Abstract: With the availability of high-resolution miniature spatial light modulators (SLMs) new methods in optical microscopy have become feasible. The SLMs discussed in this review consist of miniature liquid crystal displays with micron-sized pixels that can modulate the phase and/or amplitude of an optical wavefront. In microscopy they can be used to control and shape the sample illumination, or they can act as spatial Fourier filters in the imaging path. Some of these applications are reviewed in this article. One of them, called spiral phase contrast, generates isotropic edge enhancement of thin phase samples or spiral-shaped interference fringes for thicker phase samples, which can be used to reconstruct the phase topography from a single on-axis interferogram. If SLMs are used for both illumination control and spatial Fourier filtering, this combination for instance allows for the generalization of the Zernike phase contrast principle. The new SLM-based approach improves the effective resolution and avoids some shortcomings and artifacts of the traditional method. The main advantage of SLMs in microscopy is their flexibility, as one can realize various operation modes in the same setup, without the need for changing any hardware components, simply by electronically switching the phase pattern displayed on the SLMs.

Abstract: In this paper we develop a new statistical model for the irradiance fluctuations of an unbounded optical wavefront (plane and spherical waves) propagating through a turbulent medium under all irradiance fluctuation conditions in homogeneous, isotropic turbulence. The major advantage of the model is that leads to closed-form and mathematically-tractable expressions for the fundamental channel statistics of an unbounded optical wavefront under all turbulent regimes. Furthermore, it unifies most of the proposed statistical models for the irradiance fluctuations derived in the bibliography providing, in addition, an excellent agreement with the experimental data.

Abstract: A broadband adaptive optics scanning ophthalmoscope (BAOSO) consisting of four afocal telescopes, formed by pairs of off-axis spherical mirrors in a non-planar arrangement, is presented. The non-planar folding of the telescopes is used to simultaneously reduce pupil and image plane astigmatism. The former improves the adaptive optics performance by reducing the root-mean-square (RMS) of the wavefront and the beam wandering due to optical scanning. The latter provides diffraction limited performance over a 3 diopter (D) vergence range. This vergence range allows for the use of any broadband light source(s) in the 450-850 nm wavelength range to simultaneously image any combination of retinal layers. Imaging modalities that could benefit from such a large vergence range are optical coherence tomography (OCT), multi- and hyper-spectral imaging, single- and multi-photon fluorescence. The benefits of the non-planar telescopes in the BAOSO are illustrated by resolving the human foveal photoreceptor mosaic in reflectance using two different superluminescent diodes with 680 and 796 nm peak wavelengths, reaching the eye with a vergence of 0.76 D relative to each other.

Abstract: We demonstrate that a structured light intensity pattern can be produced at the output of a multi-mode optical fiber by shaping the wavefront of the input beam with a spatial light modulator. We also find the useful property that, as in the case for free space propagation, output intensities can be easily superimposed by taking the argument of the complex superposition of corresponding phase-only holograms. An analytical expression is derived relating output intensities ratios to hologram weights in the superposition.

Abstract: We study the focusing of light through random photonic materials using wavefront shaping. We explore a novel approach namely binary amplitude modulation. To this end, the light incident to a random photonic medium is spatially divided into a number of segments. We identify the segments that give rise to fields that are out of phase with the total field at the intended focus and assign these a zero amplitude, whereas the remaining segments maintain their original amplitude. Using 812 independently controlled segments of light, we find the intensity at the target to be 75±6 times enhanced over the average intensity behind the sample. We experimentally demonstrate focusing of light through random photonic media using both an amplitude only mode liquid crystal spatial light modulator and a MEMS-based spatial light modulator. Our use of Micro Electro-Mechanical System (MEMS)-based digital micromirror devices for the control of the incident light field opens an avenue to high speed implementations of wavefront shaping.

Abstract: We have employed ptychographic coherent diffractive imaging to completely characterize the focal spot wavefield and wavefront aberrations of a high-resolution diffractive X-ray lens. The ptychographic data from a strongly scattering object was acquired using the radiation cone emanating from a coherently illuminated Fresnel zone plate at a photon energy of 6.2 keV. Reconstructed images of the object were retrieved with a spatial resolution of 8 nm by combining the difference-map phase retrieval algorithm with a non-linear optimization refinement. By numerically propagating the reconstructed illumination function, we have obtained the X-ray wavefield profile of the 23 nm round focus of the Fresnel zone plate (outermost zone width, Δr = 20 nm) as well as the X-ray wavefront at the exit pupil of the lens. The measurements of the wavefront aberrations were repeatable to within a root mean square error of 0.006 waves, and we demonstrate that they can be related to manufacturing aspects of the diffractive optical element and to errors on the incident X-ray wavefront introduced by the upstream beamline optics.

Abstract: Optical aberrations due to the inhomogeneous refractive index of tissue degrade the resolution and brightness of images in deep-tissue imaging. We introduce a confocal fluorescence microscope with adaptive optics, which can correct aberrations based on direct wavefront measurements using a Shack-Hartmann wavefront sensor with a fluorescent bead used as a point source reference beacon. The results show a 4.3× improvement in the Strehl ratio and a 240% improvement in the signal intensity for fixed mouse tissues at depths of up to 100 μm.

Abstract: We study the focusing of light through random photonic materials using wavefront shaping. We explore a novel approach namely binary amplitude modulation. To this end, the light incident to a random photonic medium is spatially divided into a number of segments. We identify the segments that give rise to fields that are out of phase with the total field at the intended focus and assign these a zero amplitude, whereas the remaining segments maintain their original amplitude. Using 812 independently controlled segments of light, we find the intensity at the target to be 75 +/- 6 times enhanced over the average intensity behind the sample. We experimentally demonstrate focusing of light through random photonic media using both an amplitude only mode liquid crystal spatial light modulator and a MEMS-based spatial light modulator. Our use of Micro Electro-Mechanical System (MEMS)-based digital micromirror devices for the control of the incident light field opens an avenue to high speed implementations of wavefront shaping.

Abstract: We introduce a new algorithm for calculating computer generated hologram (CGH) using ray-sampling (RS) plane. RS plane is set at near the object and the light-rays emitted by the object are sampled at the plane. Then the light-rays are transformed into the wavefront with using the Fourier transforms. The wavefront on the CGH plane is calculated by wavefront propagation simulation from RS plane to CGH plane. The proposed method enables to reproduce high resolution image for deep 3D scene with angular reflection properties such as gloss appearance.

Abstract: We demonstrate coherent combining (phase locking) of seven laser beams emerging from an adaptive fiber-collimator array over a 7 km atmospheric propagation path using a target-in-the-loop (TIL) setting. Adaptive control of the piston and the tip and tilt wavefront phase at each fiber-collimator subaperture resulted in automatic focusing of the combined beam onto an unresolved retroreflector target (corner cube) with precompensation of quasi-static and atmospheric turbulence-induced phase aberrations. Both phase locking (piston) and tip–tilt control were performed by maximizing the target-return optical power using iterative stochastic parallel gradient descent (SPGD) techniques. The performance of TIL coherent beam combining and atmospheric mitigation was significantly increased by using an SPGD control variation that accounts for the round-trip propagation delay (delayed SPGD).

Abstract: The past decade has seen a significant growth in research targeted at space based observatories for imaging exo-solar planets. The challenge is in designing an imaging system for high-contrast. Even with a perfect coronagraph that modifies the point spread function to achieve high-contrast, wavefront sensing and control is needed to correct the errors in the optics and generate a "dark hole". The high-contrast imaging laboratory at Princeton University is equipped with two Boston Micromachines Kilo-DMs. We review here an algorithm designed to achieve high-contrast on both sides of the image plane while minimizing the stroke necessary from each deformable mirror (DM). This algorithm uses the first DM to correct for amplitude aberrations and the second DM to create a flat wavefront in the pupil plane. We then show the first results obtained at Princeton with this correction algorithm, and we demonstrate a symmetric dark hole in monochromatic light.

Abstract: The Shack-Hartmann wavefront sensor (SHWS) spots upon which ocular aberration measurements depend have poor quality in mice due to light reflected from multiple retinal layers. We have designed and implemented a SHWS that can favor light from a specific retinal layer and measured monochromatic aberrations in 20 eyes from 10 anesthetized C57BL/6J mice. Using this instrument, we show that mice are myopic, not hyperopic as is frequently reported. We have also measured longitudinal chromatic aberration (LCA) of the mouse eye and found that it follows predictions of the water-filled schematic mouse eye. Results indicate that the optical quality of the mouse eye assessed by measurement of its aberrations is remarkably good, better for retinal imaging than the human eye. The dilated mouse eye has a much larger numerical aperture (NA) than that of the dilated human eye (0.5 NA vs. 0.2 NA), but it has a similar amount of root mean square (RMS) higher order aberrations compared to the dilated human eye. These measurements predict that adaptive optics based on this method of wavefront sensing will provide improvements in retinal image quality and potentially two times higher lateral resolution than that in the human eye.

Abstract: Most studies investigating the acoustic radiation force upon a target are based on symmetry considerations between the object and the incident beam. Even so, this symmetry condition is not always fulfilled in several cases. An expression for the radiation force is obtained as a function of the beam-shape and the scattering coefficients of an incident wave and the object, respectively. The expression for the radiation force caused by a plane wave on a rigid sphere is used to validate the formula. This method represents a theoretical advance permitting different interpretations and predictions concerned to the acoustic radiation force phenomenon.

Abstract: We have developed an alternative (new) method to produce common-image gathers in the incident-angle domain by calculating wavenumbers directly from the P-wave polarization rather than using the dominant wavenumber as the normal to the source wavefront. In isotropic acoustic media, the wave propagation direction can be directly calculated as the spatial gradient direction of the acoustic wavefield, which is parallel to the wavenumber direction (the normal to the wavefront). Instantaneous wavenumber, obtained via a novel Hilbert transform approach, is used to calculate the local normal to the reflectors in the migrated image. The local incident angle is produced as the difference between the propagation direction and the normal to the reflector. By reordering the migrated images (over all common-source gathers) with incident angle, common-image gathers are produced in the incident-angle domain. Instantaneous wavenumber takes the place of the normal to the reflector in the migrated image. P- and S-wave separ...

Abstract: The weak-lensing science of the Large Synoptic Survey Telescope (LSST) project drives the need to carefully model and separate the instrumental artifacts from the intrinsic shear signal caused by gravitational lensing. The dominant source of the systematics for all ground-based telescopes is the spatial correlation of the point-spread function (PSF) modulated by both atmospheric turbulence and optical aberrations in the telescope and camera system. In this article, we present a full field-of-view simulation of the LSST images by modeling both the atmosphere and the system optics with the most current data for the telescope and camera specifications and the environment. To simulate the effects of atmospheric turbulence, we generated six-layer Kolmogorov/von Karman phase screens with the parameters estimated from the on-site measurements. LSST will continuously sample the wavefront, correcting the optics alignment and focus. For the optics, we combined the ray-tracing tool ZEMAX and our simulated focal-plane data to introduce realistic residual aberrations and focal-plane height variations. Although this expected focal-plane flatness deviation for LSST is small compared with that of other existing cameras, the fast focal ratio of the LSST optics cause this focal-plane flatness variation and the resulting PSF discontinuities across the CCD boundaries to be significant challenges in our removal of the PSF-induced systematics. We resolve this complication by performing principal component analysis (PCA) CCD by CCD and by interpolating the basis functions derived from the analysis using conventional polynomials. We demonstrate that this PSF correction scheme reduces the residual PSF ellipticity correlation below 10-7 over the cosmologically interesting (dark-matter-dominated) scale 10'-3°. From a null test using the Hubble Space Telescope (HST) Ultra Deep Field (UDF) galaxy images without input shear, we verify that the amplitude of the galaxy ellipticity correlation function, after the PSF correction, is consistent with the shot noise set by the finite number of objects. We conclude that the current optical design and specification for the accuracy in the focal-plane assembly are sufficient to enable the control of the PSF systematics required for weak-lensing science with LSST.

Abstract: We study the effect of frequency detuning on light focused through turbid media. By shaping the wavefront of the incident beam light is focused through an opaque scattering layer. When detuning the laser we observe a gradual decrease of the focus intensity, while the position, size,and shape of the focus remain the same within experimental accuracy. The frequency dependence of the focus intensity follows a measured speckle correlation function. We support our experimental findings with calculations based on transport theory. Our results imply wavefront shaping methods can be generalized to allow focusing of optical pulses in turbid media.

Abstract: Generation of a nondiffracting transversally polarized beam by means of transmitting an azimuthally polarized beam through a multibelt spiral phase hologram and then highly focusing by a high-NA lens is presented. A relatively long depth of focus (∼4.84λ) of the electric field with only radial and azimuthal components is achieved. The polarization of the wavefront near the focal plane is analyzed in detail by calculating the Stokes polarization parameters. It is found that the polarization is spatially varying and entirely transversally polarized, and the polarization singularity disappears at the beam center, which makes the central bright channel possible.

Abstract: We analyze the resolution and statistical fluctuations of images when the ambient medium is random and scattering can be modeled primarily by wavefront distortion. We compare the coherent interferometric imaging method to the widely used Kirchhoff migration and show how the latter loses statistical stability at an exponential rate with the distance of propagation. In Kirchhoff migration we form images by superposing the array data back-propagated to the image domain. In coherent interferometry, we back-propagate local cross-correlations of the array data. This is a denoising process that enhances the signal-to-noise ratio of images but also reduces the resolution. We quantify analytically the trade-off between enhanced stability and reduced resolution in coherent interferometric imaging.

Abstract: A large number of degrees of freedom are required to produce a high quality focus through random scattering media. Previous demonstrations based on spatial phase modulations suffer from either a slow speed or a small number of degrees of freedom. In this work, a high speed wavefront determination technique based on spatial frequency domain wavefront modulations is proposed and experimentally demonstrated, which is capable of providing both a high operation speed and a large number of degrees of freedom. The technique was employed to focus light through a strongly scattering medium and the entire wavefront was determined in 400 milliseconds, ~three orders of magnitude faster than the previous report.

Abstract: Wavefront sensorless adaptive optics (AO) systems have been widely studied in recent years To reach optimum results, such systems require an efficient correction method In this paper, a general model-based correction method for a wavefront sensorless AO system is presented The general model-based approach is set up based on a relationship wherein the second moments (SM) of the wavefront gradients are approximately proportionate to the FWHM of the far-field intensity distribution The general model-based method is capable of taking various common sets of functions as predetermined bias functions and correcting the aberrations by using fewer photodetector measurements Numerical simulations of AO corrections of various random aberrations are performed The results show that the Strehl ratio is improved from 007 to about 090, with only N + 1 photodetector measurement for the AO correction system using N aberration modes as the predetermined bias functions

Abstract: Ptychographic x-ray diffraction microscopy is a lensless imaging technique with a large field of view and high spatial resolution, which is also useful for characterizing the wavefront of an x-ray probe. The performance of this technique is degraded by positioning errors due to the drift between the sample and illumination optics. We propose an experimental approach for correcting the positioning errors and demonstrate success by two-dimensionally reconstructing both the wavefront of the focused x-ray beam and the complex transmissivity of the weakly scattering objects at the pixel resolution of better than 10 nm in the field of view larger than 5 $\ensuremath{\mu}$m. This method is applicable to not only the observation of organelles inside cells or nano-mesoscale structures buried within bulk materials but also the characterization of probe for single-shot imaging with x-ray free electron lasers.

Abstract: In this paper we develop a new statistical model for the irradiance fluctuations of an unbounded optical wavefront (plane and spherical waves) propagating through a turbulent medium under all irradiance fluctuation conditions in homogeneous, isotropic turbulence. The major advantage of the model is that leads to closed-form and mathematically-tractable expressions for the fundamental channel statistics of an unbounded optical wavefront under all turbulent regimes. Furthermore, it unifies most of the proposed statistical models for the irradiance fluctuations derived in the bibliography providing, in addition, an excellent agreement with the experimental data.

Abstract: In this paper we describe the basic principle of FlexWave, a new high resolution wavefront manipulator, and discuss experimental data on imaging, focus and overlay. For this we integrated the FlexWave module in a 1.35 NA immersion scanner. With FlexWave we can perform both static and dynamic wavefront corrections. Wavefront control with FlexWave minimizes lens aberrations under high productivity usage of the scanner, hence maintaining overlay and focus performance, but moreover, the high resolution wavefront tuning can be used to compensate for litho related effects. Especially now mask 3D effects are becoming a major error component, additional tuning is required. Optimized wavefront can be achieved with computational lithography, by either co-optimizing source, mask, and Wavefront Target prior to tape-out, or by tuning Wavefront Targets for specific masks and scanners after the reticle is made.

Abstract: A phase microscopy method based on the use of a refractive glass pyramid to determine the wavefront generated by a transparent microscopic sample is presented. The method uses the incoherent illumination of the sample to statically extend the sensor dynamic range. A description, experimental demonstration, and preliminary results are presented.

Abstract: One-dimensional compression waves in a collision-free plasma are studied using the adiabatic two-fluid model. It is supposed that an initial magnetic field makes an arbitrary angle θ with the direction of wave propagation and e2 denotes the electron-ion mass ratio. An extensive study of the steady flows is carried out which is particularly full in the limiting cases e = 0 or 1; the effect of introducing a friction term in the equations is also considered. Then an asymptotic treatment is found to provide a simple but qualitatively correct picture of the dependence of small amplitude waves on e and θ between these extremes. Finally the picture is filled in by solving the piston problem numerically. It is found that two types of wave occur: roughly when tan θ > e−1 − e, the usual flow consists of a main wavefront followed by an oscillatory wave train; while, in the contrary case, the wave front is preceded by an oscillatory precursor. This precursor is on the scale of the ion gyromagnetic radius while the wa...

Abstract: Two-photon (2P) microscopy is widely used in neuroscience, but the optical properties of brain tissue are poorly understood. We have investigated the effect of brain tissue on the 2P point spread function (PSF2P) by imaging fluorescent beads through living cortical slices. By combining this with measurements of the mean free path of the excitation light, adaptive optics and vector-based modeling that includes phase modulation and scattering, we show that tissue-induced wavefront distortions are the main determinant of enlargement and distortion of the PSF2P at intermediate imaging depths. Furthermore, they generate surrounding lobes that contain more than half of the 2P excitation. These effects reduce the resolution of fine structures and contrast and they, together with scattering, limit 2P excitation. Our results disentangle the contributions of scattering and wavefront distortion in shaping the cortical PSF2P, thereby providing a basis for improved 2P microscopy.

Abstract: Measuring the deviation of a wavefront from a sphere provides valuable feedback on lens alignment and manufacturing errors. We demonstrate that these aberrations can be accurately measured at hard x-ray wavelengths, from far-field intensity measurements, using phase retrieval with a moveable structure in the beam path. We induce aberrations on a hard x-ray kinoform lens through deliberate misalignment and show that the reconstructed wavefronts are in good agreement with numerical simulations. Reconstructions from independent data, with the structure at different longitudinal positions and significantly separated from the beam focus, agreed with a root mean squared error of 0.006 waves.

Abstract: Time-reversed ultrasonically encoded (TRUE) optical focusing was recently proposed to deliver light dynamically to a tight region inside a scattering medium. In this letter, we report the first development of a reflection-mode TRUE optical focusing system. A high numerical aperture light guide is used to transmit the diffusely reflected light from a turbid medium to a phase-conjugate mirror (PCM), which is sensitive only to the ultrasound-tagged light. From the PCM, a phase conjugated wavefront of the tagged light is generated and conveyed by the same light guide back to the turbid medium, subsequently converging to the ultrasonic focal zone. We present experimental results from this system, which has the ability to focus light in a highly scattering medium with a round-trip optical penetration thickness (extinction coefficient multiplied by round-trip depth) as large as 160.

Abstract: X-ray grating interferometry is a well established technique to perform differential phase contrast imaging on conventional x-ray tubes. So far, the application of this technique in commercial micro computed tomography scanners has remained a major challenge due to the compact setup geometry. In this letter, we report on the design of a compact imaging setup using a microfocus source. Due to the extreme wave front curvature, the gratings are fabricated on a flexible substrate, enabling precise cylindrical shaping. A laboratory setup and a modified SCANCO μCT100 scanner have been built, allowing high resolution and large field of view imaging.