A method is proposed to measure the photon polarisation parameter \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _{\gamma }$$\end{document} λ γ in \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{b}} \!\rightarrow {s} {\gamma } $$\end{document} b → s γ transitions using an amplitude analysis of \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B\!\rightarrow K\pi \pi {\gamma } $$\end{document} B → K π π γ decays. Simplified models of the \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K} {\pi } {\pi } $$\end{document} K π π system are used to simulate \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{B} ^+}} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^+} {\gamma } $$\end{document} B + → K + π - π + γ and \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{B} ^0} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^0} {\gamma } $$\end{document} B 0 → K + π - π 0 γ decays, validate the amplitude analysis method, and demonstrate the feasibility of a measurement of the \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _{\gamma }$$\end{document} λ γ parameter irrespective of the model parameters. Similar sensitivities to \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _{\gamma }$$\end{document} λ γ are obtained with both the charged and neutral hadronic systems. In the absence of any background and distortion due to experimental effects, the statistical uncertainty expected from an analysis of \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{B} ^+}} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^+} {\gamma } $$\end{document} B + → K + π - π + γ decays in an LHCb data set corresponding to an integrated luminosity of 9  \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,\hbox {fb}^{-1}$$\end{document} fb - 1 is estimated to be 0.009. A similar measurement using \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{B} ^0} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^0} {\gamma } $$\end{document} B 0 → K + π - π 0 γ decays in a Belle II data sample corresponding to an integrated luminosity of 5  \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {\,ab}^{-1}$$\end{document} ab - 1 would lead to a statistical uncertainty of 0.018.