Undersampled Digital Holographic Interferometry

In digital holography, primary holographic fringes are recorded using a matricial CCD sensor. Because of the low spatial resolution of currently available CCD arrays, the angle between the reference and object beams must be limited to a few degrees. Namely, due to the digitization involved, the Shannon's criterion imposes that the Nyquist sampling frequency be at least twice the highest signal frequency. This means that, in the case of the recording of an interference fringe pattern by a CCD sensor, the inter-fringe distance must be larger than twice the pixel period. This in turn limits the angle between the object and the reference beams. If this angle, in a practical holographic interferometry measuring setup, cannot be limited to the required value, aliasing will occur in the reconstructed image. In this work, we demonstrate that the low spatial frequency metrology data could nevertheless be efficiently extracted by careful choice of twofold, and even threefold, undersampling of the object field. By combining the time-averaged recording with subtraction digital holography method, we present results for a loudspeaker membrane interferometric study obtained under strong aliasing conditions. High-contrast fringes, as a consequence of the vibration modes of the membrane, are obtained.