A method is given for the evaluation, in transmission electron microscopy, of the amplitude and phase from the intensity distribution of an electron micrograph. The method requires a minimum of two micrographs taken under different defocus conditions. The iterative scheme requires only the relative defocus between micrographs, and the procedure is valid both in bright-field and dark-field microscopy for any specified coherence of the electron source. Assumptions on the scattering properties of the specimen, such as the weak-phase-weak-amplitude object, are not required. For a complete determination of the amplitude-phase distribution for electron transmission through the specimen, the electron micrograph must be corrected for the effect of lens aberrations and defocusing to give the electron wavefunction immediately after transmission; only in the case of a weak-phase object can this wavefunction be directly related to the projected potential distribution in the object. Inelastic electron scattering is explicitly omitted from the analysis presented.

Comment onA method for the solution of the phase problem in electron microscopy

Shearography is a full-field speckle interferometric technique used to determine surface displacement derivatives. For an interferometric technique, shearography is particularly resilient to environmental disturbances and has hence become an invaluable measurement tool outside of the optics laboratory. Furthermore, the inclusion of additional measurement channels has turned shearography from a qualitative inspection tool into a system suitable for quantitative surface strain measurement. In this review article we present a comprehensive overview of the technique, describing the principle of operation, optical configurations, image processing algorithms and applications, with a focus on more recent technological advances.

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Shearography technology and applications: a review

We present a detailed analysis of image formation in digital Fresnel holography. The mathematical modeling is developed on the basis of Fourier optics, making possible the understanding of the different influences of each of the physical effects invoked in digital holography. Particularly, it is demonstrated that spatial resolution in the reconstructed plane can be written as a convolution product of functions that describe these influences. The analysis leads to a thorough investigation of the effect of the width of the sensor, the surface of pixels, the numerical focusing, and the aberrations of the reference wave, as well as to an explicit formulation of the Shannon theorem for digital holography. Experimental illustrations confirm the proposed theoretical analysis.

General theoretical formulation of image formation in digital Fresnel holography

The recording of the volume speckle field from an object at different planes combined with the wave propagation equation allows the reconstruction of the wavefront phase and amplitude without requiring a reference wave. The main advantage of this single-beam multiple-intensity reconstruction (SBMIR) technique is the simple experimental setup because no reference wave is required as in the case of holography. The phase retrieval technique is applied to the investigation of diffusely transmitting and reflecting objects. The effects of different parameters on the quality of reconstructions are investigated by simulation and experiment. Significant enhancements of the reconstructions are observed when the number of intensity measurements is 15 or more and the sequential measurement distance is 0.5 mm or larger. Performing two iterations during the reconstruction process using the calculated phase also leads to better reconstruction. The results from computer simulations confirm the experiments. Analysis of transverse and longitudinal intensity distributions of a volume speckle field for the SBMIR technique is presented. Enhancing the resolution method by shifting the camera a distance of a half-pixel in the lateral direction improves the sampling of speckle patterns and leads to better quality reconstructions. This allows the possibility of recording wave fields from larger test objects.

Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field

In this paper, a novel accurate deformation distribution measurement technique by using sampling moire method is proposed. The basic principle and an experimental result of a steel beam in symmetric three-point bending are reported. In this method, the measurement area of a target is attached with an adhesive tape of a known pitch grating firstly. An ordinary CCD camera is installed on a fixed point to record the image during deformation. The captured image is analyzed by performing easy image processing, i.e., thinning-out and linear interpolation, to obtain the multiple phase-shifted moire patterns. Then, the phase distribution of the moire pattern can be calculated using phase-shifting method. Finally, the deformation distribution is calculated by the grating pitch times the phase difference of before deformation and after deformation. The experimental results in symmetric three-point bending test show that the displacement of the steel beam at loading point agree well with those obtained by an accurate displacement sensor. The average error of displacement measurement is less than 4 μm when 2 mm grating pitch is used, and it corresponds to 1/500 of the grating pitch accuracy. This indicates that noncontact deformation distribution measurement is possible by simple and easy procedure with high accuracy, high speed, and low cost for the structural evaluation of infrastructures.

Sampling Moiré Method for Accurate Small Deformation Distribution Measurement

Speckle pattern decorrelation reduces the accuracy of interferometric shape and deformation measurements. We introduce a technique for the reduction of speckle noise in digital holography. The method is not based on classical filtering techniques such as median filters. Instead it utilizes the shift theorem of the Fourier transform. For this method several holograms of the same object under test are recorded. The reconstruction leads to a set of object wave fields with different speckle patterns. A proper averaging procedure, taking into account the properties of the wrapped phases, leads to an improvement of the accuracy in the resulting phase difference. The theory of the applied method is described and our first results for technical components with an improvement of accuracy up to 1/57 of the wavelength are presented.

Improvement of accuracy in digital holography by use of multiple holograms

A miniaturized sensor head for endoscopic measurements based on digital holography is described. The system was developed to measure the shape and the three-dimensional deformation of objects located at places to which there is no access by common measurement systems. A miniaturized optical sensor, including a complete digital holographic interferometer with a CCD camera, is placed at the end of a flexible endoscope. The diameter of the head is smaller than 10 mm. The system enables interferometric measurements to be made at speeds of as many as five reconstructions per second, and it can be used outside the laboratory under normal environmental conditions. Shape measurements are performed with two wavelengths for contouring, and the deformation is measured by digital holographic interferometry. To obtain full three-dimensional data in displacement measurements we illuminate the object sequentially from three different illumination directions. To increase the lateral resolution we use temporal phase shifting.

Miniaturized digital holography sensor for distal three-dimensional endoscopy.

Spatial light modulators (SLMs) can be used to optically reconstruct the complex amplitude of a wavefield. The reconstructed wavefield in the far-field is corrupted by effects arising from the non-ideal modulation properties and the discrete nature of SLMs. These effects are regarded as drawbacks and particularly disturb the visual impression and reduce the light efficiency of the reconstruction in the region of interest. In this paper we present a novel method to improve the quality of the reconstructed light field by eliminating the higher diffraction orders and by modifying hologram data based on the characteristic modulation properties of the SLM. We achieve the elimination of the higher orders optically using only one lens in a 4f configuration with an appropriate amplitude mask inserted in the Fourier plane. For compensating the non-ideal modulation properties of the SLM we characterize the device to alter the digital hologram data in an appropriate way. The basic principle of this technique and its experimental verification are described.

https://iopscience.iop.org/article/10.1088/1464-4258/11/10/105405/pdf

Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator

Analytical expressions to describe the phase gradient of monochromatic light by means of the three-dimensional intensity distribution are derived. With these formulas it is shown that the two-dimensional phase gradient in a plane can be completely determined from noninterferometric intensity measurements if the light propagates strictly in one direction. The analytical expressions are verified by means of numerical investigations on simulated speckle fields, and the results are discussed with respect to common deterministic phase retrieval approaches.

Ervin Kolenovic

Papers

Improvement of accuracy in digital holography by use of multiple holograms

Miniaturized digital holography sensor for distal three-dimensional endoscopy.

Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator

Correlation between intensity and phase in monochromatic light

Speckle shearography using a multiband light source