Three-dimensional measurements by using deflectometry and the double Hilbert transform

Abstract

An improved phase retrieval method based Hilbert transform is introduced to quantitatively calculate the phase distribution from distorted fringe pattern. Also phase measurement deflectomety are widely used in specular type samples. The background noise or bias should be suppressed prior to apply Hilbert transform. A method for suppression background noise double Hilbert transform is presented, which requires only one image. The method is easy to implement, and it is able to conducting automated fast measurements. We have demonstrated the double Hilbert transform method to retrieve the phase and background suppression by computer simulation and experiment in phase measuring deflectometry method. Numbers.; 42. 30. Rx, 42. 30. Kq PACS

Deflectometry for specular surfaces: an overview

“…Surfaces may be reconstructed in Fourier (Freischlad and Koliopoulos, 1986) or Hilbert space (Na et al, 2016), where it is also possible to formulate integrability requirements (Frankot and Chellappa, 1988) (in this case, for SFS data). The integration itself may be iterative (Huang et al, 2015b) or deterministic (Bon et al, 2012).…”

Analysis of red blood cell parameters by Talbot-projected fringes

“…The diffraction intensity distribution of the grating G1 at the Talbot plane, after passing through the object (RBCs) is given as 31,32 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 6 3 ; 5 3 1 IðxÞ ¼ AðxÞ þ B cos 2πmx a þ ϕðxÞ…”

“…A real function and its Hilbert-transformed function are related to each other in such a way that they together create an analytical signal, which can be written with an amplitude and phase, and the derivative of the phase can be identified as the instantaneous frequency. 4,32,33 The background intensity must be eliminated prior to the application of HT for retrieving the phase. To isolate the sinusoidal term and to eliminate the background intensity, Eq.…”

“…The complex analytical signal ZðxÞ exhibits rapid phase modulation with spatial frequency 1∕a; thus, Δϕ is strongly wrapped. Finally, the phase ϕðxÞ associated with the presence of the object is extracted as 4,32,33 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 3 2 6 ; 7 5 2 ϕðxÞ ¼ Δϕ − qðxÞ; where qðxÞ ¼ 2πm a :…”