Self-consistent, unbiased root-mean-square emittance analysis

We present a self-consistent method for analyzing measured emittance data that yields unbiased estimates for the root-mean-square (rms) emittance. The self-consistent, unbiased elliptical exclusion analysis uses an ellipse to determine the bias from the data outside the ellipse, before calculating the rms emittance from the bias-subtracted data within the ellipse. Increasing the ellipse size until the rms emittance estimate saturates allows for determining the minimum elliptical area that includes all real signals, even those buried in the noise. Variations of the ellipse shape and orientations are used to test the robustness of the results. Background fluctuations cause fluctuations in the rms emittance estimate, which are an estimate of the uncertainty incurred through the analysis