The heights of the tilted block were also measured using the laser displacement sensor on the top surface at a total of 17 points spaced at an equal interval of 10 mm. The height data of laser measurement were also linear fitted using the least-squares method and tilt angle was obtained from the gradient of the linear fitted data. The tilt angle calculated using phase shifting technique was compared with the tilt angle calculated using laser measurement as shown in Fig. 8(a)–(c). The data were linear fitted, and the tilt angle was calculated from the gradient value of each tilted block data set. The tilt angle calculated from the laser measurement data for block A, B and C were, respectively, 0.46°,0.57° and 0.72°. The maximum difference was for block C
(15%).
Figures 8(a)–(c) show that the difference between the profile measured using the phase-shift method and laser measurement is greater towards the end of the block length where the height is greatest. The difference in measurement increases with the increase in tilt angle. However, for small tilt angle the laser and phase shifting measurement agree closely. The possible source of error in measurement for blocks B and C is due to the scaling factor and inaccuracy of the θ-L relationship. This is because the actual scaling factor changes with height of the block, but in this case the scaling factor used was for the reference block height. The
scaling factor was assumed fixed for the tilted blocks because its value cannot be computed for a tilted block if the height is not known. The other source of error is the θ-L relationship that was derived for the reference block height. However, in a tilted surface the relationship between θ -L varies because θ is also a function of the height y. The difference between the two results for block B and C in Fig. 8(b)–(c) could be due to the linear fitting process on the phase-shift data. However, accuracy in small angle measurement is more crucial as large angle tilts rarely occur
in an actual PCBA.
3 Connector tilt measurement on PCBA
This part of the work was done to demonstrate the capability of the phase-shift technique in detecting tilts on actual PCBA connectors. Due to the protruding leads on the underside of the PCBA, the best horizontal position was created by attaching several bolts of 11.76 mm thickness underneath. Figure 9(a) shows a plan view of the connectors superimposed with projected fringes. A total of five PCI connectors (A to E) were inspected. The connector
heights were approximately 12 mm each and the scaling factor calculated is 0.264 mm/pixel. The relationship between θ and L, derived for the height 11.57 mm from the reference table, is given by（一个数学公式）
Figures 8(a)–(c) show that the difference between the profile measured using the phase-shift method and laser measurement is greater towards the end of the block length where the height is greatest. 图8（a）－（c）表明，用相位偏移法和激光测量法测得的分布之间的差别，朝玻璃块长度的末端比较大，在那里，高度是最高的。The difference in measurement increases with the increase in tilt angle. 测量值的差别随着倾角的增大而增大。However, for small tilt angle the laser and phase shifting measurement agree closely. 可是对于小的倾角来说，激光测量和相位偏移测量密切一致。The possible source of error in measurement for blocks B and C is due to the scaling factor and inaccuracy of the θ-L relationship. 在B块和C块的测量中可能的误差源是由于θ-L 关系的比例因子和不精确引起的。This is because the actual scaling factor changes with height of the block, but in this case the scaling factor used was for the reference block height. 这是因为，实际的比例因子随着玻璃块的高度而变化，但是在这一情况下，所用的比例因子是针对参考玻璃块的。The scaling factor was assumed fixed for the tilted blocks because its value cannot be computed for a tilted block if the height is not known. 我们假设比例因子对于倾斜的玻璃块是固定的，因为如果高度未知的话，对于一块倾斜玻璃块来说，它的值就不能计算。 The other source of error is the θ-L relationship that was derived for the reference block height. 另一个误差来源是针对参考玻璃块的高度推导出的θ-L 关系。However, in a tilted surface the relationship between θ -L varies because θ is also a function of the height y. 然而，在一个倾斜的表面上，θ-L 之间的关系会变化，因为θ也是高度y的一个函数。The difference between the two results for block B and C in Fig. 8(b)–(c) could be due to the linear fitting process on the phase-shift data. 图8（b）－（C）中B块和C块两个结果之间的差别可以因相移数据的线性拟合过程而引起。However, accuracy in small angle measurement is more crucial as large angle tilts rarely occur in an actual PCBA. 不过，由于大角度倾斜在实际的印制电路板（PCBA）组件中很少发生，所以小角度测量中的精度更为关键。
3 Connector tilt measurement on PCBA
3. PCBA上连接器倾角的测量
This part of the work was done to demonstrate the capability of the phase-shift technique in detecting tilts on actual PCBA connectors. 进行这一部分研究是为了实验验证相位偏移技术在检测实际PCBA连接器的倾角的能力。Due to the protruding leads on the underside of the PCBA, the best horizontal position was created by attaching several bolts of 11.76 mm thickness underneath. 由于在PCBA下侧突出的引线，所以最好的水平位置是通过在下面附上若干11.76mm厚度的螺栓来创造的。Figure 9(a) shows a plan view of the connectors superimposed with projected fringes. 图9（a）示出了与投影条纹叠加的连接器的平面图。 A total of five PCI connectors (A to E) were inspected. 一共检验了5个PCI连接器（A到E）。The connector heights were approximately 12 mm each and the scaling factor calculated is 0.264 mm/pixel. 连接器的高度每个大约为12mm，计算得到的比例因子为0.264mm/像素。The relationship between θ and L, derived for the height 11.57 mm from the reference table, is given by在11.57mm高度由参考表推导出的θ 和 L之间的关系给出如下：（一个数学公式）
里面的专业词汇如果百度里找不到合适的结果你可以去学术网站你看看，例如中国知网。
是个学生吧，其实英语的能力是很重要的，我曾经利用两整天30个小时翻译过一篇我们的专业论文，翻译的时候是痛苦的，翻译后的笑容是甜的。加油吧！多加强英语的学习！
（ 15 ％ ） 。
数字8条（ a ） - （三）表明，形象之间的差异来衡量使用相移法和激光测量更大接近年底时块长度的高度，是最大的。测量中的差异的增加而增加的倾斜角度。然而，小倾角的激光和相移测量同意密切。可能的来源，测量误差在区块B和C是由于尺度因子和不准确的θ左旋关系。这是因为实际的比例因子的变化与高度块，但在这种情况下，扩大的因素是使用的参考块的高度。那个
尺度因子假定固定的倾斜块，因为它的价值无法计算的倾斜块的高度，如果不知道。其他来源的错误是θ左旋关系，推导出的参考块的高度。然而，在表面倾斜的关系θ左旋不同，因为θ也是一个功能高度元两者之间的差额结果B座和C图。第8 （ b ） - （三）可能是由于线性拟合进程相移数据。然而，精度在小角度测量是更关键的是大角度倾斜很少发生
在实际组件。
3连接器倾斜测量组件
这部分的工作是证明能力的相移技术在倾斜检测的实际组件连接器。由于突出导致下方的组件，最好的水平位置是由附加几个螺栓一十一点七六毫米厚度下方。图9 （一）表明一个计划期的连接器叠加，预计边缘。共有五个PCI连接器（ A至E ）进行了视察。连接器
高度约为12毫米的每个尺度因子计算是0.264毫米/像素。 θ之间的关系和L ，导出了高度十一点五七毫米从参考表，给出了（一个数学公式）
（ 15 ％ ） 。
数字8条（ a ） - （三）表明，形象之间的差异来衡量使用相移法和激光测量更大接近年底时块长度的高度，是最大的。测量中的差异的增加而增加的倾斜角度。然而，小倾角的激光和相移测量同意密切。可能的来源，测量误差在区块B和C是由于尺度因子和不准确的θ左旋关系。这是因为实际的比例因子的变化与高度块，但在这种情况下，扩大的因素是使用的参考块的高度。那个
尺度因子假定固定的倾斜块，因为它的价值无法计算的倾斜块的高度，如果不知道。其他来源的错误是θ左旋关系，推导出的参考块的高度。然而，在表面倾斜的关系θ左旋不同，因为θ也是一个功能高度元两者之间的差额结果B座和C图。第8 （ b ） - （三）可能是由于线性拟合进程相移数据。然而，精度在小角度测量是更关键的是大角度倾斜很少发生
在实际组件。
3连接器倾斜测量组件
这部分的工作是证明能力的相移技术在倾斜检测的实际组件连接器。由于突出导致下方的组件，最好的水平位置是由附加几个螺栓十一点七六毫米厚度下方。图9 （一）表明一个计划期的连接器叠加，预计边缘。共有五个PCI连接器（ A至E ）进行了视察。连接器
高度约为12毫米的每个尺度因子计算是0.264毫米/像素。 θ之间的关系和L ，导出了高度十一点五七毫米从参考表，给出了（一个数学公式）
这个是网上翻译的，不知道行不行？
