Thomas Dipl.-Ing. Meinecke

Information extraction from digital holograms for particle flow analysis

The goal of our project is to observe the distribution of steady and moving colloidal polystyrene particles within a micro-optofluidic canal system. To this end, we apply a classical in-line holographic setup with a magnifying telescope and a digital camera sensor. The capabilities of numerical hologram reconstruction and the subsequent image processing offer new possibilities concerning the digital hologram analysis. We demonstrate new concepts for a four-dimensional particle flow observation using a captured holographic video as well as the potentials for information extraction.

Two-step phase-shift interferometry with known but arbitrary reference waves: a graphical interpretation

There are many applications in biology and metrology where it is important to be able to measure both the amplitude and phase of an optical wave field. There are several different techniques for making this type of measurement, including digital holography and phase retrieval methods. In this paper we propose an analytical generalization of this two-step phase-shifting algorithm. We investigate how to reconstruct the object signal if both reference waves are different in phase and amplitude. The resulting equations produce two different solutions and hence an ambiguity remains as to the correct solution. Because of the complexity of the generalized analytical expressions we propose a graphical-vectorial method for solution of this ambiguity problem. Combining our graphical method with a constraint on the amplitude of the object field we can unambiguously determine the correct result. The results of the simulation are presented and discussed.

Iterative Phase Retrieval and the Important Role Played by Initial Conditions

Recovering the complex amplitude of a coherent wave field has many important applications in modern optics from practical metrology problems to basic diffraction research. Although several techniques exist, in this manuscript, we will examine the iterative Phase Retrieval (PR) [1-6] exclusively. To recover the phase information with this approach several intensity distributions, diffracted from the object of interest, are recorded at different optical planes. A significant advantage of the PR is the relative simplicity of the optical setup, compared with an interferometric approach. With this approach, noise sources such as an imperfect reference wave can be avoided. PR techniques are an ill-posed inverse problem and hence initial conditions play an important and relatively poorly understood role.

Digital holography and phase retrieval: a theoretical investigation.

Iterative Phase Retrieval (PR) techniques represent an alternative means to Digital Holography (DH) for estimating the complex amplitude of an optical wavefront. To achieve a high-resolution reconstruction from a digital hologram, one must use Phase-Shifting Interferometric (PSI) techniques to remove the DC and twin image terms that are a feature of holographic recordings. Unfortunately this approach is not suitable for imaging dynamic events, since a minimum of 3 sequential captures, are typically required and the scene cannot change during this recording process. PR algorithms may provide a solution to this dynamic imaging problem, however these algorithms provide solutions that are not unique and hence cannot ensure an accurate solution to the problem.

Freeform characterization based on nanostructured diffraction gratings

The in-line characterization of freeform optical elements during the production cycle is challenging. Recently, we presented a compact sensor setup for the characterization of the wavefront generated by freeform optical elements in transmission. The sensor is based on a common-path interferometer consisting of diffractive components and Fourier filtering being adapted to the subsequent numerical post processing. Additionally, it offers several degrees of freedom for enlarging the measurement range of the wavefront gradients. In this contribution, we propose an advanced sensor setup for the measurement of wavefronts generated by freeform elements in reflection. The main advantage is the uni-axial illumination of the test object and the measuring system without the need for conventional beamsplitters. Due to this uni-axial arrangement, the main challenge is to avoid the effect of stray light and back reflections on the measurement signal-to-noise ratio. This is achieved by implementing a highly absorbing amplitude grating based on nanostructured silicon. We demonstrate the experimentally realized measurement system and compare its performance to a commercial Shack-Hartmann sensor.

Wavefront sensing by numerical evaluation of diffracted wavefields

A novel wavefront sensor principle based on diffraction theory and Fourier analysis with a modified angular spectrum propagator has been developed. We observe the propagation of a wavefront behind a two-dimensional cross grating and derive a universal method to extract the phase gradient directly from a captured intensity image. To this end the intensity distribution is analyzed in the spectral domain, and the processing is simplified by an appropriate decomposition of the propagator kernel. This method works for arbitrary distances behind the grating. Our new formulation is verified through simulations. The wavefront generated by a freeform surface is measured by the new method and compared with measurements from a commercial Shack–Hartmann wavefront sensor.

Axial Decorrelation of Paraxial Wavefields: Theory and Experiment

Coherent optical systems are widely used in modern non-contact metrology [1]. To understand and design these systems appropriately, it is of utmost importance to be able to relate the optical field at the input of the system to that at the output of the system. Many different models exist for achieving this goal. Here however, we assume that the paraxial approximation is valid for the analysis. The paraxial model generally strikes a reasonable balance between calculating an accurate solution while maintaining a relatively simple description of the physical process. For general speckle metrology systems, consisting of many lenses, Gaussian apertures, and sections of free space, the ABCD-matrix-diffraction approach by Yura et. al. [2] provides an excellent design framework [3].

A theoretical comparison of Fresnel based digital holography and phase retrieval from the transport of intensity equation

Optical systems that can recover both the amplitude and phase of a scattered wave eld are important for a range of di erent practical imaging and metrology applications. In this manuscript we examine two di erent techniques: (A) Fresnel based digital holography and (B) Teagues transport of intensity phase retrieval technique, using a special analytical function that serves to act as the scattered wave eld we would like to recover. Nowadays both systems use modern CCD or CMOS arrays to make the necessary intensity measurements. In system (A) an ideal plane wave reference eld is required and should overlap, and interfere, with the scattered eld at at the CCD plane. The resulting intensity distribution recorded by the CCD is a digital hologram. If several captures are recorded, where the phase of the reference has been changed (stepped) between captures, it is possible to recover an approximation to the complex amplitude of the scattered wave eld. In system (B) no reference eld is needed, which is a signi cant advantage from a practical implementation point of view. Rather, the intensity of the scattered wave eld has to be measured at two axially displaced planes. We expect that the performance of both systems will be fundamentally limited by at least three separate factors, (i) the nite extent of CCD array, (ii) the nite extent of the CCD pixels which average the light intensity incident upon them, and (iii) the sampling operation which occurs because the intensity is recorded at a set of uniformly displaced discrete locations. In this manuscript, we examine how factors (i) and (iii), e ect the imaging performance of each system by varying the spatial frequency extent of the scattered wave eld. We nd that system A has superior performance compared to system B.