Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors

Practical approach for optimizing off-axis telecentric digital holographic microscope design

Digital holographic microscopy (DHM) has become an attractive imaging tool for the analysis of living cells and histological tissues. Telecentric DHM (TDHM) is a configuration of DHM that reduces the computational demands through a priori aberration corrections. However, TDHM requires a well-aligned optical pipeline to optimize its resolution and image quality (IQ), which has traditionally complicated the alignment process. Derived from optical interference functions, we offer here a set of methodologies to simplify TDHM design and alignment by determining the optimal +1-order position, which depends on the object-reference beam angle and the interference plane rotation angle. The methods are then experimentally tested and verified on a TDHM system by imaging living HeLa cells in suspension.

Linearity and Optimum-Sampling in Photon-Counting Digital Holographic Microscopy

In the image plane configurations frequently used in digital holographic microscopy (DHM) systems, interference patterns are captured by a photo-sensitive array detector located at the image plane of an input object. The object information in these patterns is localized and thus extremely sensitive to phase errors caused by nonlinear hologram recordings (grating profiles are either square or saturated sinusoidal) or inadequate sampling regarding the information coverage (undersampled around the Nyquist frequency or arbitrarily oversampled). Here, we propose a solution for both hologram recording problems through implementing a photon-counting detector (PCD) mounted on a motorized XY translation stage. In such a way, inherently linear (because of a wide dynamic range of PCD) and optimum sampled (due to adjustable steps) digital holograms in the image plane configuration are recorded. Optimum sampling is estimated based on numerical analysis. The validity of the proposed approach is confirmed experimentally.

Dual-directional shearography based on a modified common-path configuration using spatial phase shift

This paper describes a dual-directional shearography system to address the issue of two-dimensional characterization of the surface strain. A common-path configuration coupled with an additional light path is used to provide the shearing in two directions. One of the three interfering beams is shared by both directional shearograms to improve the light efficiency and enhance the robustness of the system. The two directional shearograms are carried by different spatial carriers to distinguish one from the other. The spatial carrier is introduced by the single-aperture-lens Wollaston prism configuration. Rather than the conventional method in which the aperture is fixed at the front focal point of the imaging lens, a general case is considered by introducing a variable distance between the aperture and the imaging lens. The influence of the aperture-lens distance on the spatial carrier is then analyzed, which enables the separate control of the shearing amount and the spatial carrier. Two types of dual-directional shearography are presented to demonstrate the feasibility and the flexibility of the system. Type I is the simultaneous dual lateral shearography in orthogonal directions, and Type II is the simultaneous lateral and radial shearography. The spatial carrier introduced by the single-aperture-lens Wollaston prism configuration is discussed, and a configuration in which the Wollaston prism and the aperture are located at different sides of the lens is recommended for further shearography applications.

From speckle pattern photography to digital holographic interferometry [Invited]

Speckles are inherently an interference phenomenon produced when an optically rough surface or a turbulent medium introduces some degree of randomness to a reflected or a transmitted electromagnetic field. Speckles are often nuisance in coherent image formation. Speckle patterns are however a useful tool for displacement and deformation as well as vibration and stress analysis. The development of speckle photography to speckle interferometry and digital holographic interferometry is described in this paper.

High-precision three-dimensional shape reconstruction via digital refocusing in multi-wavelength digital holography

Three-dimensional (3D) shape reconstructions and metrology measurements are often limited by depth-of-field constraints. Current focus-detection-based techniques are insufficient to profile out-of-focus 3D objects with high axial accuracy. Extended-focus imaging (EFI) techniques can improve the range and precision of such measurements. By incorporating digital refocusing with multiwavelength interferometry, a holographic imaging solution is presented in this paper to accurately measure 3D objects over a large depth range. Accuracy and repeatability of the proposed EFI technique are validated by digital simulations and refocusing experiments. A reconstruction example demonstrates the feasibility of high-precision 3D measurements of objects deeper than the system's classical depth of field.

Phase noise optimization in temporal phase-shifting digital holography with partial coherence light sources and its application in quantitative cell imaging

In temporal phase-shifting-based digital holographic microscopy, high-resolution phase contrast imaging requires optimized conditions for hologram recording and phase retrieval. To optimize the phase resolution, for the example of a variable three-step algorithm, a theoretical analysis on statistical errors, digitalization errors, uncorrelated errors, and errors due to a misaligned temporal phase shift is carried out. In a second step the theoretically predicted results are compared to the measured phase noise obtained from comparative experimental investigations with several coherent and partially coherent light sources. Finally, the applicability for noise reduction is demonstrated by quantitative phase contrast imaging of pancreas tumor cells.

Two-wavelength method for endoscopic shape measurement by spatial phase-shifting speckle-interferometry

A two-wavelength method for endoscopic topography reconstruction is introduced that can be applied to out-of-plane sensitive electronic-speckle-pattern interferometry systems based on rigid endoscope imaging systems. The surface measurement is performed by detection of the phase-difference distribution affected by a change in the applied laser wavelength. Furthermore, the off-axis endoscopic illumination geometry is taken into account by an approximation. Experimental results of the characterization of the endoscopic surface reconstruction technique and the measurement accuracy obtained are described and discussed. Finally, the applicability of the method is demonstrated with results from the topographic reconstruction of a free-form surface.

Complex-wave retrieval from a single off-axis hologram

We present a new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera. First, we retrieve the complex object wave in the acquisition plane from the hologram's samples. In a second step, if required, we propagate the wave front by using a digital Fresnel transform to achieve proper focus. This algorithm is sufficiently general to be applied to sophisticated optical setups that include a microscope objective. We characterize and evaluate the algorithm by using simulated data sets and demonstrate its applicability to real-world experimental conditions by reconstructing optically acquired holograms.

Speckle interferometry: three-dimensional deformation field measurement with a single interferogram

An electronic speckle interferometer, arranged for out-of-plane sensitivity and with an off-axis reference beam to produce spatial phase bias, is used for three-dimensional deformation field measurements. The complex amplitude of the object wave is calculated by application of a Fourier-transform method to a single interferogram. The change in phase after object deformation yields the out-of-plane component of the displacement field. The two in-plane components are obtained by cross correlation of subimages of the reconstructed object wave's intensity, a method that is also referred to as digital speckle photography. The Fourier-transform algorithm is extended and modified, leading to random measurement errors that are below widely accepted theoretical limits and also to an extended measuring range. These properties and the mutually combined information improve the accuracy of both methods compared with their usual single implementation. The performance is evaluated in experiments with pure out-of-plane, pure in-plane, and combined deformations and compared with theoretical values. An example of a practical application is given.

Spatial versus temporal phase shifting in electronic speckle-pattern interferometry: noise comparison in phase maps

Temporal and spatial phase shifting in electronic speckle-pattern interferometry are compared quantitatively with respect to the quality of the resultant deformation phase maps. On the basis of an analysis of the noise in sawtooth fringes a figure of merit is defined and measured for various in-plane and out-of-plane sensitive electronic speckle-pattern interferometry configurations. Varying quantities like the object-illuminating intensity, the beam ratio, the speckle size and shape, and the fringe density allows characteristic behaviors of both phase-shifting methods to be explored.

Complex division as a common basis for calculating phase differences in electronic speckle pattern interferometry in one step

We point out that all formulas for calculating the phase map ofobject deformations in one step can be described by the same simpleformalism of a complex division.

Spatial phase shifting for pure in-plane displacement and displacement-derivative measurements in electronic speckle pattern interferometry (ESPI)

Hitherto no method, to our knowledge, was known to incorporate spatial phase shifting for the measurement of pure in-plane displacements. We demonstrate that the modified Duffy two-aperture configuration [Opt. Lett. 22, 1958 (1996)], which is sensitive to only the in-plane displacement component and offers increased sensitivity, lends itself to measurement with spatial phase shifting. The configuration can also be used for obtaining displacement derivatives by the introduction of shear with the tilt of a mirror.