Yingjie Yu

Least-squares calibration method for fringe projection profilometry

This paper presents a novel calibration approach for determining the mapping relationship between the depth map and the phase difference in fringe projection profilometry. This approach is based on a simple nonlinear function, which is deduced by analyzing the geometry of measurement system and hence perfectly describes the mapping between the depth map and the phase-difference distribution. The calibration is implemented by translating a target plane to a sequence of given positions with known depths, and measuring its phase distributions. A least-squares estimation algorithm with linear computation is deduced to retrieve the related parameters and to reconstruct the mapping function. Both computer simulation and experiment are carried out to demonstrate the validity of this technique.

Blind phase shift estimation in phase-shifting interferometry

A blind phase shift estimation algorithm that allows simultaneous calculation of phases and phase shifts from three or more interferograms is presented. In phase-shifting interferometry, the phase shift errors introduce specific correlations between the calculated background intensity distribution and the fringe component. These correlations can be measured with a cross-power spectrum. By minimization of an objective function based on this cross-power spectrum, the actual phase shifts are estimated and used for phase recovery. The validity of this algorithm is verified by both the numerical simulation and the experiment results.

Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine

Stitching interferometry is a common method for measuring the figure error of high numerical aperture optics. However, subaperture measurement usually requires a fringe-nulling routine, thus making the stitching procedure complex and time-consuming. The challenge when measuring a surface without a fringe-nulling routine is that the rays no longer perpendicularly hit the surface. This violation of the null-test condition can lead to high fringe density and introduce high-order misalignment aberrations into the measurement result. This paper demonstrates that the high-order misalignment aberrations can be characterized by low-order misalignment aberrations; then, an efficient method is proposed to separate the high-order misalignment aberrations from subaperture data. With the proposed method, the fringe-nulling routine is not required. Instead, the subaperture data is measured under a nonzero fringe pattern. Then, all possible misalignment aberrations are removed with the proposed method. Finally, the full aperture map is acquired by connecting all subaperture data together. Experimental results showing the feasibility of the proposed procedure are presented.

Holographic imaging of full-color real-existing three-dimensional objects with computer-generated sequential kinoforms

We propose a computational method for generating sequential kinoforms of real-existing full-color threedimensional (3D) objects and realizing high-quality 3D imaging. The depth map and color information are obtained using non-contact full-color 3D measurement system based on binocular vision. The obtained full-color 3D data are decomposed into multiple slices with RGB channels. Sequential kinoforms of each channel are calculated and reconstructed using a Fresnel-diffraction-based algorithm called the dynamicpseudorandom-phase tomographic computer holography (DPP-TCH). Color dispersion introduced by different wavelengths is well compensated by zero-padding operation in the red and green channels of object slices. Numerical reconstruction results show that the speckle noise and color-dispersion are well suppressed and that high-quality full-color holographic 3D imaging is feasible. The method is useful for improving the 3D image quality in holographic displays with pixelated phase-type spatial light modulators (SLMs).

Analytical method for designing gradient-index fiber probes

An analytical method was investigated to design the gradient-index (GRIN) fiber probe based on characteristic parameters of a Gaussian beam propagating through the probe. First, a typical model of the GRIN fiber probe was presented, consisting of a single mode fiber, a no-core fiber (NCF), and a GRIN fiber lens. Second, a complex beam parameter matrix transformation method was adopted to derive the mathematical expressions of characteristic parameters, such as beam waist location, beam waist radius, and Rayleigh range. Then, MATLAB software was used to analyze the impact of the length of NCF and the length of the GRIN fiber lens on the characteristic parameters. Finally, performance comparison was performed between the calculation results and the experimental data published previously. The calculation results are in agreement with the experimental data and thus validate the presented analytical method for designing GRIN fiber probes. In addition, the characteristic parameters of a Gaussian beam going through the GRIN fiber probe will stay the same when the length of the GRIN fiber lens increases every 1/2 pitch length, which could be used to decrease the fabrication complication of GRIN fiber probes by increasing the length of GRIN fiber lens periodically.

Novel multiview connection method based on virtual cylinder for 3-D surface measurement

In optical 3-D measurements, two steps are generally required to obtain the whole-body 3-D shapes of objects: measuring the 3-D shape from different views, and afterwards connecting them together. The multiview overlapping scanning connection technique in a cylindrical coordinate system is an effective method for measuring a surface with a rotation axis, e.g., a 360-deg shape. However, there are great difficulties in measuring a more complex surface, such as those with concavities or composed of several discontinuous patches, because a complex surface generally cannot be explicitly represented in cylindrical coordinates. To solve these problems, a novel multiview connection method based on virtual cylinders for measurement of 3-D surfaces is proposed. In a Cartesian coordinate system, the virtual cylinders are determined by least-squares fitting to the local overlapping surface patches. The error movements are obtained from a linear equation system based on the virtual cylinders. The connection of adjacent views is then performed by coordinate transformation in 3-D space. Both computer simulation and experimental results are presented to verify the effectiveness of the suggested method.

Three-dimensional profile measurement using a flexible new multiview connection method

A novel multi-view connection method is proposed for whole field three-dimensional (3D) profile measurement. Firstly 3D profiles of tested object from different views can be measured by using the digital fringe projection profilometry, and then these profiles are transformed into the common coordinate by applying transform matrix. With the help of a new determination method for the revolution axis of rotary stage, the direction vector and one point of the axis are achieved. To improve the computability and feasibility of coordinate transformation, the quaternion method is also used to get the transform matrix. Considering the error movements between the views, an effective method based on multi-aperture overlap scanning technique (MAOST) is presented, which can determine the relationship between two adjacent views from their overlapping areas. The connection of adjacent views is performed accurately in 3D space. Both computer simulation and experimental results are presented to verify the feasibility of proposed method.

Method for removing longitudinal chromatism in full color holographic projection system

Hologram, as a type of diffractive optical element, is sensitive to wavelength in the process of optoelectronic reconstruction. Due to the different wavelengths of three prime colors used in full color holographic projections, there are chromatisms which badly spoil the reconstructed image. The chromatisms are composed of transverse and longitudinal chromatisms. For a computer generated hologram, transverse chromatism can be compensated by resampling the object information. However, it becomes more complex for longitudinal chromatism. This paper analyzes how the image is reconstructed from the phase-type hologram in a holographic projection system and the causations of longitudinal chromatism. To remove it, this paper proposes loading a specially designed phase distribution on a phase-type hologram. The advantage of this method is that it can be achieved by computer calculation and without adding any hardware such as achromatic optical element. A time-sharing system for a full-color hologram projection is developed in this paper. Comparisons have been made between the reconstructed images with and without chromatism. The experimental result shows that the method is effective in removing longitudinal chromatism and the quality of the reconstructed image is improved.

Recent developments of multi-aperture overlap-scanning technique

In this paper, the multi-aperture overlap-scanning technique (MAOST) and its recent developments are presented. In the first instance, MAOST is used in interferometry, and the principle of MAOST for interferometry is that, a tested large-scale plane is covered by an array of interferometric subapertures, and the relationship between each couple of adjacent subapertures is determined from their overlapping areas by a least squares method, and then the profile of tested plane is obtained by connecting all the subapertures together. Recently, to meet the requirements of advanced manufacturing, the idea of MAOST has been extended to precision three-dimensional (3-D) measurement. In practice, a whole-body 3-D shape is acquired by two steps: first measuring the 3-D shape from different views and afterwards connecting all the views together. In order to accurately determine the position and orientation of every single-view in a common coordinate system, an iterative algorithm based on MAOST concept is utilized.

A least squares calibration method for fringe projection profilometry

This paper presents a novel least squares calibration approach for fringe projection profilometry. This approach is based on a simple nonlinear function, which is deduced by analyzing the geometry of measurement system and perfectly describes the mapping relationship between the depth map and phase distribution. The calibration is implemented by translating a target plane to a sequence of given positions with known depths, and measuring its phase distributions. Based on least squares estimation, an algorithm with linear computation is deduced to retrieve the related parameters, by which the burden of computational complexity is effectively alleviated. In experiment, a plaster statue is measured to demonstrate the validity of the principle.