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Resolution realities: what size telescope do you need to shoot astrophotos that resolve subarcsecond detail on solar-system bodies?

THE BEST PHOTOGRAPHS from any telescope are limited by issues that include diffraction, optical quality, image motion, digital-camera noise, and especially atmospheric turbulence. Together these create obstacles that hide fine details. While powerful image-processing algorithms can rescue some of the detail compromised by these conditions, there are claims that super-resolution--finer detail than that allowed by diffraction theory--is achievable. I wondered how much is truly possible and decided to investigate on my own.

Controlled Conditions

To test how accurately astrophotographers can capture exceedingly small detail in planetary pictures, I attempted to image tiny features under controlled conditions. Rather than shooting objects in the sky, I made diffraction-limited pictures of targets indoors. I placed printed images of Jupiter's moons Ganymede and Io and Saturn's rings 10 meters (33 feet) away from a 105-millimeter camera lens stopped down enough to make diffraction the dominant factor limiting image resolution. This eliminated problems with optical quality, image motion, and atmospheric turbulence from the tests. I also used the same camera and processing techniques as many planetary astrophotographers: a Philips ToUcam recorded five frames per second, stacking the individual frames to create a final image. Cyanogen's MaxIm DL 4 (www.cyanogen.com) was used for camera control, image stacking, and processing.

I placed a small pinhole next to my targets to simulate a star so that I could measure a point-spread function (PSF), which defines blur within an image and is used for advanced image-processing techniques. The test images were recorded with lens focal ratios of f/5.6, f/32, and f/64, which, in my setup, corresponded to diffraction-limited sky images obtained with telescope apertures of 14, 9.3, and 5.8 inches, respectively, in the green region of the spectrum.

Stacking 300 frames increases the signal-to-noise ratio (SNR) to about 600:1 in my tests. This is probably a larger SNR than most astronomical images would exhibit, but since the purpose of these tests is to determine the best-possible case, the high SNR was reasonable. After I combined the 8-bit images (255 values of gray) from the webcam, I stretched the pixel values to 16 bits (65,536 values) to eliminate digitization artifacts in subsequent processing steps.

Deconvolution

Image-processing algorithms that use deconvolution work by measuring the PSF and image noise to calculate the best reconstruction of details. Ideally, a star image is measured to find an accurate PSF. Two highly popular deconvolution algorithms are maximum entropy and Lucy-Richardson. Because images of the planets are often devoid of stars, these programs can use a process of trial and error to achieve a suitable PSF.

In my case, I obtained the PSF from the simulated star in each image. Each stacked image was resampled by a factor of 2 to reduce pixelation artifacts before processing. Each one was then processed separately with Lucy-Richardson and maximum-entropy deconvolution, iterating the processing until the details converged to a common result. Although the images were probably overprocessed, I wanted to get maximum resolution, not the most beautiful images.

The illustration at top right shows Ganymede and Io images comparing raw and processed versions recorded at f/64, which represents a 5.8-inch telescope. The originals show no apparent features, but the deconvolved images show some slight shape changes. Proof that the deconvolution process worked properly is demonstrated by the simulated star image, which becomes essentially pointlike after processing. There's no visible difference between the Lucy-Richardson and maximum-entropy results. The processed Ganymede images show a brighter top and bottom, in agreement with reality. Io shows a darker lower hemisphere, but no more conclusions can be drawn. Based on these results, recording meaningful detail on Io or Ganymede requires a telescope larger than 6 inches.

The images made at f/32 represent a 9.3-inch telescope. This size instrument is imilar to the 10-inch I've used for my Jupiter and Saturn imaging in recent years. Many people, including me, have seen visible shading on Ganymede with this aperture under very good seeing. The processed versions again appear nearly identical. The two bright spots are now resolved but do not appear smaller than the star image, so super-resolution still isn't obtained. The unprocessed Io image shows no evidence of surface structure, but the processed image does show some mottling, in agreement with reality, though nothing exceptional. Images taken with 91/4-inch telescopes under ideal conditions and strongly processed can thus show some real detail on these moons that approaches the diffraction limit.

The views made at f/5.6 (equal to those obtained with a 14-inch telescope) finally show some strong features in the unprocessed files. Ganymede displays more than simple shading, and Io shows definite mottling. After processing, the contrast seems increased, but I don't see any new features, especially finer than those resolved at the diffraction limit. The processing was overdone--Io is not even round--in an attempt to bring out more detail.

Saturn's Encke Division

Since the Encke Division in Saturn's rings is a linear feature, some people think that it is easier to resolve. This is never true; if the feature is narrower than the diffraction limit, it can never be resolved, but it can still be seen. Its visibility, however, does depend on the quality and contrast of the image. The images show the Encke Division recorded by the same setup used for the Galilean moons but at a different scale, which equates to slightly larger telescopes. The images recorded at f/64, representing a 6-inch aperture, show no Encke Division. After processing, a black line is visible at the proper position, but this is a processing artifact that shows as "ringing" throughout the ring structure.

While the processed star image gets much smaller, the Encke Division does not appear.

Using a 10-inch telescope, represented here by the f/32 images, the Encke Division is now unambiguous. While the contrast is not very high, the black line appears with a slightly higher contrast than in the original image after processing.

At f/5.6, representing a 16-inch aperture, the original image shows good contrast. The width of the Encke Division in the original image is about the same width as the star in the same image; it can't be any narrower! The processed images have sharper edges, but there are still some artifacts due to diffraction.

Conclusions

With good seeing, optics, and imaging techniques, amateurs using small telescopes can image details on Ganymede and Io and can also detect Saturn's Encke Division. A 14-inch aperture is a significant improvement over 10-inch telescopes, more than the simple diameter ratio of the apertures suggests. Any imaging technique that helps achieve the diffraction limit (short exposures, stacking multiple images, deconvolution) is essential to recording real detail. Image-processing steps using deconvolution will help bring out details to the diffraction limit, but exceeding that limit on nonstellar images seems impossible. Care in processing will prevent generating artifacts that pose for real features. As for my future imaging plans, I'm replacing my 10-inch scope with a 16-inch model.

Don Bruns gives more details on the experimental procedures used for the tests described here on his Web site at www.stellarproducts.com.
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Author:Bruns, Donald
Publication:Sky & Telescope
Geographic Code:1USA
Date:Dec 1, 2005
Words:1188
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