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+.EQ
+delim	$$
+.EN
+.OM
+.TO
+IRAF ONEDSPEC Users
+.FR
+Frank Valdes
+.SU
+SENSFUNC Corrections
+.LP
+This memorandum describes the meaning of the corrections
+computed by the \fBonedspec\fR task \fBsensfunc\fR.
+The basic equation is
+
+.EQ (1)
+I( lambda )~=~I sub obs ( lambda )~10 sup {0.4~(s( lambda )~+
+~A~e( lambda )~+~roman {fudge~terms})}
+.EN
+
+where $I sub obs$ is the observed spectrum corrected to counts per second,
+$I$ is the flux calibrated spectrum, $s( lambda )$ is the sensitivity
+correction needed to produce
+flux calibrated intensities, $A$ is the air mass at the time of the
+observation, $e( lambda )$ is a standard extinction function, and,
+finally, additional terms appropriately called \fIfudge\fR terms.  Expressed
+as a magnitude correction this equation is
+
+.EQ (2)
+DELTA m( lambda )~=s( lambda )~+~A~e( lambda )~+~roman {fudge~terms}
+.EN
+
+In \fBsensfunc\fR the standard extinction function is applied so that ideally
+the $DELTA m$ curves (defining the sensitivity function) obtained from
+observations of different stars and at different air masses are identical.
+However, at times this is not the case because the observations were taken
+through non-constant or nonstandard extinction.
+
+There are two types of fudge terms used in \fBsensfunc\fR, called \fIfudge\fR
+and \fIgrey\fR.  The \fIfudge\fR correction is a separate constant,
+independent of wavelength or air mass, applied to each observation to shift
+the sensitivity curves to the same level on average.  This is done to
+determine the shape of the sensitivity curve only.
+The fudge correction for each observation is obtained by determining
+the average magnitude shift over all wavelenths relative to the observation
+with the smallest sensitivity correction.  A composite sensitivity curve
+is then determined from the average of all the fudged observations.
+The fudge terms are not incorporated in the sensitivity or extinction
+corrections applied to calibrate the spectra.  Thus, after applying the
+sensitivity and extinction corrections to the standard star spectra there
+will be absolute flux scale errors due to the observing conditions.
+
+If the observer believes that there is an actual calibratible error in
+the standard extinction then \fBsensfunc\fR can be used to determine a
+correction which is a linear function of the air mass.  This is done by
+relating the fudge values (the magnitude shifts needed to bring observations
+to the same sensitivity level) to the air mass of the observations.
+The \fIgrey\fR term is obtained by the least square fit to 
+
+.EQ (3)
+f sub i~=~G~DELTA A sub i~=~G~A sub i~+~C
+.EN
+
+where the $f sub i$ are the fudge values relative to the observation with
+the smallest sensitivity correction and the $DELTA A sub i$ are the
+air mass differences relative to this same observation.  The slope constant
+$G$ is what is refered to as the \fIgrey\fR term.  The constant term,
+related to the air mass of the reference observation to which the other
+spectra are shifted, is absorbed in the sensitivity function.
+The modified equation (2) is
+
+.EQ (4)
+DELTA m( lambda )~=~s ( lambda ) + A~(e( lambda )~+~G)
+.EN
+
+It is important to realize that equation (3) can lead to erroneous results
+if there is no real relation to the air mass or the air mass range is
+too small.  In other words applying the grey term correction will produce
+some number for $G$ but it may be worse than no correction.  A plot of
+the individual fudge constants, $f sub i$, and the air mass or
+air mass differences would be useful to evaluate the validity of the
+grey correction.  The actual magnitude of the correction is not $G$
+but $DELTA A~G$ where $DELTA A$ is the range of observed air mass.