Diffraction-limited 800nm imaging with the NOT


This article is based on a recently accepted paper to Astronomy and Astrophysics entitled `Diffraction-limited 800nm imaging with the 2.56m Nordic Optical Telescope' by J.E. Baldwin, et al  [1] (postscript copy).

Described here is an exciting new technique to acquiring diffraction-limited images in the visible waveband from medium size telescopes. It exploits the property that for nominal seeing on a good site (approx 0.5 arcseconds) there is a probability that occasionally for short periods the atmosphere will produce a sharp image. If these sharp images are identified, selected and co-added by shift and add, then an image close to the diffraction limit of the telescope can be obtained.

The principle behind the method is to take many short exposure images and to select the good ones for construction of the final picture. The occurrence of a "lucky exposure" will be when the phase variations due to the atmosphere are less than ~1 radian across the aperture of the telescope. Fried [2] calculated the probability P, of having a phase variation across a given aperture D of less than 1 radian for a seeing defined by the spatial scale r0:

P ~ 5.6exp(-0.1557(D/r0)2)

For the NOT given a seeing of 0.5 arcseconds at 800nm then D/r0 will be 7, giving a probability of getting one exposure with a Strehl ratio greater than 0.37 to be one in 350. For a telescope of 3.6m diameter the probability at 800nm will fall to only one in 1000000, implying the technique can only realistically be carried out on medium sized telescopes (<2.5m) with a well adjusted primary mirror.

Observations and Analysis

To demonstrate the technique a camera with a frame transfer 512x512 15um CCD run by a AstroCam 4100 controller and capable of frame rates greater than 150Hz was mounted on the NOT with some simple reimaging optics to produce an image scale of 41~milliarcseconds/pixel giving a FWHM of the diffraction-limited image of 66~milliarcseconds at 800nm, with the HiRAC i filter centred at 810nm with a bandwidth of 120nm defining the band.

Observations where made during the two technical nights 12-13 May 2000, typically at zenith angles < 20 degrees  though angles up to 50 degrees where explored. The seeing during these two nights was around 0.5 arcseconds.

A brief description of the analysis of the data procedure is: Using only runs with known good images, the FWHM and total stellar flux was determined, then each frame was interpolated to give a factor of 4 times greater resolution. The Strehl ratio for each frame was derived and all ``good'' frames selected with a Strehl ratio greater than some chosen value, shifted so the peak pixels where superimposed and stacked to produce a single image.

To go to fainter objects successive short exposure frames were added together without image motion correction to give longer exposure times. It has been found that periods as long as 30ms could be used with only a small reduction of the observed Strehl ratio.


Figure 1 shows an example image of zeta Bootis created using the best 1% of exposures from a dataset of 23200 frames. The image shows a diffraction limited central peak (Strehl = 0.26, FWHM = 83x94 milliarcseconds) and first airy ring superposed on a faint halo for each star. 300 milliarcseconds from the component stars the surface brightness of the halo reaches only 2% of that in the stellar disks. The high dynamic range of this technique is evident from the contour plot of the same image (Figure 2). The fluctuations in the halo reach only 0.1% of the peak brightness 700 milliarcseconds from the stars.

Figure 1 : The best 1% of exposures of zeta Bootis, shifted and added.

Contour plot of the image of $\zeta$ Bo\"{o}tis. Contour levels at0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 40, 60, 80\% peak intensity.

Figure 2 : Contour plot of the image of zeta Bootis.

Contour levels at 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 40, 60, 80% peak intensity.

Figure 3 : Image of epsilon Aquilae showing its first airy ring.

Figure 3 show an image of  epsilon Aquilae and its first airy ring. The image has a Strehl ratio of 0.3 and a FWHM of 79x94 milliarcseconds.

Conclusions and Future Prospects

The observations described here show that the selection of short exposure images can reliably provide diffraction limited images with Strehl ratios of 0.25 - 0.30 at wavelengths as short as 0.8um with 2.5m telescopes. The relatively high readout noise of the present camera (~100e-) sets a limiting magnitude of +11.5 for 30ms exposures. Current development of extremely low noise high quantum efficiency CCD's (Mackay etal. 2001 [3]) will allow this technique to be extended to reference stars as faint as +15.5 and fainter  than +23 for unresolved objects in the same isoplanatic patch. Potentially for good seeing (less than 0.5arcseconds) for a dominate turbulent atmospheric layer at 2.5km then 100% sky coverage is obtainable with usable reference stars for a 2.5m telescope.


[1] Baldwin J. E., Tubbs R. N., Cox G. C., Mackay C. D., Wilson R. W., & Andersen M. I., 2000, A& A (in press)

[2] Fried, D. L. 1978, Optical Society of America Journal, 68, 1651

[3] Mackay, C. D., Bell, R., Burt, D., Moody, I. & Tubbs, R. N., 2001, SPIE Proceedings, 4306, (in press)