When does Lucky Imaging Work Better Than Adaptive Optics Techniques?

There is no doubt that Adaptive Optics techniques have been successful in certain areas. When the reference star is bright enough it has been possible to achieve very high Strehl ratios, and Adaptive Optics has been used extensively in the near infrared where we have not yet tried to apply Lucky Imaging techniques due to the lack of suitable detector systems. However there are a number of circumstances where the achievements of Lucky Imaging have exceeded those of Adaptive Optics. In order to understand the circumstances under which Lucky imaging excels we need to look at the way that Adaptive Optic systems generally work.

Adaptive Optics works by breaking up the telescope aperture into cells of size of the order of r₀ and detecting the reference star in each cell. This is most often done with the Shack Hartmann sensor:

The images produced show an array of image is of a star, one from each of the lenslets in the Shack Hartmann sensor.

A movie showing a typical image sequence can be seen (1.3 MBtyes) by clicking on the image. This shows images from the 4.2m William Herschel Telescope on La Palma using an 8x8 lenslet array in a Shack-Hartmann sensor (JOSE Camera).

The relative motions and positions of the star within each cell are then used to work out what the phase errors in the wavefront are at any instant and a computer controlled flexible mirror is distorted to compensate for these phase errors. A schematic of such a system is shown below, where the blue light from the star is used for the wavefront sensor to give an image like those shown above, and the deduced wavefront errors drive a wavefront corrector (here a flexible mirror) to remove the errors in the input wavefront, and therefore pass a corrected (and ideally diffraction limited) wavefront on to the science instrument.

(Image from Gordon Love, Durham).

If the reference star is very bright then it may be possible to work out what the phase errors are and to correct them before they change (and remember that they are changing very rapidly on timescales of the order of milliseconds). The reference star has to be very bright anyway because it must be detected with good signal-to-noise in each of the cells of the sensor rather than over the whole aperture of the telescope as is the case with the Lucky Imaging technique. Typically perhaps 20 cells in the sensor would be used with a 2.5 metre telescope. In practice it means that there is a very small probability that a reference star will be found close enough to the object of scientific interest for adaptive optics to be usable whereas with Lucky Imaging we are able to work with very much fainter reference stars. We find that we therefore have a much higher probability of finding a reference star within our field of view. For more information on reference star magnitudes and availability click here.

Isoplanatic Patch Size

The other problem which greatly affects the application of Adaptive Optics is the limited isoplanatic patch. There are a few cases in astronomy when we are happy simply to resolve two objects. We may wish to look at a very close pair of stars so that we can separate the components and look at their relative motions. However virtually all astronomy depends on comparing the brightness of the object under study with others in the field so that we can measure positions and brightnesses with useful accuracy. The problem with adaptive optics is that the shape of the star images changes very rapidly with the distance of an object from the reference star. This arises because adaptive optics tries to compensate for the phase fluctuations in the atmosphere at every instant, including when they are particularly bad. The poorer these conditions are the more rapidly the image shape changes with distance from the reference star. With Lucky Imaging we discard images formed when the phase fluctuations are bad and only use those which are least affected. This gives us star image profiles that vary much more slowly across the image. Not only does this mean that we get images that are much easier to work with for astronomers but we are also able to find reference stars over a much larger area of sky than is possible with adaptive optics.  This larger area to search for reference stars means that we have a much higher probability of finding one. The mean size of the isoplanatic patch measured at Paranal, the site of the European Southern Observatory VLT, is only about 2.6 arc seconds in V band (equivalent to about 4.5 arcsec in I-band at 850nm) whereas our measurements given isoplanatic patch approaching one arc minute in diameter. For more information on why Lucky imaging gives an isoplanatic patch so much larger than does Adaptive Optics click here.

Atmospheric Turbulence Model Problems

One final problem which is only becoming clear now that Adaptive Optics systems are being commissioned and found to be less good than expected is due to the fact that although atmospheric turbulence has a power spectrum very similar to that predicted by models based on Kolmogorov turbulence theory, the turbulence actually found in practice is significantly different in a way that makes the construction of Adaptive Optic systems very much harder. For more information on the complexities of atmospheric turbulence click here.

Reference Star Magnitudes and Availability

Both Adaptive Optics and Lucky Imaging require the presence in the field of view of a reference star bright enough for the system to use to derive the wavefront errors (in the case of Adaptive Optics) or to provide an image quality indicator (in the case of Lucky Imaging). With Adaptive Optics it is imperative to run the wavefront sensor much faster than the characteristic seeing timescale so that the system can effectively compensate for the seeing before it all changes again. With characteristic seeing de-correlation timescales in the range of 10-30 milliseconds sensors are usually operated with readout frame times in the 1-10 millisecond range. In addition, in order to get a significant number of measurement points across the telescope aperture for the phase errors to allow a meaningful interpolation so as to deduce the wavefront errors, the light from the telescope must be divided amongst a large number of sensors. In typical systems the sensor scale corresponds to the square grid of approximately 50 centimetres per sensor. This means that with a 2.5 metre telescope the light is shared amongst perhaps 20 sensors.

With Lucky Imaging all the light from the reference star entering the telescope is used by a single sensor. In addition Lucky Imaging only needs to run at a speed that is fast enough to give a reasonable probability that the reference star is imaged as being close to the limiting resolution of the telescope. It might be thought that with characteristic seeing de-correlation timescales in the range of 10-30 milliseconds that Lucky Imaging has to operate with frame times in this range. However because we are seeking those moments with good seeing, when the wavefront errors across the whole telescope are small, it also turns out that the de-correlation timescales around the moment of good seeing are significantly longer than this and we have been surprised that we are able to do so much work on typical nights even with frame rates as low as 12 frames per second (80 millisecond frame time).

The net effect is that Lucky Imaging is able to use reference stars that are more than three magnitudes fainter (because the light is not split amongst many individual sensors) plus a further 1.5-2.5 magnitudes fainter because we are able to run our sensor significantly more slowly. This difference of typically more than five magnitudes is critical for a practical system because of the sky surface densities of reference stars as a function of magnitude. This is shown in the figure below.

(Courtesy: D. Simons, Gemini)

Here we see that the probability of finding a reference star that is bright enough for an Adaptive Optic system, typically a 12-13 magnitude star, is extremely small whereas the probability of finding one that is bright enough for Lucky Imaging within our isoplanatic field area and which is typically a 17 magnitude star with a back illuminated, photon counting EMCCD, is dramatically greater.

Isoplanatic Patch Size Differences between Lucky Imaging and Adaptive Optics

The isoplanatic patch is not a term that is precisely defined and we have to be careful in making and comparisons between Lucky Imaging and Adaptive Optics. The isoplanatic patch is the name given to the area of sky over which the wavefront errors are closely correlated. If we look at two objects which are separated by an angular distance of Θ then as Θ becomes larger we will find that we are looking increasingly through different turbulent cells in the atmosphere. We know that Θ is related to r₀ and given a characteristic height D of the turbulent layer above the ground then we find that very roughly Θ = r₀/D. The isoplanatic patch size will be different from that of the isoplanatic patch size for Lucky or that for speckle imaging (e.g. http://www.iop.org/EJ/abstract/0150-536X/13/2/002/ ), for the following reasons.

Adaptive Optics tries to measure the wavefront errors at all times, even when they are at their most extreme, and to correct for them and use the light from the science object all the time. With Lucky Imaging, however, we preferentially select those images where the wavefront is at its least distorted across the whole aperture of the telescope and in this case we find that the angular distance Θ between two objects where the phase variations due to the atmospheric turbulence become significantly de-correlated is very much larger. This is equivalent to saying that the isoplanatic patch size is very large for the lowest power spectrum frequencies in the atmospheric turbulence and become smaller and smaller as we move to higher and higher frequency disturbances in the atmosphere. Lucky Imaging simply avoids using those frames substantially affected by the higher frequency disturbances and only works with those dominated by the lowest power spectrum frequencies.

As a consequence we find that Lucky Imaging gives isoplanatic patch sizes that are very much larger than routinely obtained with adaptive optics, typically 5-15 times the size depending on the fraction of images used in creating the final image.

An example of the actual isoplanatic patch sizes obtained with AO we look at the beautiful image of part of NGC3603 obtained with the NAOS/CONICA system on the VLT.

This image was taken in K-band (2.2 microns) with one of the VLT 7.5m telescopes, in 0.5 arcsec seeing. so this image is highly comparable with those obtained with our Lucky Imaging runs on the NOT, a 2.5m telescope in I-band (850nm). This uses an extremely bright star (V=8) as reference in the centre of this exceptionally crowded field, and we see that the images close to the reference star show faint Airy rings round them. Below is a section of the above image very close to the reference star.

However, at a radial distance of only 10 arcsec from the reference star, equivalent to only 3.5 arcsec if this had been taken in I-band as we have done on the NOT, the images are very different in character.

These images are obviously very much more diffuse, and it is clear that it would be extremely difficult to undertake accurate photometry of this field even over 10 arcsec in K-band, unless the object under study were so well separated that there was no confusion from overlapping haloes of nearby stars.

This demonstrates clearly why isoplanatic patch size is so critical for genuine astronomical studies.  With Lucky Imaging we find isoplanatic patch sizes of 50 arcsec diameter in I-band, equivalent to 160 arcsec diameter in K-band, or well over one hundred times the area accessible with AO.