Single fringe projection profilometry based on sinusoidal intensity normalization and subpixel fitting

A novel fringe projection profilometry using a single sinusoidal fringe pattern projected is proposed. Computer-generated sinusoidal fringe and uniform intensity patterns are firstly projected on a testing object by a liquid crystal display projector. The variable reflection intensity of a fringe pattern is then roughly normalized by division operation applied to the grabbed fringe and uniform intensity patterns projected. Fringe intensity is further normalized by employing an interpolation algorithm. The deformed sinusoidal pattern encoding object shape is converted to a wrapped phase map without using phase-shifting or Fourier transform. Computer simulation and experimental performance are evaluated to demonstrate the validity of the proposed method. The experimental results compared with those of the four-step phase-shifting and fast Fourier transform methods are also presented.

Research Highlights
► To reduce the number of fringe patterns for phase extraction and speed up the measurement, a novel fringe projection method was proposed for shape measurement. The approach needs only one deformed sinusoidal fringe patterns without phase-shifting for determination of the object shape.
► Compared with one of our previous research works [6], the present method evaluates an object’s shape based on one fringe pattern and subpixel fitting. The shape measurement is much more accurate than that using the method presented in Ref. [6].
► On the other hand, the proposed technique employs Akima interpolation for fringe intensity fitting and phase extraction on subpixel scale [10]. Only data from the next neighbor points is used to determine the coefficients of the interpolation polynomial. It obviously saves much more time than that using our previous method shown in Ref. [7]. While the latter employs a differential algorithm for phase evaluation based on global interpolation of fringe gray level on a subpixel scale.
► Compared with the Fourier transform method (FTM), the proposed method is fully automated.