Specifications

AUTOSTAR CCD PHOTOMETRY 61
Where:
i
o
, r
o,
v
o, and
i
o
are magnitudes corrected for extinction
k'
vi
= (v–i) Extinction Coefficient
k'
v
= (v) Extinction Coefficient
k'
vr
= (v–r) Extinction Coefficient
k'
bv
= (b–v) Extinction Coefficient
k'
ri
= (r–i) Extinction Coefficient
X = Air Mass for the observation
The BVRI system defined here uses one simple magnitude, V, and
four simple color indices, (V – I), (V – R), (R – I), and (B – V). In
some texts, the system is defined not only in these terms but also
by an alternative set consisting of the four simple magnitudes, B,
V, R, and I.
Note: (V – I) is used in the following equations, but actually is
not necessary as final values for (V – I) can be determined from
the (V – R) and (R – I) values.
Determining the Extinction Coefficients
There are three cases for determining extinction coefficients: data
used for differential photometry; data when color transformation
coefficients are not known; and data when they are known. In each
case, the equations are of the form for a straight line:
Y = MX + B
Where: M is the slope and is equal to the filter band's extinction
coefficient. Because we are only interested in extinction for use in
determining the color coefficients, we will just use the first case as
it is simpler:
Slope = Δ Magnitude / Δ Air Mass
For this case, a single standard star is used. The star should be
observed at varying air masses (X = 1.0 to 1.5 or greater). A
minimum of four and if possible a dozen or more data point are
suggested. We have chosen to use the M67 star cluster to obtain
data on stars that have well-determined magnitudes.