Helix 250 - CCD optimized
Kaf-11000 CCD chip with 11 million pixels of 
9 x 9 micron. The Helix 250 has been designed for the new generation large format CCD-camera's.
This resulted in a camera with a large flat field, unprecedented optical quality and a focal length that satisfies the Nyquist criterion.
The optical constrains for our new camera were very heavy and many calculations were necessary to get small enough spot-sizes across the field. Spot diagrams are used to analyze the image of a star in focus. They are used to measure the quality of the optical system. The smaller the spots, the sharper the image

Of course the questions arises of how small the spots must be. The exposure time for an astrocamera is long so the sharpness of the image will be determined by seeing (a). A second important factor, of course, is tracking (b). We also have the tolerances of the mechanical construction and optical imperfections of the camera (c).
If we assume a perfectly optical system, we can than calculate the effect of (a), (b) and (c) on the image quality:
  • Example 1: We assume a very good seeing of only 2 and a guiding error of 1 and an error of 2 due to mechanical and optical imperfections. The theoretical deterioration of the image quality is then the square root of 2**2 + 1**1 + 2**2 equals 3 . At focus this corresponds to a spot size of 11 micron.
  • Example 2: A more realistic estimate of seeing conditions of 4 and a guiding error of 2 and a mechanical and optical error of 2 gives an total error of 4.9. This translates into 18 micron at focus.
  • Example 3: If we take 6 for the seeing and a 4 tracking error, the overall error adds up to 7.5 and 27.8 micron at focus.

The Helix 250 has been especially designed for modern large format CCD-cameras. These cameras have a large chips and small pixels.

As an example, we take a pixel size of 9x9 micron. According to the Nyquist theorem the optimum spot size must then be 18 micron. If we take the three cases, one can easily see that the seeing and tracking fully determine the optical quality of the image if we succeed in keeping the spot sizes very small.

The spot size of a diffraction limited optical system at F/3 for a wavelength of 500 nm is about 4 micron. It is not possible to get smaller spot sizes due to the wave character of light.
We are very proud to say that Harrie Rutten succeeded in designing the optical system in such a way that the camera is almost diffraction limited across the entire spectral range.

If we return to the three examples we can see the consequences. For simplicity we assume that the spot size is 5 micron for the optical system. To calculate the overall spot sizes we must add this 5 micron. This leads to 12, 18.7 and 28.3 micron for resp, (1), (2) and (3).

From this we may conclude that the Helix 250 is an extremely good camera to use with CCD-chips with small pixels. Its focal length of 750 mm makes a perfect match between spot size and pixel size. For larger instruments seeing effects, guiding and mechanical errors will  determine the image quality while smaller instruments will not be as sharp as the Helix 250.

Using 9 x 9 micron pixels lead to over sampling in larger instruments and under sampling in smaller instruments. With a focal length of 750 mm the Helix 250 matches the Nyquist theorem perfectly.