Influence of corneal astigmatism on near and far vision in eyes with bifocal intraocular lenses.

Here, we present a full wave propagation model that quantitatively assesses the effect of astigmatism on visual functions in eyes with diffractive bifocal IOLs. The proposed model with bifocal IOLs evaluated the image quality of each focus at varying degrees of corneal astigmatism with the metrics of modulation transfer function and light-in-the-bucket. The results show that corneal astigmatism alters the distance-near image quality balance. Positive (negative) astigmatism has more detrimental effects on far (near) vision. Additionally, bifocal IOLs are more vulnerable to corneal astigmatism, highlighting the need to consider multifocal toric IOLs with astigmatism greater than 1.0 D. The numerical results closely agreed with previous relevant clinical findings, suggesting the clinical usability of the presented method in predicting the postoperative visual function of patients.

Time-resolved detection of early-arriving ballistic waves in a quasi-diffusive regime.

Ballistic waves directly carry image information in imaging through a scattering medium, but they are often obscured by much intense multiple-scattered waves. Detecting early arriving photons has been an effective method to extract ballistic waves in the transmission-mode imaging. However, it has been difficult to identify the temporal distribution of ballistic waves relative to the multiple scattering waves in the quasi-diffusive regime. Here, we present a method to separately quantify ballistic and multiple-scattered waves at their corresponding flight times even when multiple scattering is much stronger than the ballistic waves. This is realized by measuring the transmission matrix of an object embedded within scattering medium and comparing the coherent accumulation of ballistic waves with their incoherent addition. To further elucidate the temporal behavior of ballistic waves in quasi-diffusive regime, we analyze the flight time difference between ballistic and multiple-scattered waves and the effect of coherence gating on their relative intensities for the scattering medium of different thicknesses. The presented method to distinctively detect the temporal behavior of ballistic and multiple-scattered waves will lay a foundation to exploit multiple-scattered waves for deep-tissue imaging.

Time-gated iterative phase conjugation for efficient light energy delivery in scattering media.

Light waves propagating through complex biological tissues are spatially spread by multiple light scattering, and this spread limits the working depth in optical bioimaging, phototherapy, and optogenetics. Here, we propose the iterative phase conjugation of time-gated backscattered waves for enhancing the light energy delivered to a target object embedded in a scattering medium. We demonstrate the enhancement of light energy delivered to a target object hidden behind a 200-µm-thick mouse skull by more than ten times in comparison with the initial random input. The maximum enhancement was reached in only 10 iterations, more than a hundred times smaller than existing methods based on either a time-gated reflection matrix or iterative feedback optimization of the time-gated reflection intensity. Consequently, the proposed method is less sensitive to sample perturbations. Furthermore, the number of images required for optimization remained almost unchanged with an increase in the illumination area, unlike existing methods, where the convergence time scales with the illumination area. The proposed method provides high operation speed over a wide illumination area, which can facilitate the use of wavefront shaping in practical applications.

Analyzing the relationship between decorrelation time and tissue thickness in acute rat brain slices using multispeckle diffusing wave spectroscopy.

Novel techniques in the field of wavefront shaping have enabled light to be focused deep inside or through scattering media such as biological tissue. However, most of these demonstrations have been limited to thin, static samples since these techniques are very sensitive to changes in the arrangement of the scatterers within. As the samples of interest get thicker, the influence of the dynamic nature of the sample becomes even more pronounced and the window of time in which the wavefront solutions remain valid shrinks further. In this paper, we examine the time scales upon which this decorrelation happens in acute rat brain slices via multispeckle diffusing wave spectroscopy and investigate the relationship between this decorrelation time and the thickness of the sample using diffusing wave spectroscopy theory and Monte Carlo photon transport simulation.

Model for estimating the penetration depth limit of the time-reversed ultrasonically encoded optical focusing technique.

The time-reversed ultrasonically encoded (TRUE) optical focusing technique is a method that is capable of focusing light deep within a scattering medium. This theoretical study aims to explore the depth limits of the TRUE technique for biological tissues in the context of two primary constraints - the safety limit of the incident light fluence and a limited TRUE's recording time (assumed to be 1 ms), as dynamic scatterer movements in a living sample can break the time-reversal scattering symmetry. Our numerical simulation indicates that TRUE has the potential to render an optical focus with a peak-to-background ratio of ~2 at a depth of ~103 mm at wavelength of 800 nm in a phantom with tissue scattering characteristics. This study sheds light on the allocation of photon budget in each step of the TRUE technique, the impact of low signal on the phase measurement error, and the eventual impact of the phase measurement error on the strength of the TRUE optical focus.

Method for auto-alignment of digital optical phase conjugation systems based on digital propagation.

Optical phase conjugation (OPC) has enabled many optical applications such as aberration correction and image transmission through fiber. In recent years, implementation of digital optical phase conjugation (DOPC) has opened up the possibility of its use in biomedical optics (e.g. deep-tissue optical focusing) due to its ability to provide greater-than-unity OPC reflectivity (the power ratio of the phase conjugated beam and input beam to the OPC system) and its flexibility to accommodate additional wavefront manipulations. However, the requirement for precise (pixel-to-pixel matching) alignment of the wavefront sensor and the spatial light modulator (SLM) limits the practical usability of DOPC systems. Here, we report a method for auto-alignment of a DOPC system by which the misalignment between the sensor and the SLM is auto-corrected through digital light propagation. With this method, we were able to accomplish OPC playback with a DOPC system with gross sensor-SLM misalignment by an axial displacement of up to~1.5 cm, rotation and tip/tilt of ~5° and in-plane displacement of ~5 mm (dependent on the physical size of the sensor and the SLM). Our auto-alignment method robustly achieved a DOPC playback peak-to-background ratio (PBR) corresponding to more than ~30 % of the theoretical maximum. As an additional advantage, the auto-alignment procedure can be easily performed at will and, as such, allows us to correct for small mechanical drifts within the DOPC systems, thus overcoming a previously major DOPC system vulnerability. We believe that this reported method for implementing robust DOPC systems will broaden the practical utility of DOPC systems.

Large-volume focus control at 10 MHz refresh rate via fast line-scanning amplitude-encoded scattering-assisted holography.

The capability of focus control has been central to optical technologies that require both high temporal and spatial resolutions. However, existing varifocal lens schemes are commonly limited to the response time on the microsecond timescale and share the fundamental trade-off between the response time and the tuning power. Here, we propose an ultrafast holographic focusing method enabled by translating the speed of a fast 1D beam scanner into the speed of the complex wavefront modulation of a relatively slow 2D spatial light modulator. Using a pair of a digital micromirror device and a resonant scanner, we demonstrate an unprecedented refresh rate of focus control of 31 MHz, which is more than 1,000 times faster than the switching rate of a digital micromirror device. We also show that multiple micrometer-sized focal spots can be independently addressed in a range of over 1 MHz within a large volume of 5 mm × 5 mm × 5.5 mm, validating the superior spatiotemporal characteristics of the proposed technique - high temporal and spatial precision, high tuning power, and random accessibility in a three-dimensional space. The demonstrated scheme offers a new route towards three-dimensional light manipulation in the 100 MHz regime.

Optical phase conjugation (OPC)-assisted isotropic focusing.

Isotropic optical focusing - the focusing of light with axial confinement that matches its lateral confinement, is important for a broad range of applications. Conventionally, such focusing is achieved by overlapping the focused beams from a pair of opposite-facing microscope objective lenses. However the exacting requirements for the alignment of the objective lenses and the method's relative intolerance to sample turbidity have significantly limited its utility. In this paper, we present an optical phase conjugation (OPC)-assisted isotropic focusing method that can address both challenges. We exploit the time-reversal nature of OPC playback to naturally guarantee the overlap of the two focused beams even when the objective lenses are significantly misaligned (up to 140 microns transversely and 80 microns axially demonstrated). The scattering correction capability of OPC also enabled us to accomplish isotropic focusing through thick scattering samples (demonstrated with samples of ~7 scattering mean free paths). This method can potentially improve 4Pi microscopy and 3D microstructure patterning.

DeepPhaseCut: Deep Relaxation in Phase for Unsupervised Fourier Phase Retrieval.

Fourier phase retrieval is a classical problem of restoring a signal only from the measured magnitude of its Fourier transform. Although Fienup-type algorithms, which use prior knowledge in both spatial and Fourier domains, have been widely used in practice, they can often stall in local minima. Convex relaxation methods such as PhaseLift and PhaseCut may offer performance guarantees, but these algorithms are usually computationally expensive for practical use. To address this problem, here we propose a novel unsupervised feed-forward neural network for Fourier phase retrieval which generates high quality reconstruction immediately. Unlike the existing deep learning approaches that use a neural network as a regularization term or an end-to-end blackbox model for supervised training, our algorithm is a feed-forward neural network implementation of physics-driven constraints in an unsupervised learning framework. Specifically, our network is composed of two generators: one for the phase estimation using PhaseCut loss, followed by another generator for image reconstruction, all of which are trained simultaneously without matched data. The link to the classical Fienup-type algorithms and the recent symmetry-breaking learning approach is also revealed. Extensive experiments demonstrate that the proposed method outperforms all existing approaches in Fourier phase retrieval problems.

Deep tissue space-gated microscopy via acousto-optic interaction.

To extend the imaging depth of high-resolution optical microscopy, various gating operations-confocal, coherence, and polarization gating-have been devised to filter out the multiply scattered wave. However, the imaging depth is still limited by the multiply scattered wave that bypasses the existing gating operations. Here, we present a space gating method, whose mechanism is independent of the existing methods and yet effective enough to complement them. Specifically, we reconstruct an image only using the ballistic wave that is acousto-optically modulated at the object plane. The space gating suppresses the multiply scattered wave by 10-100 times in a highly scattering medium, and thus enables visualization of the skeletal muscle fibers in whole-body zebrafish at 30 days post fertilization. The space gating will be an important addition to optical-resolution microscopy for achieving the ultimate imaging depth set by the detection limit of ballistic wave.

Wavefront shaping with disorder-engineered metasurfaces.

Recently, wavefront shaping with disordered media has demonstrated optical manipulation capabilities beyond those of conventional optics, including extended volume, aberration-free focusing and subwavelength focusing. However, translating these capabilities to useful applications has remained challenging as the input-output characteristics of the disordered media (P variables) need to be exhaustively determined via O(P) measurements. Here, we propose a paradigm shift where the disorder is specifically designed so its exact input-output characteristics are known a priori and can be used with only a few alignment steps. We implement this concept with a disorder-engineered metasurface, which exhibits additional unique features for wavefront shaping such as a large optical memory effect range in combination with a wide angular scattering range, excellent stability, and a tailorable angular scattering profile. Using this designed metasurface with wavefront shaping, we demonstrate high numerical aperture (NA > 0.5) focusing and fluorescence imaging with an estimated ~2.2×108 addressable points in an ~8 mm field of view.

Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light.

Noninvasive light focusing deep inside living biological tissue has long been a goal in biomedical optics. However, the optical scattering of biological tissue prevents conventional optical systems from tightly focusing visible light beyond several hundred micrometers. The recently developed wavefront shaping technique time-reversed ultrasonically encoded (TRUE) focusing enables noninvasive light delivery to targeted locations beyond the optical diffusion limit. However, until now, TRUE focusing has only been demonstrated inside nonliving tissue samples. We present the first example of TRUE focusing in 2-mm-thick living brain tissue and demonstrate its application for optogenetic modulation of neural activity in 800-µm-thick acute mouse brain slices at a wavelength of 532 nm. We found that TRUE focusing enabled precise control of neuron firing and increased the spatial resolution of neuronal excitation fourfold when compared to conventional lens focusing. This work is an important step in the application of TRUE focusing for practical biomedical uses.

Optical phase conjugation assisted scattering lens: variable focusing and 3D patterning.

Variable light focusing is the ability to flexibly select the focal distance of a lens. This feature presents technical challenges, but is significant for optical interrogation of three-dimensional objects. Numerous lens designs have been proposed to provide flexible light focusing, including zoom, fluid, and liquid-crystal lenses. Although these lenses are useful for macroscale applications, they have limited utility in micron-scale applications due to restricted modulation range and exacting requirements for fabrication and control. Here, we present a holographic focusing method that enables variable light focusing without any physical modification to the lens element. In this method, a scattering layer couples low-angle (transverse wave vector) components into a full angular spectrum, and a digital optical phase conjugation (DOPC) system characterizes and plays back the wavefront that focuses through the scattering layer. We demonstrate micron-scale light focusing and patterning over a wide range of focal distances of 22-51 mm. The interferometric nature of the focusing scheme also enables an aberration-free scattering lens. The proposed method provides a unique variable focusing capability for imaging thick specimens or selective photoactivation of neuronal networks.

Optical focusing inside scattering media with time-reversed ultrasound microbubble encoded light.

Focusing light inside scattering media in a freely addressable fashion is challenging, as the wavefront of the scattered light is highly disordered. Recently developed ultrasound-guided wavefront shaping methods are addressing this challenge, albeit with relatively low modulation efficiency and resolution limitations. In this paper, we present a new technique, time-reversed ultrasound microbubble encoded (TRUME) optical focusing, which can focus light with improved efficiency and sub-ultrasound wavelength resolution. This method ultrasonically destroys microbubbles, and measures the wavefront change to compute and render a suitable time-reversed wavefront solution for focusing. We demonstrate that the TRUME technique can create an optical focus at the site of bubble destruction with a size of ∼2 µm. We further demonstrate a twofold enhancement in addressable focus resolution in a microbubble aggregate target by exploiting the nonlinear pressure-to-destruction response of the microbubbles. The reported technique provides a deep tissue-focusing solution with high efficiency, resolution, and specificity.

Focusing through dynamic tissue with millisecond digital optical phase conjugation.

Digital optical phase conjugation (DOPC) is a new technique employed in wavefront shaping and phase conjugation for focusing light through or within scattering media such as biological tissues. DOPC is particularly attractive as it intrinsically achieves a high fluence reflectivity in comparison to nonlinear optical approaches. However, the slow refresh rate of liquid crystal spatial light modulators and limitations imposed by computer data transfer speeds have thus far made it difficult for DOPC to achieve a playback latency of shorter than ~200 ms and, therefore, prevented DOPC from being practically applied to thick living samples. In this paper, we report a novel DOPC system that is capable of 5.3 ms playback latency. This speed improvement of almost 2 orders of magnitude is achieved by using a digital micromirror device, field programmable gate array (FPGA) processing, and a single-shot binary phase retrieval technique. With this system, we are able to focus through 2.3 mm living mouse skin with blood flowing through it (decorrelation time ~30 ms) and demonstrate that the focus can be maintained indefinitely-an important technological milestone that has not been previously reported, to the best of our knowledge.

Relation between speckle decorrelation and optical phase conjugation (OPC)-based turbidity suppression through dynamic scattering media: a study on in vivo mouse skin.

Light scattering in biological tissue significantly limits the accessible depth for localized optical interrogation and deep-tissue optical imaging. This challenge can be overcome by exploiting the time-reversal property of optical phase conjugation (OPC) to reverse multiple scattering events or suppress turbidity. However, in living tissue, scatterers are highly movable and the movement can disrupt time-reversal symmetry when there is a latency in the OPC playback. In this paper, we show that the motion-induced degradation of the OPC turbidity-suppression effect through a dynamic scattering medium shares the same decorrelation time constant as that determined from speckle intensity autocorrelation - a popular conventional measure of scatterer movement. We investigated this decorrelation characteristic time through a 1.5-mm-thick dorsal skin flap of a living mouse and found that it ranges from 50 ms to 2.5 s depending on the level of immobilization. This study provides information on relevant time scales for applying OPC to living tissues.

Iterative time-reversed ultrasonically encoded light focusing in backscattering mode.

The Time-Reversed Ultrasound-Encoded (TRUE) light technique enables noninvasive focusing deep inside scattering media. However, the time-reversal procedure usually has a low signal-to-noise ratio because the intensity of ultrasound-encoded light is intrinsically low. Consequently, the contrast and resolution of TRUE focus is far from ideal, especially in the backscattering geometry, which is more practical in many biomedical applications. To improve the light intensity and resolution of TRUE focus, we developed an iterative TRUE (iTRUE) light focusing technique that employs the TRUE focus itself as a signal source (rather than diffused light) for subsequent TRUE procedures. Importantly, this iTRUE technique enables light focusing in backscattering mode. Here, we demonstrate the concept by focusing light in between scattering layers in a backscattering configuration and show that the light intensity at the focus is progressively enhanced by a factor of ~20. By scanning across a fluorescent bead between these two scattering layers, the focusing resolution in the ultrasound axial and lateral directions was improved ~2-fold and ~3-fold, respectively. We further explored the application of iTRUE in biological samples by focusing light between 1 mm thick chicken tissue and cartilage, and light intensity enhancements of the same order were also observed.