This paper presents a mathematical methodology for deriving optimal margin and edge-enhanced intensity maps in radiation therapy to counteract dose blurring caused by motion and uncertainty. The authors analyze how to design intensity maps that ensure tumour coverage while minimizing the total dose delivered. They show that if the tumour size is small relative to the standard deviation of motion (t/σ ≤ 2.28), an optimal intensity map is simply a pure scaling of the static intensity map without margins or edge-enhancements. However, if the tumour size is larger than this threshold, margins and edge-enhancements are preferred. The authors derive formulae to calculate the exact dimensions of these intensity maps. The study also extends the analysis to scenarios where the parameters of the motion distribution are uncertain. In these cases, the authors derive a similar threshold to determine the structure of an optimal margin intensity map. They also analyze edge-enhanced intensity maps, which provide increased intensity near the tumour edge to offset dose blurring. The authors find that if the tumour size is small relative to the standard deviation of motion (t/σ ≤ 2.11), an optimal intensity map is again a pure scaling of the static intensity map. However, if the tumour size is larger than this threshold, edge-enhancements are preferred. The authors also discuss the importance of robustness in the presence of motion uncertainty. They show that when motion parameters are uncertain, the optimal margin intensity map must account for the range of possible values of the mean and standard deviation of the motion distribution. They derive a modified threshold based on the effective tumour size and maximum standard deviation to determine whether a positive margin or pure intensity scaling is optimal. The paper concludes that optimal margin and edge-enhanced intensity maps can be derived using mathematical formulations that account for motion and uncertainty. These maps ensure tumour coverage while minimizing the total dose delivered. The results provide guidelines for treatment planning decisions, showing that for small tumours, pure intensity scaling may be sufficient to compensate for dose blurring due to motion. For larger tumours, margins or edge-enhancements are preferred. The study also highlights the importance of robustness in the presence of motion uncertainty and provides a framework for designing optimal intensity maps in such scenarios.This paper presents a mathematical methodology for deriving optimal margin and edge-enhanced intensity maps in radiation therapy to counteract dose blurring caused by motion and uncertainty. The authors analyze how to design intensity maps that ensure tumour coverage while minimizing the total dose delivered. They show that if the tumour size is small relative to the standard deviation of motion (t/σ ≤ 2.28), an optimal intensity map is simply a pure scaling of the static intensity map without margins or edge-enhancements. However, if the tumour size is larger than this threshold, margins and edge-enhancements are preferred. The authors derive formulae to calculate the exact dimensions of these intensity maps. The study also extends the analysis to scenarios where the parameters of the motion distribution are uncertain. In these cases, the authors derive a similar threshold to determine the structure of an optimal margin intensity map. They also analyze edge-enhanced intensity maps, which provide increased intensity near the tumour edge to offset dose blurring. The authors find that if the tumour size is small relative to the standard deviation of motion (t/σ ≤ 2.11), an optimal intensity map is again a pure scaling of the static intensity map. However, if the tumour size is larger than this threshold, edge-enhancements are preferred. The authors also discuss the importance of robustness in the presence of motion uncertainty. They show that when motion parameters are uncertain, the optimal margin intensity map must account for the range of possible values of the mean and standard deviation of the motion distribution. They derive a modified threshold based on the effective tumour size and maximum standard deviation to determine whether a positive margin or pure intensity scaling is optimal. The paper concludes that optimal margin and edge-enhanced intensity maps can be derived using mathematical formulations that account for motion and uncertainty. These maps ensure tumour coverage while minimizing the total dose delivered. The results provide guidelines for treatment planning decisions, showing that for small tumours, pure intensity scaling may be sufficient to compensate for dose blurring due to motion. For larger tumours, margins or edge-enhancements are preferred. The study also highlights the importance of robustness in the presence of motion uncertainty and provides a framework for designing optimal intensity maps in such scenarios.