Elizabeth Daly

Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors

The main applications of adaptive optics are the correction of the effects of atmospheric turbulence on ground-based telescopes and the correction of ocular aberrations in retinal imaging and visual simulation. The requirements for the wavefront corrector, usually a deformable mirror, will depend on the statistics of the aberrations to be corrected; here we compare the spatial statistics of wavefront aberrations expected in these two applications. We also use measured influence functions and numerical simulations to compare the performance of eight commercially available deformable mirrors for these tasks. The performance is studied as a function of the size of the optical pupil relative to the actuated area of the mirrors and as a function of the number of modes corrected. In the ocular case it is found that, with the exception of segmented mirrors, the performance is greatly enhanced by having a ring of actuators outside the optical pupil, as this improves the correction of the pupil edge. The effect is much smaller in the case of Kolmogorov wavefronts. It is also found that a high Strehl ratio can be obtained in the ocular case with a relatively low number of actuators if the stroke is sufficient. Increasing the number of actuators has more importance in the Kolmogorov case, even for the relatively weak turbulence considered here.

Linearity of the pyramid wavefront sensor.

The pyramid wavefront sensor is very similar to the Fourier knife-edge test, but employs dynamic modulation to quantify the phase derivative. For circular modulation, we compare approximate geometrical optics calculations, more exact diffraction calculations, and experimental results. We show that both the sinusoidal and the approximate linear relationship between wavefront derivative and wavefront sensor response can be derived rigorously from diffraction theory. We also show that geometrical, diffraction and experimental results are very similar, and conclude that the approximate geometrical predictions can be used in place of the more complex diffraction results.

Wavefront correction through image sharpness maximisation

A key component of any adaptive optics system (AO) for the correction of wavefront aberrations, is the wavefront sensor(WFS). Many systems operate in a mode where a WFS measures the aberrations present in the incoming beam. The required corrections are determined and applied by the wavefront corrector - often a deformable mirror (DM). We wish to develop a wavefront sensor-less correcting system, as derived from the original adaptive optics system of Muller and Buffington. In this experiment we employ a method in which a correcting element with adjustable segments is driven to maximise some function of the image. We employ search algorithms to find the optimal combination of actuator voltages to maximise a certain sharpness metric. The “sharpness” is based on intensity measurements taken with a CCD camera. Results have been achieved using a Nelder-Mead variation of the Simplex algorithm. Preliminary results show that the Simplex algorithm can minimise the aberrations and restore the Airy rings of the imaged point source. Good correction is achieved within 50-100 iterations of the Simplex algorithm. The results are repeatable and so-called “blind” correction of the aberrations is achieved. The correction achieved using various sharpness algorithms laid out by Muller and Buffington are evaluated and presented.

Ophthalmic wavefront measurements using a versatile pyramid sensor

We describe the operation of a pyramid wavefront sensor used to measure and correct aberrations of the human eye. The system is designed for maximum speed when running in closed loop but can also provide calibrated open-loop measurements of aberrations with a range of sampling options. A detailed characterization of the system was performed to ensure measurement accuracy. Ocular aberrations after correction had root-mean-square errors consistently less than 0.1μm over a 6mm pupil for all subjects tested. The system frame rate is 83Hz in both open- and closed-loop modes.

Task-based assessment of deformable mirrors

A performance comparison is made using a number of commercially available Deformable Mirrors(DM) in fitting both ocular and atmospheric wavefronts. Least squares phase fitting simulations are performed for five mirrors using experimentally obtained mirror influence functions. The DMs used cover a range of DM technologies with varying size and cost. The phase fitting performance of these mirrors is found to be a function of influence function shape, actuator density and available mirror stroke.

Supplementary active optics for illumination within an adaptive optics system

The use of additional adaptive optics to manipulate the beacon in an adaptive optics system for the human eye opens up many opportunities. Possibilities include better beacon creation, correction of gross aberrations that the beam acquires as it passes into the eye, symbiotic beams to guide or locate a probe or medical beam, and examination of the higher order aberrations experienced by the beam as it enters the eye. We describe the use of active optics for creation of the beacon in an adaptive optics system that incorporates a fundus imaging arm. In describing the possibilities for beacon shaping and steps that may be employed to use this to create a sharper or more versatile beacon, we determine the effects of such shaping on the performance of the system. Results are presented for both model and human eyes. The beacon shaping incorporates Bessel beam creation with tip-tilt and defocus correction from a mask on a spatial light modulator. Visual feedback from images of the beacon as it appears at the retina is used to refine it.

Measuring phase aberrations using a pyramid wave front sensor

The pyramid wavefront sensor (PWS) was initially proposed by astronomers to measure aberrations introduced by the atmosphere. More recently it has been used to measure aberrations of the human eye, and has been successfully incorporated into an adaptive optics loop to correct those aberrations. The raw sensor signal can be used as feedback to control a wavefront correcting device, or with appropriate scaling, to reconstruct the wavefront map in the pupil. In practice, use of dynamic modulation allows one to tune the sensitivity and range of the sensor to best suit the particular application. We describe a PWS primarily designed to perform in-vivo measurements of human eyes. The sensor is calibrated over a wide range of settings allowing one to choose those best suited to a specific task. For example, enhanced-sensitivity measurements of very small aberrations require small range (closed loop adaptive optics). Alternatively, if one wants to measure the aberrations of the eye without any correction, the range required is subject-dependent and can be large; the price paid is in reduced sensitivity . We present in-vivo measurements of human eyes taken at a number of experimental settings and compare the performance of the PWS at each.

Wave-front correction of a femtosecond laser using a deformable mirror

Typical applications of ultra-high-power femtosecond lasers include precision drilling and surface micro-machining of metals, and micro-structuring of transparent materials. However, high peak-power pulsed lasers are difficult to focus close to the diffraction limit because of aberrations that induce deviations from a perfect spatial wave-front. The sources of these aberrations include thermally induced and nonlinear optical distortions, as well as static distortions such as those introduced by gratings used in chirped-pulse amplification (CPA). A spatially clean beam is desirable to achieve the highest possible intensity on-target, and to minimize the energy deposited outside the central focus. One way to achieve this is to correct the wave-front using an adaptive optical element such as a deformable mirror, a more cost-effective solution than increasing peak intensity by providing further pulse amplification. The wave-front of the femtosecond system is measured using a Hartmann-Shack wave-front sensor, and corrected with a 37-channel deformable membrane mirror used slightly off-axis. The deformable mirror has been tested with a FISBA OPTIK μPhase HR digital interferometer, which is also used to calibrate the performance of the wave-front sensor. The influence of fluctuations of the laser on the measurement is minimised by averaging the centroid positions obtained from several consecutive frames. The distorted wave-front is compared to a reference flat wave-front which is obtained from a collimated laser diode operating at the same wavelength as the femtosecond system. The voltages on the deformable mirror actuators are then set to minimise the difference between the measured and reference wave-fronts using a simple least squares approach. Wave-front sensor and correction software is implemented in Matlab.

Improved fixation quality provided by a Bessel beacon in an adaptive optics system

We investigate whether a structured probe beam that creates the beacon for use in a retinal imaging adaptive optics system can provide useful side effects. In particular we investigate whether a Bessel beam that is seen by the subject as a set of concentric rings has a dampening effect on fixation variations of the subject under observation. This calming effect would allow longer periods of observation, particularly for patients with abnormal fixation.

Requirements for MEMS mirrors for adaptive optics in the eye

MEMS is one of several emerging technologies for fabricating wavefront correctors for use in adaptive optics systems. Each technology has its own advantages and disadvantages. In order to compare devices, it is useful to define a task and make a comparison based upon the effectiveness of each device for this task. Such an approach implies, of course, that device A might be better suited for task X whereas device B is better suited for task Y. In adaptive optics, this situation is already known: deformable mirrors that are relatively effective at compensating for atmospheric turbulence are not necessarily the mirrors that one would choose for correction of the aberrations of the eye. This is essentially because the statistical modal distribution of the aberrated wavefronts in each case are different. In this talk, we shall present a method for systematically evaluating the effectiveness of different mirror (or transmissive) technologies in adaptive optics in the eye. It uses a model for the aberrations of the eye (such as that developed by Thibos et al1) and a least squares fitting procedure. Results will be presented for at least 4 mirrors, including a 12x12 MEMS device. The key point is that it is the effectiveness of each actuator signal that is important, not the raw number of actuators.