Microscopes are now widely used in the field of three-dimensional measurements for their high magnification and changeable physical focal length. However, the small depth of focus restricts the camera from taking clear images with apparent tilts. To set the camera in focus, the calibration board should be near-parallel to the imaging plane. As a result, the traditional calibration methods are not practical for a normal lens, which requires multiple views of the calibration board. For this, a method in which a digital camera with a microscope is calibrated precisely under the near-parallel condition is proposed. In this method, the magnification rate of the imaging system, which is equal to the rate of image distance to object distance, is calculated precisely and utilized to calculate camera parameters. Due to the invariance of the magnification rate, the parameters calculated by this method are accurate and stable. In addition, to solve the problem that the physical focal length cannot be calibrated by one image, the magnification method is adopted to measure it. Finally, the stability and accuracy are evaluated by simulations and experiments.
In order to improve the stability of the calibration method based on a single parallel plane, we propose a robust calibration method based on the calculation of traditional homography matrix and Gaussian imaging model. This method first uses a convenient and accurate method to calculate the physical focal length of the entire microscope optical system, and then uses the Gaussian imaging model to calculate the effective focal length and intrinsic matrix of the camera. Then, the camera’s extrinsic parameters can be easily calculated from the homography matrix. Finally, all camera parameters can be optimized along with the lens distortion through a nonlinear optimization process. In this method, only two images of the parallel calibration plate need to be captured to complete the calibration. The proposed method overcomes the problem of instability of the existing microscope calibration methods and significantly improves the robustness and accuracy of the whole calibration process.
KEYWORDS: Phase shift keying, Reflectivity, Error analysis, Modulation, Fringe analysis, Cameras, Digital cameras, High dynamic range imaging, Signal to noise ratio, Imaging systems
Measuring objects with drastic texture variation is a big challenge for fringe projection profilometry (FPP) systems. In this paper, the reasons why textures on measured objects' surface influence the measurement accuracy are thoroughly analyzed and an effective phase error compensation method is proposed. Due to the existence of various random noises, the reconstruction accuracy will be negatively affected by the textures with different reflectivity. As an intrinsic feature of digital cameras, random noises be hardly removed by mathematical solutions. In this paper, it is mathematically proved that image pixels with the same fringe modulation have the same noise variance and the same phase error variance. With the aid of fringe orientations calculated in the phase map, pixels which satisfy the following two conditions are picked out as a group: 1. They should have the same phase. 2. They have almost the equivalent modulation values. Then the phase values of this group of pixels are averaged and this mean phase is the compensated phase value. Experiments demonstrate that the proposed method can effectively reduce phase errors caused by random noises and textures with small reflectivity.
KEYWORDS: Fringe analysis, Cameras, High dynamic range imaging, Projection systems, Binary data, 3D metrology, Phase shifts, Image processing, Reflectivity, Signal to noise ratio
Fringe projection profilometry is a popular optical method for three-dimensional (3-D) shape measurement because of its high accuracy, fast measurement speed, and full-field inspection nature. However, due to the limited dynamic range of the digital camera, saturated pixels in the captured images will lead to serious phase errors and measurement errors when the measured object has a drastic texture variation. To deal with such a problem, an adaptive digital fringe projection technique for high dynamic 3-D shape measurement is proposed. In this method, phase-shifting fringes are adaptively generated with the aid of a coordinates mapping process and binary-search technique to eliminate saturation. Compared with previous adaptive fringe projection techniques, the camera response function and homographic mapping between the camera and projector are not needed, making the whole measurement easier to carry out and less laborious. Experiments validate the effectiveness and superiority of the proposed method for high-dynamic range 3-D shape measurement.
KEYWORDS: 3D metrology, Phase measurement, High dynamic range imaging, Cameras, 3D displays, Digital cameras, Phase shifts, Projection systems, 3D image processing
Fringe Projection Profilometry (FPP) is a popular optical method for 3D shape measurement because of its high accuracy, fast measurement speed and full-field inspection nature. However, due to the limited dynamic range of the digital camera, saturated and dark pixels in the captured images will lead to serious phase error and measurement error when the measured object has a drastic texture variation. To deal with such problem, a novel adaptive digital fringe projection technique for high dynamic 3D shape measurement is proposed. In this method, phase-shifting fringes are adaptively generated with the aid of a coordinates mapping process and binary-search technique. Compared with previous adaptive fringe projection techniques, the camera response function and homographic mapping between the camera and projector are not needed, making the whole measurement easier to carry out and less laborious. Experiments validate the effectiveness and superiority of the proposed method for high dynamic range 3D shape measurement
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