## 3 System Configuration  
According to the measurement methodology described above, a light bar with sharp edges is required. In the measurement system, the prolonged light bar is adopted so that the heights of multiple bumps are simultaneously calculated in a single scanning measurement process, which requires a linear structured light with high performance in the illumination intensity and intensity distribution along the length of the stripe. The intensity distribution can be altered when different light sources are used, while different imaging processing methods should be used accordingly. In our illumination model, a high-power metal arc lamp is used as the light source, which not only ensures the high illumination intensity required due to the reduction of exposure time during the fast scanning process, but also improves the measurement accuracy, as its incoherent property can effectively minimize the speckle effect caused by traditional coherent light sources. The light beam passing through the optical fiber is truncated by a precision slit aperture, which is manufactured by etching on thin glass coated with an opaque coating; a light stripe with the same shape of the slit aperture is formed. Strict quality requirements for the width and edges of the slit ensure the quality of light stripe. As shown in Figure 5, a slit aperture with a length of 30 mm and a width of 0.05 is installed with optic fiber. Subsequently, a set of optical filters are used to cut off the infrared ray to protect the wafer surface coating from the infrared light. Finally, passing through a group of lenses consisting of a collimating lens and a flat apochromatic microscope objective, an optimal light stripe is formed, and a narrow powerful line with a length of 2 mm and width of 0.025 mm is focused on the measured wafer surface. A microscope imaging optical path with fixed magnification composed of an apochromatic microscope objective and a tube lens, with focus length \(f_{objective}=40\) mm and \(f_{tube}=200\) mm, respectively, was used. The reflected light from the wafer surface is recorded by a plane array camera. The shift of the reflected light strip from the top of bumps and the wafer surface in the image implies the height variations of the measured bumps. Combined with the system parameter calibration, the bump heights will be accurately calculated on a computer workstation according to Equation (3), as described above. Figure 5 shows the schematic diagram of the bump height measurement system. The illuminating model is arranged at 45\({}^{\circ}\) relative to the wafer surface, and the imaging model is symmetrically disposed to ensure reliable data of the whole measurement range is gathered, in view of short depth of focus of the microscope. To achieve the full field bump height measurement of the whole wafer, a scanning path generating algorithm was researched based on the field of view and wafer size. As shown in Figure 6. The parameter \(W\) represents the scanning step. The row numbers of the scanning path \(N\) are determined by the diameter of the wafer D and scanning step \(W\):  
\[N=D/W \tag{5}\]  
Figure 5: Schematic of the experimental setup for height measurement of micro bumps on a wafer. The length of scanning path of each row Li is determined by Equation (6):  
\[L_{\rm i}=2\sqrt{\left(\frac{D}{2}\right)^{2}-\left(\frac{D}{2}-i*W\right)^{2}} \,\left(i=-\frac{N}{2},-\frac{N}{2}+1,-\frac{N}{2}+2,\cdots,\cdots,\frac{N}{2}- 1,\frac{N}{2}\right) \tag{6}\]  
The scanning path of each row is prolonged to align the turning point with that of the next row, thereby forming a continuous scanning path. In addition, another critical parameter is the sampling interval. High measurement accuracy can be obtained in a small-step scanning model, as smaller sampling intervals mean more bump data and finer resolution of measurement. On the contrary, rapid scanning in large-step models achieves a relatively low accuracy. During the scanning process, each image contains multiple bump shadows.