PSF broadening due to fluorescence emission

Fluorescent structures are nowadays commonly used in the field of biological imaging. However the emission of fluorescence is always given within a finite spectrum. When the imaging systems point spread function is measured, this can be described as an incoherent summation of individual single-wavelength PSFs, weighted by the emission spectrum. As the full-width-half-maximum of the PSF scales inversely with the wavelength and most emission spectra exhibit a fluorescence tail at longer wave-lengths, this contributes significantly to lateral broadening. In our work we theoretically quantify this effect by deriving an analytic expression, which has been verified against some numerical simulations (rel. error on average 3 %). We report a FWHM-broadening on the order of 10 nm and additionally propose a way to overcome this broadening by splitting the emission spectrum into multiple wavelength segments. The corresponding image data is recombined in Fourier space by weighted averaging, leading to an improved signal-to-noise ratio at high spatial frequencies and a reduction of the FWHM of up to 8 nm (relative reduction of the broadening by {approx} 70 %). We also introduce a corrected wavelength, which in combination with already existing PSF calculation tools, describes a theoretical PSF which incorporates the aforementioned broadening effect.