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The troposphere is considered as one of the major error sources in space geodetic techniques. Thus, accurate troposphere delay models are essential to provide high-quality products, such as reference frames, satellite orbits, or Earth rotation parameters. In this paper, a new troposphere delay model for satellite laser ranging, the Vienna Mapping Functions 3 for optical frequencies (VMF3o), is introduced. The model parameters are derived from ray-traced delays generated by an in-house ray-tracing software. VMF3o comprises not only zenith delays and mapping functions, but also linear horizontal gradients, which are not part of the standard SLR analysis yet. The model parameters are dedicated to a signal wavelength of 532 nm. Since some SLR stations operate also with other wavelengths, VMF3o provides a correction formula to transform the model parameters to any requested wavelength between 350 and 1064 nm. A test demonstrates that the correction formula approximates slant delays calculated at different wavelengths very accurately. The remaining error for slant delays at a wavelength of 1064 nm adds up to only a few millimetres at    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$10^{\circ }$$\end{document}    10  ∘elevation angle. A comparison study of the modelled delays that are derived from VMF3o and ray-traced delays was carried out to examine the quality of the model approach. The remaining differences of modelled and ray-traced delays are expressed as mean absolute error. At    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$5^{\circ }$$\end{document}    5  ∘elevation angle, the mean absolute error is only a few millimetres. At    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$10^{\circ }$$\end{document}    10  ∘elevation angle, it is at the 1 mm level. The results of the comparison also reveal that introducing linear horizontal gradients reduces the mean absolute error by more than 80% for low elevation angles.

VMF3o: the Vienna Mapping Functions for optical frequencies