THEORETICAL ANALOGIES AND PRACTICAL DIFFERENCES BETWEEN IMAGING AND LENSLESS INTERFEROMETRIC METHODS

Interferometry is ubiquitous in dimensional measurement as it constitutes an extremely sensitive and highly versatile metrological tool. Depending on the configuration, it can be used for the characterization of surface topologies, distances or vibrations. Many of these applications require spatially resolved measurements. This can either be achieved by classical imaging of the object to the detector using an objective lens or by a lensless (or non-imaging) holographic setup. Accordingly, either an image of the object plane or its farfield distribution is superimposed with the reference beam and thereby characterized. Both methods can also be implemented in off-axis-configuration, which sacrifices some spatial resolution to enable single-shot measurements instead of the sequential phase shifting required for an inline-configuration. Apart from the required post-processing, imaging and lensless methods thus offer identical performance in theory. In practice however, depending on the properties of the measurement object, one method may lead to a more efficient use of the detector than the other. Fig. 1 illustrates this idea by an example.

If the surface of the object is assumed to be smooth, the image of the object directly resembles the object itself. The farfield distribution on the other hand shows a diffraction pattern, mostly spread into the vertical and horizontal direction according to the two most prominent orientations found in the object. The intensity is thus distributed very unevenly and most regions are illuminated only weakly while the center of the frame is strongly pronounced. The ratio between the mean intensity across the whole frame and the maximum value constitutes a measure of homogeneity and amounts to only 9.9e-6 in this case. The limited dynamic range of the detector is used very inefficiently for most pixels, as a large portion of the frame is basically black if the image is not supposed to be overexposed in the center. For the imaging system, a ratio of 1.5e-1 is obtained instead and thus makes use of the detector more efficiently for this specific object. For an object with the same USAF reflectivity distribution, but an optically rough surface, the intensity ratio for the imaging system is deteriorated by speckle noise to a value of now 1.2e-2. The spatially homogeneous far field distribution across the whole frame partially compensates for the speckle noise and the calculated intensity ratio of 7.7e-2 indicates that the lensless system operates more efficiently for this object. In our contribution, we present a more thorough theoretical investigation as well as real-world examples encountered in a holographic vibrometry laboratory setup.