Mathematical Principles of Object 3D Reconstruction by Shape-from-Focus Methods

Martišek, Dalibor; Mikulášek, Karel

doi:10.3390/math9182253

Cited by 3 publications

(1 citation statement)

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“…Along the optical axis, the distribution of focus data is similar to a parabola, where the pixel points corresponding to the maximum value on the parabola have the best clarity. Curve fitting techniques such as Gaussian fitting [8] and polynomial fitting [9] are often used to estimate the peak value. By using these methods to identify all clear pixel positions, discrete 3D shapes can be reconstructed.…”

Section: Introductionmentioning

confidence: 99%

Wafer Surface Reconstruction Based on Shape From Focus

Wang,

Chen,

Shi

et al. 2024

IEEE Access

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Scanning electron microscope, atomic force microscope and other equipment play an important role in the fields of topography restoration and detection. However, these devices are generally used in nanometer-scale measurement scenarios. For wafer topography quality control scenarios ranging from microns to hundreds of microns, these technologies have problems such as high cost and slow detection speed. Therefore, developing new, low-cost, and high-precision methods is necessary. To address this problem, a wafer surface reconstruction framework is proposed based on the shape-from-focus principle. In view of the characteristics of the large area and micro-small height of the wafer, to solve the limitations of the existing shape from focus framework, which is generally based on a single field, we created a multi-field image sequence rapid acquisition system and proposed the use of pulse control methods to achieve rapid acquisition of large area images. On the other hand, this paper proposes a dual filtering framework combining the Levy flight filtering principle with the SOR algorithm in point cloud filtering to achieve a balance between smoothing the depth map and maintaining the detailed structure, reducing the impact of noise, and improving the morphology restoration accuracy. To avoid splicing seams between fields, the progressive detection multifield stitching technique is used to complete large-area depth data stitching. Experiments were conducted on both synthetic and real objects to verify the effectiveness of the proposed method. In terms of synthesized images, the accuracy of the three methods significantly improved after applying the proposed method framework. After applying the Tenenbaum method framework, its correlation and peak signal-tonoise ratio improved by 7.5% and 38.2%, respectively, and its root mean square error was reduced by 40.7%. The excellent accuracy reconstruction results of the proposed method was verified through accuracy evaluation experiments. The height errors of the three methods used were all higher than 1 μm. However, after using the proposed method framework, the maximum error was only 0.24 μm. The experimental results indicated that this method overcomes the area limitation of traditional SFF and is suitable for applying wafer surface morphology measurements.

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Section: Introductionmentioning

confidence: 99%