Optical observations by ground‐based astronomers have long been limited by the distorting effects of the Earth's atmosphere. Primary mirrors have been polished to exquisite accuracy for telescopes with apertures as large as 10 meters, but at optical wavelengths these can deliver an angular resolution typically no better than that of a 25‐cm telescope, as atmospheric turbulence deforms the image on a millisecond time scale. One (highly expensive) approach to overcome this problem has been to loft instruments such as the Hubble Space Telescope above the atmosphere. Another approach, pursued by instrument builders in the astronomy community and their counterparts in the military, has been to design electro‐optical systems that measure and undo the effects of clear‐air turbulence in real time. (See figure 1.) A number of such adaptive optic devices have already been built and operated on large ground‐based telescopes, delivering near‐diffraction‐limited performance at infrared and visible wavelengths. With th...

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Adaptive Optics in Astronomy

The problem of fitting a wave-front distortion estimate to a (single-instant) set of phase-difference measurements has been formulated as an unweighted least-square problem. The least-square equations have been developed as a set of simultaneous equations for a square array of phase-difference sensors, with phase estimates at the corner of each measurement element. (This corresponds to the standard Hartmann configuration and to one version of a shearing interferometer of a predetection compensation wave-front sensor.) The noise dependence in the solution of the simultaneous equations is found to be expressible in terms of the solution to a particular version of the measurement inputs to the simultaneous equation, a sort of “Green’s-function” solution. The noise version of the simultaneous equations is solved using relaxation techniques for array sizes from 4 × 4 to 40 × 40 phase estimation points, and the mean-square wave-front error calculated as a function of the mean-square phase-difference measurement error. It is found that the results can be approximated within a fraction of a percent accuracy by 〈(δΦ)2〉=0.6558[1+0.2444 ln(N2)]σpd2, where 〈(δΦ)2〉 is the mean-square error (rad2) in the estimation of the wave-front distortion, for a square array consisting of N2 square subaperture elements over which two phase-difference measurements are made—one phase difference across the x dimension and the other difference across the y dimension. Here σpd2 is the mean-square error (rad2) in each phase-difference measurement.

Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements

Light focusing plays a central role in biomedical imaging, manipulation and therapy. In scattering media, direct light focusing becomes infeasible beyond one transport mean free path. All previous methods used to overcome this diffusion limit lack a practical internal ‘guide star’. Here, we propose and experimentally validate a novel concept called time-reversed ultrasonically encoded (TRUE) optical focusing to deliver light into any dynamically defined location inside a scattering medium. First, diffused coherent light is encoded by a focused ultrasonic wave to provide a virtual internal guide star. Only the encoded light is time-reversed and transmitted back to the ultrasonic focus. The time-reversed ultrasonically encoded optical focus—defined by the ultrasonic wave—is unaffected by multiple scattering of light. Such focusing is particularly desirable in biological tissue, where ultrasonic scattering is ~1,000 times weaker than optical scattering. Various fields, including biomedical and colloidal optics, can benefit from TRUE optical focusing.

Time-reversed ultrasonically encoded optical focusing into scattering media.

The main advantage of confocal microscopes over their conventional counterparts is their ability to optically “section” thick specimens; the thin image slices thus obtained can be used to reconstruct three-dimensional images, a capability which is particularly useful in biological applications. However, it is well known that the resolution and optical sectioning ability can be severely degraded by system or specimen-induced aberrations. The use of high aperture lenses further exacerbates the problem. Moreover, aberrations can considerably reduce the number of photons that reach the detector, leading to lower contrast. It is rather unfortunate, therefore, that in practical microscopy, aberration-free confocal imaging is rarely achieved. Adaptive optics systems, which have been used widely to correct aberrations in astronomy, offer a solution here but also present new challenges. The optical system and the source of aberrations in a confocal microscope are considerably different and require a novel approach to wavefront sensing. This method, based upon direct measurement of Zernike aberration modes, also exhibits an axial selectivity similar to that of a confocal microscope. We demonstrate an adaptive confocal fluorescence microscope incorporating this modal sensor together with a deformable membrane mirror for aberration correction. Aberration corrected images of biological specimens show considerable improvement in contrast and apparent restoration of axial resolution.

https://www.pnas.org/content/pnas/99/9/5788.full.pdf

Adaptive aberration correction in a confocal microscope

In this work, we report a novel high capacity (number of degrees of freedom) open loop adaptive optics method, termed digital optical phase conjugation (DOPC), which provides a robust optoelectronic optical phase conjugation (OPC) solution. We showed that our prototype can phase conjugate light fields with ~3.9 x 10−3 degree accuracy over a range of ~3 degrees and can phase conjugate an input field through a relatively thick turbid medium (μsl ~13). Furthermore, we employed this system to show that the reversing of random scattering in turbid media by phase conjugation is surprisingly robust and accommodating of phase errors. An OPC wavefront with significant spatial phase errors (error uniformly distributed from – π/2 to π/2) can nevertheless allow OPC reconstruction through a scattering medium with ~40% of the efficiency achieved with phase error free OPC.

Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation

ATMOSPHERIC turbulence limits the resolution of a ground-based astronomical telescope to much worse than the diffraction limit of the instrument. An adaptive-optics system, in which some part of the optical train of the telescope can be adjusted in real time, can compensate for atmospheric turbulence, but a beacon or guide-star is needed to allow measurement of the atmospheric optical distortion. It has been suggested1 that the measurement could be achieved by means of a synthetic beacon (also called an artificial beacon, and sometimes a laser guide-star) formed by atmospheric backscatter from a ground-based laser. We have performed an experiment to demonstrate atmospheric compensation using a synthetic beacon. With a pulsed dye laser to generate the beacon and a 241-channel adaptive-optics system to perform the phase correction, we obtained almost diffraction-limited resolution of star images in the visible part of the spectrum. Our results indicate that there are no technical barriers to atmospheric compensation using synthetic beacons at ground-based observatories.

Compensation of atmospheric optical distortion using a synthetic beacon

Most atmospheric-turbulence-compensation experiments have been performed under weak-scintillation conditions; conventional phase-conjugate adaptive-optics systems usually provide good correction for these conditions. We have performed an experiment over a 5.5-km horizontal propagation path to explore the efficacy of conventional adaptive optics in strong-scintillation conditions. The experimental results showed a significant degradation in correction as the scintillation increased. The presence of branch points in the phase appears to be the primary reason for the degradation in correction as the scintillation increases.

Atmospheric-compensation experiments in strong-scintillation conditions.

We have performed what are, to our knowledge, the first measurements of wave fronts propagated through atmospheric turbulence with the use of a synthetic beacon in the mesospheric sodium layer. The synthetic-beacon wave fronts showed reasonable agreement with those from reference stars. The sodium-layer beacon performance was also compared with that of beacons produced by Rayleigh backscatter in the 6-20-km altitude range.

Atmospheric-turbulence measurements using a synthetic beacon in the mesospheric sodium layer.

A laboratory experiment has demonstrated the effectiveness of compensating for forced-convection-dominated cw thermal blooming by using a deformable mirror to add phase corrections to the laser beam. In agreement with theoretical predictions, the peak focal-plane irradiance has been increased by a factor of 3 under severely bloomed conditions.

Thermal-blooming compensation: experimental observations using a deformable-mirror system

We present experimental results that demonstrate real-time, atmospheric-turbulence compensation of a bright star with the use of two synthetic beacons. Each beacon was used to measure the phase aberrations over only part of the telescope aperture, a configuration that is suitable for reducing focal-anisoplanatism error. To our knowledge, this is the first demonstration of atmospheric compensation with the use of multiple synthetic beacons.

Charles A. Primmerman

Papers

Compensation of atmospheric optical distortion using a synthetic beacon

Atmospheric-compensation experiments in strong-scintillation conditions.

Atmospheric-turbulence measurements using a synthetic beacon in the mesospheric sodium layer.

Thermal-blooming compensation: experimental observations using a deformable-mirror system

Experimental demonstration of atmospheric compensation using multiple synthetic beacons.