Low Level Aperture Photometry Interface
One of the commonly used methods to measure fluxes of sources from an image is to sum–up the flux within some circular aperture centered on each source position. The reason for choosing circular apertures is that in most applications, point sources produce roughly circularly symmetric profiles. In general there is a trade–off that has to be made when an aperture is chosen. Large apertures result in a larger area of sky being included which contributes noise to the measurement. This particularly affects faint stars. On the other hand, smaller apertures include less flux, and hence are subject to larger Poisson noise. This is particularly important for bright stars, since their PSF dominates over the sky brightness over a much larger area of the detector. Luckily, flux measurements using many multiple apertures can be performed, resulting in optimal photometry regardless of the brightnesses of the sources.
If one were to simply add up the fluxes for any pixels that fully or partially overlap with the aperture, the area over which the flux is added will vary as the source mover around the pixel grid. As a result, unless the positions of sources are kept fixed to much better than the size of a pixel between consecutive images of a survey, this introduces scatter in the measured flux. The only way to avoid this software noise source is to always add up the flux over the same area around the source for each image. This automatically implies that photometry tools have to handle pixels which only partially overlap with the aperture.
AstroWISP performs aperture photometry, properly accounting for the PSF and non-uniform pixel sensitivity for both pixels fully within the aperture and pixels straddling the aperture boundary. If no PSF information is available, the flux over each pixel is assumed uniformly distributed. If not pixel sensitivity information is available, pixels are assumed uniformly sensitive.
The flux (\(F\)) and its Poisson error (\(\delta F\)) are estimated as \(F=\sum_p k_p m_p - \pi r^2B\) and \(\delta F=\sqrt{\sum_p k_p^2 m_p g_p^{-1}} + \pi r^2\delta B^2\), where the \(p\) index iterates over all pixels which at least partially overlap with the aperture, \(m_p\) are the measured (after bias, dark and flat field corrections) values of the pixels in ADU, \(g_p\) are the gains of the pixels in electrons/ADU (including the effects of the pre–applied flat field correction), \(k_p\) are constants which account for the sub–pixel sensitivity map and the partial overlaps between the pixel and the aperture, \(r\) is the size of the aperture, and \(B\) and \(\delta B\) are the background estimate and its associated error for the source.
If the sub–pixel sensitivity map is \(S(x,y)\ (0<x<1, 0<y<1)\), the PSF is \(f(x,y)\) (\(x\) and \(y\) are relative to the input position of the source center), and \(l_p\)/\(b_p\) is the horizontal/vertical distance between the left/bottom boundary of the \(p\)-th pixel and the source location, then the \(k_p\) constants are given by:
where the integral in the numerator is performed over the part of the pixel that is inside the aperture, and \(A\) is the overall scaling constant by which the PSF must be multiplied in order to reproduce the pixel values on the image (see Low Level PSF/PRF Fitting Interface for a description of how \(A\), \(B\) and the PSF parameters are estimated).