New approach to partial coherence single beam phase retrieval techniques:
Phase retrieval based on the Transport of Intensity Equation have recently emerged as a practical tool for recovering the phase of non absorbing specimens and are routinely employed over a wide range of wavelengths starting from the optical to the x-ray regime. These techniques only require a series of single beam propagated intensities for recovering the phase information. In this way, the TIE solver provides big robustness against mechanical and environmental instabilities. However, the major difficulty in applying TIE based techniques is the requirement of large Signal to Noise Ratio (SNR) in the capturing system.
In this research project we are planning to develop a novel methodology for TIE techniques when employing Partial Coherent Illumination (PCI). This new methodology is planned to increase the SNR in the capturing system. The breakthroughs of the project address this issue by employing Partially Coherent Modulated Object Illumination (PCMOI), which 1) allow capturing only the desired frequency spectrum maximizing the SNR requirement, and 2) removing speckle noise completely, and by consequence, mitigating Low Frequency Artifacts (LFAs) from the retrieved phase, which is major source of error for TIE solvers. The performed study is devoted to: optimization of the illumination coherence function for the applied non equidistant capturing plane separation strategy and development of phase retrieval algorithms based on the TIE. The developed optimization and the phase retrieval techniques will be based on extracting the individual spatial frequencies only from these planes where the error is lowest. Thus, the suppression of LFA will be efficiently done from the retrieved phase without employing regularization techniques. The proposed methodology plans to obtain an accurate phase reconstruction by employing unequal plane separations and an image formation system with PCI.
NCN Preludium 8 – Maciej Trusiak
Modern optical metrology methods enable noncontact, noninvasive, accurate and fast examination of objects/phenomena, varying from nano to macro scale, static and dynamic, with full-field data acquisition and processing. Information about the measurand (2D/3D shape, refractive index distribution, in-plane and out-of-plane displacements, vibration amplitude etc.) is encoded in the phase and/or amplitude distribution of the output intensity distribution called a fringe pattern. To decode the phase and amplitude distribution automatic fringe pattern analysis (AFPA) methods are used. Their effectiveness defines the accuracy and uncertainty provided by versatile and widely used optical measurement techniques.
Research project objective concerns accuracy improvements in optical metrology techniques by developing more efficient algorithmic solutions for data analysis. We propose to advance functionality, efficiency and precision of optical metrology methods without resorting to hardware development, which a very promising approach but costly and time consuming. In this research project we aim at developing adaptive AFPA algorithms based on the notion of the Hilbert-Huang transform (HHT), which adjusts its working principle to the data under study in almost “intelligent” manner, with no a priori assumptions. Implementation and modification of novel algorithms will significantly advance the AFPA in terms of data filtering and accurate decoding the measured information encoded as the image phase and amplitude distribution. Novel numerical methods are expected to provide single-frame phase and amplitude demodulation with increased accuracy and efficiency in comparison with classical approaches (i.e., single-frame Fourier transform and multipleframe temporal phase shifting approach).
The research hypotheses concern: (1) developing novel methods utilizing the HHT to deepen the state of knowledge in the field of adaptive data analysis techniques and examine the similarities and differences between this approach and iterative linear Gaussian filtration; (2) theoretical and experimental studies of the reconstruction process in digital holography (in macro scale) employing HHT based algorithmic solutions to increase the hologram phase demodulation accuracy (comparative studies against the mostly used classical temporal phase shifting method); (3) numerical and experimental analysis of the possibility to increase accuracy of the complex object field demodulation (phase and amplitude information) in optical diffraction tomography and holographic microscopy applying developed HHT-based algorithmic solutions (comparative studies against classical Fourier transform method); (4) examine the influence of data filtration utilizing HHT algorithms on systematic and random error reduction in subpixel displacement fields determination using popular and attractive digital image correlation method.
Replacing classical analysis schemes with novel automatic adaptive algorithmic solutions based on the Hilbert-Huang transform is expected to improve the accuracy and broaden the functionalities of optical metrology methods employed to examine biological and technical objects. A significant step from visualization towards metrology is expected to be accomplished. Proposed studies in the field of digital holography, optical diffraction tomography, holographic microscopy and digital image correlation will constitute pioneering works aiming at theoretical and experimental verification of the possibility to decrease stringent limitations and improve accuracy, efficiency and attractiveness of the noninvasive optical measurements using adaptive data analysis. Proposed single-frame processing perfectly matches the requirement to monitor fast-changing dynamic events, the issue of great scientific interest. Potential results which are expected in the proposed PRELUDIUM 8 research project can be transferred, in natural way, to other science tasks, e.g., medical imaging, geophysics, image recognition, remote sensing, virtual reality etc.
NCN Preludium 9 – Julianna Kostencka
Holography gives impression of depths (parallax), however is unable of revealing the interior of a sample. For this reason it is often called a 2½D imaging technique. However, the fully 3D imaging can be achieved using holographic tomography. In this technique, a series of holographic measurements is performed for various angular positions of a rotating sample. Then, the captured data is numerically combined, which results in reconstruction of three-dimensional distribution of refractive index within a sample. This project aims at advancing the described technique by overcoming its two main weaknesses – poor spatial resolution and 3D image deformation due to inaccuracies of the sample rotation system. This is achieved by introducing a simple modification to the tomographic measurement system, where the conventional type of the sample illumination applying a single laser beam is replaced with the two-beam illumination. The proposed modification allows achieving the so-called superresolution effect, which enables visualization of fine details of a sample. Furthermore, the two-beam illumination facilitate reliable sample tracking, which allows accurate numerical correction of the rotation errors. The proposed solution provides significant improvement in accuracy and resolution of the 3D refractive index measurement and thus enables investigation of very challenging samples such as photonic fibers.
NCN Preludium 9 – Wojciech Krauze
New approach to determination of three-dimensional refractive index distribution from object projections acquired within a limited angular range:
For years analysis of single biological cells that are subject to different pharmacological substances has constituted the basis for the development of medicine and pharmacology. Until recently, the basic method used for observation of biological cells was classic optical microscopy, where a measured sample is observed visually through the microscopic objective. This method provides only approximated information about how different cell structures absorb light. Over time, information about absorption only was insufficient.
The objective of this project is to develop a new method for investigation of biological cells. The new technique will be based on optical tomography methods. This will allow reconstructing three-dimensional refractive index distribution of biological cells that are placed in a Petri dish, on which these cells are usually grown. Also, an algorithm for calculation of a three-dimensional refractive index distribution from projections that are acquired within a limited angular range will be developed.