Are digital adaptive optics possible?

Question

Adaptive optics generally apply slight changes to mirrors to account for atmospheric turbulence. These generally require either a mirror to be broken up into smaller mirrors, each with their own actuator, or for a single large mirror to be slightly deformed by many different actuators.

Is it possible to do much of this digitally?

Couldn't software slightly attenuate or amplify each pixel at each time-slice collected from a passive mirror? These changes would depend on the distortions measured by a guide star or laser (this digital system would still require a guiding light)? I suspect this would probably be less accurate than true adaptive optics, but it would also be far less expensive (as you wouldn't need so many actuators).

Has this approach been studied and dropped? Is it ridiculous and not even theoretically possible? I'm curious if anything has researched this idea.

Answer 1

The problem with your approach is that the deformable mirror changes the phase of the light across the mirror, where the light is not focussed. The light at the sensor array is focussed, and what you get is the intensity which is, roughly, the Fourier Transform of the phase front at the mirror. By the time you have intensity, the phase information has been lost.

edit for clarity:

The sensor array measures the intensity, at which point the phase info is irretrievable. If you remove the sensor array and re-measure past the focal plane, yes, you can get phase info -- see "Plenoptic cameras."

Now, there are other techniques -- you might be interested in searching for papers on "Lucky Imaging" , which basically takes as many images as possible and throws away the distorted ones.

Answer 2

Each part of the mirror contributes to every pixel in the image, and the pockets of atmospheric distortion may be only 10-20 cm wide. If you look at a bright planet through a 30+ cm telescope in poor seeing conditions, the image looks like a stack of several sub-images shifting in and out of alignment, each from a different part of the mirror. To oversimplify, adaptive optics systems continually tweak the mirror segments to keep those sub-images aligned.

If you can accept a much higher detector cost in exchange for eliminating the actuator cost, it's possible to make an array of small telescopes, each with its own video camera, and align the shifting sub-images in software. But then diffraction by the smaller apertures would limit the system resolution unless you built an optical interferometer, which has its own category of difficulties to overcome.

Answer 3

@CarlWitthoft's answer is misleading if not wrong.

The Fourier transform of a field does not lose phase information. If you let the light drift another focal length and then use an identical mirror, you completely recover the initial electric field distribution incident at the telescopes entrance aperture. Information is not lost here.

The problem is not related to the optics at all.

The problem is that the detector (silicon CCD or photographic plate or whatever) measures time-averaged intensity of the light, which is the absolute value squared of the field at the detector's surface. It's this squaring and averaging in conventional detection schemes that makes phase information unrecoverable.

There is a whole field of research into trying to make phase-sensitive pixels for cameras but it's pretty academic, and you lose significantly in resolution and other performance metrics when you try to do this.

But what about longer wavelengths?

Your idea can and indeed does work in radio astronomy, even for microwaves and millimeterwaves. This is because the electric field received by each pixel (which is one dish antenna of an array of them) can indeed be absolutely digitized. They down-convert frequencies as high as a THz to one or two GHz and then amplify and digitize it with extremely fast ADCs.

Once that is done, you can correct for distortions in the wavefront arriving at your array of antennas in software. This process is explained further in answers to Would Adaptive Optics be Useful in Radio Astronomy?

Answer 4

With enough computational power every pixel of a camera sensor could be processed individually. Outputs amplified or reduced to compensate for variations of light levels across the sensor. Stacking algorithms can discard those pixels that do not receive a constant input.

Photo shopping to the max. Make the Astro Photographers life easier. The problem for everyone else would be in deciding where science becomes art.