Off-axis Digital Holography Research Articles

High-precision phase extraction of biological tissues based on lateral shear with zig-zag scanning in off-axis digital holography

We propose a method combining off-axis digital holography (DH) with one-dimensional (1D) lateral shear based on Zig-zag scanning to extract high-precision phase distribution of biological tissues. Firstly, object wavefront is reconstructed using the numerical reconstruction algorithm from digital hologram. Secondly, Zig-zag scanning is introduced to reorder the object wavefront from matrix to 1D vector, allowing the retrieved phase value to change smoothly without value saltation. Then, 1D lateral shear process is performed to acquire the shear vector, from which the phase difference vector is extracted by arctangent calculation. Given the small amount of shear, the phase difference vector is extracted without unwrapping process. Afterwards, the phase vector is obtained through numerical accumulation. Finally, the real phase distribution matrix is retrieved by inverse Zig-zag scanning. The proposed method has high precision in phase extraction of biological tissues. The simulated and experimental results demonstrate the feasibility and precision superiority of the proposed method.

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

Windowing the Fourier spectra is usually used to filter the zero-order and twin image in off-axis digital holography (DH). However, during the filtering process, manual operation is often needed. In our work, we present an automatic filtering method. The filtered zone is a circle in the Fourier domain. The point with the highest intensity in the +1st order is chosen as its center, the location of which is related to the angle between the reference and the objective beams. Considering that the size of the zero-order spectra is twice of that of the +1st order, the radius of the circle is set to be a third of the distance between the circle center and the very center of the Fourier spectra. With this filtering method, the desired spectra can be filtered out automatically and noniteratively. This method has been tested and validated on several samples. Compared with the iterative filtering method, it spends about 2‰ of the processing time and obtains the reconstructed images with high similarity. This approach can result in real-time use of the off-axis DH and holographic microscopy.

Super-Bandwidth Two-Step Phase-Shifting Off-Axis Digital Holography by Optimizing Two-Dimensional Spatial Frequency Sampling Scheme

The presence of the auto correlation and twin cross correlation noises restrict the available spatial bandwidth of the holographic microscopy to much less than the available bandwidth of the digital sensor. Therefore, in order to record the same image area as conventional 2D intensity imaging techniques, several images should be taken. We present two-step phase-shifting off-axis digital holography with maximum space-bandwidth product for three-dimensional (3D) digital holography. Removing the autocorrelation term using a two-step phase-shifting technique significantly increases the available bandwidth for off-axis interferometry. An optimizing super-diagonal two-dimensional (2D) spatial frequency sampling scheme at the sub-Nyquist frequency is employed for performing off-axis interferometry in the absence of the autocorrelation term. The spatial bandwidth of the proposed two-step phase-shifting technique is 400% of that in square scheme off-axis digital holography. Experimental results demonstrate the feasibility of this technique in extracting the 3D morphology of transparent microscopic objects with a larger bandwidth.

Variable Wavefront Curvature Phase Retrieval Compared to Off-Axis Holography and Its Useful Application to Support Intraoperative Tissue Discrimination

Quantitative phase imaging can reveal morphological features without having to stain the biological sample. This property has important implications for intraoperative applications since the time spent during histopathology can be reduced from a few minutes to a few seconds. However, most common quantitative phase imaging techniques are based on the interferometric principle, which makes them more prone to disturbing environmental influences, such as temperature drift and air turbulence. In the last decade, with the advance of computing power, many different iterative quantitative phase imaging techniques, which only require the recording of the diffracted wavefield, and therefore offer increased robustness towards environmental disturbances, have been proposed. These are particularly well-suited for the application outside the well-controlled lab environment such as an operating theatre. The optical performance of our developed iterative phase retrieval method based on variable wavefront curvature will be evaluated by reference to off-axis digital holography and applied for intraoperative discrimination of tissue.

Variable Wavefront Curvature Phase Retrieval Compared to Off-Axis Holography and Its Useful Application to Support Intraoperative Tissue Discrimination

Quantitative phase imaging can reveal morphological features without having to stain the biological sample. This property has important implications for intraoperative applications since the time spent during histopathology can be reduced from a few minutes to a few seconds. However, most common quantitative phase imaging techniques are based on the interferometric principle, which makes them more prone to disturbing environmental influences, such as temperature drift and air turbulence. In the last decade, with the advance of computing power, many different iterative quantitative phase imaging techniques, which only require the recording of the diffracted wavefield, and therefore offer increased robustness towards environmental disturbances, have been proposed. These are particularly well-suited for the application outside the well-controlled lab environment such as an operating theatre. The optical performance of our developed iterative phase retrieval method based on variable wavefront curvature will be evaluated by reference to off-axis digital holography and applied for intraoperative discrimination of tissue.

Phase sensitivity of off-axis digital holography.

In off-axis digital holography, the Fourier transform-based algorithm is commonly used for signal processing. Here, we derive the theoretical phase sensitivity of this algorithm, which can be calculated from a single 2D hologram. This algorithm sensitivity represents the best achievable sensitivity of a system using this algorithm. Our derivation treats the signal in its most general form, considering non-uniform illumination and the effect of sideband filtering. As a result, phase sensitivity varies spatially, determined by local signal-to-noise ratio. Sensitivity expressions for both shot noise and uniform noise models are given. These results are validated with simulations and experiments. Significantly, this theoretical sensitivity can serve as a baseline metric for assessing performance of a phase-imaging system, such as experimental sensitivity and hardware stability, which are critical for high-sensitivity quantitative phase imaging. In addition, the results are equally applicable to other interferometric techniques with similar interferogram patterns and signal processing algorithms.

Characteristics of vibration frequency measurement based on sound field imaging by digital holography

We present the characteristics of indirect frequency measurement system based on off-axis digital holography (DH) for vibrating objects, which works on phase change characteristics of a medium where sound wave propagates. The sound field measurement method using off-axis DH already proposed by the author’s group is applied to the measurement of vibration frequency of arbitrary sound sources. In DH based sound imaging for frequency measurement, object wave passes near to vibrating object and the interference patterns are recorded in digital holograms as a function of time. After using inverse Fresnel calculation, acousto-optic data processing, and Fourier analysis, vibration frequency of an object of interest can be measured. In this paper, the measurement capability of vibration frequency for different objects and quantitative characteristics of the sound power are evaluated experimentally. The frequency range of the experimental results are from hundreds Hz to tens of kHz that covers audible range. The comparison with microphone recording and the analysis have also been carried out to check the strength and stability of the proposed scheme.

Highly stable wide-field common path digital holographic microscope based on a Fresnel biprism interferometer

Quantitative phase imaging (QPI) of biological cells and tissues is an important technique useful in the determination of many biophysical parameters such as morphology, refractive index, thickness, cell dry mass, hemoglobin concentration, etc. Off-axis digital holography has been ideal for the QPI of microscopic specimens, but it has lower temporal stability compared to on-axis and common path digital holographic microscopes, which offer higher temporal stability. In this paper, we present a very simple, easy to align yet highly stable common path digital holographic microscope based on a Fresnel biprism interferometer. The system uses a biprism to divide the incoming beam into reference and object beams without the loss of optical power, unlike diffraction phase microscopy. Two methods are proposed, one by utilizing the spatial filtering mode and the other by the self-referencing mode. It offers the advantage that the reference beam can be easily created simply by translating the object in the focal plane of the microscopic objective or by spatially filtering one of the object beams in the Fourier domain. The proposed setup offers no power loss and a high phase stability of approximately 0.006 rad (6 mrad) without using any vibration isolation. The experiments on industrial and biological samples are reported demonstrating its application both for static and dynamic samples.

Quantifying single plasmonic nanostructure far-fields with interferometric and polarimetric k-space microscopy

Optically resonant nanoantennae are key building blocks for metasurfaces, nanosensors, and nanophotonic light sources due to their ability to control the amplitude, phase, directivity, and polarization of scattered light. Here, we report an experimental technique for the full recovery of all degrees of freedom encoded in the far-field radiated by a single nanostructure using a high-NA Fourier microscope equipped with digital off-axis holography. This method enables full decomposition of antenna-physics in its multipole contributions and gives full access to the orbital and spin angular momentum properties of light scattered by single nano-objects. Our results demonstrate these capabilities through a quantitative assessment of the purity of the “selection rules” for orbital angular momentum transfer by plasmonic spiral nanostructures.

Continuous-wave off-axis and in-line terahertz digital holography with phase unwrapping and phase autofocusing

Continuous-wave terahertz digital holography is a practical tool to obtain the complete wave-front information of a sample in the terahertz region that has offered unique advantages in various fields. The propagation distance plays a decisive role in the numerical reconstruction of both in-line and off-axis digital holograms. Only when a terahertz hologram is propagated back to a focal object plane can the authentic amplitude and phase distribution be reconstructed, which is actually a troublesome task. In this manuscript, the combination of hologram enhancement, spectrum filtering, phase retrieval and phase unwrapping algorithms is illustrated and organized to benefit the decision-making process of the autofocusing method not only for the amplitude distribution but also for the phase image. To guarantee the accuracy of the autofocusing results, the noise of the hologram, the intrinsic twin image in the amplitude and phase results and the wrapped ambiguity in the phase distribution are suppressed or lessened by using the four techniques stated above. The focused amplitude and unwrapped phase distributions of the sample are reconstructed, and experimental verification confirms that the present hybrid autofocusing method is a feasible, effective and promising technology with broad application prospects.

High-precision spherical subaperture stitching interferometry based on digital holography

A novel subaperture stitching interferometry is proposed to measure the high-numerical-aperture sphericity for workshop testing, which combined digital holographic technology, subaperture stitching algorithm and systemic aberration calibration. Each subaperture is fleetly measured by the digital off-axis holography with a single shot so that the influence of measurement environment can be effectively reduced. The high-precision full aperture shape is obtained by stitching these subapertures, meanwhile, the subaperture alignment errors and the systemic aberration can be correctly compensated by the method of least-squares with the Zernike polynomial fitting. The approach is verified by testing three spherical surfaces, including a concave sphere, a convex sphere, and a hemisphere, in general environment. Moreover, the measurement results are compared with full aperture results by using a large aperture interferometer of Zygo and stitching result by using a subaperture stitching interferometer of QED. The results based on the proposed approach are consistent with the commercial interferometers. Specifically, the relative deviations of RMS are 0.009 λ and 0.02 λ for testing a concave and a convex spheres, and that is 0.011 λ for testing a hemisphere. Our method not only has the comparable measurement accuracy with the commercial interferometers but also is more robust, feasibility and inexpensive than other subaperture stitching interferometry. We provide an anti-interference way to test spherical surfaces in workshop environment.

Simultaneous two-wavelength tri-window common-path digital holography

Two-wavelength common-path off-axis digital holography is proposed with a tri-window in a single shot. It is established using a standard 4f optical image system with a 2D Ronchi grating placed outside the Fourier plane. The input plane consists of three windows: one for the object and the other two for reference. Aided by a spatial filter together with two orthogonal linear polarizers in the Fourier plane, the two-wavelength information is encoded into a multiplexed hologram with two orthogonal spatial frequencies that enable full separation of spectral information in the digital Fourier space without resolution loss. Theoretical analysis and experimental results illustrate that our approach can simultaneously perform quantitative phase imaging at two wavelengths.

Comparison of the refocus criteria for the phase, amplitude, and mixed objects in digital holography

For digital holographic applications, we have studied the refocus criteria operating on the high-pass filtered and the nonfiltered reconstructed complex amplitudes (RCAs), respectively. A set of 10 criteria have been investigated for applications on phase, amplitude, and mixed objects in off-axis digital holography. Without filtering, the criteria always exhibit opposite behaviors for amplitude and phase objects and cannot work normally for mixed ones. With high-pass filtering on the RCAs, most of the criteria can be used regardless of the phase or amplitude nature of the objects without noises. But, in real applications with noises, they show different robustness. The investigations indicate that the criterion based on the integrated amplitude shows good exactitude and strong robustness, exhibiting a great potential in real applications, especially for multiobject systems.

Off-axis digital holography with multiplexed volume Bragg gratings.

We report on an optical imaging design based on common-path off-axis digital holography, using a multiplexed volume Bragg grating. In the reported method, a reference optical wave is made by deflection and spatial filtering through a volume Bragg grating. This design has several advantages, including simplicity, stability, and robustness against misalignment.

Real-Time Amplitude and Phase Imaging of Optically Opaque Objects by Combining Full-Field Off-Axis Terahertz Digital Holography with Angular Spectrum Reconstruction

Terahertz digital holography (THz-DH) has the potential to be used for non-destructive inspection of visibly opaque soft materials due to its good immunity to optical scattering and absorption. Although previous research on full-field off-axis THz-DH has usually been performed using Fresnel diffraction reconstruction, its minimum reconstruction distance occasionally prevents a sample from being placed near a THz imager to increase the signal-to-noise ratio in the hologram. In this article, we apply the angular spectrum method (ASM) for wavefront reconstruction in full-filed off-axis THz-DH because ASM is more accurate at short reconstruction distances. We demonstrate real-time phase imaging of a visibly opaque plastic sample with a phase resolution power of λ/49 at a frame rate of 3.5 Hz in addition to real-time amplitude imaging. We also perform digital focusing of the amplitude image for the same object with a depth selectivity of 447 μm. Furthermore, 3D imaging of visibly opaque silicon objects was achieved with a depth precision of 1.7 μm. The demonstrated results indicate the high potential of the proposed method for in-line or in-process non-destructive inspection of soft materials.

Dual-plane slightly off-axis digital holography based on a single cube beam splitter.

In order to recover the holographic object information, a method based on the recording of two digital holograms, not only at different planes but also in a slightly off-axis scheme, is presented. By introducing a π-phase shift in the reference wave, the zero-order diffracted term and the twin image are removed in the frequency domain during the processing of the recorded holograms. We show that the zero-order elimination by the phase-shifted holograms is better than working with weak-order beam and average intensity removal methods. For recording experimentally two π-shifted holograms at different planes slightly off-axis, a single cube beam splitter is used. Computer simulations and experimental results, carried out to validate our proposal, show a high accuracy of π/14 that can be comparable with phase-shifting digital holography. For high fringe spacing, our proposal could be applied in electron holography, avoiding high voltage in a biprism.

Steep large film thickness measurement with off-axis terahertz digital holography reconstructed by a direct Fourier and Hermite polynomial.

In this paper, we enhance the steepness of film thickness edge in terahertz off-axis digital holography by employing a reconstruction method based on a direct Fourier and Hermite polynomial function. The method is applied to samples of 110 μm and 80 μm step heights to extract the phase images in real time. Use of this method reduces the resolution factor by around one half, representing around a 50% decrease in critical dimension as compared with conventional measurements. The method is very promising and opens the route to potential applications in the fields of microlithography.

One-Shot Measurement of the Three-Dimensional Electromagnetic Field Scattered by a Subwavelength Aperture Tip Coupled to the Environment

Near-field scanning optical microscopy (NSOM) achieves subwavelength resolution by bringing a nanosized probe close to the surface of the sample. This extends the spectrum of spatial frequencies that can be detected with respect to a diffraction limited microscope. The interaction of the probe with the sample is expected to affect its radiation to the far field in a way that is often hard to predict. Here we address this question by proposing a general method based on full-field off-axis digital holography microscopy which enables to study in detail the far-field radiation from a NSOM probe as a function of its environment. A first application is demonstrated by performing a three-dimensional (3D) tomographic reconstruction of light scattered from the subwavelength aperture tip of a NSOM, in free space or coupled to transparent and plasmonic media. A single holographic image recorded in one shot in the far field contains information on both the amplitude and the phase of the scattered light. This is suffi...

Single-shot dual-wavelength in-line and off-axis hybrid digital holography

We propose an in-line and off-axis hybrid holographic real-time imaging technique. The in-line and off-axis digital holograms are generated simultaneously by two lasers with different wavelengths, and they are recorded using a color camera with a single shot. The reconstruction is carried using an iterative algorithm in which the initial input is designed to include the intensity of the in-line hologram and the approximate phase distributions obtained from the off-axis hologram. In this way, the complex field in the object plane and the output by the iterative procedure can produce higher quality amplitude and phase images compared to traditional iterative phase retrieval. The performance of the technique has been demonstrated by acquiring the amplitude and phase images of a green lacewing's wing and a living moon jellyfish.

Spatially incoherent common-path off-axis color digital holography.

We describe a new method for recording spatially incoherent common-path off-axis color digital holograms. We present the theoretical and experimental evidence to demonstrate an incoherent common-path off-axis color digital holographic (ICOCH) system capable of capturing information from three-dimensional color objects under incoherent illumination, both in transmission and reflection modes. Fresnel incoherent correlation holography (FINCH), a common-path system, is a frequently used incoherent holography technique. Our proposed system is conceptually similar to an advanced form of FINCH; moreover, it has three advantages over this advanced form of FINCH. First, removal of the spatial light modulator makes our system simpler and more cost-effective. Second, removal of the polarizer or analyzer allows for greater light throughput. Third, the off-axis optical configuration enables separation of zero-order and twin images with only a single exposure per color rather than requiring three exposures per color for in-line holography FINCH. Therefore, we believe that this simple and cost-effective system with high light throughput can acquire incoherent holograms for different colors involving single exposure for each color, which makes the ICOCH system suitable for many applications.