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We present a new technique for fast form measurement based on imaging with partially coherent illumination. It consists of a 4f-imaging system with a digital micro-mirror device (DMD) located in the Fourier plane of its two lenses. The setup benefits from spatially partially coherent illumination that allows for depth discrimination and a DMD that enables a fast depth scan. Evaluating the intensity contrast, the 3D form of an object is reconstructed. We show that the technique additionally offers extended depth of focus imaging in microscopy and short measurement times of less than a second.

We propose a fast method for measuring optical properties, e.g., the refractive index profile and birefringence, of fibers. It is based on recovering the phase distribution of light refracted by a fiber sample at the recording plane from a single-shot digital hologram. During the recovering process, an optimized approach based on the spatial carrier frequency method was utilized. The proposed approach enhances affects that arise from the limited spatial extent of the bandpass filter associated with the implementation of the spatial carrier frequency method. In contrast to the low spatial resolution of off-axis digital holograms, the method ensures the best utilization of the camera support. From the recovered phase information, the optical path difference is measured; thus, the refractive index profile, the mean refractive index, and the birefringence of isotactic polypropylene (IPP) are determined. Experimental results are given for illustration.

Generally, wave field reconstructions obtained by phase-retrieval algorithms are noisy, blurred, and corrupted by various artifacts such as irregular waves, spots, etc. These distortions, arising due to many factors, such as nonidealities of the optical system (misalignment, focusing errors), dust on optical elements, reflections, and vibration, are hard to localize and specify. It is assumed that there is a cumulative disturbance called “background,” which describes mentioned distortions in the coherent imaging system manifested at the sensor plane. Here we propose a novel iterative phase-retrieval algorithm compensating for these distortions in the optical system. An estimate of this background is obtained via special calibration experiments, and then it is used for the object reconstruction. The algorithm is based on the maximum likelihood approach targeting on the optimal object reconstruction from noisy data and imaging enhancement using a priori information on the object amplitude. In this work we demonstrate the compensation of the distortions of the optical trace for a complex-valued object with a binary amplitude. The developed algorithm results in state-of-the-art filtering, and sharp reconstruction imaging of the object amplitude can be achieved.

For deterministic phase retrieval, the problem of insignificant axial intensity variations upon defocus of a smooth object wavefront is addressed. Our proposed solution is based on the use of a phase diffuser facilitating the formation of a partially-developed speckle field (i.e., a field with both scattered-wave and unperturbed-wave components). The smooth test wavefront impinges first on the phase diffuser producing the speckle field. Then two speckle patterns with different defocus are recorded at the output plane of a 4f-optical filtering setup with a spatial light modulator (SLM) in the common Fourier domain. The local variations of the recorded speckle patterns and the defocus distance approximate the axial intensity derivative which, in turn, is required to recover the wavefront phase via the transport of intensity equation (TIE). The SLM setup reduces the speckle recording time and the TIE allows direct (i.e., non-iterative) calculation of the phase. The pre-requisite partially-developed speckle field in our technique facilitates high image contrast and significant axial intensity variation. Wavefront reconstruction for the 3D refractive test object used demonstrates the effectiveness of the technique.

In this paper, the issue of misalignment in phase retrieval by means of optical linear filtering is discussed. The filtering setup is based on a 4f configuration with a spatial light modulator (SLM) as an active element, located in the Fourier domain. From the analysis, crucial parameters for the alignment procedure of the setup’s optical axes and the center of the SLM are identified. Furthermore, a method to automatically as well as electronically compensate such effects by modifying the phase pattern displayed on the SLM is introduced. Experimental results are presented that validate the compensation approach.

Recently we have proposed the conception of an innovative experimental scheme for phase retrieval from a set of consecutive intensity measurements. It is based on a 4f-optical filter with a reflective phase-only spatial light modulator (SLM) located in the Fourier domain. The main advantage of this scheme is the greatly reduced measurement time since no mechanical shift is required throughout the capturing process. To recover the phase, the captured intensities have been subjected to an iterative process based on generalized projections. Here, we investigate the influence of misalignment, between the optical axes of the setup, on the performance of the iterative scheme's solution. It is demonstrated that if misalignments is present, measurement errors will be propagated in the iterative process and thus affect the accuracy and the rate of convergence of the phase retrieval. The concept is demonstrated by investigating the wavefield diffracted by the U.S. Air Force resolution target. In the case of an aligned setup, it is shown that only 5 planes and 10 iterations give good reconstructions.

We present an experimental configuration for phase retrieval from a set of intensity measurements. The key component is a spatial light modulator located in the Fourier domain of an imaging system. It performs a linear filter operation that is associated to the process of propagation in the image plane. In contrast to the state of the art, no mechanical adjustment is required during the recording process, thus reducing the measurement time considerably. The method is experimentally demonstrated by investigating a wave field scattered by a diffuser, and the results are verified by comparing them to those obtained from standard interferometry.

We present a robust method to inspect a typical composite material constructed of carbon fiber reinforced plastic (CFRP). It is based on optical surface contouring using the spatial light modulator (SLM)-based phase retrieval technique. The method utilizes multiple intensity observations of the wave field, diffracted by the investigated object, captured at different planes along the optical axis to recover the phase information across the object plane. The SLM-based system allows for the recording of the required consecutive intensity measurements in various propagation states across a common recording plane. This overcomes the mechanical shifting of a camera sensor required within the capturing process. In contrast to existing phase retrieval approaches, the measuring time is considerably reduced, since the switching time of the SLM is less than 50 ms. This enables nondestructive testing under thermal load. Experimental results are presented that demonstrate the approach can be used to assess structural properties of technical components made from CFRP.

A technique for enhanced deterministic phase retrieval using a partially developed speckle field (PDSF) and a spatial light modulator (SLM) is demonstrated experimentally. A smooth test wavefront impinges on a phase diffuser, forming a PDSF that is directed to a 4f setup. Two defocused speckle intensity measurements are recorded at the output plane corresponding to axially-propagated representations of the PDSF in the input plane. The speckle intensity measurements are then used in a conventional transport of intensity equation (TIE) to reconstruct directly the test wavefront. The PDSF in our technique increases the dynamic range of the axial intensity derivative for smooth phase objects, resulting in a more robust solution to the TIE. The SLM setup enables a fast and accurate recording of speckle intensity. Experimental results are in good agreement with those obtained using the iterative phase retrieval and digital holographic methods of wavefront reconstruction.