Reply to Comment: ‘A novel method for fast and robust estimation of fluorescence decay dynamics using constrained least-square deconvolution with Laguerre expansion’

In this response we underscore that the instrumentation described in the original publication (Liu et al 2012 Phys. Med. Biol. 57 843-65) was based on pulse-sampling technique, while the comment by Zhang et al is based on the assumption that a time-correlated single photon counting (TCSPC) instrumentation was used. Therefore the arguments made in the comment are not applicable to the noise model reported by Liu et al. As reported in the literature (Lakowicz 2006 Principles of Fluorescence Spectroscopy (New York: Springer)), while in the TCSPC the experimental noise can be estimated from Poisson statistics, such an assumption is not valid for pulse-sampling (transient recording) techniques. To further clarify this aspect, we present here a comprehensive noise model describing the signal and noise propagation of the pulse sampling time-resolved fluorescence detection. Experimental data recorded in various conditions are analyzed as a case study to demonstrate the noise model of our instrumental system. In addition, regarding the statement of correcting equation (3) in Liu et al (2012 Phys. Med. Biol. 57 843-65), the notation of discrete time Laguerre function in the original publication was clear and consistent with literature conventions (Marmarelis 1993 Ann. Biomed. Eng. 21 573-89, Westwick and Kearney 2003 Identification of Nonlinear Physiological Systems (Hoboken, NJ: Wiley)). Thus, it does not require revision