We present the thermal expansion coefficient （TEC） measurement technology of compensating for the effect of variations in the refractive index based on a Nd： YA G laser feedback system, the beam frequency is shifte...We present the thermal expansion coefficient （TEC） measurement technology of compensating for the effect of variations in the refractive index based on a Nd： YA G laser feedback system, the beam frequency is shifted by a pair of aeousto-optic modulators and then the heterodyne phase measurement technique is used. The sample measured is placed in a muffle furnace with two coaxial holes opened on the opposite furnace walls. The measurement beams hit perpendicularly and coaxially on each surface of the sample. The reference beams hit on the reference mirror and the high-refiectivity mirror, respectively. By the heterodyne configuration and computing, the influences of the vibration, distortion of the sample supporter and the effect of variations in the refractive index are measured and largely minimized. For validation, the TECs of aluminum samples are determined in the temperature range of 29-748K, confirming not only the precision within 5 × 10-7 K-1 and the accuracy within 0.4% from 298K to 448K but also the high sensitivity non-contact measurement of the lower reflectivity surface induced by the sample oxidization from 448 K to 748 K.展开更多
Unique expansions in non-integer bases have been investigated in many papers during the last thirty years.They are often conveniently generated by labeled directed graphs.We give a precise description of the set of se...Unique expansions in non-integer bases have been investigated in many papers during the last thirty years.They are often conveniently generated by labeled directed graphs.We give a precise description of the set of sequences generated by these graphs.This provides a geometric explanation of many former abstract results in this domain.Our results are illustrated by many examples.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No F050306
文摘We present the thermal expansion coefficient （TEC） measurement technology of compensating for the effect of variations in the refractive index based on a Nd： YA G laser feedback system, the beam frequency is shifted by a pair of aeousto-optic modulators and then the heterodyne phase measurement technique is used. The sample measured is placed in a muffle furnace with two coaxial holes opened on the opposite furnace walls. The measurement beams hit perpendicularly and coaxially on each surface of the sample. The reference beams hit on the reference mirror and the high-refiectivity mirror, respectively. By the heterodyne configuration and computing, the influences of the vibration, distortion of the sample supporter and the effect of variations in the refractive index are measured and largely minimized. For validation, the TECs of aluminum samples are determined in the temperature range of 29-748K, confirming not only the precision within 5 × 10-7 K-1 and the accuracy within 0.4% from 298K to 448K but also the high sensitivity non-contact measurement of the lower reflectivity surface induced by the sample oxidization from 448 K to 748 K.
基金supported by National Natural Science Foundation of China(Grant Nos.11871348 and 61972265)Natural Science Foundation of Guangdong Province of China(Grant No.2020B1515310008)+1 种基金Project of Educational Commission of Guangdong Province of China(Grant No.2019KZDZX1007)Shenzhen Key Laboratory of Advanced Machine Learning and Applications.
文摘Unique expansions in non-integer bases have been investigated in many papers during the last thirty years.They are often conveniently generated by labeled directed graphs.We give a precise description of the set of sequences generated by these graphs.This provides a geometric explanation of many former abstract results in this domain.Our results are illustrated by many examples.
