Separation of lobes in Multispectral Digital Holography

• Main Author: Hjartarson, Örn
• Format: Others
• Language: English
• Published: Umeå universitet, Institutionen för fysik 2013
• Subjects: Holography Holographic Optics Lobes Electromagnetism Non-invasive
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-64314

Through a holographic recording a property from the third dimension, the depth, is obtained in the form of a phase map of the incident light. One wavelength holography will have a unique phase for the depth range corresponding to the wavelength of the light and outside this range the real depth can not be resolved. By introducing more wavelengths to the measurement the unique phase combination of the waves will have a wider range and larger objects can be resolved. Up to six wavelengths can be simultaneous recorded by making them occupy different spatial frequencies. A set of spatial frequencies together describing a property of the wave is referred to as a lobe. For more than 6 wavelengths and a larger depth range produced by a more seldom repeated unique phase combination the individual waves will occupy the same frequencies, i.e. the lobes overlap. The separation of overlapping lobes is essential in order to make precise and time independent measurements of large and/or moving objects. To separate the lobes the complex fields, i.e. the phases together with the amplitudes, were simulated to propagate a distance and again recorded. The propagation leads to a phase shift of the spatial frequencies which reveals the complex fields in the case of two overlapping wavelengths. For three overlapping wavelengths the resolution, i.e spatial frequencies describing the object, has to be reduced in order to determine the individual complex fields. Since the propagation is a linear transformation for the frequencies that do not overlap, only the overlapping elements whose propagation is nonlinear produce new information. The new information gained is therefore independent of the number of wavelengths used which limits the exact determination of the fields to two wavelengths. Through the holographic recording another property of the complex field is obtained which is the superimposed individual intensities. This bounds the complex fields to certain values, i.e. restricts the possible amplitude of the waves. The recording in the two planes produces two intensity distributions which both must be satisfied by the complex fields. The optimization model for this was formulated and a simple optimization algorithm was implemented. Instead of an equality constraint of the intensities the inequality constraint was implemented, mainly due to that the optimization process was out of the scope of the thesis and the inequality constraint resulted in a simple implementation. The result pointed out important properties even though the optimization could not separate the fields satisfactorily for more than three wavelengths. The inequality constraint contains enough information to solve the case of three overlapping wavelengths.