Terahertz holography for imaging amplitude and phase objects

Real-time millimeter wave holography with an arrayed detector

Millimeter and terahertz wave imaging has emerged as a powerful tool for applications such as security screening, biomedical imaging, and material analysis. However, intensity images alone are often insufficient for detecting variations in the dielectric constant of a sample, and extraction of material properties without additional phase information requires extensive prior knowledge of the sample. Digital holography provides a means for intensity-only detectors to reconstruct both amplitude and phase images. Here we utilize a commercially available source and detector array, both operating at room temperature, to perform digital holography in real-time for the first time in the mm-wave band (at 290 GHz). We compare the off-axis and phase-shifting approaches to digital holography and discuss their trade-offs and practical challenges in this regime. Owing to the low pixel count, we find phase-shifting holography to be the most practical and high fidelity approach for such commercial mm-wave cameras even under real-time operational requirements.

Making the Invisible Visible: Toward High-Quality Terahertz Tomographic Imaging via Physics-Guided Restoration

Terahertz (THz) tomographic imaging has recently attracted significant attention thanks to its non-invasive, non-destructive, non-ionizing, material-classification, and ultra-fast nature for object exploration and inspection. However, its strong water absorption nature and low noise tolerance lead to undesired blurs and distortions of reconstructed THz images. The diffraction-limited THz signals highly constrain the performances of existing restoration methods. To address the problem, we propose a novel multi-view Subspace-Attention-guided Restoration Network (SARNet) that fuses multi-view and multi-spectral features of THz images for effective image restoration and 3D tomographic reconstruction. To this end, SARNet uses multi-scale branches to extract intra-view spatio-spectral amplitude and phase features and fuse them via shared subspace projection and self-attention guidance. We then perform inter-view fusion to further improve the restoration of individual views by leveraging the redundancies between neighboring views. Here, we experimentally construct a THz time-domain spectroscopy (THz-TDS) system covering a broad frequency range from 0.1 to 4 THz for building up a temporal/spectral/spatial/material THz database of hidden 3D objects. Complementary to a quantitative evaluation, we demonstrate the effectiveness of our SARNet model on 3D THz tomographic reconstruction applications.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11263-023-01812-y.

Single-pixel three-dimensional imaging of the terahertz-wave by complex-field synthesis

We propose a novel three-dimensional (3D) imaging technique by terahertz (THz) waves. Specifically, we modulate the THz wave using diffusers to produce three different speckle-like illumination patterns. The object is raster scanned by the three illumination patterns to generate three raw images via the single-pixel detection method. Subsequently, we synthesize a complex field using the three raw images. Finally, the retrieved image is calculated using the phase correlation of the complex point spread function. The proposed imaging system is simple and highly cost-effective. Therefore, it is a promising technique that can be adopted for industrial inspection and security screening.

Full-field high-resolution terahertz imaging based on a high-resistance silicon solid immersion lens

The spatial resolution of the direct imaging system depends on the wavelength and the numerical aperture. In the terahertz (THz) waveband, the wavelength is relatively large, and the higher numerical aperture of the imaging system usually promises the possibility of achieving higher spatial resolution. Solid immersion technique is an effective method to expand the numerical aperture. We design and fabricate a hemisphere lens with high-resistance silicon to achieve the effect of solid immersion, and obtain full-field, high-resolution focal-plane imaging. The characteristics of the direct refraction imaging and the secondary reflection imaging are analyzed by ray-tracing calculations. And the field curvature of the equivalent object plane and the spot diagram on the vertical image plane of the lens are quantifiably evaluated. It is shown that the secondary reflection imaging can effectively reduce the geometric distortion and achieve more ideal imaging quality. The method of blocking different regions before and after the solid immersion lens is proposed to obtain a clear magnified image of a two-dimensional grating with the period of 300 µm. This method provides a powerful tool for THz full-field microscopic imaging.

Generation of complicated millimeter-wave beams based on a wideband high-transmission polarization-independent complex-amplitude metasurface

Complex amplitude modulation metasurfaces (CAMM) that can independently control both amplitude and phase have fostered a broad research interest worldwide due to its more robust wave manipulation capability than metasurfaces that can only adjust phase. Although many CAMM structures have been reported, they still suffer from limitations such as low transmittance, complicated structure, polarization dependence, high cost, and difficulty in fabrication. This work proposes a high-transmission polarization-independent CAMM operating in an ultra-wide millimeter-wave frequency range from 30 to 50 GHz realized by cost-effective and easily implementable manners. Three CAMMs are designed to generate complicated millimeter-wave beams like holographic imaging beam, Airy beam, and vortex knot beam. The presented simulation and experimental results clearly demonstrate the effectiveness of the CAMMs. This work presents a new paradigm for CAMM that can be readily extended to other frequency bands. It may also advance further applications of millimeter-wave beams in communication, imaging and detection.

Spatial coherence in 2D holography

Holography is a long-established technique to encode an object's spatial information into a lower-dimensional representation. We investigate the role of the illumination's spatial coherence properties in the success of such an imaging system through point spread function and Fourier domain analysis. Incoherent illumination is shown to result in more robust imaging performance free of diffraction artifacts at the cost of incurring background noise and sacrificing phase retrieval. Numerical studies confirm that this background noise reduces image sensitivity as the image size increases, in agreement with other similar systems. Following this analysis, we demonstrate a 2D holographic imaging system realized with lensless, 1D measurements of microwave fields generated by dynamic metasurface apertures.

Route to Intelligent Imaging Reconstruction via Terahertz Nonlinear Ghost Imaging

Terahertz (THz) imaging is a rapidly emerging field, thanks to many potential applications in diagnostics, manufacturing, medicine and material characterisation. However, the relatively coarse resolution stemming from the large wavelength limits the deployment of THz imaging in micro- and nano-technologies, keeping its potential benefits out-of-reach in many practical scenarios and devices. In this context, single-pixel techniques are a promising alternative to imaging arrays, in particular when targeting subwavelength resolutions. In this work, we discuss the key advantages and practical challenges in the implementation of time-resolved nonlinear ghost imaging (TIMING), an imaging technique combining nonlinear THz generation with time-resolved time-domain spectroscopy detection. We numerically demonstrate the high-resolution reconstruction of semi-transparent samples, and we show how the Walsh-Hadamard reconstruction scheme can be optimised to significantly reduce the reconstruction time. We also discuss how, in sharp contrast with traditional intensity-based ghost imaging, the field detection at the heart of TIMING enables high-fidelity image reconstruction via low numerical-aperture detection. Even more striking-and to the best of our knowledge, an issue never tackled before-the general concept of "resolution" of the imaging system as the "smallest feature discernible" appears to be not well suited to describing the fidelity limits of nonlinear ghost-imaging systems. Our results suggest that the drop in reconstruction accuracy stemming from non-ideal detection conditions is complex and not driven by the attenuation of high-frequency spatial components (i.e., blurring) as in standard imaging. On the technological side, we further show how achieving efficient optical-to-terahertz conversion in extremely short propagation lengths is crucial regarding imaging performance, and we propose low-bandgap semiconductors as a practical framework to obtain THz emission from quasi-2D structures, i.e., structure in which the interaction occurs on a deeply subwavelength scale. Our results establish a comprehensive theoretical and experimental framework for the development of a new generation of terahertz hyperspectral imaging devices.

Route to Intelligent Imaging Reconstruction via Terahertz Nonlinear Ghost Imaging

Terahertz (THz) imaging is a rapidly emerging field, thanks to many potential applications in diagnostics, manufacturing, medicine and material characterisation. However, the relatively coarse resolution stemming from the large wavelength limits the deployment of THz imaging in micro- and nano-technologies, keeping its potential benefits out-of-reach in many practical scenarios and devices. In this context, single-pixel techniques are a promising alternative to imaging arrays, in particular when targeting subwavelength resolutions. In this work, we discuss the key advantages and practical challenges in the implementation of time-resolved nonlinear ghost imaging (TIMING), an imaging technique combining nonlinear THz generation with time-resolved time-domain spectroscopy detection. We numerically demonstrate the high-resolution reconstruction of semi-transparent samples, and we show how the Walsh-Hadamard reconstruction scheme can be optimised to significantly reduce the reconstruction time. We also discuss how, in sharp contrast with traditional intensity-based ghost imaging, the field detection at the heart of TIMING enables high-fidelity image reconstruction via low numerical-aperture detection. Even more striking-and to the best of our knowledge, an issue never tackled before-the general concept of "resolution" of the imaging system as the "smallest feature discernible" appears to be not well suited to describing the fidelity limits of nonlinear ghost-imaging systems. Our results suggest that the drop in reconstruction accuracy stemming from non-ideal detection conditions is complex and not driven by the attenuation of high-frequency spatial components (i.e., blurring) as in standard imaging. On the technological side, we further show how achieving efficient optical-to-terahertz conversion in extremely short propagation lengths is crucial regarding imaging performance, and we propose low-bandgap semiconductors as a practical framework to obtain THz emission from quasi-2D structures, i.e., structure in which the interaction occurs on a deeply subwavelength scale. Our results establish a comprehensive theoretical and experimental framework for the development of a new generation of terahertz hyperspectral imaging devices.

Air-Coupled Ultrasound Time Reversal (ACU-TR) For Subwavelength Nondestructive Imaging

Air-coupled ultrasound (ACU) is increasingly used for nondestructive testing (NDT). With ACU, no contact or coupling agent (e.g., water and ultrasound gel) is needed between transducers and test sample, which provides high measurement reproducibility. However, for testing in production, a minimum separation is often necessary between the sample and the transducers to avoid contamination or transducer damage. Due to wave diffraction, the collimation of the ultrasound beam decreases for larger propagation distances, and ACU images become blurred and show lower defect lateral resolution with increasing sample-transducer separation. This is especially critical to thick composites, where large-size planar sources are used to bridge the large ACU transmission loss with good collimation. In this work, ACU reradiation in unbounded media is extended to NDT of multilayered composites. The extended method is named ACU time reversal (ACU-TR) and significantly improves the defect resolution of ACU imaging. With ACU-TR, the complete pressure distribution radiated by large ACU source is measured with point receivers (RXs) in one plane arbitrarily separated from the sample. By applying acoustic holography physics, it is then possible to quantitatively reconstruct the pressure field directly at arbitrary sample defect planes, which compensates for undesired diffraction phenomena and improves minimum detectable defect size, thereby achieving subwavelength lateral resolution. We tested the method on complex wood-based composite samples based on the ACU far-field measurements at a separation of 160 mm between the sample and the RX transducer. With the proposed method, it is possible to detect surface defects as well as inner defects within composite boards. In the future, by using point RX arrays instead of a scanned microphone, both data acquisition and evaluation can be potentially implemented in real time.

Continuous-wave terahertz self-referencing digital holography based on Fresnel's mirrors

Continuous-wave terahertz digital holography (TDH) is a booming full-field phase-contrast imaging method validated in both in-line and Mach-Zehnder off-axis geometries. In this Letter, a self-referencing TDH approach is proposed based on the Fresnel's mirrors, by which the object wavefront is partitioned and reflected. Two beams interfere with each other to form an off-axis hologram. The proposed recording configuration is immune from a superposed twin image and has higher temporal stability than Mach-Zehnder interferometers. To evaluate the phase-contrast imaging performance, different types of samples are measured.

Time-domain terahertz compressive imaging

We present an implementation of the single-pixel imaging approach into a terahertz (THz) time-domain spectroscopy (TDS) system. We demonstrate the indirect coherent reconstruction of THz temporal waveforms at each spatial position of an object, without the need of mechanical raster-scanning. First, we exploit such temporal information to realize (far-field) time-of-flight images. In addition, as a proof of concept, we apply a typical compressive sensing algorithm to demonstrate image reconstruction with less than 50% of the total required measurements. Finally, the access to frequency domain is also demonstrated by reconstructing spectral images of an object featuring an absorption line in the THz range. The combination of single-pixel imaging with compressive sensing algorithms allows to reduce both complexity and acquisition time of current THz-TDS imaging systems.

THz coherent lensless imaging

Imaging with THz radiation has proved an important tool for both fundamental science and industrial use. Here we review a class of THz imaging implementations, named coherent lensless imaging, that reconstruct the coherent response of arbitrary samples with a minimized experimental setup based only on a coherent source and a camera. After discussing the appropriate sources and detectors to perform them, we detail the fundamental principles and implementations of THz digital holography and phase retrieval. These techniques owe a lot to imaging with different wavelengths, yet innovative concepts are also being developed in the THz range and are ready to be applied in other spectral ranges. This makes our review useful for both the THz and imaging communities, and we hope it will foster their interaction.

Iterative phase-retrieval-assisted off-axis terahertz digital holography

In terahertz digital holography, the off-axis configuration is the appropriate choice when the investigated object is non-sparse and complex. The limitation of recording distance in the off-axis configuration restricts the imaging quality. Either low-resolution or spectra overlap can potentially occur. We propose an iterative phase-retrieval approach to improve the quality of reconstruction results obtained from an off-axis hologram. One additional capture of object wave intensity is recorded to perform iterative phase retrieval with off-axis reconstruction as the initial guess. Apodization operation can be applied to the object wave intensity capture to suppress undesired border diffraction effects. The image quality using the proposed method has been improved both from simulation and experimental verification.

Visualization of internal structure and internal stress in visibly opaque objects using full-field phase-shifting terahertz digital holography

We construct a full-field phase-shifting terahertz digital holography (PS-THz-DH) system by use of a THz quantum cascade laser and an uncooled, 2D micro-bolometer array. The PS-THz-DH enables us to separate the necessary diffraction-order image from unnecessary diffraction-order images without the need for spatial Fourier filtering, leading to suppress the decrease of spatial resolution. 3D shape of a visibly opaque object is visualized with a sub-millimeter lateral resolution and a sub-µm axial resolution. Also, the digital focusing of amplitude image enables the visualization of internal structure with the millimeter-order axial selectivity. Furthermore, the internal stress distribution of an externally compressed object is visualized from the phase image. The demonstrated results imply a possibility for non-destructive inspection of visibly opaque non-metal materials.

Hyperspectral data denoising for terahertz pulse time-domain holography

We investigated data denoising in hyperspectral terahertz pulse time-domain holography. Using the block-matching algorithms adapted for spatio-temporal and spatio-spectral volumetric data we studied and optimized parameters of these algorithms to improve phase image reconstruction quality. We propose a sequential application of the two algorithms oriented on work in temporal and spectral domains. Experimental data demonstrate the improvement in the quality of the resultant time-domain images as well as phase images and object's relief. The simulation results are proved by comparison with the experimental ones.

Sparsity-based continuous wave terahertz lens-free on-chip holography with sub-wavelength resolution

We demonstrate terahertz (THz) lens-free in-line holography on a chip in order to achieve 40 μm spatial resolution corresponding to ~0.7λ with a numerical aperture of ~0.87. We believe that this is the first time that sub-wavelength resolution in THz holography and the 40 μm resolution were both far better than what was already reported. The setup is based on a self-developed high-power continuous wave THz laser at 5.24 THz (λ = 57.25 μm) and a high-resolution microbolometer detector array (640 × 512 pixels) with a pitch of 17 μm. This on-chip in-line holography, however, suffers from the twin-image artifacts which obfuscate the reconstruction. To address this problem, we propose an iterative optimization framework, where the conventional object constraint and the L₁ sparsity constraint can be combined to efficiently reconstruct the complex amplitude distribution of the sample. Note that the proposed framework and the sparsity-based algorithm can be applied to holography in other wavebands without limitation of wavelength. We demonstrate the success of this sparsity-based on-chip holography by imaging biological samples (i.e., a dragonfly wing and a bauhinia leaf).

Increasing the resolution of the reconstructed image in terahertz pulse time-domain holography

In this paper, we present a novel numerical approach for increasing the resolution of retrieved images of objects after their diffraction patterns are recorded via terahertz pulse time-domain holography (THz PTDH). THz PTDH allows for spectrally resolved imaging with high spatial resolution and does not require the fine alignment of complex optics in the THz path. The proposed data post-processing method opens up the possibility to reconstruct holograms recorded with spatially restricted THz detectors, and overcome the diffraction limit even for the lower-frequency spectral components. The method involves an iterative procedure of backward-forward wavefront propagation to simulate the field distribution beyond the initially recorded hologram area. We show significant improvement in both the object reconstruction and contrast across the whole spectrum, with qualitative resolution enhancement at lower frequency spectral components.

Video-rate terahertz digital holographic imaging system

Terahertz (THz) imaging has been demonstrated in numerous applications from medical to non-destructive evaluation (NDE), but current systems require expensive components, provide slow frame-rates and low resolutions. THz holography offers a potentially low-cost, high-performance alternative. Here we demonstrate the first full video-rate THz digital holography system at 2.52 THz (118.8 µm) using low-cost optical components. 2D digital reconstructions of samples are performed at frame-rates of 50 Hz - an order of magnitude higher than previous systems, whilst imaging of samples concealed in common packaging types demonstrates suitability for NDE applications. A lateral resolution of 250 µm was determined using a 1951 USAF target.

Terahertz ptychography

We realized a phase retrieval technique using terahertz (THz) radiation as an alternative to THz digital holography, named THz ptychography. Ptychography has been used in x-ray imaging as a groundbreaking improvement of conventional coherent diffraction imaging. Here we show that ptychography can be performed at THz frequencies too. We reconstructed an amplitude and a phase object with both simulated and real data. Lateral resolution accounts to <2λ, while depth variations as low as λ/30 can be assessed.

Bicontrollable terahertz metasurface with subwavelength scattering elements of two different materials

Transmission of a normally incident plane wave through a metasurface with bicontrollable subwavelength scattering elements was simulated using a commercial software. Some pixels composing the H-shaped scattering elements were made of a magnetostatically controllable material whereas the remaining pixels were made of a thermally controllable material, the metasurface designed to operate in the terahertz spectral regime. The copolarized transmission coefficients were found to exhibit stopbands that shift when either a magnetostatic field is applied or the temperature is increased or both. Depending on spectral location of the stopband, either the magnetostatic field gives coarse control and temperature gives fine control or vice versa. The level of magnetostatic control depends on the magnetostatic-field configuration.

Topography of hidden objects using THz digital holography with multi-beam interferences

We present a method for the separation of the signal scattered from an object hidden behind a THz-transparent sample in the framework of THz digital holography in reflection. It combines three images of different interference patterns to retrieve the amplitude and phase distribution of the object beam. Comparison of simulated with experimental images obtained from a metallic resolution target behind a Teflon plate demonstrates that the interference patterns can be described in the simple form of three-beam interference. Holographic reconstructions after the application of the method show a considerable improvement compared to standard reconstructions exclusively based on Fourier transform phase retrieval.

Resolution and quality enhancement in terahertz in-line holography by sub-pixel sampling with double-distance reconstruction

We demonstrate the enhancement of resolution and image quality in terahertz (THz) lens-free in-line digital holography by sub-pixel sampling with double-distance reconstruction. Multiple sub-pixel shifted low-resolution (LR) holograms recorded by a pyroelectric array detector (100 μm × 100 μm pixel pitch, 124 × 124 pixels) are aligned precisely to synthesize a high-resolution (HR) hologram. By this method, the lateral resolution is no more limited by the pixel pitch, and lateral resolution of 150 μm is obtained, which corresponds to 1.26λ with respect to the illuminating wavelength of 118.8 μm (2.52 THz). Compared with other published works, to date, this is the highest resolution in THz digital holography when considering the illuminating wavelength. In addition, to suppress the twin-image and zero-order artifacts, the complex amplitude distributions of both object and illuminaing background wave fields are reconstructed simultaneously. This is achieved by iterative phase retrieval between the double HR holograms and background images at two recording planes, which does not require any constraints on object plane or a priori knowledge of the sample.

Comparison of Thermal Detector Arrays for Off-Axis THz Holography and Real-Time THz Imaging

In terahertz (THz) materials science, imaging by scanning prevails when low power THz sources are used. However, the application of array detectors operating with high power THz sources is increasingly reported. We compare the imaging properties of four different array detectors that are able to record THz radiation directly. Two micro-bolometer arrays are designed for infrared imaging in the 8-14 μm wavelength range, but are based on different absorber materials (i) vanadium oxide; (ii) amorphous silicon; (iii) a micro-bolometer array optimized for recording THz radiation based on silicon nitride; and (iv) a pyroelectric array detector for THz beam profile measurements. THz wavelengths of 96.5 μm, 118.8 μm, and 393.6 μm from a powerful far infrared laser were used to assess the technical performance in terms of signal to noise ratio, detector response and detectivity. The usefulness of the detectors for beam profiling and digital holography is assessed. Finally, the potential and limitation for real-time digital holography are discussed.

Synthetic aperture in terahertz in-line digital holography for resolution enhancement

Terahertz digital holography is a combination of terahertz technology and digital holography. In digital holography, the imaging resolution is the key parameter in determining the detailed quality of a reconstructed wavefront. In this paper, the synthetic aperture method is used in terahertz digital holography and the in-line arrangement is built to perform the detection. The resolved capability of previous terahertz digital holographic systems restricts this technique to meet the requirement of practical detection. In contrast, the experimental resolved power of the present method can reach 125 μm, which is the best resolution of terahertz digital holography to date. Furthermore, the basic detection of a biological specimen is conducted to show the practical application. In all, the results of the proposed method demonstrate the enhancement of experimental imaging resolution and that the amplitude and phase distributions of the fine structure of samples can be reconstructed by using terahertz digital holography.

Real-time terahertz digital holography with a quantum cascade laser

Coherent imaging in the THz range promises to exploit the peculiar capabilities of these wavelengths to penetrate common materials like plastics, ceramics, paper or clothes with potential breakthroughs in non-destructive inspection and quality control, homeland security and biomedical applications. Up to now, however, THz coherent imaging has been limited by time-consuming raster scanning, point-like detection schemes and by the lack of adequate coherent sources. Here, we demonstrate real-time digital holography (DH) at THz frequencies exploiting the high spectral purity and the mW output power of a quantum cascade laser combined with the high sensitivity and resolution of a microbolometric array. We show that, in a one-shot exposure, phase and amplitude information of whole samples, either in reflection or in transmission, can be recorded. Furthermore, a 200 times reduced sensitivity to mechanical vibrations and a significantly enlarged field of view are observed, as compared to DH in the visible range. These properties of THz DH enable unprecedented holographic recording of real world dynamic scenes.

THz holography in reflection using a high resolution microbolometer array

We demonstrate a digital holographic setup for Terahertz imaging of surfaces in reflection. The set-up is based on a high-power continuous wave (CW) THz laser and a high-resolution (640 × 480 pixel) bolometer detector array. Wave propagation to non-parallel planes is used to reconstruct the object surface that is rotated relative to the detector plane. In addition we implement synthetic aperture methods for resolution enhancement and compare Fourier transform phase retrieval to phase stepping methods. A lateral resolution of 200 μm and a relative phase sensitivity of about 0.4 rad corresponding to a depth resolution of 6 μm are estimated from reconstructed images of two specially prepared test targets, respectively. We highlight the use of digital THz holography for surface profilometry as well as its potential for video-rate imaging.

Terahertz in-line digital holography of human hepatocellular carcinoma tissue

Terahertz waves provide a better contrast in imaging soft biomedical tissues than X-rays, and unlike X-rays, they cause no ionisation damage, making them a good option for biomedical imaging. Terahertz absorption imaging has conventionally been used for cancer diagnosis. However, the absorption properties of a cancerous sample are influenced by two opposing factors: an increase in absorption due to a higher degree of hydration and a decrease in absorption due to structural changes. It is therefore difficult to diagnose cancer from an absorption image. Phase imaging can thus be critical for diagnostics. We demonstrate imaging of the absorption and phase-shift distributions of 3.2 mm × 2.3 mm × 30-μm-thick human hepatocellular carcinoma tissue by continuous-wave terahertz digital in-line holography. The acquisition time of a few seconds for a single in-line hologram is much shorter than that of other terahertz diagnostic techniques, and future detectors will allow acquisition of meaningful holograms without sample dehydration. The resolution of the reconstructions was enhanced by sub-pixel shifting and extrapolation. Another advantage of this technique is its relaxed minimal sample size limitation. The fibrosis indicated in the phase distribution demonstrates the potential of terahertz holographic imaging to obtain a more objective, early diagnosis of cancer.

Phase derivative method for reconstruction of slightly off-axis digital holograms

A phase derivative (PD) method is proposed for reconstruction of off-axis holograms. In this method, a phase distribution of the tested object wave constrained within 0 to pi radian is firstly worked out by a simple analytical formula; then it is corrected to its right range from -pi to pi according to the sign characteristics of its first-order derivative. A theoretical analysis indicates that this PD method is particularly suitable for reconstruction of slightly off-axis holograms because it only requires the spatial frequency of the reference beam larger than spatial frequency of the tested object wave in principle. In addition, because the PD method belongs to a pure local method with no need of any integral operation or phase shifting algorithm in process of the phase retrieval, it could have some advantages in reducing computer load and memory requirements to the image processing system. Some experimental results are given to demonstrate the feasibility of the method.

Fast reconstruction of off-axis digital holograms based on digital spatial multiplexing

A method for fast reconstruction of off-axis digital holograms based on digital multiplexing algorithm is proposed. Instead of the existed angular multiplexing (AM), the new method utilizes a spatial multiplexing (SM) algorithm, in which four off-axis holograms recorded in sequence are synthesized into one SM function through multiplying each hologram with a tilted plane wave and then adding them up. In comparison with the conventional methods, the SM algorithm simplifies two-dimensional (2-D) Fourier transforms (FTs) of four N*N arrays into a 1.25-D FTs of one N*N arrays. Experimental results demonstrate that, using the SM algorithm, the computational efficiency can be improved and the reconstructed wavefronts keep the same quality as those retrieved based on the existed AM method. This algorithm may be useful in design of a fast preview system of dynamic wavefront imaging in digital holography.