中国剩余定理工程化求解方法及其应用  

Engineering solution method and application of Chinese remainder theorem

作　　者：于晓洋[1] 王洋[1] 于双[1] 吴海滨[1] 陈德运[1] 

机构地区：[1]哈尔滨理工大学测控技术与仪器黑龙江省高校重点实验室,哈尔滨150080

出　　处：《仪器仪表学报》2014年第7期1630-1638,共9页Chinese Journal of Scientific Instrument

基　　金：国家自然科学基金(61071051);黑龙江省自然科学基金(F201020)资助项目

摘　　要：为了在多频相位测距技术中利用中国剩余定理进行相位解模糊,将该定理从整数域推广到实数域和模存在公约数的情况;然后提出一种余数测量值取整判据,在限定余数测量误差的前提下,根据各余数测量值的小数部分之差来确定余数测量值取整公式,形成了一种中国剩余定理工程化求解方法。该方法的理论分析、仿真验证和三周期相移结构光三维测量实验结果表明:满足余数测量误差限定条件时,实数解存在且其误差小于余数测量误差;平面景物的测量误差小于0.4%;实现了表面复杂景物的三维测量,测量结果视觉效果好。该方法具有较强的抗干扰能力、运算简单、计算量小、求解精度高,适用于工程中多频相位解模糊。In order to utilize Chinese remainder theorem to realize phase unwrapping in the field of muhi-frequency phase ranging, the theorem was extended from integer domain to real domain and to the situation in which common divisors exist among the modules, and then a remainder rounding criterion was proposed. Under the premise of setting a remainder measurement error limit, the rounding formula of remainder measurement value was determined based on the difference of the fractional parts of the measured remainders ; and the engineering solution of the Chinese remainder theorem was formed. Theoretical analysis, simulation verification and the experiment result of three-periodic phase shift structured light measurement show that when satisfying the remainder measurement error limit, the real solution exists and the error is less than the remainder measurement error; the measurement error of the plane scene is less than 0.4%. When measuring the scene with complex surface, a smooth and delicate three-dimensional reconstruction surface can be realized. The proposed method has some advantages, such as strong anti-interference ability, simple operation, less computation, and high solution precision, and is applicable to the multi-frequency phase unwrapping in engineering application.

关 键 词：中国剩余定理 取整判据 相位解模糊 多频相位测距 光学三维测量 

分 类 号：TH741[机械工程—光学工程]