Multidimensional imaging using compressive Fresnel holography

Tunable image projection spectrometry

We present tunable image projection spectrometry (TIPS), a Fourier-domain line-scan spectral imager with a tunable compression ratio. Compared to state-of-the-art spatial-domain pushbroom hyperspectral cameras, TIPS requires much fewer measurements and provides a higher light throughput. Using a rotating Dove prism and a cylindrical field lens, TIPS scans an input scene in the Fourier domain and captures a subset of multi-angled one-dimensional (1D) en face projections of the input scene, allowing a tailored data compression ratio for a given scene. We demonstrate the spectral imaging capability of TIPS with a hematoxylin and eosin (H&E) stained pathology slide. Moreover, we showed the spectral information obtained can be further converted to depths when combining TIPS with a low-coherence full-field spectral-domain interferometer.

High-quality compressed sensing imaging with limited detector bits using sparse measurements and multiple dithers

High-flux measurement characteristics of compressed sensing (CS) imaging causes the imaging system prone to be disturbed by quantization. To realize high-quality CS imaging with limited detector bits, an improved imaging method combining sparse measurements and multiple dithers is proposed to reduce the dynamic range of the measured signals and increase that of effective detection. Simulations and experiments show that compared with traditional CS imaging, the proposed system decreases reconstruction errors caused by quantization distortions and may reduce the required number of detector bits to 1. The effects of detector noise and system parameters are discussed to validate the feasibility and performance of this method.

Snapshot hyperspectral light field tomography

We present snapshot hyperspectral light field tomography (Hyper-LIFT), a highly efficient method in recording a 5D (x, y, spatial coordinates; θ, φ, angular coordinates; λ, wavelength) plenoptic function. Using a Dove prism array and a cylindrical lens array, we simultaneously acquire multi-angled 1D en face projections of the object like those in standard sparse-view computed tomography. We further disperse those projections and measure the spectra in parallel using a 2D image sensor. Within a single snapshot, the resultant system can capture a 5D data cube with 270 × 270 × 4 × 4 × 360 voxels. We demonstrated the performance of Hyper-LIFT in imaging spectral volumetric scenes.

Influence of sparse constraint functions on compressive holographic tomography

In this paper, we quantified and analyzed the impact of the l₁ norm and total variation (TV) norm sparse constraints on the reconstruction quality under different interlayer spacings, sampling rates, and signal-to-noise ratios. For high-quality holograms, the results of compressive-sensing reconstruction using l₁ norm achieved higher quality than those by the TV norm. In contrast, for low-quality holograms, the quality of TV-norm-based reconstruction results was relatively stable and better than that of l₁ norm. In addition, we explained why interlayer spacing cannot be smaller and recommend the use of axial resolution of the digital holography system as the interlayer spacing. The conclusions are valuable in the choice of sparse constraints in compressive holographic tomography.

Axial resolution analysis in compressive digital holographic microscopy

Digital holographic microscopy with compressive sensing (CDHM) has successfully achieved tomography and has been applied in many fields. However, the enhancement of axial resolution in CDHM remains to be elucidated. By deducing accurate formulas for the lateral and axial resolutions without paraxial approximation, we quantized the elongation effect of a digital holography (DH) system in this study. Thus, we revealed that the elongation effect, which is affected only by the system's numerical aperture (NA), is an inherent property of DH systems. We present a detailed analysis herein on the physical significance of the coherence parameter, which is the ratio of a system's limit axial resolution to the interlayer spacing more thoroughly than in previous research. Further, we achieved the tomography of a fiber by using a DH system with a 10 × microscope, with CS to eliminate the elongation effect, and experimentally validated our theoretical results. By applying these theoretical guidelines, we distinguished crossed fibers at distances of 36.4 μm and 48.5 μm, respectively, using the same experimental setup. There would be potential applications of this theory in tomography and observation of microscale objects in the areas of biological and fluid.

Single-shot optical multiple-image encryption by jointly using wavelength multiplexing and position multiplexing

A single shot large-capacity optical multiple-image encryption method based on wavelength multiplexing and position multiplexing is proposed. In the encryption process of the proposed method, multiple plane waves of different wavelengths are adopted to illuminate secret images that are placed at different positions along the optical axis. All the secret images are encoded into a single grayscale intensity-only image that is recorded by a monochromic camera by applying a diffractive-imaging based double random phase encoding (DRPE) system. In the decryption process, high accuracy images are decrypted without crosstalk from the intensity image through a multimode phase retrieval algorithm and a two-step iterative shrinkage/thresholding (TwIST) algorithm. The feasibility of the proposed method is demonstrated by numerical simulations.

Coded aperture structured illumination digital holographic microscopy for superresolution imaging

This paper proposes a coded aperture structured illumination (CASI) technique in digital holographic microscopy (DHM). A CASI wave is generated using two binary phase codes (0° and 120°) for spatial phase shifting. The generated CASI wave then interferes with a reference wave to form a coded Fresnel hologram at a single exposure with compressive sensing (CS) to avoid the temporal phase-shifting process of the structured illumination (SI). The CS algorithm is applied to retrieve the missing data of decoded phase-shifted SI-modulated waves, which are used to separate overlapped spatial frequencies for obtaining a larger spatial frequency coverage to provide superresolution imaging. Two phase-only spatial light modulators are applied to generate a directional SI pattern for obtaining a coded aperture with a suitable size to perform one-shot acquisition in the DHM system.

Tunable time-resolved tick-tock pulsed digital holographic microscopy for ultrafast events

This study presents a time-resolved imaging technique for detecting ultrafast events in the sample with tunable tick-tock pulses in common-path digital holographic microscopy. The tick-tock pulses are generated from the same single femtosecond pulse source and manipulated through a spatial-multiplexing encoding/decoding scheme with two complementary binary codes for digital hologram recording and reconstruction. The spatial-multiplexing encoding/decoding scheme with compressive sensing on the Fresnel digital hologram is used to recover missing data and achieve high-fidelity wavefront reconstruction. The elapsed time of tick-tock pulses can be adjusted by changing the optical path difference between the pulse pair arms for dynamic observation at various timescales. The proposed method is applied to explore the ultrafast physical phenomenon by quantitative phase imaging with a stopwatch-like tunable timescale ranging from nanoseconds to femtoseconds.

GPU-accelerated compressive holography

In this paper, we show fast signal reconstruction for compressive holography using a graphics processing unit (GPU). We implemented a fast iterative shrinkage-thresholding algorithm on a GPU to solve the ℓ₁ and total variation (TV) regularized problems that are typically used in compressive holography. Since the algorithm is highly parallel, GPUs can compute it efficiently by data-parallel computing. For better performance, our implementation exploits the structure of the measurement matrix to compute the matrix multiplications. The results show that GPU-based implementation is about 20 times faster than CPU-based implementation.

Experimental demonstration of single-shot phase imaging with a coded aperture

We experimentally demonstrated single-shot phase imaging with a coded aperture (SPICA), which connects digital holography and coherent diffractive imaging based on compressive sensing to realize the advantages of both methods simultaneously. SPICA allows the observation of a complex field with a simple, single-shot optical setup that does not need reference light and does not suffer from losses associated with the field-of-view and spatial resolution. Experiments showed the promising capabilities of SPICA for single-shot holographic imaging.

Multidimensional object acquisition by single-shot phase imaging with a coded aperture

We propose a generalized framework for quantitatively acquiring multidimensional complex objects based on single-shot phase imaging with a coded aperture (SPICA). In multidimensional SPICA, a propagating field from a multidimensional complex object is sieved by a coded aperture, the sieved field is modulated by an optical element, which is called coding optics, and then the resultant field is captured by a monochrome image sensor. The original complex field is reconstructed from the single captured intensity image by a phase retrieval algorithm with a support constraint of the coded aperture and a sparsity-based reconstruction algorithm based on compressive sensing. We also present theoretical conditions for the proposed method. As a demonstration, we numerically verified an application of this generalized framework for single-shot acquisition of depth-variant multispectral objects.

Digital holography based on multiwavelength spatial-bandwidth-extended capturing-technique using a reference arm (Multi-SPECTRA)

Single-shot digital holography based on multiwavelength spatial-bandwidth-extended capturing-technique using a reference arm (Multi-SPECTRA) is proposed. Both amplitude and quantitative phase distributions of waves containing multiple wavelengths are simultaneously recorded with a single reference arm in a single monochromatic image. Then, multiple wavelength information is separately extracted in the spatial frequency domain. The crosstalk between the object waves with different wavelengths is avoided and the number of wavelengths recorded with both a single-shot exposure and no crosstalk can be increased, by a large spatial carrier that causes the aliasing, and/or by use of a grating. The validity of Multi-SPECTRA is quantitatively, numerically, and experimentally confirmed.

Single-shot phase imaging with a coded aperture

We present a method of quantitatively acquiring a large complex field, containing not only amplitude information but also phase information, based on single-shot phase imaging with a coded aperture (SPICA). In SPICA, the propagating field from an object illuminated by partially coherent visible light is sieved by a coded mask, and the sieved field propagates to an image sensor, where it is captured. The sieved field is recovered from the single captured intensity image via a phase retrieval algorithm with an amplitude support constraint using the mask pattern, and then the object's complex field is reconstructed from the recovered sieved field by an algorithm employing a sparsity constraint based on compressive sensing. The system model and the theoretical bounds of SPICA are derived. We also verified the concept with numerical demonstrations.

Quantization error and dynamic range considerations for compressive imaging systems design

A natural field of application for compressive sensing theory is imaging. Indeed, numerous compressive imaging (CI) systems and applications have been developed during the last few years. This work addresses the quantization effect in CI, which is fundamental for most CI architectures. In this paper, the implications of sensor quantization on universal CI are investigated theoretically and demonstrated with numerical experiments. It is shown that employing a CI framework may set severe requirements on the quantization depth of the optical sensor used. The quantization depth overhead requirement may be prohibitive in many optical imaging scenarios employing typical CI architectures. Practical solutions that significantly alleviate this requirement are suggested.

Feasibility study for compressive multi-dimensional integral imaging

This paper describes a generalized framework for single-exposure acquisition of multi-dimensional scene information using integral imaging system based on compressive sensing. In the proposed system, a multi-dimensional scene containing a plurality of information such as 3D coordinates, spectral and polarimetric data is captured by integral imaging optics. The image sensor uses pixel-wise filtering elements arranged randomly. The multi-dimensional original object is reconstructed using an algorithm with a sparsity constraint. The proposed system is demonstrated with simulations and feasible optical experiments based on synthetic aperture integral imaging using multi-dimensional objects including 3D coordinates, spectral, and polarimetric information.

Overview of compressive sensing techniques applied in holography [Invited]

In recent years compressive sensing (CS) has been successfully introduced in digital holography (DH). Depending on the ability to sparsely represent an object, the CS paradigm provides an accurate object reconstruction framework from a relatively small number of encoded signal samples. DH has proven to be an efficient and physically realizable sensing modality that can exploit the benefits of CS. In this paper, we provide an overview of the theoretical guidelines for application of CS in DH and demonstrate the benefits of compressive digital holographic sensing.