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Of Pixel Size and Focal Reducers
by Dennis di Cicco

Focal reducers
Focal reducers come in all shapes and sizes. The author feels they are one of the most important accessories for digital imaging since they are ideal for adjusting a telescope’s effective focal length to a CCD’s pixel size.
Sky & Telescope / Chuck Baker

Focal Reducers

During the past 20 years numerous focal reducers have appeared on the market. Most observers think of these in terms of decreasing a telescope’s f/number to make it "faster" photographically. But, as the name implies, these accessories work by reducing a telescope’s effective focal length. They are excellent for helping match image scale and pixel size. This is especially useful for Schmidt-Cassegrain telescopes.

In the past the challenge was to design a system with high-quality images across a large field. But since CCDs are relatively small this tolerance can be relaxed, and many focal reducers suitable for digital imaging can be made from simple achromatic lenses such as those scavenged from a old pair of binoculars. (An excellent source of information about the design and function of focal reducers is an article by the late Alan Gee on page 367 of this magazine’s April 1984 issue.)

Today, however, designing a custom focal reducer is necessary only in unusual situations. Commercial units, particularly those for Schmidt-Cassegrain telescopes, offer many options -- especially when the resulting focal length is tweaked by adjusting the spacing between the reducer and CCD.

Diagram
The compression factor of popular focal reducers can be varied somewhat by adjusting the spacing between the reducer’s back mounting surface and the CCD. The author derived this graph using Celestron and Meade f/6.3 reducers, which are designed for a spacing of 105 mm.
Sky & Telescope diagram.
Popular f/6.3 reducers sold by Celestron and Meade for their f/10 Schmidt-Cassegrains are designed to be used with a 105-mm separation between the back surface of the reducer and the detector (be it film, CCD, or whatever). As the accompanying graph indicates, altering this spacing changes the compression factor — great for fine-tuning a CCD system. Increasing the separation increases the amount of compression and thus reduces the effective focal length. Ideally we could increase the separation enough to accommodate small pixels. In practice, however, either image quality or, more likely, mechanical restrictions imposed by the telescope’s focusing system will limit the amount of compression that can be obtained.

There is one notable exception. Optec’s MAXfield unit is specifically designed to compress the field of an f/10 Schmidt-Cassegrain to a remarkable f/3.3 for CCD work. The spacing between the reducer and chip is critical, however, and changing it by even a millimeter degrades images. Also, the reducer has a maximum usable field about 11 mm across, too small for large chips.

SCHMIDT-CASSEGRAIN FOCAL LENGTHS
Instrument
Focal length (millimeters)
  Nominal f/3.3 reducer f/6.3 reducer
8" f/10 2,032 670 1,050—1,400
8" f/6.3 1,280 -- 800
9.25" f/10 2,350 775 1,200—1,650
10" f/10 2,540 838 1,350—1,800
10" f/6.3 1,600 -- 1000
11" f/10 2,800 924 1,500—1,950
12" f/10 3,050 1,005 1,600—2,100
14" f/11 3,910 1,290 2,050—2,700
16" f/10 4,060 1,340 2,100—2,850
 
   
There are also a few caveats for observers planning to use focal reducers with Meade’s 8- and 10-inch f/6.3 Schmidt-Cassegrain telescopes. I have found that the MAXfield focal reducer, while in theory yielding an f/2 system when attached to these instruments, will not give satisfactory star images — it works only with f/10 telescopes. The f/6.3 focal reducers, on the other hand, will compress the f/6.3 telescopes to about f/4 with very acceptable results. But experience suggests that changing the spacing to obtain other compression ratios is not recommended and is the reason for the single focal-length entries in the table at left.

Of the many comments I’ve heard about focal reducers, no one has ever mentioned their cost-saving benefit. Consider this example. I do much of my deep-sky imaging with a Meade 16-inch LX200 Schmidt-Cassegrain. The telescope’s nominal f/10 (4,000-mm) focal length is long even for large pixels. Adding a f/6.3 focal reducer drops the effective focal length to about 2,500 mm — a good match for the 18-micron pixels available with a KAF-1600 chip binned 2x2. Such a setup would yield an image scale of 1.49" per pixel and a field of view measuring roughly 19 by 13 arcminutes.

By switching to the f/3.3 focal reducer, however, I can get nearly identical sky coverage and imaging performance from an unbinned KAF-0400 detector. This chip has the KAF-1600’s same 9-micron pixels but is only one-quarter as large, with a 768-by-512-pixel array. What is really attractive about this arrangement, however, is that cameras equipped with the smaller chip cost about half as much as those with the KAF-1600, amounting to a savings of $2,500 to $3,000 depending on make and model! Similar results are possible with today’s 12- and 14-inch Schmidt-Cassegrain telescopes.



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