## 1 Introduction  
Augmented Reality (AR) is an innovative technology that overlays computer-generated 2D and 3D objects onto a real-world camera view, creating an immersive and interactive experience [1]. In rehabilitation, AR has gained significant attention due to its unique ability to provide immediate, real-time feedback and foster engaging training environments [2, 3]. This real-time interactive nature of AR facilitates precise movements by enabling users to concurrently adjust their actions while following virtual model demonstrations. Consequently, AR proves highly effective for rehabilitation training by seamlessly integrating motivating and engaging content, which is crucial for patient adherence and progress [2]. Notably, AR has consistently demonstrated significant utility for patients requiring rehabilitation by effectively incorporating key therapeutic elements such as repetitive practice, immediate feedback, and enhanced motivation [1]. Individuals who have undergone leg amputation due to accident or illness typically ambulate using a prosthesis. Rehabilitation training is multifaceted, encompassing foundational exercises like strengthening residual limb muscles and improving balance, progressing to complex tasks such as weight shifting, standing up, and navigating stairsand ramps [4, 5]. A fundamental and critical element in prosthetic training is achieving effective weight-bearing on the prosthetic side. However, post-amputation, patients frequently experience pain, edema, and skin issues in the residual limb [6], creating significant barriers to early weight-bearing, which is otherwise crucial for symptom alleviation and quicker prosthetic adaptation [7]. Rehabilitation commonly begins with static standing exercises aimed at even weight distribution, gradually advancing to more dynamic tasks like inducing weight-bearing on the amputated side via healthy leg movements, or standing on the amputated leg while the healthy leg is elevated on a step box [5]. While physical therapists primarily guide these exercises with verbal instructions, the inherent asymmetry between the two legs often leads to considerable balance challenges for patients. Relying solely on verbal cues can thus limit the achievement of accurate movements and sufficient weight-bearing, particularly during the initial stages of prosthetic use where finer motor control and psychological adjustment are paramount [7]. Recognizing these limitations, researchers have explored advanced technologies to augment traditional rehabilitation approaches. Previous studies show that diverse forms of feedback, including mirrors, verbal cues, and augmented sensory feedback, effectively aid weight-bearing and balance training for individuals with lower limb amputations [7, 8, 9]. Authors of one study specifically suggested that visual feedback is particularly beneficial for controlling sway in amputees, advocating for its inclusion in rehabilitation plans [7]. Furthermore, studies have reported that visual feedback improves gait asymmetry [8], and biofeedback training incorporating visual feedback assists in retraining equal weight-bearing [9]. The provision of diverse feedback is essential for optimizing correct movement execution during rehabilitation [10]. Specifically, visual feedback stimulates proprioception, offering neurological benefits, and the visual confirmation of achieving target movement trajectories has been shown to result in more accurate exercise performance and enhanced motor learning [3]. Building on these insights, AR technology emerges as a compelling solution, offering real-time visual guidance that could directly address the balance and accuracy challenges faced by lower limb amputees, thereby fostering greater engagement and more effective rehabilitation outcomes. Existing research shows promising results for AR-based rehabilitation training across various patient populations. Numerous studies on stroke patients indicate AR's effectiveness in enhancing upper and lower limb functional recovery [11].