \bibitem[\protect\astroncite{{Kaneda} et~al.}{2002}]{Kaneda02}
Kaneda, H., et al. 2002,
{\em Adv. in Space Res.} {\bf 30} (9), 2105

\reference % \bibitem[\protect\astroncite{{Kester} et~al. }{2003}]{LC_Kester}
{Kester}, D., {Beintema}, D.~A., and {Lutz}, D. 2003, in {\em ESA SP-481}

\reference % \bibitem[\protect\astroncite{Malaiz\'e}{2003}]{Malaize2003}
Malaiz\'e, J. 2003,
{\em Probl\`emes inverses en imagerie spatiale~: Projet {SIRTF}
  {MIPS} canal \`a 160 $\mu$m},
Stage de 2i\`eme ann\'ee {I}ng\'enieur, LSS, Supelec

\reference % \bibitem[\protect\astroncite{{Matsuura} et~al.}{2002}]{SW1}
Matsuura, S., et al. 2002,
%\newblock {\em Proc. of SPIE} {\bf 4850}, 902
{\em Proc. of SPIE} {\bf 4850}, 902

\reference % \bibitem[\protect\astroncite{{Takahashi} et~al.}{2000}]{Takahashi00}
Takahashi, H., et al. 2000, 
%\newblock {\em Proc. of SPIE} {\bf 4013}, 47
{\em Proc. of SPIE} {\bf 4013}, 47

\reference % \bibitem[\protect\astroncite{{Takahashi} et~al.}{2003}]{Takahashi03}
{Takahashi}, H., et al. 2003,
%\newblock {\em Proc. of SPIE} {\bf 4850}, 191
{\em Proc. of SPIE} {\bf 4850}, 191

\reference % \bibitem[\protect\astroncite{Vinokurov and Fouks}{1991}]{VinoFouks91}
Vinokurov, L.~A. and Fouks, B.~I. 1991,
%\newblock {\em Sov. Phys. Semicond.} {\bf 25(11)}, 1207
{\em Sov. Phys. Semicond.} {\bf 25(11)}, 1207

\reference % \bibitem[\protect\astroncite{{Young} et~al.}{2003}]{Young03}
{Young}, E.~T., et al. 2003,
%\newblock {\em Proc. of SPIE} {\bf 4850}, 98
{\em Proc. of SPIE} {\bf 4850}, 98

\end{references} 	%\end{thebibliography}
%\end{references}

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