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THE EFFECT OF BACKGROUND ON LOCALIZATION UNCERTAINTY IN SINGLE EMITTER IMAGING Bernd Rieger and Sjoerd Stallinga Quantitative Imaging Group, Department of Imaging Science and Technology Delft University of Technology, Lorentzweg 1, 2628 CJ, Delft, The Netherlands Email: [email protected] KEY WORDS: point spread function, maximum likelihood estimation, Cramer-Rao lower bound, free dipole emitter We analyze singe emitter localization at high background levels. Thompson, Larson and Webb have published a widely quoted formula for the localization accuracy as a function of signal and background photon count [1] for Least Mean Squares (LMS) fitting. In the presence of shot noise LMS fitting is not appropriated and should be replaced by Maximum Likelihood Estimation (MLE). The latter estimation closely follows the Cramer-Rao lower bound (CRLB) for a wide range of signal photon counts and up to very large background levels and can be computed in real time using graphics cards [2]. The use of an idealized Gaussian to fit measured spots that originate from freely and rapidly rotating dipole emitters appears to work well for all parameters considered [3]. Mortensen and co-workers presented an exact but not closed form expression for the localization uncertainty [4] that applies to MLE and thus corrects the widely used formula of [1]. We propose the following analytical approximation for the localization uncertainty for MLE fitting: σ2 ⎛ 2τ ⎞ (Δx) 2 = a ⎜⎜1 + 4τ + ⎟, N ⎝ 1 + 4τ ⎟⎠ τ = 2πσ a2b / ( Na 2 ), σ a2 = σ 2 + a 2 /12 Here a is the camera pixel size, N is the total signal photon count, b the background photon count per pixel and σ is the width of the Gaussian that is used to fit the PSF. This relatively simple closed-form expression approximates the minimum achievable localization uncertainty excellently for all signal and background levels. We present simulation results that prove the validity and usefulness of our formula for an idealized Gaussian ground truth PSF model or a realistic free dipole ground truth PSF model [3]. [1] R.E. Thompson, D.R. Larson, and W.W. Webb, Biophysical Journal, 82:2775–2783, 2002. [2] C.S. Smith, N. Joseph, B. Rieger, and K.A. Lidke, Nature Methods, 7(5):373–375, 2010. [3] S. Stallinga, and B. Rieger, Optics Express, 18(24):24461-24476, 2010. [4] K.I. Mortensen, L.S. Churchman, J.A. Spudich, and Flyvbjerg, Nature Methods, 7(5):377 –384, 2010.