First, the error for each target and comparison star is individually
calculated using equation 25 in MERLINE, W. & HOWELL, S.B.,
1995, EXP. ASTRON., 6, 163. The error value is reported as
Source_Error_Xnn in the measurements table and accounts for CCD
gain, read out noise (RON), dark current, quantization noise, and
poisson statistics in the source and sky background signals. As of
release 2.1.5, scintillation noise is not included in the error
calculation.
The error equation is:
SourceError = SquareRoot(IntSourceCnts * Gain + NSourcePixels * (1.0
+ NSourcePixels / NSkyPixels) * (SkyPerPixel * Gain + DarkPerPixel +
RON * RON + Gain * Gain * 0.083521)) / Gain;
where:
IntSourceCnts = net integrated source counts (calculated by AIJ)
SkyPerPixel = average sky background per pixel (calculated by AIJ)
NSourcePixels = number of pixels within the sources aperture
(calculated by AIJ)
NSkyPixels = number of pixel within the sky background annulus
(calculated by AIJ)
DarkPerPixel = total dark counts per pixel (entered by user on set
aperture panel as [e-/pix/sec], which is then multiplied internally
by the exposure time found in the FITS header {or by 1.0 if no
exposure time header info is found}, or is read from the FITS header
keyword specified in the set aperture panel, but in this case should
be in [e-/pix] in the header {i.e. is not multiplied by exposure
time in this case})
RON = CCD read out noise [e-] (entered by user on set aperture
panel)
Gain = CCD gain (entered by user on set aperture panel)
For relative photometry error calculations, the individual source
errors are propagated through the summations and divisions using
standard error propagation techniques assuming independent variables
(see
http://en.wikipedia.org/wiki/Propagation_of_uncertainty ). Thus,
the error in the comparison star ensemble is calculated by summing
the individual comparison star errors in quadrature {i.e. in the
measurements table, tot_C_err = SquareRoot(Source_Error_C1^2 +
Source_Error_C2^2 + ... + Source_Error_CN^2)}. When forming the
relative flux terms, error is propagated through the division and
reported in the measurements table as rel_flux_err_Xnn. For example,
rel_flux_err_T1 = (Source-Sky_T1 / tot_C_cnts) * SquareRoot(
Source_Error_T1^2 / Source-Sky_T1^2 + tot_C_err^2 / tot_C_cnts^2).
If data are normalized or converted to magnitude in the plot window,
error is normalized or converted to magnitude before plotting as
well. For normalization, the error value is divided by the same
baseline average value used to normalize the data. For conversion to
magnitude, the following calculation is used: rel_flux_error_T1(mag)
= 2.5 * Log_base10 (1.0 + rel_flux_err_T1/rel_flux_T1).
Normalized error and/or error in magnitude can be saved to the
measurements table by using the "New Col" button ( ) on the
left-hand side of the "Multi-plot Y-data" panel corresponding to the
displayed curve that shows the normalized or magnitude converted
data.
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