# Non-Contact Measurement of Small-Module Gears Using Optical Coherence Tomography
## 1 Introduction  
Micro gears with a modulus of 0.05 mm to 0.5 mm are widely used in precision measuring tools, navigation instruments, and chronometer clocks [1]. In addition, it also widely used as a key precision driving part in defense industry and the manufacturing of micro machinery [2]. In the process of transmission, if the tooth surface is damaged, it will affect the normal operation of machine maintenance and mechanical transmission. Because the quality of the tooth surface of the micro gears affects the precision, noise, and life of the instrument, the precision and quality of the measurement of small gears has higher requirements than that of the normal one. If traditional contact measurement technology and instruments are used to measure small gears, even a thin and small measurement head is difficult to insert into the teeth, resulting in the difficulty in carrying out measurements; also, the contact measurement head sometimes damage the teeth. In addition, the rigidity of the measuring rod is poor, it is difficult to determine the deformation error caused by the measuring rod, the error is difficult to read, the measurement accuracy and repeatability are difficult to guarantee, and sometimes it is impossible to do the measurement at all. Because of the small modulus, it is difficult to obtain the tooth profile with the naked eye. It needs to be aligned under the microscope, which is inconvenient for the measurement [3]. Therefore, high-automation requirements of the measuring instrument are required. Some studies introduced the contact gear measuring instrument developed recently, it is found that the minimum gear modulus can be measured as 0.2 mm, and the diameter of the measuring rod is 0.25 mm [2]. In 2003, the researcher from Ogashihara company has found that it was difficult to measure the gears with modules that are less than 0.3 mm using contact instruments [4]. Therefore, the existing contact measurement techniquesand instruments are still unable to meet the requirements of the precision micro gear, especially the precision measurement of micro gears that are produced by mass production [2]. Contact CNC (Computer Numerical Control) micro-gear measurement based on the coordinate method [5] is one of the current methods of detections for small-module gears. This method has high precision, high measurement efficiency, and a wide application range [6], but the tooth profile detected by this contact measurement cannot be too small, and therefore, it cannot meet the requirements of micro gear measurement. Non-contact measurement technology based on CCD (Charge Coupled Device) measurement [7; 8] is the second common technique that has the advantages of non-contact, fast speed, and strong anti-interference ability in the field. However, it also has the problem that only the tooth profile of the end face of the gear can be detected, and it is difficult to detect the tooth profile in the direction of tooth width. Contact measurement technology based on an optical fiber probe [9; 10] and gear meshing measurement technology is employed. Although the fiber optic probe has begun to be applied to measure the small-module gear, the main problem of the optical fiber probe is its measuring efficiency and its value transfer [3]. Optical coherence tomography (OCT) is a technique to measure and process the interference intensity of scattered light in the measured sample with the reference light by using the light interference principle. Subsequently, a high-resolution depth image is reformed to express the internal microstructure of the sample [11]. The technique has the ability of biopsy, with a resolution up to micrometers, and it can obtain non-invasive two-dimensional and three-dimensional images [12], and now it has been used in in industrial fields for the measurement of tablet coatings [12], fiber composites, MEMS (Micro Electro Mechanical Systems) devices [13], thin sheets and artworks, etc.