Single-shot digital multiplexed holography for the measurement of deep shapes

Abstract

This work develops a single-shot holographic profilometer that enables shape characterization of discontinuous deep surfaces. This is achieved by combining hologram frequency multiplexing and an illumination technique of complex amplitude in multi-incidence angle profilometer. Object illumination is carried out from seven directions simultaneously, where the radial angular coordinates of illumination plane waves obey the geometric series. It is shown that: (i) the illumination pattern provides the required frequency separation of all object wavefronts in transverse frequency space, which is necessary for hologram demultiplexing, and (ii) numerical generation of longitudinal scanning function (LSF) is possible, which has large measurement range, high axial resolution, and small side lobes. Low side lobes of LSF and the developed multiplexed field dependent aberration compensation method are essential to minimize the negative influence of speckle noise of single-shot capture on the measurement result. The utility of the proposed method is demonstrated with experimental measurement of heights of two step-like objects.

Multi-Incidence Holographic Profilometry for Large Gradient Surfaces with Sub-Micron Focusing Accuracy

“…The limitations found in OC and MAI have been addressed and solved by the multi-incident digital holographic profilometry (MIDHP) [ 10 , 13 ]. MIDHP assembles the set of object fields from the captured holograms for numerical generation of the longitudinal scanning function (LSF) [ 5 , 10 , 14 , 15 , 16 , 17 , 18 ].…”

“…Thus, it was sufficient to illuminate the object from one side, which means that the employed angles illumination beams were all positive. Reference [ 13 ] made effort to minimize the illumination wave components to obtain a single shot multiplexing solution.…”

“…The underlying theory of MIDHP was based on planar surface objects [ 10 , 13 ]. Thus, measured samples were intentionally selected as step-like objects (a set of flat surfaces with different heights).…”

“…Focus error introduces unproper reconstruction of the object shape. For the step-like objects, which do not require high focusing accuracy, manual focusing was sufficient to generate the LSF and complete measurement [ 10 , 13 ]. However, for objects with a continuous and high gradient shape, the accuracy of manual focusing is not sufficient.…”

“…This is due to (i) scanning with a larger number of illumination components, and (ii) the application of the proposed autofocusing algorithm. The classical generation of the LSF is based on the angular spectrum method [ 22 ], where the summation of the propagated wave is realized in the spatial domain [ 10 , 13 ]. Consequently, the LSF generation algorithm with P illumination scanning waves needs evaluation of 2P Fourier Transforms (FTs) for one propagation step.…”