## 1 Introduction  
The curved frequency selective surface (FSS) structure has many potential engineering application prospects. To the antenna radome, generally, there are some special requirements for the FSS radome materials. On the other hand, the FSS structure needs to meet certain specifications to have satisfactory performance. The ideal FSS is an infinite periodic surface structure composed of some basic elements, which have a frequency selective function for radiated electromagnetic waves and can be regarded as a spatial filter. After decades of research, the structure and performance of FSS have been improved in many aspects. The existing prefabricated mediums have many dielectric constant values to be used in a variety of FSS designs, which are mainly distributed in 2.2 to 10.2 [1; 2; 3; 4; 5; 6; 7]. The ultra-wideband properties of FSS are closely related to the periodic element structure, dielectric material property and FSS layer structure. In curved and ultra-wideband FSS cell designs, the interwoven convoluted structure can reduce the cell size and increase the bandwidth [7]. Reference [8] proposed an ultra-wideband FSS and its 3 dB bandwidth reached 12.6 GHz (5.85-18.45 GHz) at vertical incidence angle, the structure consists of three FSS patches and two 1 mm medium layers. In warped FSS, the bandwidths of different incident angles are a very important index. The planar FSS in reference [8] had a good technical performance within the 30\({}^{\circ}\) incident angle. However, this type of structure had an exacting requirement on its medium electromagnetic property. Generally speaking, a wider FSS bandwidth requires a lower medium dielectric constant, thus, there is a significant increase in costs. In terms of this issue, a method of air holes perforated through the normal medium to decrease the equivalentdielectric constant value is proposed in this paper, thus an ultra-wideband FSS can be accomplished with cheaper and lighter materials. With air through holes through the medium, the medium macroscopic dielectric constant value is obviously altered. Several methods were put forward to obtain the mixed medium dielectric constant, the effective medium theory included. These methods function by being able to define averages that hope to be representative of the system and be connected with experimental measurements in the macroscopic situation. Thus, providing the basis for the widely used Maxwell-Garnett formula [9; 10]. The modern homogenization theory is an effective method to obtain the composite dielectric constant, the multiscale homogenization method was proposed afterwards [11; 12; 13; 14; 15; 16; 17]. The effective dielectric constant of the perforated medium (PM) is computed by the multiscale method, in which the microscale field in the period unit is computed, and the macro parameters are obtained by the average of the microscale field. The results of the multiscale method can be compared with the non-perforated medium FSS, and the performances of the FSSs can be calculated. The curved FSS radome can be developed based on the PM FSS performance obtained above. In practice, the FSS needs to form a corresponding curved surface structure according to different application systems, such as the antenna reflective surface and cover, and some are oversized. Based on the application environment of the curved FSS radome, an accurate calculation method is needed to calculate the transmission coefficients of different frequencies and incident angles [18; 19; 20]. This paper adopts the vector fitting method to fit the planar FSS transmission coefficients as the function of frequency. The FSS transmission coefficients functions of different incident angles then utilize B spline interpolation to reduce the data size. The transmission coefficients functions are synthesized base on the physical optic method to analyze the curved FSS transmission coefficients.