Fig. 1. Phenomena of the parasitic reflection. (a) Transparent glass with vertical fringe; (b) Transparent glass with horizontal fringe

Fig. 2. Principle of the phase measuring deflectometry

Fig. 3. Schematic diagram of extracting main frequency information through continuous wavelet transform. (a) Amplitude distribution graph; (b) Phase distribution graph; (c) Ridge line distribution graph; (d) Schematic of frequency information

Fig. 4. Flowchart of the method of suppressing parasitic reflection by continuous wavelet transform

Fig. 5. Simulation fringe pattern. (a) Flat glass with dimensions of 80 mm×80 mm; (b) Spherical lens with a radius of 200 mm

Fig. 6. Wavelet transform plots of vertical stripes on the surface of transparent flat. (a) Amplitude distribution diagram; (b) Phase distribution diagram

Fig. 7. Phase error comparison of 2.5% noise intensity. (a) Proposed method; (b) Traditional phase-shiftng method;(c) Continuous wavelet transform method; (d) Multi-frequency phase-shifting method

Fig. 8. Effectiveness of proposed method when initial phase is poor

Fig. 9. Wavelet transform plots of vertical stripes on the front surface of the lens. (a) Amplitude distribution diagram; (b) Phase distribution diagram

Fig. 10. Phase error of lens

Fig. 11. Reconstruction simulated results. (a) Transparent flat; (b) Spherical lens

Fig. 12. Hardware diagram of the experimental system

Fig. 13. Schematic diagram of glass plate. (a) 3 mm transparent plate; (b) Parasitic reflection phenomenon of vertical fringes; (c) Parasitic reflection phenomenon of horizontal fringes

Fig. 14. Schematic diagram of the plano-convex lens. (a) Plano-convex lens; (b) Parasitic reflection phenomenon of vertical fringes; (c) Parasitic reflection phenomenon of horizontal fringes

Fig. 15. Wavelet transform plots of vertical fringes of 3 mm glass flat. (a) Amplitude distribution diagram; (b) Phase distribution diagram;(c) Wavelet ridge line diagram

Fig. 16. Surface gradients obtained by proposed method for glass plate. (a) x direction gradient; (b) y direction gradient

Fig. 17. Reconstruction results of the glass plate. (a) Reconstructed 3 mm transparent glass plate using proposed method; (b) Reconstructed 3 mm transparent glass plate using multi-frequency phase-shifting method; (c) Reconstructed 4 mm transparent glass plate using proposed method; (d) Reconstructed 4 mm transparent glass plate using multi-frequency phase-shifting method

Fig. 18. Reconstruction results of the plano-convex lens. (a) Reconstruction results using proposed method; (b) Reconstruction results using the multi-frequency phase-shifting method