Extra-detection-free monoscopic deflectometry for the in situ measurement of freeform specular surfaces

Extra detections of feature points conducted by a third-party instrument are indispensable in the monoscopic deflectometry to specify the surface position, but the measuring capability can be limited because most freeform surfaces do not contain any distinguishable and detectable feature points. In this Letter, the behaviors of the position error and form error of the measured surface are discriminated by reverse ray-tracing. A novel iterative optimization strategy is developed to position the workpiece for the in situ deflectometric measurement so that extra detections can be avoided. It is demonstrated that this method can achieve parallel measuring accuracy with conventional deflectometry, but the measuring efficiency and range of freeform surfaces can be greatly improved. A hollow off-axis parabolic mirror is measured, and its departure from the interferometric results is 139.85 nm root mean square.