## 1 Introduction  
Over the centuries, mortars have been highly used as bedding material in buildings construction and as valuable materials in frescoes and decorations. Indeed, mortars are characterized by ease of manufacture and application, a positive cost-benefit ratio, and a remarkable versatility that supported the widespread century-old use [1, 2]. Recently, the attention on the role that ancient masonry mortars play in their earthquake resistance has risen for medieval cities and villages characterized by the presence of historical buildings [3], but also for archeological sites [4], which stand on high seismic hazard zones [5; 6]. One of the main issues regarding the characterization of historical masonry buildings concerns their high heterogeneity [7; 8], in fact, these are also often characterized by poor construction, with mixed masonry, made up of rounded and/or irregular stone elements [9]. In this regard, a rapid and exhaustive characterization is necessary for both decreasing their vulnerability and identifying guidelines for advanced restoration techniques [10; 11; 12]. In this context, the determination of the mechanical parameters of the mortars, such as compressive strength and Young's modulus, is crucial in the analysis of these types of structures. However, the high cultural and artistic value of ancient buildings is in contrast with the need to obtain a representative statistics-based collection of samples for laboratory tests, because the small thickness of mortar joints makes their extraction, collection, and subsequent creation of the prismatic samples required by the standards difficult [13; 14; 15]. To this aim, the use of non-destructive tests (NDT) has been proposed by many authors [16; 17] and references therein, which have tried to provide interpretation of the deterioration mechanisms affecting these materials in a coordinated matter with the laboratory tests. The most popular ones, just to mention a few, are pulse transmission techniques, infrared tomography, tomographic imaging, and microwave radar. However, these techniques require operator experience and proper planning to provide reliable results. The methods based on rebound hardness instead, are relatively simple to conduct and the result processing is quick. At the same time, when dealing with low-strength materials such as the masonry of historical buildings, some of them such as the Schmidt hammer and the penetrometer cannot be considered as fully non-destructive. In fact, it can leave small depressions [17] or even cause fractures on the material giving no-rebound values [18]. With regards to the L-type Schmidt hammer, the impact energy (0.735 Nm) is too large for the characterization of the historical masonry mortars, and in fact, as reported by [19], it should be used with caution when the Uniaxial Compressive strength (UCS) of the material is less than 20 MPa. This value is generally one order of magnitude larger than the one of the historical mortars. At the same time, the penetrometer, which is based on the penetration of the steel needle into the masonry joint, cannot be considered as a non-destructive test when used on buildings with historical, artistic, or cultural value. For the reasons just mentioned, a rapid and non-invasive methodology for the estimation of the strength of ancient mortars is highly desirable. In this study, we propose the use of the Equotip hardness tester (EQ), a non-destructive, easy to handle, and electronic rebound-based device, originally developed in the 1970s for testing metals [20], and then extensively tested for rock hardness determination [21; 22; 23] and weathering studies [24; 25; 26; 27]. This method has been already extensively applied to the investigation of mechanical properties of weak rocks [18], natural materials that resemble the ancient mortars under several perspectives. The EQ has a low impact energy (1/66 of the Schmidt hammer) and it can be applied on materials having less than 0.1 MPa UCS [22].