Photometric Zero Point
The primary result of a photometric solution is the detector zero point. It relates the magnitude of a star or other object in a given band to the DN counts of an object. It is given by:
Where \(m\) is the magnitude of an object which has a total integrated signal of \(D\) over some time \(t\). The magnitude zero point is given by \(Z_p\). (The multiplicative constant is \(100^\frac{1}{5} \approx 2.51189\).)
We can reverse this calculation by consulting a photometric database. The photometric database gives us the magnitudes for a given band and we can use aperture photometry to determine the total counts of the objects.
This way, we can calculate an average zero point value \(Z_p\) which can be used for other photometric calculations. We use medians to avoid issues with outliers. The zero-point itself also has an error of \(Z_e\) as determined from the variation between the different calculated zero-point values from each photometric star.
Specifically for our collective set of zero points \(\mathbf{Z} = {{Z_{p,1}, {Z_{p,2}, ...}\), we have our averaged zero point given by the median:
And the error on the average provided by the standard error of the median. To avoid possible contamination from outliers in either the observations or the photometric database, we estimate the deviation using the median absolute deviation, thus (for \(n\) being the total number of observations)…
Important considerations must be taken to remove overly bright and overly dim objects. These otherwise skew the zero point measurement because of saturation or noise effects.
Calculating Magnitude
Once the zero-point \(Z_p\) and its error \(Z_e\) is determined, the original equation as provided above, can be used to determine the photometric magnitude of stars or other targets using PSF photometry.
Provided the counts (integrated over some time \(t\)) of the target which the magnitude is to be determined as \(F\), and the error to be \(E = \sqrt{F}\) as per Poisson statistics, the magnitude is given as:
Propagating the errors, we have that the error in the magnitude \(m_\sigma\) (or rather its variance \(m_\sigma^2\)) is given by:
We assume that the covariance between \(F\) and \(Z_p\) is \(\sigma_{F,Z_p} = 0\). The propagated error itself, is of course \(m_\sigma = \sqrt{m_\sigma^2}\).
Filtering Considerations
We account for overly bright and overly dim stars and other problematic targets by filtering the results from the photometric database (the PhotometryEngine). We describe the methods that we use to filter the inappropriate stars. Configuring these methods can be done by tuning their corresponding configuration files.
Limiting by Magnitude
We limit the stars considered for calculating the zero point based on magnitude. If a star has a filter magnitude (as determined by the photometric database) exceeding \(m_\text{max}\), then it is not included in the determination of the zero point. They are excluded from the set which when averaged determines the zero point and its errors.
(To “exceed” a filter magnitude, the magnitude must be less than the reference one because magnitudes are a backwards system.)