Elsevier

Precision Engineering

Volume 65, September 2020, Pages 279-286
Precision Engineering

Modified color CCD moiré method and its application in optical distortion correction

https://doi.org/10.1016/j.precisioneng.2020.05.013Get rights and content

Highlights

  • The formation mechanism of color fringes and multiplication moiré were analyzed.

  • The color CCD moiré method for correcting lens distortion was modified.

  • The color fringes in a CCD moiré pattern has been successfully simulated.

  • The modified method was then applied to characterize chromatic aberration.

Abstract

The characterization and correction of lens distortion is an important part of optical measurement. This work analyzes the formation mechanism of color fringes and multiplication moiré, and discusses modification of the color CCD moiré method for correcting lens distortion. A demosaicing algorithm was used to simulate the color fringes in a CCD moiré pattern. We then performed a detailed analysis of the carrier field, and adopted a universal polynomial distortion model to characterize lens distortion, which increased the accuracy of distortion correction. Comparison experiments verified the feasibility of the modified method and the correctness of the formation mechanism for color CCD moiré. The modified method was then applied to lens distortion correction in the DIC measurement process, effectively reducing errors in displacement measurement.

Introduction

Image sensors are widely used in transportation, communication, remote sensing, medicine, astronomy, and aerospace applications [[1], [2], [3]]. However, lens distortion interferes with image sensing, causing straight lines to be seen as curves and distorting shapes [4,5]. Moreover, distortion causes systematic errors in high-precision measurements. Typically, lens distortion is caused by characteristics of the lens, its assembly, or other built-in factors, many of which are difficult to eliminate by physical means [[6], [7], [8]]. Therefore, in practice, it is necessary to correct the distorted image using software.

Presently, two categories of techniques are available for characterizing lens distortion [[9], [10], [11]]. One is based on the relationship of coordinate points [9]; the other is based on the invariance of the properties of certain points before and after imaging [10,11]. The first method uses the correspondence between the three-dimensional coordinates of points on the external calibration object and the two-dimensional coordinates of corresponding points in the image captured by the camera to solve the distortion parameters of the camera. The checkerboard calibration method proposed by Zhang [12], which is based on this principle, has been widely used. Pan et al. achieved the calibration of lens distortion with the help of random speckle images [13]. The lens distortion calibration method with speckle is efficient and convenient. Speckle distortion correction at the micro-nano scale has unique advantages. Zhu et al. used speckle to calibrate the distortion of the microscope lens [14]. Similarly, Hou proposed a CCD moiré method [[15], [16], [17]] using a regular grating structure to characterize lens distortion [18]. This method has advantages. For instance, in the field of micro-nano measurement, it is easier to process gratings than checkerboards. However, the CCD moiré method is currently used only to correct images with large errors at the edges. Furthermore, the color CCD moiré has effects on colors that remain inadequately explained. Therefore, it is necessary to conduct in-depth research on these issues to characterize lens distortion more accurately using color CCD moiré.

In this paper, the formation mechanism of color CCD moiré is analyzed. Improvements of the color CCD moiré method for correcting lens distortion are discussed. The validity and correctness of the method are verified by comparative experiments. Finally, the application of the modified method to DIC measurement is described as well as its ability to reduce errors in displacement measurement.

Section snippets

Demosaicing algorithm

According to Li's theory [19], the formation of a monochromatic CCD moiré is a sampling process. Unlike monochromatic camera imaging, color camera imaging requires demosaicing [20,21]. Therefore, the formation of color CCD moiré mainly involves two processes: sampling and demosaicing. Details of the sampling process can be found in Refs. [19], while the demosaicing algorithm is described below.

To achieve color imaging, it is necessary to record the red, green, and blue signals from external

Simulation of color CCD moiré

Monochromatic CCD moiré is the result of a periodic light intensity entering the camera, which forms interference patterns on the target surface of the camera. Li Junfei explained the interference behavior by sampling. However, this explanation is insufficient for color CCD moiré, especially for multiplied color moiré. In this work, moiré images formed by direct sampling, bilinear interpolation, and high-quality linear interpolation were simulated, as shown in Fig. 4. The moiré formed by direct

Application: lens distortion correction for DIC measurement

The DIC method is one of the most widely used displacement measurement techniques. When using the DIC method, it is necessary to correct lens distortion. In this study, rigid body translational displacement fields were measured by the DIC method, and the lens distortion was corrected using the developed method described earlier. The experimental setup is shown in Fig. 9. A speckle-coated plate was controlled to move horizontally at the electric translation stage. The translation distance was

Chromatic aberration characterization by CCD moiré of three color channels

In order to accurately calculate the chromatic aberration between different channels, a moiré image with better quality was selected, as shown in Fig. 12(a). Extract the brightness information of the three channels along the dotted line in Fig. 12(a). The original brightness information of moiré was affected by the specimen grating, and there are large fluctuations. After filtering and smoothing, the position information of the three-channel brightness peak (peak phase of the moiré) is

Conclusion

In this work, the color CCD moiré method was analyzed and modified. The main contributions of this study can be divided into three parts. First, the formation mechanism of color CCD moiré is summarized in terms of sampling and demosaicing. The correctness of the mechanism was verified by comparing the color CCD moiré patterns collected under different pitches with the simulated patterns. Second, the color lens CCD moiré method for evaluating lens distortion was improved. By comparing different

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

National Key R&D Program of China (Grant No. 2017YFB1103900), National Natural Science Foundation of China [Grant Nos.11572041, and 11972084], National Science and Technology Major Project (2017-VI-0003-0073) and Beijing Natural Science Foundation (1192014).

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