High Frame-rate Imaging Based Photometry, Photometric Reduction of Data from Electron-multiplying Charge Coupled Devices (EMCCDs)

The EMCCD is a type of CCD that delivers fast readout times and negligible readout noise, making it an ideal detector for high frame rate applications which improve resolution, like lucky imaging or shift-and-add. This improvement in resolution can potentially improve the photometry of faint stars in extremely crowded fields significantly by alleviating crowding. Alleviating crowding is a prerequisite for observing gravitational microlensing in main sequence stars towards the galactic bulge. However, the photometric stability of this device has not been assessed. The EMCCD has sources of noise not found in conventional CCDs, and new methods for handling these must be developed. We aim to investigate how the normal photometric reduction steps from conventional CCDs should be adjusted to be applicable to EMCCD data. One complication is that a bias frame cannot be obtained conventionally, as the output from an EMCCD is not normally distributed. Also, the readout process generates spurious charges in any CCD, but in EMCCD data, these charges are visible as opposed to the conventional CCD. Furthermore we aim to eliminate the photon waste associated with lucky imaging by combining this method with shift-and-add. A simple probabilistic model for the dark output of an EMCCD is developed. Fitting this model with the expectation-maximization algorithm allows us to estimate the bias, readout noise, amplification, and spurious charge rate per pixel and thus correct for these phenomena. To investigate the stability of the photometry, corrected frames of a crowded field are reduced with a PSF fitting photometry package, where a lucky image is used as a reference. We find that it is possible to develop an algorithm that elegantly reduces EMCCD data and produces stable photometry at the 1% level in an extremely crowded field.Comment: Submitted to Astronomy and Astrophysic

Bayesian photon counting with electron-multiplying charge coupled devices (EMCCDs)

The EMCCD is a CCD type that delivers fast readout and negligible detector noise, making it an ideal detector for high frame rate applications. Because of the very low detector noise, this detector can potentially count single photons. Considering that an EMCCD has a limited dynamical range and negligible detector noise, one would typically apply an EMCCD in such a way that multiple images of the same object are available, for instance, in so called lucky imaging. The problem of counting photons can then conveniently be viewed as statistical inference of flux or photon rates, based on a stack of images. A simple probabilistic model for the output of an EMCCD is developed. Based on this model and the prior knowledge that photons are Poisson distributed, we derive two methods for estimating the most probable flux per pixel, one based on thresholding, and another based on full Bayesian inference. We find that it is indeed possible to derive such expressions, and tests of these methods show that estimating fluxes with only shot noise is possible, up to fluxes of about one photon per pixel per readout.Comment: Fixed a few typos compared to the published versio

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