# A Real-Time Automated System for Dual-Aperture Common-Path Interferometer Phase-Shifting
## 1 Introduction  
Mass production through highly automated manufacturing processes has highlighted the need for more efficient precision surface measurement systems and testing processes. In automated manufacturing, the quality of the workpiece surface is highly related to the machining process [1]. Additionally, the manufacturing of technological devices has rapidly migrated to the production of micrometric and nano-scale surfaces [2]. Currently, on-machine in-process measurement provides reliable methodologies to obtain information on machining processes. In-process measurement characteristics require high-speed, high-resolution, real-time measurement, and optical measurement systems provide reliable alternatives to perform measurements and monitoring. Interferometric approaches have been widely used for surface measurement because they can provide noncontact, high-resolution, and high-accuracy measurements [3, 4, 5]. Particularly, common-path interferometers such as Fizeau or Twyman-Green have been widely used for ex-situ surface measurement, however, for on-machine measurement it is necessary to reduce the influence of disturbances associated with the process [4, 5]. In this sense, it is necessary to develop automated measurement systems, based on optical interferometry with real-time operation, that are immune to disturbances during the measurement of noisy interferograms. In optical interferometry, phase difference between two interferograms allows physical variable quantities such as displacement [6, 7], temperature [8, 9], refractive index [9, 10], anddeformation [11; 12], among others, to be obtained. The phase difference can be obtained by applying phase-shifting methods [13; 14; 15]. These methods typically consist of introducing an additional phase by shifting either a grating or a mirror depending on the interferometric arrangement configuration [16; 17; 18]. The phase-shifting process is typically achieved manually in most cases or by using electro-mechanical actuators [19; 20; 21]. In the case of manual shifting, the use of specialized or expensive equipment is not required, however, low accuracy and repeatability of the process is obtained. Alternatively, the use of electromechanical actuators improves the accuracy and linearity of the phase-shifting step spacing; however, the implementation of such systems typically require expensive equipment and specific implementation conditions. In this regard, piezoelectric devices have been widely used to reach millimetric-sized or even nanometric phase-shift linear displacements within interferometric approaches to obtain smaller phase variations [22; 23]. Additionally, the interferometric implementation can significantly improve the accuracy when obtaining the phase difference. Particularly, the dual-aperture common-path interferometer (DACPI) is a robust interferometric system that is able to deal with mechanical disturbances better, compared with separated-path interferometers [15; 17; 24; 25]. The DACPI consists of a telecentric, 4_f_-Fourier imaging system with two windows in the object plane and a binary ruling as a spatial filter [18]. In DACPI systems, phase stepping is usually obtained by transverse translation of a Ronchi ruling placed at the Fourier plane, where the translation is typically performed manually [17]. Moreover, the phase difference obtained by a DACPI requires external digital processing, which includes the use of algorithms, usually performed separately from the capture stage. In this regard, the main disadvantages in systems such as DACPI is the significant time increase in phase calculating and related miscalibration issues. In this paper, we present an automated DACPI system for obtaining the phase difference between the probe and the reference window in real time. Furthermore, the obtaining of the phase extraction is carried out by means of a self-calibrated algorithm [26; 27], without the requirement of equal spaced consecutively captured interference patterns [13; 14; 28].