## 1 Introduction  
Many studies employ Electronic Speckle Pattern Interferometry (ESPI) for the measurement of displacements, deformations, and surface shape. The optical system used in ESPI can be configured to favour displacement measurements in a certain direction. Usually, measurements are made by observing perpendicular or parallel displacements to an observer plane. Therefore, the technique is typically divided into two types of interferometers according to the main sensitivity vector direction of the optical system: in-plane and out-of-plane sensitivity interferometers. [PERSON] et al. show several techniques based on ESPI and holographic interferometry ESPI, as well as an optical configuration for several interferometric systems [1].  
ESPI is an instrumental technique for full-field displacement and surface topography measuring when it is not possible to make contact with the object. This technique is highly accurate in recording measurements, and its resolution can be adjusted in a wide range, from nanometres to micrometres [2]. ESPI is widely used as a non-destructive test in mechanical elements [3], vibration analysis [4], dynamic deformation analysis [5; 6], and surface topometric measurement [7]. Unfortunately, optical configurations in ESPI can only record displacement in one direction, making it necessary to employ an optical system for each direction of the displacement--preferably orthogonal and simultaneous ones. To measure the mechanical stresses around a crack, it is necessary to determine the deformation in the radial direction on the edge of the crack tip [8]. Since determining the direction in which displacement occurs is essential to the study of deformations, several methods have been proposed to overcome this limitation. [PERSON] et al. [9], [PERSON] et al. [10], [PERSON] et al. [11],and [PERSON] et al. [12] show distinct approaches to simultaneous orthogonal deformation measurements based on ESPI, and using different elements, such as polarizers, alternating measurements between optical systems, and simultaneous illumination with different wavelengths and interferometers.  
On the other hand, [PERSON] et al. and [PERSON] et al. introduced a device based on two conic mirrors and collimated illumination to measure residual stresses by interferometry with radial-in-plane sensitivity [13; 14; 15]. The conic mirrors are interconnected with piezoelectric actuators, which are needed to implement the phase shift technique to find the deformation-associated optical phase. To diminish the measurement mistakes due to the wavefront of illumination, it is necessary to keep the radial direction of the sensitivity vector consistent by using collimated illumination over the full conic mirror surface. This becomes increasingly expensive if the outer diameter of the conic mirror is large because it requires a collimating lens with the same diameter. In this work, we reduce costs by introducing a radial interferometer with divergent illumination that uses a linear polarizer and a one-quarter wave retarder to perform the phase shift technique by polarization [16]. With this method, we present a proposal for a solution to the problem of collimated illumination of an extended beam diameter through a simplification of the typical optical system used in radial interferometry. To verify the functionality of the radial interferometer with divergent illumination, without the need of a collimated illumination, we performed deformation measurements in a thin aluminium plate when it was heated from the rear by a point heat source. Results are compared to a finite element analysis simulation.