Reconstructed Object Wave Research Articles

Automatic phase aberration compensation for digital holographic microscopy based on phase variation minimization.

We propose a numerical and totally automatic phase aberration compensation method in digital holographic microscopy. The phase aberrations are extracted in a nonlinear optimization procedure in which the phase variation of the reconstructed object wave is minimized. Not only phase curvature but also high-order aberrations could be corrected without extra devices. The correction is directly carried out with the wrapped phase map, which is not affected by phase unwrapping or fitting errors. Numerical simulation proves that the proposed method is more accurate than the conventional surface fitting method without selecting a cell-free background. Experimental results demonstrate the availability of the proposed method in real-time analysis of living cells.

Focusing properties of Lucas sieves

A kind of optical diffractive element named photon sieve, which is essentially Fresnel zone plate in which the transmissive rings are replaced with a large number of randomly distributed isolated pinholes, can be used to focus X-ray and extreme ultraviolet lithography spectrum into spots with sizes smaller than the diameter of the smallest circular pinhole. However, both the traditional photon sieves and Fibonacci sieves have no more than two axial foci. In order to break this limitation, the Lucas sequence is introduced into the design of photon sieves, and thus producing four axial foci. With respect to the previous Fibonacci sequence, Lucas sequence has the same recursion relation as well as the same eigenvalue of golden mean =(1 + 5)/2. The only difference between them is the first two initial seeds. Based on Fresnel-Kichhoff diffraction theory, the simulation results show that there exist four focal spots with approximately equal intensity along the optical axis on condition that the hole diameters are set to be 1.16 times the underlying Fresnel zone width. Then in order to verify the validity of our proposed model, a Lucas sieve of diameter 12.11 mm and referred focal length 180 mm is fabricated by photolithography and its focusing properties are precisely measured by the in-line phase-shifting digital holography. In experiment, a quarter wave plate is used to realize two-step phase-shift interferences, and obtain the quad-focal length by auto-focusing algorithm in holography. Meanwhile, the quad-focal spots can also be calculated through the diffraction propagation of reconstructed object wave. Compared with the theoretical values, the measurement results indicate that the maximum deviation of quad-focal lengths is less than 0.9%, and the relative errors of the full width at half maximum of four Airy spots are all less than 5%. The experimental results agree well with the theoretical analysis results. Owing to the advantages of small volume, little weight and easy processing, Lucas sieve has great potential in X-ray microscopy, array imaging for living biological cell and especially in the next generation of synchrotron light sources.

Autofocusing and resolution enhancement in digital holographic microscopy by using speckle-illumination

Sequential speckle illumination has been incorporated into digital holographic microscopy (DHM) for autofocusing and resolution enhancement. For autofocusing, the image plane is numerically determined by searching for the minimal deviation among the reconstructed images obtained by different speckle illuminations and propagating the object wave to the image plane accordingly. Furthermore, an iterative method is used to synthesize the numerical aperture from the reconstructed object waves obtained by different speckle illuminations, in order to achieve resolution enhancement. The feasibility of the proposed method is demonstrated by both simulation and experiment.

Optical voice recorder by off-axis digital holography.

An optical voice recorder capable of recording and reproducing propagating sound waves by using off-axis digital holography, as well as quantitative visualization, is presented. Propagating sound waves temporally modulate the phase distribution of an impinging light wave via refractive index changes. This temporally modulated phase distribution is recorded in the form of digital holograms by a high-speed image sensor. After inverse propagation using Fresnel diffraction of a series of the recorded holograms, the temporal phase profile of the reconstructed object wave at each three-dimensional position can be used to reproduce the original sound wave. Experimental results using a tuning fork vibrating at 440 Hz and a human voice are presented to show the feasibility of the proposed method.

Method for calculating the dynamic phase delay in holographic interferometry without phase unwrapping

A method for calculating the difference between two arbitrary spatial phase distributions reconstructed from digital holograms is presented. The method is promising for application in double-exposure digital holographic interferometry, especially for the evaluation of phase variations in heavily noised or speckle-structure-modulated digital holograms, because it does not use the phase unwrapping procedure for each reconstructed spatial phase distribution. Instead, by analogy with classical double-exposure holographic interferometry, an interference pattern formed by two reconstructed object waves is calculated first. The interferogram thus obtained is then processed as a digital hologram by the same method that was used for reconstruction of physically recorded holograms. The advantages of the proposed method are demonstrated by both by the numerical computation of the difference of the phase distributions of speckle-structure-modulated wavefronts and the experimental observation of the laser-induced temperature gradients in an aqueous solution of a photosensitizer.

Advanced split-illumination electron holography without Fresnel fringes

Advanced split-illumination electron holography was developed by employing two biprisms in the illuminating system to split an electron wave into two coherent waves and two biprisms in the imaging system to overlap them. A focused image of an upper condenser-biprism filament was formed on the sample plane, and all other filaments were placed in its shadow. This developed system makes it possible to obtain precise reconstructed object waves without modulations due to Fresnel fringes, in addition to holograms of distant objects from reference waves.

Autofocusing of digital holographic microscopy based on off-axis illuminations

An auto-focusing method for digital holographic microscopy has been proposed by employing two off-axis illumination beams. When specimens are illuminated by two plane waves in different directions, it is found that the farther the reconstruction plane is from the image plane, the wider the two reconstructed images are separated from each other. Thus, the image plane can be determinated by finding the minimum of the variation between the two reconstructed object waves on both the amplitude and phase distributions. The feasibility of the proposed method is demonstrated by the corresponding simulation and experiment.

Optimum aberration coefficients for recording high-resolution off-axis holograms in a Cs-corrected TEM

Amongst the impressive improvements in high-resolution electron microscopy, the Cs-corrector also has significantly enhanced the capabilities of off-axis electron holography. Recently, it has been shown that the signal above noise in the reconstructable phase can be significantly improved by combining holography and hardware aberration correction. Additionally, with a spherical aberration close to zero, the traditional optimum focus for recording high-resolution holograms ("Lichte's defocus") has become less stringent and both, defocus and spherical aberration, can be selected freely within a certain range. This new degree of freedom can be used to improve the signal resolution in the holographically reconstructed object wave locally, e.g. at the atomic positions. A brute force simulation study for an aberration corrected 200 kV TEM is performed to determine optimum values for defocus and spherical aberration for best possible signal to noise in the reconstructed atomic phase signals. Compared to the optimum aberrations for conventional phase contrast imaging (NCSI), which produce "bright atoms" in the image intensity, the resulting optimum values of defocus and spherical aberration for off-axis holography enable "black atom contrast" in the hologram. However, they can significantly enhance the local signal resolution at the atomic positions. At the same time, the benefits of hardware aberration correction for high-resolution off-axis holography are preserved. It turns out that the optimum is depending on the object and its thickness and therefore not universal.

Real-time monitoring of the solution concentration variation during the crystallization process of protein-lysozyme by using digital holographic interferometry

We report a real-time measurement method of the solution concentration variation during the growth of protein-lysozyme crystals based on digital holographic interferometry. A series of holograms containing the information of the solution concentration variation in the whole crystallization process is recorded by CCD. Based on the principle of double-exposure holographic interferometry and the relationship between the phase difference of the reconstructed object wave and the solution concentration, the solution concentration variation with time for arbitrary point in the solution can be obtained, and then the two-dimensional concentration distribution of the solution during crystallization process can also be figured out under the precondition which the refractive index is constant through the light propagation direction. The experimental results turns out that it is feasible to in situ, full-field and real-time monitor the crystal growth process by using this method.

Resolution improvement of digital holographic images based on angular multiplexing with incoherent beams in orthogonal polarization states

We present a method to improve the resolution of digital holographic images based on angular multiplexing with incoherent beams from two orthogonal polarized components of natural light. Two incoherent subholograms are synchronously recorded by two pairs of incoherent object waves and reference waves with orthogonal polarization states, in which the object is illuminated by two incoherent beams from different directions. The increase in resolution is obtained through phase correction and superposition of two reconstructed object waves. Experimental results show that the resolution and quality of the reconstructed image can be effectively improved.

Algorithm of the non-interpolation wave-front reconstruction of the color digital holography

In the research of the color digital holography and digital holography measurement with multi-wavelength illumination, how to avoid the interpolation error in the wave-front reconstruction with variable magnification is an important subject to be studied. Since the Fresnel diffraction integral can be expressed as Fourier transformation as well as convolution form, there are two reconstruction approaches, one is the relay algorithm which divides the reconstruction distance into two parts, the other is the convolution algorithm which uses the spherical wave as reconstruction wave. In this paper, the two algorithms are theoretically analyzed and experimentally studied, and the condition satisfying the sampling theorem for the reconstruction calculation is discussed. The results show that the convolution approach satisfies the sampling theorem more readily, while higher quality reconstructed object wave field can be obtained with the convolution approach.

Phase correction and resolution improvement of digital holographic image in numerical reconstruction with angular multiplexing

A phase correction method is presented to remove the phase slope of the sub-holograms caused by the multi-direction illumination on object in digital holography. To improve the resolution of the reconstructed holographic images, two sub-holograms are recorded by using angular multiplexing and their phase slope parameter is obtained by theoretical analysis. Introducing a phase correction parameter to this phase slope, the ideal complex reconstructed image can be obtained by superposing the reconstructed object wave fields of the two sub-holograms. Experimental results demonstrate that the resolution of the reconstructed image can be effectively enhanced.

Automated three-dimensional tracking of living cells by digital holographic microscopy

Digital holographic microscopy (DHM) enables a quantitative multifocus phase contrast imaging that has been found suitable for technical inspection and quantitative live cell imaging. The combination of DHM with fast and robust autofocus algorithms enables subsequent automated focus realignment by numerical propagation of the digital holographically reconstructed object wave. In combination with a calibrated optical imaging system, the obtained propagation data quantify axial displacements of the investigated sample. The evaluation of quantitative DHM phase contrast images also enables an effective determination of lateral cell displacements. Thus, 3-D displacement data are provided. Results from investigations on sedimenting red blood cells and HT-1080 fibrosarcoma cells in a collagen tissue model demonstrate that DHM enables marker-free automated quantitative dynamic 3-D cell tracking without mechanical focus adjustment.

Phase-shifting digital holography in image reconstruction

A phase-shifting digital holography scheme developed to investigate internal defects in artworks is described. Phase-shifting is utilized to obtain a clear reconstructed object wave from a rough surface texture. A reverse-transform algorithm is employed to reconstruct the object wave on its original position of unknown distance or the imaging position from the object wave information on the holographic plane. To get the clearest reconstruction the exact registration of the unknown distance is determined by applying the intensity sum as the auto-focusing function. The spatial resolution of the reconstruction image is also investigated for a variety of affecting factors. Laboratory results of reconstruction images under deformation are presented.

Correction of wave-front errors caused by the slight tilt of a reference beam in phase-shifting interferometry.

In standard phase-shifting interferometry the reference beam is supposed to be a plane wave exactly normal to the recording plane. A slight tilt of the reference beam, however, may occur in practice, and it will introduce phase distortion for the reconstructed object wave front. The effects of reference wave tilt on the wave reconstruction are analyzed, and a novel method is proposed to correct the errors caused by this tilt. This method is simple and convenient without the need of any additional optical devices and measurements, and it can be used for both the smooth and the diffuse object surfaces. The effectiveness of this method is verified by a series of computer simulations.

Simultaneous measurement of displacement and its spatial derivatives with a digital holographic method

A digital holographic method for simultaneous measurement of the displacement and its spatial derivatives is described. In this method, two holograms are first recorded in the undeformed and deformed states of the specimen; then two object waves related to the two states of the specimen are numerically reconstructed. The phase maps of the displacement and its derivatives can be generated simultaneously from these two reconstructed object waves with a numerical method. This proposed method offers a simple experimental setup, flexibility in handing the data, and high quality of phase maps.

Sensitivity adjustable contouring by digital holography and a virtual reference wavefront

A new method of contouring using digital holography and a virtual reference wavefront is reported. In this method, an object wave is first recorded and then digitally reconstructed. At the same time, a reference wave is digitally introduced to interfere with the reconstructed object wave to form a contour pattern. Since the form or curvature of the reference wave can be arbitrarily designed and artificially generated by a computer, the contouring sensitivity (the depth interval) can be easily adjusted for different purpose. The effectiveness of this method has been verified by computer simulations with both the conventional off-axis hologram and the phase-shifting hologram. The simplicity of optical setup and the unique ability of changing contouring sensitivity in this technique make it attractive potential in practical measurements.

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.

Exit wave reconstruction using a conventional transmission electron microscope

Exit wave reconstruction of a focus series of Ge in [110] using the PAM–MAL algorithm was performed on a conventional electron microscope. The simulated images using the reconstructed object wave match very well with those obtained experimentally. Amplitudes from the complex wave function were extracted by means of local Fourier transformation. Crystal thickness and tilt were determined locally by quantitative comparison of the reconstructed amplitudes with amplitudes from multislice calculations. Detailed analysis yields the quasicoherent imaging approach used in the PAM–MAL algorithm to produce the largest error in the analysis. For the Ge crystal specimen parameters were quantified to spatial frequencies of 5 nm−1. In the case of an object producing strong diffracted beams, the reconstruction may fail because the quasicoherent approximation will not describe correctly the nonlinear image formation.

Generation of squeezed states by holography

A scheme for generating squeezed-state light by combining the reconstructed object wave of a hologram and its phase-conjugate wave is suggested. The method of generating the light is relatively simple, and good squeezing is possible, as our calculations show.