Correction of anisoplanatic phase errors in digital holography

The quality of coherent images computed from digital holography or heterodyne array data is sensitive to phase errors of the reference and/or object beams. A number of algorithms exist for correcting phase errors in or very near the hologram plane. In the case of phase errors introduced a nonnegligible distance away from hologram plane, the resulting imagery exhibits anisoplanatism. A feature of coherent imaging is that such phase errors may be corrected by simply propagating the aberrated fields (from the object) from the hologram plane to the plane where the phase errors were introduced and applying the phase-error correction algorithms to the fields in that plane. We present experimental results that demonstrate correction of such anisoplanatic phase errors.     

Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: influence of digital phase mask position

Introducing a microscope objective in an interferometric setup induces a phase curvature on the resulting wavefront. In digital holography, the compensation of this curvature is often done by introducing an identical curvature in the reference arm and the hologram is then processed using a plane wave in the reconstruction. This physical compensation can be avoided, and several numerical methods exist to retrieve phase contrast images in which the microscope curvature is compensated. Usually, a digital array of complex numbers is introduced in the reconstruction process to perform this curvature correction. Different corrections are discussed in terms of their influence on the reconstructed image size and location in space. The results are presented according to two different expressions of the Fresnel transform, the single Fourier transform and convolution approaches, used to propagate the reconstructed wavefront from the hologram plane to the final image plane.     

Spatial filtering in digital holographic microscopy

Abstract

An optical system based on digital holography suitable for microscopic investigations is described. A lensless digital hologram of the object under test is recorded on a CCD faceplate. The reference point source and the object are equidistant from the CCD. The point source for the illumination of the transparent microscopic object is located in another plane some millimetres behind the object. For digital reconstruction of the wavefronts the Sommerfeld propagation relation is used. The particular recording arrangement allows one to perform spatial filtering. Examples of amplitude filtering are presented.     

Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope

Single-exposure on-line (SEOL) digital holography is a recently proposed technique for monitoring, visualization, and recognition of three-dimensional (3D) objects. In contrast to traditional multi-exposure on-line digital holography, it uses only one exposure, which makes it particularly suitable for imaging and recognizing moving micro-organisms. However, the cost of using only one exposure is the superposition of a conjugate image on the desired reconstructed image. The influence of the conjugate image on the visualization and recognition performance is investigated. The conditions for which the cross-talk noise induced by the conjugate image is negligible are derived. It is demonstrated that with conditions common in imaging of microscopic 3D biological objects, SEOL digital holography is highly tolerant of cross-talk noise induced by the conjugate image.     

Aberration compensation of holographic particle images using digital holographic microscopy

Characterisation of small and large-scale vortices in turbulent flows demands a system with high spatial resolution. The measurement of high spatial resolution, three-dimensional vector displacements in fluid mechanics using holography, is usually hampered by aberration. Aberration poses some problems in particle image identification due to low fidelity of real image reconstruction. Phase mismatch between the recording and the reconstruction waves was identified as the main source of aberration in this study. This paper demonstrates how aberration compensation can be achieved by cross-correlating the complex amplitude of an aberrated reconstructed object with the phase conjugate of a known reference object in the plane of the hologram (frequency space). Results favourably show significant increase in Strehl ratio and suppression of background noise that are more pronounced for particle images of 10 and 5 microns. It is clear from the work conducted that wavefront aberration measurement and compensation of holographic microscopic objects are now possible with the use of a variant digital holographic microscope.     

单次相移数字全息中相移值的提取

为了消除相移误差对数字全息中再现像的像质的影响,本文时单次相移数字全息进行了研究.基于相位统计特性,提出了一种有效消除相移误差的新方法,该方法能够对任意未知相移量进行提取,并利用数字全息图所有抽样点的强度偏差之和作为评价标准,通过逐步改变计算得到的初始相移值来寻找正确的实际相移角.计算机模拟得到了很好的再现结果,证明了该方法的可行性和有效性.     

Optical sectioning by optical scanning holography and a Wiener filter

I propose a novel digital technique that reduces defocus noise in the reconstruction of the sectional images from the complex hologram of a thick object. In three-dimensional microscopy applications of holography, reducing the defocused light scattered from outside the focused plane is an important issue. In this technique I first extract a complex hologram of a thick object by using optical scanning holography. After that, I separate the power spectra of the focused and defocused planes from the complex hologram. Finally, I construct a Wiener filter by use of the power spectra. The Wiener filter reduces the defocus noise in the reconstruction of the sectional image of the focused plane. Computer simulations show that the proposed Wiener filter reduces the defocus noise and provides the sectional images.     

Fourier-domain digital holographic optical coherence imaging of living tissue

Digital holographic optical coherence imaging is a full-frame coherence-gated imaging approach that uses a CCD camera to record and reconstruct digital holograms from living tissue. Recording digital holograms at the optical Fourier plane has advantages for diffuse targets compared with Fresnel off-axis digital holography. A digital hologram captured at the Fourier plane requires only a 2D fast Fourier transform for numerical reconstruction. We have applied this technique for the depth-resolved imaging of rat osteogenic tumor multicellular spheroids and acquired cross-section images of the anterior segment and the retinal region of a mouse eye. A penetration depth of 1.4 mm for the tumor spheroids was achieved.     

Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging

An approach is proposed for removing the wavefront curvature introduced by the microscope imaging objective in digital holography, which otherwise hinders the phase contrast imaging at reconstruction planes. The unwanted curvature is compensated by evaluating a correcting wave front at the hologram plane with no need for knowledge of the optial parameters, focal length of the imaging lens, or distances in the setup. Most importantly it is shown that a correction effect can be obtained at all reconstruction planes. Three different methods have been applied to evaluate the correction wave front and the methods are discussed in detail. The proposed approach is demonstrated by applying digital holography as a method of coherent microscopy for imaging amplitude and phase contrast of microstructures.     

Application of the correlation coefficient method for determination of the focal plane to digital particle holography

The correlation coefficient (CC) method, which was proposed by our research group, is applied to digital particle holography to locate the focal plane of particles. It uses the fact that the CC is maximum at the focal plane. The factors influencing this method are discussed with a numerical simulation of holograms. For real holograms, the Wiener filter was proposed to process both recorded holograms and reconstructed images. The application results using the dot array target showed that the Wiener filter is a very effective tool for processing holography-related images. The effects of the dot size and the object distance on the errors in the determination of the focal plane by the CC method were investigated by using the calibration target.     

小波变换在数字全息中的应用

数字全息是通过数字重构来同时获取被测物强度与相位,但记录时的激光散斑效应和重构时的零级衍射斑成为了这种方法的瓶颈。将小波变换引入数字全息,可直接消除零级衍射像,无需相移,也不需要采集多幅图像;小波非线性滤波器还可消除散斑噪声。模拟和实验结果表明,小波分析的引入,可以消除零级衍射影响,改善图像质量,提高测试分辨率。     

Quantization noise and its reduction in lensless Fourier digital holography

Digital holography is an imaging technique that enables recovery of topographic 3D information about an object under investigation. In digital holography, an interference pattern is recorded on a digital camera. Therefore, quantization of the recorded hologram is an integral part of the imaging process. We study the influence of quantization error in the recorded holograms on the fidelity of both the intensity and phase of the reconstructed image. We limit our analysis to the case of lensless Fourier off-axis digital holograms. We derive a theoretical model to predict the effect of quantization noise and we validate this model using experimental results. Based on this, we also show how the resultant noise in the reconstructed image, as well as the speckle that is inherent in digital holography, can be conveniently suppressed by standard speckle reduction techniques. We show that high-quality images can be obtained from binary holograms when speckle reduction is performed.     

Parallel three-step phase-shifting digital holography

We propose parallel three-step phase-shifting digital holography as a technique capable of noiseless instantaneous measurement of three-dimensional objects based on phase-shifting interferometry. The proposed digital holography carries out three-step phase shifting at the same time by using a phase-shifting array device located in the reference beam. The array device has a periodic three-step phase distribution, and its configuration is simplified compared with that required for conventional parallel phase-shifting digital holography. Therefore the optical system of the proposed parallel phase-shifting digital holography is more suitable for the realization of the proposed holography. We conduct both a numerical simulation and a preliminary experiment. The results of the simulation and experiment agree well with those of the conventional phase-shifting method and are superior to the results obtained by conventional digital holography by using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.     

Studies of digital microscopic holography with applications to microstructure testing

We propose an in-line digital microscopic holography system for testing of microstructures. With the incorporation of a long-distance microscope with digital holography, the system is capable of imaging test microstructures with high resolution at sufficient working distances to permit good illumination of samples. The system, which was developed in an in-line configuration, achieves high imaging capacity and exhibits properties that are favorable for micromeasurement. We demonstrate the performance of the system with experiments to determine the displacement of a silicon microcantilever and with investigations of the microscopic resolution capability.     

Pixel-size-maintained image reconstruction of digital holograms on arbitrarily tilted planes by the angular spectrum method

We present an effective method for the pixel-size-maintained reconstruction of images on arbitrarily tilted planes in digital holography. The method is based on the plane wave expansion of the diffraction wave fields and the three-axis rotation of the wave vectors. The images on the tilted planes are reconstructed without loss of the frequency contents of the hologram and have the same pixel sizes. Our method shows good results in the extreme cases of large tilting angles and in the region closer than the paraxial case. The effectiveness of the method is demonstrated by both simulation and experiment.     

Holographic digital Fourier microscopy for selective imaging of biological tissue

We present an application of digital Fourier holography for selective imaging of scatterers with different sizes in turbid media such as biological tissues. A combination of Fourier holography and high‐resolution digital recording, digital Fourier microscopy (DFM) permits crucial flexibility in applying filtering to highlight scatterers of interest in the tissue. The high‐resolution digital hologram is a result of the collation of Fourier holographic frames to form a large‐size composite hologram. It is expected that DFM has an improved signal‐to‐noise ratio as compared to conventional direct digital imaging, e.g., phase microscopy, as applied to imaging of small‐size objects. The demonstration of the Fourier filtering capacity of DFM using a biological phantom represents the main focus of this article. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 14, 253–258, 2004; Published online inWiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20031     

Encrypting three-dimensional information with digital holography

A method for optical encryption of three-dimensional (3D) information by use of digital holography is presented. A phase-shifting interferometer records the phase and amplitude information generated by a 3D object at a plane located in the Fresnel diffraction region with an intensity-recording device. Encryption is performed optically by use of the Fresnel diffraction pattern of a random phase code. Images of the 3D object with different perspectives and focused at different planes can be generated digital or optically after decryption with the proper key. Experimental results are presented.     

General theoretical formulation of image formation in digital Fresnel holography

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.     

Underwater digital holography for studies of marine plankton

Conventional and digital holographies are proving to be increasingly important for studies of marine zooplankton and other underwater biological applications. This paper reports on the use of a subsea digital holographic camera (eHoloCam) for the analysis and identification of marine organisms and other subsea particles. Unlike recording on a photographic film, a digital hologram (e-hologram) is recorded on an electronic sensor and reconstructed numerically in a computer by simulating the propagation of the optical field in space. By comparison with other imaging techniques, an e-hologram has several advantages such as three-dimensional spatial reconstruction, non-intrusive and non-destructive interrogation of the recording sampling volume and the ability to record holographic videos. The basis of much work in optics lies in Maxwell's electromagnetic theory and holography is no exception: we report here on two of the numerical reconstruction algorithms we have used to reconstruct holograms obtained using eHoloCam and how their starting point lies in Maxwell's equations. Derivation of the angular spectrum algorithm for plane waves is provided as an exact method for the in-line numerical reconstruction of digital holograms. The Fresnel numerical reconstruction algorithm is derived from the angular spectrum method. In-line holograms are numerically processed before and after reconstruction to remove periodic noise from captured images and to increase image contrast. The ability of the Fresnel integration reconstruction algorithm to extend the reconstructed volume beyond the recording sensor dimensions is also shown with a 50% extension of the reconstruction area. Finally, we present some images obtained from recent deployments of eHoloCam in the North Sea and Faeroes Channel.     

Pulsed digital holography for deformation measurements on biological tissues

Digital holograms are recorded of biological tissues by use of a Q-switched double-pulsed ruby laser. An image-plane digital holography setup is used with a CCD camera for capturing two holograms with a short time separation (20-800 mus). Subtraction of the phase distribution in two digital holograms yield a fringe phase map that shows the change in deformation of the tissue surface between the recordings. Experiments are performed on tissue from a pig that was excited by a short-shock pulse and on a human hand that was excited by sinusoidal stimulation. Results when the object is imaged through an endoscope are also presented. The technique could be an approach for measuring parameters like elasticity on biological tissues.