Intensity error correction for 3D shape measurement based on phase-shifting method

In-situ 3-D shape measurements with submicron shape uncertainty of fast rotating objects in a cutting lathe are expected, which can be achieved by simultaneous distance and velocity measurements. Conventional tactile methods, coordinate measurement machines, only support ex-situ measurements. Optical measurement techniques such as triangulation and conoscopic holography offer only the distance, so that the absolute diameter cannot be retrieved directly. In comparison, laser Doppler distance sensors (P-LDD sensor) enable simultaneous and in-situ distance and velocity measurements for monitoring the cutting process in a lathe. In order to achieve shape measurement uncertainties below 1 μm, a P-LDD sensor with a dual camera based scattered light detection has been investigated. Coherent fiber bundles (CFB) are employed to forward the scattered light towards cameras. This enables a compact and passive sensor head in the future. Compared with a photo detector based sensor, the dual camera based sensor allows to decrease the measurement uncertainty by the order of one magnitude. As a result, the total shape uncertainty of absolute 3-D shape measurements can be reduced to about 100 nm.

In this paper, a whole-field and high-speed optical three-dimensional (3D) shape measurement for the vibration pattern of a drumhead based on Fourier Transform Profilometry (FTP) is presented and verified by experiment. A projected sinusoidal fringe pattern on the surface of measured drumhead is dynamically deformed with the vibration of the membrane and grabbed by a high-speed camera. The 3D shape deformation of the drumhead at each sampling instant can be recovered from demodulating the phase of this obtained sequence of fringe patterns. The vibration of the membrane of a Chinese drum has been measured with a high-speed sampling rate (1,000 fps) and a standard deviation (0.075 mm). This method should be helpful in studying the acoustic characteristic and the manufacture technique of the percussion instrument.

In this paper, a three-dimensional (3D) shape measurement method based on structured light field imaging is proposed, which contributes to the biomedical imaging. Generally, light field imaging is challenging to accomplish the 3D shape measurement accurately, as the slope estimation method based on radiance consistency is inaccurate. Taking into consideration the special modulation of structured light field, we utilize the phase information to substitute the phase consistency for the radiance consistency in epi-polar image (EPI) at first. Therefore, the 3D coordinates are derived after light field calibration, but the results are coarse due to slope estimation error and need to be corrected. Furthermore, the 3D coordinates refinement is performed based on relationship between the structured light field image and DMD image of the projector, which allows to improve the performance of the 3D shape measurement. The necessary light field camera calibration is described to generalize its application. Subsequently, the effectiveness of the proposed method is demonstrated with a sculpture and compared to the results of a conventional PMP system.

Binary coding methods have been widely used for three-dimensional (3D) shape measurement. However, traditional binary coding methods always require a sequence of binary patterns to encode the fringe order. This paper presents a spatial-temporal binary coding (STBC) method for 3D shape measurement with three binary patterns, including a spatial pattern and two temporal patterns. Specifically, the spatial pattern is used to encode a 4-bit spatial code, and the temporal patterns are used to encode the 2-bit temporal code. By combining the spatial code and the temporal code, 6-bit code words can be obtained that distinguish 26=64 fringe periods of sinusoidal phase-shifting patterns. A robust dual-region labeling decoding scheme is also developed to extract the 6-bit code word for fringe order determination, and then absolute-phase unwrapping can be carried out. Experiments have been conducted, and their results confirm that the STBC method can reliably reconstruct the 3D shapes of measured objects with only three binary patterns.

Fourier transform profilometry (FTP) is one of the frequently adopted three-dimensional (3D) shape measurement methods due to its ability to recover single-shot 3D shapes, yet it is challenging to retrieve the absolute phase map solely from one single grayscale fringe image. This paper presents a computational framework that overcomes this limitation of FTP with digital fringe projection (DFP). By using geometric constraints, an absolute phase map can be retrieved point-by-point from one single grayscale fringe image. Experiments demonstrate the success of our proposed framework with single-shot absolute 3D shape measurement capability.

Rapid and automatic optimal exposure control for digital fringe projection technique

Color-coded fringe projection profilometry (FPP) is one of the most important single-frame three-dimensional (3D) shape measurement techniques. Transverse chromatic aberration (TCA) in a color-coded FPP system yields imaging deviations, which will result in 3D shape measurement error. In this work, a TCA compensation method for color-coded FPP is proposed. The proposed method establishes the relationship among phase, pixel deviation, and imaging position for decreasing the 3D shape measurement error introduced by TCA. Compared to existing methods that use the relationship among depth, pixel deviation, and imaging position or polynomial fitting for each pixel, the proposed method offers the merits of precise and simple implementation, since it voids the cumulative error in-depth calculation and removes the time-consuming process of polynomial fitting for each pixel. For validation, a color-coded FPP system is established and calibrated. Two verification experiments, including a translation test and 3D shape measurement of a regular spherical object, are conducted with the calibrated system. Experimental results demonstrate that the proposed TCA compensation method is capable of effectively reducing the 3D shape measurement error caused by TCA.

A height estimating function is proposed based on geometric analysis for a three-dimensional (3-D) measurement system using a digital light processing (DLP) projector and a camera. The proposed 3-D shape measurement method is a hybrid method that combines the geometric parameter measuring method and the least squares method. This method uses the phase-to-height relationship for one line by plane analysis, and the related parameters are estimated using the least squares method. The proposed method has one function per image line instead of one function per image pixel. Sinusoidal fringe patterns of the projector are projected on the object, and the phase of the measuring point is calculated from the camera image. Then, the relationship between the phase by fringe patterns and the height of the measuring point is described as a parameter of the horizontal coordinate on the image plane. Thus, the 3-D shape of the object can be obtained. Our experiments show that the error of the modeling function is within ±0.1 mm when the x-z working range is 100×50 mm. Therefore, the proposed method can dramatically reduce the number of mapping functions needed for 3-D measurement using the geometric relationship between the projector and camera.

Vignetting refers to a position dependent loss of light in the output of an optical system causing gradual fading out of an image near the periphery. In this paper, we propose a method for correcting vignetting distortion by introducing nonlinear model fitting of a proposed vignetting distortion function. The proposed method aims for embedded digital imaging applications as well as conventional image enhancement. We could obtain a light intensity profile distribution without precisely controlled illumination and considerably reduce memory requirement for vignetting correction compared with the traditional lookup table (LUT) methods. We show the effectiveness of the proposed method by presenting the experimental results obtained from commercial digital cameras.

The phase-coding method is useful in 3D shape measurement due to its low sensitivity to surface contrast and camera noise. However, as the number of fringe periods increases, the wrapped phase recovered from the sinusoidal phase-shifting patterns is always misaligned with the fringe order calculated by the stair-coding patterns. To solve this, an improved dual-frequency phase-coding fringe projection method is designed to realize absolute phase retrieval. Specifically, the auxiliary fringe order determined by phase-shifting is used to get the absolute phase, which can eliminate fringe-order errors. Moreover, to increase speed and the number of codewords, this paper presents a scheme that only requires seven patterns, including a uniform gray image, two high-frequency sinusoidal fringe patterns, two low-frequency sinusoidal fringe patterns and two phase-coding fringe patterns. Therefore, this method requires fewer patterns to realize high-resolution measurement than existing methods. The success of the proposed method can be proved by experiments.

Optical full-field measurement techniques have been widely studied in academia and applied to many actual fields of automated inspection, reverse engineering, cosmetic surgery, and so on. With the advent of color CCD cameras and DMD (Digital Micromirror Device) based color DLP (Digital Light Processing) projectors, their major red, green, and blue channels have been used as a carrier to code fringe patterns. Since three fringe patterns can be simultaneously projected and captured at one shot, the acquisition time reduces to 1/3 of the value by the gray fringe pattern projection. This chapter will introduce two kinds of applications of red, green, and blue as a carrier: 1) modulation and demodulation method of coding sinusoidal fringe patterns into RGB channels of a composite color image; and 2) modulation and demodulation method of coding sinusoidal and binary fringe patterns into RGB channels of multiple composite color images. Experiments on testing the two kinds of applications were carried out by measuring the shape of objects’ surface. The results confirm that red, green, and blue channels can be used as a carrier to reduce the acquisition time.

In fringe projection profilometry, temporal phase unwrapping is an essential procedure to recover an unambiguous absolute phase even in the presence of large discontinuities or spatially isolated surfaces. In this work, a dual-sensitivity profilometry technique is presented, which is based on defocused projection of binary and sinusoidal fringe patterns with a high and low-frequency spatial carrier, respectively. The binary defocusing techniques (based on PWM or square-wave profile patterns, whose pitch is relatively narrow) have demonstrated successful for high-quality three-dimensional shape measurement when the projector presents a nonlinear response. But they suffer if pitch fringe is wide. On the other hand, using dual sensitivity profilometry, the quality of the unwrapped phase is determined by the high-frequency carrier. Thus, working with only one binary pattern, one can use a single defocusing level (low) in order to reduce the data acquisition time and maintain the quality of the unwrapped phase. Experimental results are presented to verify the success of the proposed method.

Measurement methods of 3D shape of large-scale complex surfaces based on computer vision: A review

3-D shape measurement systems by contactless method are required in the quality inspections of metal molds and electronic parts in industrial fields. A grating projection method with phase-shifting method has advantages of high precision and high speed. Recently, the size of a BGA (ball grid array) becomes smaller. So the pitch of a grating pattern projected onto the specimen should be smaller. In conventional method, fringe pattern is projected using an imaging lens. The focal depth becomes smaller in the case of reduced projection. It is therefore difficult to project a grating pattern with small pitch onto an object with large incident angles. Authors recently proposed a light source stepping method using a linear LED device. It is easy to shrink the projected grating pitch with a lens because this projection method does not use an imaging lens. The pitch of the projected grating depends on the width of the light source. There is a limit to shrink the projected grating pitch according to the size of the LED chip. In this paper, a small pitch fringe projection method with multiple linear fiber arrays for 3D shape measurement is proposed. The width of the fiber array is 30μm. It is one digit smaller than the width of the LED chip. The experimental result of 3-D shape measurement with small pitch projection with large incident angles is shown.

Blade is the key component of the aero-engine. In generally, it requires precise size and accurate shape, so the three-dimensional shape measurement of the blade is very important. Fringe projection profilometry is generally used to measure the 3D shape of an object, because of the advantages of non-contact operation, full-field acquisition, high resolution, and fast data processing. In this paper, 3D shape measurement method based on surface structured light that combination of gray-code and phase-shift projection is proposed. The wrapped phase of the blade is got by the four-step phase-shift method. In the projection process of the gray-code, due to the ambient light, different surface reflectance and surface physical discontinuous, the edge of gray-code becomes smooth, leading to decode error, so that the gray-code pattern must be binaried before decode. Through the accurate binarization of the blade gray-code pattern, the decoding cycle of the blade is achieved, and the unwrapped phase is achieved by phase unwrapping. Then the unwrapped phase difference between the blade and reference plane is got, the height of the blade can be obtained by the relationship between the phase difference and the height. The experimental and simulation results show that the proposed method can achieve a high precision, high speed and low cost 3D shape measurement of the blade. The measurement accuracy reaches 0.03 mm. The proposed method extends the reliability and practicality of the fringe projection profilometry.