Thepaper investigates the properties of the Lambert equivalent azimuthal projection,which is often used in normal aspect in atlases for maps of the northern and southern hemispheres.The field of research is theoretica...Thepaper investigates the properties of the Lambert equivalent azimuthal projection,which is often used in normal aspect in atlases for maps of the northern and southern hemispheres.The field of research is theoretical in nature and assumes a mastery of mathematics because it deals with map projections.The transverse aspect is commonly used for eastern and western hemisphere atlas maps.In addition,the Hammer projection was created fromthe transverse aspect of that projection.Therefore,if we want to get to know the Hammer projection better,we must first investigate the Lambert equivalent azimuthal projection in detail.While investigating this projection,it was observed that the equations of the transverse aspect can be represented in several ways.After that,it was necessary to determine the most suitable form of the equations of that projection for the calculation of partial derivatives,which are necessary for determining distortions.The article presents the distribution of factors of local linear scales along the(pseudo)meridians and(pseudo)parallels,and found that in the Lambert equivalent azimuthal projection,there can exist only one point where the distortion is equal to zero.The general case of a normal and transverse Lambert equivalent azimuthal projection has not been observed so far,and that is the new contribution of this article.展开更多
Based on the acoustic radiation theory of a dipole source, the influence of the transducer reception pattern is studied for magnetoacoustic tomography with magnetic induction（MAT-MI）. Numerical studies are conducted...Based on the acoustic radiation theory of a dipole source, the influence of the transducer reception pattern is studied for magnetoacoustic tomography with magnetic induction（MAT-MI）. Numerical studies are conducted to simulate acoustic pressures, waveforms, and reconstructed images with unidirectional, omnidirectional, and strong directional transducers.With the analyses of equivalent and projection sources, the influences of the model dimension and the layer effect are qualitatively analyzed to evaluate the performance of MAT-MI. Three-dimensional simulation studies show that the strong directional transducer with a large radius can reduce the influences of equivalent sources, projection sources, and the layer effect effectively, resulting in enhanced pressure and improved image contrast, which is beneficial for boundary pressure extraction in conductivity reconstruction. The reconstructed conductivity contrast images present the conductivity boundaries as stripes with different contrasts and polarities, representing the values and directions of the conductivity changes of the scanned layer. The favorable results provide solid evidence for transducer selection and suggest potential practical applications of MAT-MI in biomedical imaging.展开更多
文摘Thepaper investigates the properties of the Lambert equivalent azimuthal projection,which is often used in normal aspect in atlases for maps of the northern and southern hemispheres.The field of research is theoretical in nature and assumes a mastery of mathematics because it deals with map projections.The transverse aspect is commonly used for eastern and western hemisphere atlas maps.In addition,the Hammer projection was created fromthe transverse aspect of that projection.Therefore,if we want to get to know the Hammer projection better,we must first investigate the Lambert equivalent azimuthal projection in detail.While investigating this projection,it was observed that the equations of the transverse aspect can be represented in several ways.After that,it was necessary to determine the most suitable form of the equations of that projection for the calculation of partial derivatives,which are necessary for determining distortions.The article presents the distribution of factors of local linear scales along the(pseudo)meridians and(pseudo)parallels,and found that in the Lambert equivalent azimuthal projection,there can exist only one point where the distortion is equal to zero.The general case of a normal and transverse Lambert equivalent azimuthal projection has not been observed so far,and that is the new contribution of this article.
基金Project supported by the National Basic Research Program of China(Grant No.2011CB707900)the National Natural Science Foundation of China(Grant Nos 11274176 and 11474166)the Priority Academic Program Development of Jiangsu Higher Education Institutions,China
文摘Based on the acoustic radiation theory of a dipole source, the influence of the transducer reception pattern is studied for magnetoacoustic tomography with magnetic induction（MAT-MI）. Numerical studies are conducted to simulate acoustic pressures, waveforms, and reconstructed images with unidirectional, omnidirectional, and strong directional transducers.With the analyses of equivalent and projection sources, the influences of the model dimension and the layer effect are qualitatively analyzed to evaluate the performance of MAT-MI. Three-dimensional simulation studies show that the strong directional transducer with a large radius can reduce the influences of equivalent sources, projection sources, and the layer effect effectively, resulting in enhanced pressure and improved image contrast, which is beneficial for boundary pressure extraction in conductivity reconstruction. The reconstructed conductivity contrast images present the conductivity boundaries as stripes with different contrasts and polarities, representing the values and directions of the conductivity changes of the scanned layer. The favorable results provide solid evidence for transducer selection and suggest potential practical applications of MAT-MI in biomedical imaging.
