Enhanced sampling of 2D interference patterns.

We propose a simple analysis to improve the resolution of interference patterns which consist of straight fringes. As the pattern is rotated with respect to the detector, each row or column in the camera perceives it in a slightly shifted manner. We support this proposed method by analyzing both simulated and experimental interference patterns, and verify it using an interferogram obtained from a spectrally complex light source. The results imply that this technique could be implemented in different aspects of image analysis common in many fields in physics.

Beyond the diffraction limit via optical amplification.

In a previous article [Astron. Astrophys.561, A118 (2014)], we suggested a method to overcome the diffraction limit behind a telescope. We discuss and extend recent numerical simulations and test whether it is indeed possible to use photon amplification to enhance the angular resolution of a telescope or a microscope beyond the diffraction limit. An essential addition is the proposal to select events with an above-average ratio of stimulated to spontaneous photons. The analysis shows that the diffraction limit of a telescope is surpassed by a factor of 10 for an amplifier gain of 200, if the analysis is restricted to a tenth of the incoming astronomical photons. A gain of 70 is sufficient with a hundredth of the photons. More simulations must be performed to account for the bunching of spontaneous photons.

Point spread function estimation from projected speckle illumination.

The resolution of an imaging apparatus is ideally limited by the diffraction properties of the light passing through the system aperture, but in many practical cases, inhomogeneities in the light propagating medium or imperfections in the optics degrade the image resolution. Here we introduce a powerful and practical new approach for estimating the point spread function (PSF) of an imaging system on the basis of PSF Estimation from Projected Speckle Illumination (PEPSI). PEPSI uses the fact that the speckles' phase randomness cancels the effects of the aberrations in the illumination path, thereby providing an objective pattern for measuring the deformation of the imaging path. Using this approach, both wide-field-of-view and local-PSF estimation can be obtained by calibration-free, single-speckle-pattern projection. Finally, we demonstrate the feasibility of using PEPSI estimates for resolution improvement in iterative maximum likelihood deconvolution.

Phasing a segmented telescope.

A crucial part of segmented or multiple-aperture systems is control of the optical path difference between the segments or subapertures. In order to achieve optimal performance we have to phase subapertures to within a fraction of the wavelength, and this requires high accuracy of positioning for each subaperture. We present simulations and hardware realization of a simulated annealing algorithm in an active optical system with sparse segments. In order to align the optical system we applied the optimization algorithm to the image itself. The main advantage of this method over traditional correction methods is that wave-front-sensing hardware and software are no longer required, making the optical and mechanical system much simpler. The results of simulations and laboratory experiments demonstrate the ability of this optimization algorithm to correct both piston and tip-tilt errors.

Müller cells separate between wavelengths to improve day vision with minimal effect upon night vision.

Vision starts with the absorption of light by the retinal photoreceptors-cones and rods. However, due to the 'inverted' structure of the retina, the incident light must propagate through reflecting and scattering cellular layers before reaching the photoreceptors. It has been recently suggested that Müller cells function as optical fibres in the retina, transferring light illuminating the retinal surface onto the cone photoreceptors. Here we show that Müller cells are wavelength-dependent wave-guides, concentrating the green-red part of the visible spectrum onto cones and allowing the blue-purple part to leak onto nearby rods. This phenomenon is observed in the isolated retina and explained by a computational model, for the guinea pig and the human parafoveal retina. Therefore, light propagation by Müller cells through the retina can be considered as an integral part of the first step in the visual process, increasing photon absorption by cones while minimally affecting rod-mediated vision.

Color sorting by retinal waveguides.

Light is being detected by the two distinct types of photoreceptors in the human retina: cones and rods. Before light arrives at the photoreceptors, it must traverse the whole retina, along its array of higher-index Müller cells serving as natural waveguides. Here we analyze this optical process of light propagation through Müller cells by two independent optical methods: numerical beam propagation and analytical modal analysis. We show that the structure and refractive index profile of the Müller cells create a unique spatio-spectral distribution of light. This distribution corresponds to the positions and spectral sensitivities of both cones and rods to improve their light absorption.

Improving retinal image resolution with iterative weighted shift-and-add.

High-resolution retinal imaging requires dilating the pupil, and therefore exposing more aberrations that blur the image. We developed an image processing technique that takes advantage of the natural movement of the eye to average out some of the high-order aberrations and to oversample the retina. This method was implemented on a long sequence of retinal images of subjects with normal vision. We were able to resolve the structures of the size of single cells in the living human retina. The improvement of resolution is independent of the acquisition method, as long as the image is not warped during scanning. Consequently, even better results can be expected by implementing this technique on higher-resolution images.

Centroid distortion of a wavefront with varying amplitude due to asymmetry in lens diffraction.

It is often of interest to measure the centroid of a light intensity pattern in order to deduce physical properties. Examples are the Hartmann-Shack sensor, which measures the wavefront slopes, and position sensors. We investigate whether amplitude changes of the incoming electromagnetic field can affect the location of the centroid, and we show that the effect is strongly dependent on the relative size of the diffraction pattern in relation to the lenslet size. We show that if the phase varies slowly in space-and the focal spot size relative to the centroid integration area approaches zero-this variation does not affect the centroid. This is a consequence of symmetry properties of the Fresnel operator. We then show that when the focal width is not infinitely small, changes in the field amplitude can exacerbate distortion of the centroid results.

Acousto-optic wavefront sensing and reconstruction.

We employ an acousto-optic cell as a tunable-pitch wavefront sensor and study its performance. The index of refraction of two cross-standing waves forms, in the near field, an adjustable array of caustics. These caustics, similar to the lenslets used for Hartmann-Shack sensing, were measured to have an extended focal relief of 200 times their pitch. We discovered a strong interaction between the caustics and source speckle, so much so that we had to modulate the beam to reduce it. We measured ocular wavefronts at different frequencies and established the consistency and reliability of the reconstruction.

Fainter and closer: finding planets by symmetry breaking.

Imaging of planets is very difficult, due to the glare from their nearby, much brighter suns. Static and slowly-evolving aberrations are the limiting factors, even after application of adaptive optics. The residual speckle pattern is highly symmetrical due to diffraction from the telescope's aperture. We suggest to break this symmetry and thus to locate planets hidden beneath it. An eccentric pupil mask is rotated to modulate the residual light pattern not removed by other means. This modulation is then exploited to reveal the planet's constant signal. In well-corrected ground-based observations we can reach planets six stellar magnitudes fainter than their sun, and only 2-3 times the diffraction limit from it. At ten times the diffraction limit, we detect planets 16 magnitudes fainter. The stellar background drops by five magnitudes.

Wide-angle chromatic aberration corrector for the human eye.

The human eye is affected by large chromatic aberration. This may limit vision and makes it difficult to see fine retinal details in ophthalmoscopy. We designed and built a two-triplet system for correcting the average longitudinal chromatic aberration of the eye while keeping a reasonably wide field of view. Measurements in real eyes were conducted to examine the level and optical quality of the correction. We also performed some tests to evaluate the effect of the corrector on visual performance.

Comparison of Hartmann analysis methods.

Analysis of Hartmann-Shack wavefront sensors for the eye is traditionally performed by locating and centroiding the sensor spots. These centroids provide the gradient, which is integrated to yield the ocular aberration. Fourier methods can replace the centroid stage, and Fourier integration can replace the direct integration. The two--demodulation and integration--can be combined to directly retrieve the wavefront, all in the Fourier domain. Now we applied this full Fourier analysis to circular apertures and real images. We performed a comparison between it and previous methods of convolution, interpolation, and Fourier demodulation. We also compared it with a centroid method, which yields the Zernike coefficients of the wavefront. The best performance was achieved for ocular pupils with a small boundary slope or far from the boundary and acceptable results for images missing part of the pupil. The other Fourier analysis methods had much higher tolerance to noncentrosymmetric apertures.

Adaptive optics implementation with a Fourier reconstructor.

Adaptive optics takes its servo feedback error cue from a wavefront sensor. The common Hartmann-Shack spot grid that represents the wavefront slopes is usually analyzed by finding the spot centroids. In a novel application, we used the Fourier decomposition of a spot pattern to find deviations from grid regularity. This decomposition was performed either in the Fourier domain or in the image domain, as a demodulation of the grid of spots. We analyzed the system, built a control loop for it, and tested it thoroughly. This allowed us to close the loop on wavefront errors caused by turbulence in the optical system.

Wavefront reconstruction from its gradients.

Wavefronts reconstructed from measured gradients are composed of a straightforward integration of the measured data, plus a correction term that disappears when there are no measurement errors. For regions of any shape, this term is a solution of Poisson's equation with Dirichlet conditions (V = 0 on the boundaries). We show that for rectangular regions, the correct solution is not a periodic one, but one expressed with Fourier cosine series. The correct solution has a lower variance than the periodic Fourier transform solution. Similar formulas exist for a circular region with obscuration. We present a near-optimal solution that is much faster than fast-Fourier-transform methods. By use of diagonal multigrid methods, a single iteration brings the correction term to within a standard deviation of 0.08, two iterations, to within 0.0064, etc.

Hartmann-Shack analysis errors.

A theoretical model for reconstruction errors in the Hartmann-Shack wave-front sensor was constructed. The measured pattern of a regulargrid of spots can be analyzed by their individual centroiding or by a globalFourier demodulation. We investigate pixelization errors in the cameraand Poisson errors in the camera pixels. We show that by the Fourier demodulation technique it is possible to overcome pixelization errors which occur in the traditional centroid technique. By supporting simulations we show that the two methods coincide for an infinite number of pixels per spot.

Reduction of laser spot elongation in adaptive optics.

Adaptive optics systems measure the wave front to be corrected by use of a reference source, a star, or a laser beacon. Such laser guide stars are a few kilometers long, and when observed near the edges of large telescopes they appear elongated. This limits their utility significantly. However, with more sophisticated launch optics their shape and length can be controlled. We propose to string around the rim of a telescope a number of small telescopes that will add laser beams in the scattering medium to create a compact spot. The method could also be adapted for ocular adaptive optics.

Direct demodulation of Hartmann-Shack patterns.

Hartmann-Shack wave-front sensors produce a distorted grid of spots whose deviation from perfection is linear with the wave-front gradient. Usually, the centroid of each spot is calculated to provide that deviation, but it is also possible to perform the calculation by Fourier demodulation of the spot pattern [Opt. Commun. 215, 285, 2003]. We show that this demodulation can be performed directly on the grid, without reverting to Fourier transforms. Tracking the motion of each centroid individually is limited to well-defined spots with motions smaller than their pitch. In contrast, our method treats the image as a whole, is not limited to non-overlapping or sharp spots, and allows large spot motions. By replicating the array of spots slightly beyond the edge of the aperture, we reduce the chance for boundary phase dislocations in the reconstruction of the wave front. The method is especially suited to very large arrays.

Separating atmospheric layers in adaptive optics.

Several optical schemes have been proposed to measure the separate contributions of atmospheric layers for astronomical adaptive optics. I show here that simple conjugation of the wave-front sensors to the layers is sufficient. Although a larger camera is required for a larger field of view, only the pixels that sense stars are being read out. The nearly periodic Hartmann data are analyzed by Fourier filtering so that the signals from all stars are added up while most of the noise is excluded. Acoustic Hartmann wave-front sensors [Opt. Lett. 26, 1834 (2001)1 that switch between layers improve flexibility and sensitivity.