I. Introduction
Recently, human–machine interface (HMI) devices, such as touch screens and video presentation devices that transmit information between humans and machines owing to the development of virtual reality technology, have become more complex and diversified. Thus, the development of HMI devices that can be easily operated by humans is required. Furthermore, the number of input operations that require display response confirmation of the operations is increasing. Various studies have focused on the display responses of devices. For example, during device operations in environments that assume an augmented reality or virtual reality space, delays in display responses lead to discomfort in humans, reducing immersiveness [1],[2]. Therefore, a lower display delay response characteristic is required during operation in a highly immersive environment. Numerous studies have also investigated the sense of agency (SoA), which is the sense that "I am the one who is causing or generating an action" [3] while operating the device [4]. These studies have reported that the SoA is reduced in response without delay [5],[6]. Other studies have investigated the delay response that humans can perceive [7]. In experiments concerning delay recognition of self-body images, a response delay of 230 ms or more is recognizable [8]; in touch screen operation, humans can recognize a delay of 10 ms or less [9]. According to the results of these studies, the delay recognition and SoA to the response of the device differ based on the operation target and environment; a lower delayed response to human operation sensation is not optimal. Previous studies have also investigated brain activity, SoA, and delayed recognition [10],[11]. However, several human operation sensations to the response of device operation have been qualitatively evaluated through subjective information, and few studies have examined quantitative evaluations based on objective indicators.