Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

Universal linear intensity transformations using spatially incoherent diffractive processors

Under spatially coherent light, a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view (FOVs) if the total number (N) of optimizable phase-only diffractive features is ≥~2NiNo, where Ni and No refer to the number of useful pixels at the input and the output FOVs, respectively. Here we report the design of a spatially incoherent diffractive optical processor that can approximate any arbitrary linear transformation in time-averaged intensity between its input and output FOVs. Under spatially incoherent monochromatic light, the spatially varying intensity point spread function (H) of a diffractive network, corresponding to a given, arbitrarily-selected linear intensity transformation, can be written as H(m, n; m', n') = |h(m, n; m', n')|2, where h is the spatially coherent point spread function of the same diffractive network, and (m, n) and (m', n') define the coordinates of the output and input FOVs, respectively. Using numerical simulations and deep learning, supervised through examples of input-output profiles, we demonstrate that a spatially incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation between its input and output if N ≥ ~2NiNo. We also report the design of spatially incoherent diffractive networks for linear processing of intensity information at multiple illumination wavelengths, operating simultaneously. Finally, we numerically demonstrate a diffractive network design that performs all-optical classification of handwritten digits under spatially incoherent illumination, achieving a test accuracy of >95%. Spatially incoherent diffractive networks will be broadly useful for designing all-optical visual processors that can work under natural light.

Experimental optimization of lensless digital holographic microscopy with rotating diffuser-based coherent noise reduction

Laser-based lensless digital holographic microscopy (LDHM) is often spoiled by considerable coherent noise factor. We propose a novel LDHM method with significantly limited coherent artifacts, e.g., speckle noise and parasitic interference fringes. It is achieved by incorporating a rotating diffuser, which introduces partial spatial coherence and preserves high temporal coherence of laser light, crucial for credible in-line hologram reconstruction. We present the first implementation of the classical rotating diffuser concept in LDHM, significantly increasing the signal-to-noise ratio while preserving the straightforwardness and compactness of the LDHM imaging device. Prior to the introduction of the rotating diffusor, we performed LDHM experimental hardware optimization employing 4 light sources, 4 cameras, and 3 different optical magnifications (camera-sample distances). It was guided by the quantitative assessment of numerical amplitude/phase reconstruction of test targets, conducted upon standard deviation calculation (noise factor quantification), and resolution evaluation (information throughput quantification). Optimized rotating diffuser LDHM (RD-LDHM) method was successfully corroborated in technical test target imaging and examination of challenging biomedical sample (60 µm thick mouse brain tissue slice). Physical minimization of coherent noise (up to 50%) was positively verified, while preserving optimal spatial resolution of phase and amplitude imaging. Coherent noise removal, ensured by proposed RD-LDHM method, is especially important in biomedical inference, as speckles can falsely imitate valid biological features. Combining this favorable outcome with large field-of-view imaging can promote the use of reported RD-LDHM technique in high-throughput stain-free biomedical screening.

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.

Low-intensity illumination for lensless digital holographic microscopy with minimized sample interaction

Exposure to laser light alters cell culture examination via optical microscopic imaging techniques based on label-free coherent digital holography. To mitigate this detrimental feature, researchers tend to use a broader spectrum and lower intensity of illumination, which can decrease the quality of holographic imaging due to lower resolution and higher noise. We study the lensless digital holographic microscopy (LDHM) ability to operate in the low photon budget (LPB) regime to enable imaging of unimpaired live cells with minimized sample interaction. Low-cost off-the-shelf components are used, promoting the usability of such a straightforward approach. We show that recording data in the LPB regime (down to 7 µW of illumination power) does not limit the contrast or resolution of the hologram phase and amplitude reconstruction compared to regular illumination. The LPB generates hardware camera shot noise, however, to be effectively minimized via numerical denoising. The ability to obtain high-quality, high-resolution optical complex field reconstruction was confirmed using the USAF 1951 amplitude sample, phase resolution test target, and finally, live glial restricted progenitor cells (as a challenging strongly absorbing and scattering biomedical sample). The proposed approach based on severely limiting the photon budget in lensless holographic microscopy method can open new avenues in high-throughout (optimal resolution, large field-of-view, and high signal-to-noise-ratio single-hologram reconstruction) cell culture imaging with minimized sample interaction.

Off-axis propagation algorithm for partial reconstruction of wide-angle computer-generated holograms

A method for reconstruction of partial off-axis areas of arbitrary size for wide-angle viewing computer generated holograms is presented. Proposed method employs paraxial spherical phase factors and modified propagation kernels. This significantly reduces the numerical space-bandwidth product needed for off-axis wave field calculations, which makes it an efficient propagation method. As a result, propagated wavefields of high-off axis and large size output windows can be obtained. To that end, a phase-space analysis for obtaining the proper condition for implementing spatial-frequency zero-padding for accurate wavefield propagation is carried out. Hence, suppression of aliased components and high spatial resolution is possible. Nevertheless, proposed algorithm faces a computer memory bottleneck when reconstructing very large off-axis areas due to too extensive zero-padding needed. To solve this problem, a memory optimized tiling implementation is introduced. Utility of the developed propagation tools are proven by partial reconstructions from a high-resolution hologram. The size of the reconstructions areas ranges from 100 × 100 mm² up to 550 × 550 mm².

Non-uniform angular spectrum method in a complex medium based on iteration

The traditional angular spectrum method has an inherent problem that the region of diffraction propagation should be homogeneous. However, in some cases, the medium of the diffraction propagation region is inhomogeneous. In this Letter, based on iteration we proposed the non-uniform angular spectrum method for diffraction propagation calculation in a complex medium. By phase pre-processing in the spatial domain and diffraction calculation in the spatial frequency domain, the diffraction propagation problem of the light field in a complex medium is solved. Theoretical formulation and numerical examples as well as experimental investigation are presented to confirm the validity of the proposed method. The advantages of this method include faster computation, smaller memory requirement, and the ability to compute a larger area compared with the finite element method as well as the ability to compute the non-paraxial case compared with the standard fast Fourier transform beam propagation method.

Versatile optimization-based speed-up method for autofocusing in digital holographic microscopy

We propose a speed-up method for the in-focus plane detection in digital holographic microscopy that can be applied to a broad class of autofocusing algorithms that involve repetitive propagation of an object wave to various axial locations to decide the in-focus position. The classical autofocusing algorithms apply a uniform search strategy, i.e., they probe multiple, uniformly distributed axial locations, which leads to heavy computational overhead. Our method substantially reduces the computational load, without sacrificing the accuracy, by skillfully selecting the next location to investigate, which results in a decreased total number of probed propagation distances. This is achieved by applying the golden selection search with parabolic interpolation, which is the gold standard for tackling single-variable optimization problems. The proposed approach is successfully applied to three diverse autofocusing cases, providing up to 136-fold speed-up.

Wide angle holographic video projection display

Holographic projection displays provide high diffraction efficiency. However, they have a limited projection angle. This work proposes a holographic projection display with a wide angle, which gives an image of size 306mm×161mm at 700 mm and reduced speckle noise. The solution uses single Fourier lens imaging with a frequency filter and hologram generation utilizing complex coding and nonparaxial diffraction. The experiment was performed with a 4K phase-only spatial light modulator (SLM) to prove the high efficiency of the developed numerical tools. Optical reconstruction shows high resolution and high image quality achieved from a single frame. Hence, displaying video at a full frame rate of the SLM is possible.

Incoherent digital holography simulation based on scalar diffraction theory

Incoherent digital holography (IDH) enables passive 3D imaging through the self-interference of incoherent light. IDH imaging properties are dictated by the numerical aperture and optical layout in a complex manner [Opt. Express27, 33634 (2019)OPEXFF1094-408710.1364/OE.27.033634]. We develop an IDH simulation model to provide insight into its basic operation and imaging properties. The simulation is based on the scalar diffraction theory. Incoherent irradiance and self-interference holograms are numerically represented by the intensity-based summation of each propagation through finite aperture optics from independent point sources. By comparing numerical and experimental results, the applicability, accuracy, and limitation of the simulation are discussed. The developed simulation would be useful in optimizing the IDH setup.

Fourier horizontal parallax only computer and digital holography of large size

Registration and reconstruction of high-quality digital holograms with a large view angle are intensive computer tasks since they require the space-bandwidth product (SBP) of the order of tens of gigapixels or more. This massive use of SBP severely affects the storing and manipulation of digital holograms. In order to reduce the computer burden, this work focuses on the generation and reconstruction of very large horizontal parallax only digital holograms (HPO-DHs). It is shown that these types of holograms can preserve high quality and large view angle in x direction while keeping a low use of SBP. This work first proposes a numerical technique that allows calculating very large HPO-DHs with large pixel size by merging the Fourier holography and phase added stereogram algorithm. The generated Fourier HPO-DHs enable accurate storing of holographic data from 3D objects. To decode the information contained in these Fourier HPO-DHs (FHPO-DHs), a novel angular spectrum (AS) technique that provides an efficient use of the SBP for reconstruction is proposed. Our reconstruction technique, which is called compact space bandwidth AS (CSW-AS), makes use of cylindrical parabolic waves that solve sampling issues of FHPO-DHs and AS. Moreover, the CSW-AS allows for implementing zero-padding for accurate wavefield reconstructions. Hence, suppression of aliased components and high spatial resolution is possible. Notably, the imaging chain of Fourier HPO-DH enables efficient calculation, reconstruction and storing of HPO holograms of large size. Finally, the accuracy and utility of the developed technique is proved by both numerical and optical reconstructions.

A Skull-Removed Chronic Cranial Window for Ultrasound and Photoacoustic Imaging of the Rodent Brain

Ultrasound and photoacoustic imaging are emerging as powerful tools to study brain structures and functions. The skull introduces significant distortion and attenuation of the ultrasound signals deteriorating image quality. For biological studies employing rodents, craniotomy is often times performed to enhance image qualities. However, craniotomy is unsuitable for longitudinal studies, where a long-term cranial window is needed to prevent repeated surgeries. Here, we propose a mouse model to eliminate sound blockage by the top portion of the skull, while minimum physiological perturbation to the imaged object is incurred. With the new mouse model, no craniotomy is needed before each imaging experiment. The effectiveness of our method was confirmed by three imaging systems: photoacoustic computed tomography, ultrasound imaging, and photoacoustic mesoscopy. Functional photoacoustic imaging of the mouse brain hemodynamics was also conducted. We expect new applications to be enabled by the new mouse model for photoacoustic and ultrasound imaging.

Gauging diffraction patterns: field of view and bandwidth estimation in lensless holography

The purpose of this work is to provide a theoretically grounded assessment on the field of view and bandwidth of a lensless holographic setup. Indeed, while previous works have presented results with super-resolution and field-of-view extrapolation, there are no well-established rules to determine them. We show that the theoretical field of view can be large with a spatial-frequency bandwidth only limited by the wavelength, leading to an unthinkable number of degrees of freedom. To keep a realistic field of view and bandwidth, we propose several practical bounds based on a few setup properties, namely, the noise level and spatiotemporal coherence of the source.

Frequency sampling strategy for numerical diffraction calculations

Diffraction calculations play an essential role in Fourier optics and computational imaging. Conventional methods only consider the calculation from the perspective of discrete computation which would either cause error or sacrifice efficiency. In this work, we provide a unified frequency response analysis from the joint physics-mathematics perspective and propose corresponding adaptive frequency sampling strategies for five popular diffraction calculation methods. With the proposed strategies, the calculation correctness is guaranteed and the calculation efficiency is improved. Such an idea of unified frequency response study would help researchers make a do-it-yourself analysis for various diffraction calculation tasks and choose or develop a method for accurate and efficient computations of the diffraction fields.

Analysis of numerical diffraction calculation methods: from the perspective of phase space optics and the sampling theorem

Diffraction calculations are widely used in applications that require numerical simulation of optical wave propagation. Different numerical diffraction calculation methods have their own transform and sampling properties. In this study, we provide a unified analysis where five popular fast diffraction calculation methods are analyzed from the perspective of phase space optics and the sampling theorem: single fast Fourier transform-based Fresnel transform, Fresnel transfer function approach, Fresnel impulse response approach, angular spectrum method, and Rayleigh-Sommerfeld convolution. The evolutions of an input signal's space-bandwidth product (SBP) during wave propagation are illustrated with the help of a phase space diagram (PSD) and an ABCD matrix. It is demonstrated that all of the above methods cannot make full use of the SBP of the input signal after diffraction; and some transform properties have been ignored. Each method has its own restrictions and applicable range. The reason why different methods have different applicable ranges is explained with physical models. After comprehensively studying and comparing the effect on the SBP and sampling properties of these methods, suggestions are given for choosing the proper method for different applications and overcoming the restrictions of corresponding methods. The PSD and ABCD matrix are used to illustrate the properties of these methods intuitively. Numerical results are presented to verify the analysis, and potential ways to develop new diffraction calculation methods are also discussed.

Band-extended angular spectrum method for accurate diffraction calculation in a wide propagation range

The band-extended angular spectrum method (ASM) is proposed in this Letter for both near- and far-field diffraction calculation with high accuracy. Due to the aliasing problem of the transfer function (TF), the ASM is not suitable for far-field diffraction calculation. For band-limited ASM, the non-aliased bandwidth of the TF would shrink rapidly with the increase of the propagation distance, which would reduce the calculation accuracy in the far field. For the proposed band-extended ASM, the non-aliased bandwidth is significantly extended by rearranging the sampling points in the spatial frequency domain. Therefore, more frequency components of the TF contribute to the wave-field calculation, leading to a much wider propagation range and a higher computational accuracy.

Fourier rainbow holography

We present Fourier rainbow holographic imaging approach. It involves standard laser holographic recording and novel horizontal parallax only holographic display. In the display, the rainbow effect is introduced in an illumination module by high-frequency diffraction grating and white light LED source. The display is addressed by Fourier rainbow digital hologram (FRDH) encoding defocused object field with removed spatial frequency components in one direction by hologram slitting and without spherical phase factor. Theoretically and experimentally it is shown that the method extends the viewing zone of the classical viewing window display in vertical and longitudinal directions, thus the comfort of observation is improved. It is also numerically and experimentally validated that the numerical slitting applied within FRDH generation improves reconstruction depth of the display, here up to 400 mm.

Decomposition method for fast computation of gigapixel-sized Fresnel holograms on a graphics processing unit cluster

A parallel computation method for large-size Fresnel computer-generated hologram (CGH) is reported. The method was introduced by us in an earlier report as a technique for calculating Fourier CGH from 2D object data. In this paper we extend the method to compute Fresnel CGH from 3D object data. The scale of the computation problem is also expanded to 2 gigapixels, making it closer to real application requirements. The significant feature of the reported method is its ability to avoid communication overhead and thereby fully utilize the computing power of parallel devices. The method exhibits three layers of parallelism that favor small to large scale parallel computing machines. Simulation and optical experiments were conducted to demonstrate the workability and to evaluate the efficiency of the proposed technique. A two-times improvement in computation speed has been achieved compared to the conventional method, on a 16-node cluster (one GPU per node) utilizing only one layer of parallelism. A 20-times improvement in computation speed has been estimated utilizing two layers of parallelism on a very large-scale parallel machine with 16 nodes, where each node has 16 GPUs.

Digital hologram transformations for RGB color holographic display with independent image magnification and translation in 3D

A new framework for in-plane transformations of digital holograms (DHs) is proposed, which provides improved control over basic geometrical features of holographic images reconstructed optically in full color. The method is based on a Fourier hologram equivalent of the adaptive affine transformation technique [Opt. Express18, 8806 (2010)OPEXFF1094-408710.1364/OE.18.008806]. The solution includes four elementary geometrical transformations that can be performed independently on a full-color 3D image reconstructed from an RGB hologram: (i) transverse magnification; (ii) axial translation with minimized distortion; (iii) transverse translation; and (iv) viewing angle rotation. The independent character of transformations (i) and (ii) constitutes the main result of the work and plays a double role: (1) it simplifies synchronization of color components of the RGB image in the presence of mismatch between capture and display parameters; (2) provides improved control over position and size of the projected image, particularly the axial position, which opens new possibilities for efficient animation of holographic content. The approximate character of the operations (i) and (ii) is examined both analytically and experimentally using an RGB circular holographic display system. Additionally, a complex animation built from a single wide-aperture RGB Fourier hologram is presented to demonstrate full capabilities of the developed toolset.

Accurate shape measurement of focusing microstructures in Fourier digital holographic microscopy

This paper proposes a measurement method of focusing objects with a high gradient shape of a small and large radius of curvature. The measurements are carried out on a Fourier digital holographic microscope with optimized illumination conditions maximizing the usage of the system's numerical aperture. The obtained fringe patterns are the result of interference of deformed spherical object and spherical reference waves. The key elements of the method are the aberration compensation and calibration procedures. They provide accurate reconstruction of the object wave and determination of the focus position of the sample. The shape is calculated in two steps. First, the object wave is reconstructed at the plane of the object focus using single or multiframe phase extraction algorithm and the specialized propagation method. The step includes compensation for spherical aberration. In the second step, the sample shape is computed with the local ray approximation approach. The proposed method is experimentally validated with measurements of challenging, high gradient shapes (convex, concave) of different radiuses of curvature.

Defect detection based on a lensless reflective point diffraction interferometer

We propose a defect detection system to identify phase defects on optics based on a lensless reflective point diffraction interferometer (LRPDI). The optics under test are illuminated by a collimated beam to produce a signal wavefront carrying the defect information, and then the signal wavefront is recorded in a high carrier interferogram using the LRPDI. By lensless imaging, amplitude and phase defects, as well as the accurate phase of a phase defect, can be identified. The simulation and experiment demonstrate the success of the proposed system in detecting phase defects, and its high-accuracy and high-resolution dynamic detection abilities are verified.

Phase extraction from fringe pattern via light propagation

A phase demodulation method via light propagation is proposed, where one or two fringe patterns are viewed as the superposition of complex amplitudes, and then the phase is reconstructed by separating the light field via light propagation. Simulation and experimental results indicated that the proposed method can extract the phase from a single shot effectively, thereby realizing dynamic phase retrieval. In addition, the accuracy of phase reconstruction can be improved by adding another fringe pattern with an unknown phase shift. The carrier requirement is relatively low, and, thus, the proposed method can be applied to the measurements with an environment disturbance, an inaccurate phase shift, and the requirement of a high speed capture.

Angular spectrum method with compact space-bandwidth: generalization and full-field accuracy

A recent Letter [Opt. Lett.40, 3420 (2015)OPLEDP0146-959210.1364/OL.40.003420] reported a modified angular spectrum method that uses a sampling scheme based on a compact space-bandwidth product representation. That technique is useful for focusing and defocusing propagation cases and is generalized here for the case of propagation between two defocus planes. The proposed method employs paraxial spherical phase factors and modified propagation kernels to reduce the size of the numerical space-bandwidth product needed for wave field calculations. A Wigner distribution analysis is carried out in order to ensure high accuracy of the calculations in the entire computational domain. This is achieved by analyzing the evolution of the generalized space-bandwidth product when passing through the propagation algorithm for various space-frequency constraints. The results allow the derivations of sampling criteria, and, despite this, also show that a small amount of space/frequency zero padding significantly extends the capability of the recently reported modified angular spectrum method. Simulations validate the high accuracy of that method and verify a computational and memory gain of more than two orders of magnitude when comparing this technique with the conventional angular spectrum method.