In the papers [1–5] using synthetic methods and the facts from the conics theory in the Euclidean, pseudo-Euclidean, quasi-hyperbolic and hyperbolic planes, we have studied and proved numerous facts related to the cuspidal curves with emphasis on evolutes and Steiner’s deltoid. In this paper, the intention is to see what can be said about the curve of centers in some special pencil of conics and to show how, studying the center curves in the special pencil of conics a connection with Steiner’s deltoid curve has been found.

Microwave radiation diagnosis technology can detect thermal changes in skin tissue earlier than anatomical changes, but its detection accuracy is limited by non-target radiation interference in the measurement environment, additional measurement errors of system units, and energy scattering and transmission between skin tissues. This paper aims to address the scientific challenges of analyzing the forward and inversion modelling detection mechanism of layered accurate temperature measurement of human skin tissue based on multi-band. The study focuses on the construction of a pencil beam antenna optimization system, the optimization strategy of high-sensitivity correlated radiometer architecture, and the high-precision multi-band forward and inversion modelling detection algorithm. The key technologies include: (1) A new method of integrated modeling and multi-index optimization of antenna with high directivity and small aperture is proposed, and a priori knowledge-guided neural network of pencil beam distribution is constructed to realize the inversion model of antenna structural parameters; (2) The influence mechanism of high sensitivity correlated radiometer architecture error is analyzed, and a periodic phase shift error correction algorithm based on uniform polar circle is designed; (3) Combining deep learning theory and hyperparameter optimization framework, an iterative model is established, and the objective function modified by the penalty factor is defined to realize a new detection method combining forward and inversion. This paper presents a theoretical foundation for the industrialization of microwave radiation diagnostic technology.