Multi-level Spiral Phase Filtering in Speckle Interferometry Using Spatial Light Modulators

Electronic speckle pattern interferometry (ESPI) is widely used for displacement, stress and strain measurement [1]. Recently the introduction of Spatial Light Modulators (SLM), has allowed versatile optical systems that can overcome some of the limitations of the typical ESPI setups making them more robust and flexible [2]. For this kind of applications, the usual phase stepping techniques that require PZT can be replaced by carefully manipulating the modulator phase. Here a technique is proposed that introduces a multi-level spiral phase filter (MLSPF) allowing the extraction displacement in an out-of-plane ESPI setup. This MLSPF produce a specific speckle pattern denominated vortex-filtered speckle pattern (VF-SP), which results from the convolution of the standard speckle pattern and the MLSPF point spread function, similar to the phase contrast microscopy techniques [3-4]. This VF-SP contains within the speckle size, the phase terms of the filter, which can be controlled independently by the rotation of the MLSPF. Therefore by rotating the MLSPF, the standard phase stepping algorithms can be applied for phase extraction procedures, and for displacement measurements.