The above equation was used to obtain θ for various values of L for each The block heights were calculated using E (1) 上面的方程式用来得出每一玻璃块的不同L值时的θ。玻璃块的高度用式(1)计算。The difference between measured height and mean calculated height for the four blocks were, respectively, 16 mm, 18 mm, 07 mm and 15 4个玻璃块实测高度和平均计算高度之间的差别分别是16 mm, 18 mm, 07 mm 和 15 mm。The maximum difference was 16% and the minimum difference was 2% 最大差别是16%,而最小差别为2%。This results show that the variation of projection angle across the field of view will not introduce significant 这一结果表明,投影角跨视场的变化将不会引入明显的误差。Thus, the variation of projection angle across the FOV is not critical in height measurement using the 因此,投影角跨视场的变化在采用本装置进行高度测量时不是关键的。5 Tilt measurements on glass 5 对玻璃块的倾角测量 In the work on glass block tilt measurement, experiments were conducted using six different 在对玻璃块倾角测量的研究中,用了6个不同的隔离物进行实验。Slip gages were used as spacers to introduce tilts in the glass blocks because they can be attached easily to the glass surface by sliding 采用滑移规作为隔离物来引入玻璃块的倾角,因为它们可以用滑移动作方便地附于玻璃表面。In addition, the gages allow small differences in tilts to be 此外,滑移规还可允许引入小的倾角差别。The experiment was conducted twice with different sets of spacers to confirm 实验用两组不同的隔离物进行两次,以证实重复性。Tilts were introduced in three of the glass blocks, while one was kept in the horizontal 在三块玻璃块上引入倾角,另一块则保持水平位置。The horizontal block was referred to as the reference 该水平的玻璃块就看作参考玻璃块。The first set of spacers of thickness 0 mm, 2 mm and 4 mm were used to introduce the tilts in blocks A, B and C, respectively, shown in F 3(a) 厚度为0 mm, 2 mm 和 4 mm的第一组隔离物分别被用来引入A块、B块和C块的倾角,如图3(a)所示。 To avoid errors caused by the positioning of spacer, the glass block and spacer edges were aligned using a steel 为了避免因隔离物定位引起的误差,玻璃块和隔离物的边缘用一把钢尺对准。The same steps were followed in preparing the glass block tilt specimens for the second set of spacer 在为第二组隔离物厚度准备玻璃块倾角样本中,遵循相同的步骤。In this experiment the tilt was introduced with spacers of thickness 5 mm, 3 mm and 5 mm on block A, B and C, respectively, to verify the 在本实验中,分别在A块、B块和C块上以5 mm, 3 mm a和 5 mm厚度的隔离物引入倾角,以验证实验。The tilted heights of the three blocks were measured relative to the height of reference block using the phase shifting 这三块玻璃块的倾斜的高度用相位偏移技术,相对于参考玻璃块的高度进行测量。The relative heights were computed from the phase map shown in F 3(d) 相对高度由图3(d)中所示的相位图进行计算。The pixel coordinates on the phase map were scanned using a computer 相位图上像素的坐标用一个计算机程序进行扫描。 The x-coordinates where the scanning starts are same for all the blocks, whereas the y-coordinates vary for each 扫描开始处的x坐标对所有玻璃块来说多相同,而y坐标则每一块都变化。The scanning stops when the end of the block is 当达到玻璃块的末端时,扫描就停止。The pixel values along each tilted block were traced from the starting x-coordinate to locate the approximately same grayscale value on the reference 沿每一倾斜玻璃块的像素值从开始的x坐标起被跟踪,以定位参考玻璃块上的近似相同的灰度值。The grayscale values were matched within ± 2 gray values as 如前面那样,灰度值在±2的灰度值以内是匹配的。The program then converts the matched pixel coordinates of both blocks into physical dimensions (in mm) and calculates the shift δx for the each matched gray 于是,程序将两个玻璃块匹配像素的坐标转换成物理尺寸(以mm为单位),并计算每一匹配的灰度值的偏移δx 。Using the values of δx and the illumination angle calculated using the θ-L relationship for the particular block height, we calculated the height of the tilted block relative to the reference 采用δx 值和利用特定玻璃块高度下的θ-L关系计算得出的照明角, 我们计算了倾斜玻璃块相对于参考玻璃块的高度。The height data were fitted using the least-squares method and the tilt angles for the blocks were obtained from the gradient of the fitted 高度数据用最小二乘法拟合,玻璃块的倾角由拟合数据的梯度而得到。