Fast numerical reconstruction technique for high-resolution hybrid holographic microscopy

Multi-Illumination Single-Holographic-Exposure Lensless Fresnel (MISHELF) Microscopy: Principles and Biomedical Applications

Lensless holographic microscopy (LHM) comes out as a promising label-free technique since it supplies high-quality imaging and adaptive magnification in a lens-free, compact and cost-effective way. Compact sizes and reduced prices of LHMs make them a perfect instrument for point-of-care diagnosis and increase their usability in limited-resource laboratories, remote areas, and poor countries. LHM can provide excellent intensity and phase imaging when the twin image is removed. In that sense, multi-illumination single-holographic-exposure lensless Fresnel (MISHELF) microscopy appears as a single-shot and phase-retrieved imaging technique employing multiple illumination/detection channels and a fast-iterative phase-retrieval algorithm. In this contribution, we review MISHELF microscopy through the description of the principles, the analysis of the performance, the presentation of the microscope prototypes and the inclusion of the main biomedical applications reported so far.

Fast numerical propagation in high-NA imaging using the resampling angular spectrum method

Numerical propagation calculation is a fundamental research topic in optical engineering. The standard angular spectrum method (ASM) is accurate but time- and memory-consuming, especially for high-NA systems. In this work, we propose a fast and simple numerical propagation method, the resampling ASM (RS-ASM). Numerical propagation can be accelerated by combining a resampling technique with interpolation methods in the angular spectrum domain of a constrained object at the focal plane. RS-ASM has three main advantages: simple implementation, faster calculation than the standard ASM, and SNR enhancement. Here we validate RS-ASM using theory, simulation and experiment. Using the "bilinear" ASM with a proper resampling factor can result in a speed-up factor of up to 20x (for a transformation from the angular spectrum to the E field) and 4x (for a transformation from E field to the angular spectrum), together with a SNR improvement of approximately 2x. For an application example of Gerchberg-Saxton phase reconstruction, the "bilinear" RS-ASM can converge 2.6x faster than the standard ASM.

Measurement of a Temperature Field Generated by a Synthetic Jet Actuator using Digital Holographic Interferometry

This paper shows the possibility of the measurement of a temperature field generated by heated fluid from a synthetic jet (SJ) actuator. Digital holographic interferometry (DHI) was the main measuring method used for the experiments. A single-projection DHI was used for the visualization of the temperature field as an average temperature along the optical axis. The DHI results are compared with data obtained from constant current anemometry (CCA) experiments for the validation of the method. Principle of 3D temperature distribution using a tomographic approach is also described in this paper. A single SJ actuator, multiple continual nozzle, and the SJ actuator with two output orifices are used as a testing device for the presented experiments. The experimental configuration can measure high-frequency synthetic jets with the use of a single slow-frame-rate camera. Due to the periodic character of the SJ flow, synchronization between the digital camera, and the external trigger driving the phenomenon is performed. This approach can also distinguish between periodic and random parts of the flow.

Amplitude and phase retrieval with simultaneous diversity estimation using expectation maximization

Iterative amplitude and phase retrieval algorithms have been proven to accurately reconstruct arbitrary wavefronts from multiple intensity measurements when system parameters are known exactly, given the ability to induce phase diversity between images. Such sets of intensity images with phase diversity can be generated by moving a lens in the optical system, but any position error on the lens will degenerate the reconstruction result. We demonstrate the use of an expectation-maximization algorithm with Kalman smoothing for recovering both the complex field and the lens position from a stack of intensity images. Our method successfully reduces the mean-squared-error of the estimated wavefront in comparison to an approach without position error estimation. We present and discuss the results of using a Kalman smoother and nonlinear least-squares optimization for the estimation of the moving lens position.

Dual-wavelength digital holography with a single low-coherence light source

We propose a measurement system using dual-wavelength digital holography and low-coherence interferometry to measure micro- and nanostructure surface heights. To achieve an extended axial step-measurement range and better image quality, a single light-emitting diode generates two distinct light sources by filtering different center wavelengths and narrower bandwidths. The system can measure surface profile with higher step heights and lower speckle noise in a large field-of-view. Using single-source lighting and a simple configuration, the method supports compactly configured and lower-cost surface-topography measurement systems applicable in various fields. Experimental results for a standard step sample verify the system's performance.

Coherent diffractive imaging beyond the Fresnel approximation using a deterministic phase-retrieval method with an aperture-array filter

Previously, we have proposed a lensless coherent imaging using a nonholographic and noniterative phase-retrieval method that allows the reconstruction of a complex-valued object from a single diffraction intensity measured with an aperture-array filter. The proof-of-concept experiment of this method has been demonstrated under the Fresnel diffraction approximation. In applications to microscopy, however, the measurement of the diffraction intensity with high numerical aperture beyond the Fresnel approximation is required to obtain the object information at high spatial resolution. Thus we have also presented an extension procedure to apply the method to the cases beyond the Fresnel approximation by means of computer simulations. Here the effectiveness of the procedure is demonstrated by the experiments, in which the reconstruction with about 10 times the resolution of our previous experiment has been achieved and the object information in depth direction has been retrieved.

Lensless phase microscopy using phase retrieval with multiple illumination wavelengths

A phase retrieval method for microscopy using multiple illumination wavelengths is proposed. A fast algorithm suitable for calculations with high numerical aperture is used for the iterative retrieval of the object wavefront. The advantages and limitations of the technique are systematically analyzed and demonstrated by both simulation and experimental results.

High resolution (NA = 0.8) in lensless in-line holographic microscopy with glass sample carriers

For lensless digital in-line holographic microscopy a new state-of-the-art spatial resolution corresponding to an NA of 0.8 is shown based on the tile superposition propagation. The result is proved using a common glass sample carrier with a refraction index of 1.52. Single-shot high-resolution imaging is possible by suppression of coherent reflections in an optimized arrangement using partially coherent laser light illumination.

Superresolution imaging via ptychography

Coherent diffractive imaging of objects is made considerably more practicable by using ptychography, where a set of diffraction patterns replaces a single measurement and introduces a high degree of redundancy into the recorded data. Here we demonstrate that this redundancy allows diffraction patterns to be extrapolated beyond the aperture of the recording device, leading to superresolved images, improving the limit on the finest feature separation by more than a factor of 3.

Single-exposure two-dimensional superresolution in digital holography using a vertical cavity surface-emitting laser source array

We present a new implementation capable of producing two-dimensional (2D) superresolution (SR) imaging in a single exposure by aperture synthesis in digital lensless Fourier holography when using angular multiplexing provided by a vertical cavity surface-emitting laser source array. The system performs the recording in a single CCD snapshot of a multiplexed hologram coming from the incoherent addition of multiple subholograms, where each contains information about a different 2D spatial frequency band of the object's spectrum. Thus, a set of nonoverlapping bandpass images of the input object can be recovered by Fourier transformation (FT) of the multiplexed hologram. The SR is obtained by coherent addition of the information contained in each bandpass image while generating an enlarged synthetic aperture. Experimental results demonstrate improvement in resolution and image quality.

Common-path phase-shifting lensless holographic microscopy

We present an approach capable of high-NA imaging in a lensless digital in-line holographic microscopy layout even outside the Gabor's regime. The method is based on spatial multiplexing at the sample plane, allowing a common-path interferometric architecture, where two interferometric beams are generated by a spatial light modulator (SLM) prior to illuminating the sample. The SLM allows phase-shifting interferometry by phase modulation of the SLM diffracted beam. After proper digital processing, the complex amplitude distribution of the diffracted object wavefront is recovered and numerically propagated to image the sample. Experimental results are reported that validate the proposed method.

Superresolved digital in-line holographic microscopy for high-resolution lensless biological imaging

Digital in-line holographic microscopy (DIHM) is a modern approach capable of achieving micron-range lateral and depth resolutions in three-dimensional imaging. DIHM in combination with numerical imaging reconstruction uses an extremely simplified setup while retaining the advantages provided by holography with enhanced capabilities derived from algorithmic digital processing. We introduce superresolved DIHM incoming from time and angular multiplexing of the sample spatial frequency information and yielding in the generation of a synthetic aperture (SA). The SA expands the cutoff frequency of the imaging system, allowing submicron resolutions in both transversal and axial directions. The proposed approach can be applied when imaging essentially transparent (low-concentration dilutions) and static (slow dynamics) samples. Validation of the method for both a synthetic object (U.S. Air Force resolution test) to quantify the resolution improvement and a biological specimen (sperm cells biosample) are reported showing the generation of high synthetic numerical aperture values working without lenses.

Reconstruction of high-resolution holographic microscopic images

In in-line holographic microscopy a pinhole illuminates an object and a CCD-detector directly records the hologram in a pixel-pitch-dependent distance. A rapidly calculating exact reconstruction technique using a reorganized hologram with a low number of pixels, the tile superposition technique, is presented. The algorithm is applied on imaging of a 2 microm bead cluster, and it is compared with other reconstruction techniques. The high-contrast image corresponds to an NA of 0.7. A full 4 megapixel reconstruction with a resolution approaching the diffraction limit is possible in less than a minute. The technique is a base for high-resolution wide-field imaging by multispot illumination.

High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning

Theoretical analysis shows that, to improve the resolution and the range of the field of view of the reconstructed image in digital lensless Fourier transform holography, an effective solution is to increase the area and the pixel number of the recorded digital hologram. A new approach based on the synthetic aperture technique and use of linear CCD scanning is presented to obtain digital holographic images with high resolution and a wide field of view. By using a synthetic aperture technique and linear CCD scanning, we obtained digital lensless Fourier transform holograms with a large area of 3.5 cm x 3.5 cm (5000 x 5000 pixels). The numerical reconstruction of a 4 mm object at a distance of 14 cm by use of a Rayleigh-Sommerfeld integral shows that a theoretically minimum resolvable distance of 2.57 microm can be achieved at a wavelength of 632.8 nm. The experimental results are consistent with the theoretical analysis.

Exact analysis of the effects of sampling of the scalar diffraction field

If the sampled diffraction pattern due to a planar object is used to reconstruct the object pattern by backpropagation, the obtained pattern is no longer the same as the original. The effect of such sampling on the reconstruction is analyzed. The formulation uses the plane-wave expansion, and therefore the provided solution is exact for wave propagation in media where scalar wave propagation is valid. In contrast to the sampling effects under the Fresnel approximation, the exact solution indicates that there are no modulated replicas of the original object in the reconstructed pattern. Rather, the distortion is in the form of modulated, translated, and dispersed versions of the original.

Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution

A fast algorithm is proposed for the reconstruction of digital holograms that are recorded at high numerical aperture. The method directly evaluates the Rayleigh-Sommerfeld diffraction integral by use of a fast convolution algorithm. A shift parameter that accounts for the coordinate system's transverse displacement of the object plane and the hologram plane is introduced in a discrete representation of the diffraction kernel. Combination of the samplings reconstructed with different shift values yields diffraction-limited resolution over the full field of view. The algorithm is suitable for various applications such as holographic microscopy and metrology. Simulation and experimental results are presented.

Applications of fractional transforms to object reconstruction from in-line holograms

We propose a method for the digital reconstruction of an object whose diffraction pattern has been recorded on a hologram. The fractional Fourier transform is used for the object reconstruction. To determine the position of the object, the fractional order is scanned. The fractional cosine and fractional Hartley transforms are also employed for object reconstruction. These two transforms are real valued and allow the reconstruction to be done with lower computing complexity. Simulations and experimental results are presented.

Penalized-likelihood image reconstruction for digital holography

Conventional numerical reconstruction for digital holography using a filter applied in the spatial-frequency domain to extract the primary image may yield suboptimal image quality because of the loss in high-frequency components and interference from other undesirable terms of a hologram. We propose a new numerical reconstruction approach using a statistical technique. This approach reconstructs the complex field of the object from the real-valued hologram intensity data. Because holographic image reconstruction is an ill-posed problem, our statistical technique is based on penalized-likelihood estimation. We develop a Poisson statistical model for this problem and derive an optimization transfer algorithm that monotonically decreases the cost function at each iteration. Simulation results show that our statistical technique has the potential to improve image quality in digital holography relative to conventional reconstruction techniques.

Fourier algorithm method for reconstruction of large-aperture digital holograms based on phase compensation

To simplify the reconstruction calculation of a large-aperture digital hologram we propose a novel Fourier-transformation reconstruction algorithm. When the reconstructed wave is the same as or similar to the reference wave, the higher-order phase term of reconstruction can be compensated for. For example, the variation between the higher-order phase term and the aperture angle with a different field of view in in-line phase-shifting digital holography is analyzed.

Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm

The phase retrieval algorithm has been used in this paper for whole reconstruction of the optical wave fields. The quantitative information of the phase distribution as well as the intensity distribution of the reconstruction field at different locations along the propagation direction has been achieved from double or multi in-line holograms. Numerical reconstructions of the wave fields from experimentally recorded in-line holograms are presented. This technique can be potentially applied for aberrated wave front analyzing and 3D imaging.

Dynamic digital holographic interferometry with three wavelengths

A color digital holographic interferometry movie was produced by applying the subtraction digital holography method in a quasi-Fourier off-axis experimental setup. The movie was numerically recorded and replayed from three sets of digital holograms obtained with three different laser lines (476 nm, 532 nm, and 647 nm). The movie shows convective flows induced by thermal dissipation in a tank filled with oil.

Optical scanning holography as a technique for high-resolution three-dimensional biological microscopy

The applicability of optical scanning holography (OSH) to the field of microscopic imaging for biological applications is assessed. A generalized mathematical description of OSH that takes into account polarization effects, high numerical apertures, and generalized illumination wave fronts is presented. This description is used to show that the proposed single-beam scanning technique relaxes the restrictions under which OSH functions correctly compared with the conventional double-beam scanning method. It is also shown that, although in general OSH is restricted to thin samples, this condition can be relaxed in nonrefracting fluorescence samples, which are of importance in biological microscopy.

Short-coherence digital microscopy by use of a lensless holographic imaging system

An optical system based on short-coherence digital holography suitable for three-dimensional (3D) microscopic investigations is described. The light source is a short-coherence laser, and the holograms are recorded on a CCD sensor. The interference (hologram) occurs only when the path lengths of the reference and the object beam are matched within the coherence length of the laser. The image of the part of the sample that matches the reference beam is reconstructed by numerical evaluation of the hologram. The advantages of the method are high numerical aperture (this means high spatial resolution), detection of the 3D shape, and a lensless imaging system. Experimental results are presented.

Image formation in phase-shifting digital holography and applications to microscopy

We discuss image formation in phase-shifting digital holography by developing an analytical formulation based on the Fresnel-Kirchhoff diffraction theory. Image-plane position and imaging magnification are derived for general configurations in which a spherical reference is employed. The influences of discrete sampling of the resulting interference patterns by a CCD and numerical reconstruction on qualities of point images are investigated. Dependence of the point images on the ratio of the minimum fringe spacing to pixel pitch of the CCD is numerically analyzed. Two-point resolution and magnification are also investigated as a function of pixel numbers by a simulation using a one-dimensional model. In experiments magnified images of biological objects and a resolution target were reconstructed with the same quality as by conventional microscopy.

Whole optical wavefields reconstruction by digital holography

In this paper, we have investigated on the potentialities of digital holography for whole reconstruction of wavefields. We show that this technique can be efficiently used for obtaining quantitative information from the intensity and the phase distributions of the reconstructed field at different locations along the propagation direction. The basic concept and procedure of wavefield reconstruction for digital in-line holography is discussed. Numerical reconstructions of the wavefield from digitally recorded in-line hologram patterns and from simulated test patterns are presented. The potential of the method for analysing aberrated wave front has been exploited by applying the reconstruction procedure to astigmatic hologram patterns.

A posteriori processing of spatiotemporal digital microholograms

In an accompanying paper [G. Indebetouw and P. Klysubun, J. Opt. Soc. Am. A 18, 319 (2001)], the theoretical background of a spatiotemporal digital microholographic method was described, and some experimental results were presented. Here the usefulness of the method for microholographic imaging of biological specimens such as cells is demonstrated. The vast possibility of a posteriori processing of the microholograms is discussed. Dark-field, phase-contrast, and interference-contrast images, as well as quantitative phase maps, all obtained a posteriori from the same microhologram, are illustrated as examples.

Spatiotemporal digital microholography

We develop the theoretical background of a holographic method in which the hologram is sampled simultaneously in space and in time by a charge-coupled device (CCD) sensor. With the use of temporal heterodyning (rather than spatial heterodyning, which is employed in conventional holography), in-line, single-sideband holograms of fields having an arbitrary degree of spatial coherence are recorded in an exposure time that can theoretically be as short as four frames of the CCD. The method is applied to microholography and is shown to avoid the main drawbacks of conventional holographic microscopy, namely, the need for high-spatial-bandwidth detectors and for a high degree of spatial coherence, which unavoidably leads to speckle noise. The possibility of a posteriori aberration compensation is demonstrated, and experimental results are presented.

Hybrid holographic microscopy: visualization of three-dimensional object information by use of viewing angles

One of the attractive features of hybrid holographic microscopy, in which the hologram of a microscopic object recorded by an image sensor is numerically reconstructed with a computer, is that the three-dimensional (3-D) information of a recorded object is obtained. The 3-D information has often been extracted by means of changing the reconstruction distance in the numerical reconstruction process, but here we describe an alternative technique that allows for variable viewing angles. That is, the perspective from which the object is viewed can be varied. The approximation used enables use of the fast-Fourier-transform algorithm for numerical reconstruction even in the high-resolution case in which the Fresnel approximation is no longer valid. The resolution of the proposed technique is also discussed.

Spatial filtering for zero-order and twin-image elimination in digital off-axis holography

Off-axis holograms recorded with a CCD camera are numerically reconstructed with a calculation of scalar diffraction in the Fresnel approximation. We show that the zero order of diffraction and the twin image can be digitally eliminated by means of filtering their associated spatial frequencies in the computed Fourier transform of the hologram. We show that this operation enhances the contrast of the reconstructed images and reduces the noise produced by parasitic reflections reaching the hologram plane with an incidence angle other than that of the object wave.

Hybrid holographic microscopy free of conjugate and zero-order images

The true image area that can be used for recording microscopic objects in hybrid holographic microscopy can be increased by elimination of the conjugate image and the zero-order image. We therefore added two shutters and one phase modulator to the electro-optical holographic recording system so that we could change the recording parameters and evaluate four methods of eliminating the conjugate image and the zero-order image. We found that the methods that use only the phase modulator require the recording of fewer holograms than do the methods that use the shutters and also provide reconstructed images that are less noisy.