Statistical analysis and optimization of frequency-domain fluorescence lifetime imaging microscopy using homodyne lock-in detection

Investigation of signal-to-noise ratio in frequency-domain multiphoton fluorescence lifetime imaging microscopy

Multiphoton microscopy (MPM) combined with fluorescence lifetime imaging microscopy (FLIM) has enabled three-dimensional quantitative molecular microscopy in vivo. The signal-to-noise ratio (SNR), and thus the imaging rate of MPM-FLIM, which is fundamentally limited by the shot noise and fluorescence saturation, has not been quantitatively studied yet. In this paper, we investigate the SNR performance of the frequency-domain (FD) MPM-FLIM with two figures of merit: the photon economy in the limit of shot noise, and the normalized SNR in the limit of saturation. The theoretical results and Monte Carlo simulations find that two-photon FD-FLIM requires 50% fewer photons to achieve the same SNR as conventional one-photon FLIM. We also analytically show that the MPM-FD-FLIM can exploit the DC and higher harmonic components generated by nonlinear optical mixing of the excitation light to improve SNR, reducing the required number of photons by an additional 50%. Finally, the effect of fluorophore saturation on the experimental SNR performance is discussed.

Effect of noise on modulation amplitude and phase in frequency-domain diffusive imaging

We theoretically investigate the effect of noise on frequency-domain heterodyne and/or homodyne measurements of intensity-modulated beams propagating through diffusive media, such as a photon density wave. We assumed that the attenuated amplitude and delayed phase are estimated by taking the Fourier transform of the noisy, modulated output data. We show that the estimated amplitude and phase are biased when the number of output photons is small. We also show that the use of image intensifiers for photon amplification in heterodyne or homodyne measurements increases the amount of biases. Especially, it turns out that the biased estimation is independent of AC-dependent noise in sinusoidal heterodyne or homodyne outputs. Finally, the developed theory indicates that the previously known variance model of modulation amplitude and phase is not valid in low light situations. Monte-Carlo simulations with varied numbers of input photons verify our theoretical trends of the bias.