1. A real-time-measurement projection device comprising: a projection device that projects pattern light including a pattern image onto a projection target; an imaging device that electronically acquires a captured image of the projection target irradiated with the pattern light for each pixel for a predetermined exposure time; and a calculation device that computes pixel correspondence information between each pixel of the imaging device and each pixel of the projection device by contrasting data of the captured image with data of the pattern image, converts measurement information of each pixel obtained from the imaging device into a correspondence coordinate of the projection device on the basis of the pixel correspondence information, and generates a video to be projected onto the projection target on the basis of the measurement information of each pixel converted into the correspondence coordinate of the projection device, wherein the projection device is configured to irradiate the projection target with the video generated by the calculation device as video light in synchronization with a cycle of an exposure time in the imaging device, and wherein the imaging device temporally deviates a start point and an end point of the predetermined exposure time for each pixel.