# Influence of Surface Tilt Angle on a Chromatic Confocal Probe with a Femtosecond Laser
## 1 Introduction  
For semiconductor devices, MEMS (micro electro mechanical systems) and other precision components with microgeometry, measurement, and evaluation of three-dimensional (3D) surface profiles [1; 2] are necessary to maintain their quality. For this purpose, measuring instruments are required to have a resolution and accuracy in the order of sub-\(\upmu\)m over a measurement range of several hundred \(\upmu\)m [1; 2; 3]. Confocal probes [4; 5; 6; 7; 8; 9; 10] are non-contact 3D surface profiling instruments that satisfy these requirements. Confocal probes are used in many fields since they are capable of carrying out non-contact and high-resolution 3D shape measurement in the atmosphere. In recent years, chromatic confocal probes using a light source with a spectral width have been studied from the viewpoint of measurement efficiency and measurement range [11; 12; 13; 14; 15; 16]. Furthermore, a dual-detector confocal optical system has been proposed to achieve higher resolution and a wider measurement range for measuring the optical axis position of the object to be measured [17; 18; 19; 20; 21]. Our research group has also developed a dual-detector chromatic confocal probe using a femtosecond laser as a light source [22; 23; 24; 25; 26; 27]. At first, a new \(z\)-position detection method, which is referred to as the tracking local minimum method (TL method) [22], has been proposed. So far, the tracking local minimum method (TL method) [22], which uses the minimum point of the sidelobe of the confocal response curve, has been used to achieve an optical axis position measurement resolution of 30 nm in a measurement range of 40 \(\upmu\)m, and then a measurement range of 250 \(\upmu\)m [23; 27] has been achieved by applying the principle of the sidelobe of the confocal response curve. Here, these achievements in the references [23; 27] have focused on the measurement range expansion of \(z\)-position based on the TL methodby extending the sidelobes of the confocal response curves. After that, as another new \(z\)-position measurement method, the tracking intersection method (TI method) [26], which detects the \(z\)-position from the intersection of confocal response curves obtained with two detectors, has also been proposed and demonstrated by using the developed dual-detector chromatic confocal probe system. It should be noted that the difference is that the TL method identifies the \(z\)-position from the local minima of the confocal responses, while the TI method identifies the \(z\)-position from the intersection of the confocal responses. Both the TL method and TI method, however, enable highly accurate detection of the \(z\)-position of the measurement object without being affected by the shape of the light source spectrum. Furthermore, several investigations have been carried out to make the confocal optical system robust against temperature variation, and several works have also been carried out to improve the measurement accuracy of the proposed dual-detector chromatic confocal probe by examining the amount of detector offset [24; 25]. On the other hand, the influence of the tilt angle of the measurement object on the proposed TL method has not been investigated so far. It should be noted that the influence of the tilt angle of the measurement object on the scanning confocal response curve, from which the optical axis position of the measurement object can be detected, has been investigated by several researchers [28; 29; 30; 31; 32; 33; 34; 35; 36; 37]; for example, it has been found that the presence of a tilt angle of the measurement object changes the shape of the confocal response curve, thereby affecting the detection of the measurement object's optical axis position [28; 29; 30; 31]. However, these investigations have been conducted on scanning confocal probes with monochromatic light sources, and no investigations have been carried out on chromatic confocal probes.