High dynamic range 3D measurement based on the Butterworth low-pass filter and Hilbert transform

Due to the limited dynamic range of the camera, a measured object with non-Lambert reflection saturates the fringe pattern, which will lead to three-dimensional (3D) measurement error. In this paper, we propose a novel, to our knowledge, high dynamic range 3D measurement technique based on the Butterworth low-pass filter (BLPF) and Hilbert transform (HT), which is called BLPFHT for short. First, we analyze the Fourier transform (FT) spectrum of saturated fringe pattern. Then, we use the Butterworth low-pass filter to filter out the higher harmonic components introduced by fringe intensity saturation. BLPF leads to a non-sinusoidal fringe pattern in the saturated region, which introduces periodic phase error. Therefore, we establish a phase error model and use HT to correct the phase error. Experimental comparison confirms that the proposed BLPFHT can efficiently and accurately reconstruct the 3D shape of non-Lambert reflective surfaces without additional image or hardware assistance.