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Focal Reducers (Field reducers)and Focal Magnifiers (Barlow lens)

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PART I Focal Reducers

February 1999 update note:   Meade has released a new focal reducer/flattener as of February 1999.  This is said to be a three element reducer which will fully cover chips as large as the Kodak1600 size. (1616XT or ST-8 size)  This is encouraging since the Optec will not cover the larger chips.  The Meade reducer is also quite reasonably priced.  I have not received the Meade focal reducer, but it is reported to have a focal length of 88 mm.  This is slightly longer that the 55 mm of the Optec and thus requires a slightly greater distance between the reducer and the image plane than the Optec.  The calculated distance for a reduction of 0.33 is 59 mm.  Since the chip is behind the front of the imager body surface by 43 mm for the ST-7, and adapter tube of about 15 mm is about right.  I understand that Meade provides a variable adapter of 15 to 30 mm.   SBIG has a reducer designed specifically for their ST-5C which I have not seen.

There are significant restrictions on the positioning of focal reducers used with SCT telescopes.  These restrictions and some applications of focal reducers are discussed in this note.  Focal reducers are precision optical elements you add to the optical path and should be used according to the instructions provided with them.  They should be used at their design distance from the imaging plane and should not be stacked to get greater optical effect.  Most 0.63 focal reducers are intended for use with an f 10 SCT but will work with an f 6.3 SCT as well.  Stronger focal reducers, like the 0.33 reducer are designed specifically for f 10 telescopes.  Correct optical application of these reducers will give the best optical results.

The telescope produces a real image some distance behind the rear plate of the telescope.  This real image is normally viewed with an eyepiece or intercepted by a photographic film or CCD imager.  For objects at infinity, like stars, this image can be moved closer to or farther from the back plate by moving the mirror. This is called focussing.  As the mirror is moved back, the real image moves closer to the back plate and as the mirror is moved forward toward the secondary, the image moves farther away from the back plate. Focus can be accomplished by moving the mirror or by moving the eyepiece or CCD.

Focal reducers are positive lenses which do two things to the real image.  They move the focal point forward (toward the back plate) considerably and they reduce the image size.  It is the reduced image that is desired since it is both smaller and brighter. Thus more image fits on the film or CCD imager, which has the effect of decreasing the effective focal length of the telescope. It also increases the surface brightness of the real image thus decreasing the effective f number of the telescope.

Focal reducers are designed, optically,  to work at a fixed and specified distance from the film or CCD imager.  They are best corrected for this one distance.  For the Meade 0.63 focal reducer this distance is 87 mm from the rear of the lens (96 mm from the exit pupil) and for the Optec MAXfield 0.33 it is 29.5 mm. (from the rear of the lens structure)  In practice the MAXfield distance of 29.5 mm is measured from the rear element of the reducer but is actually about 35 mm from the nodal point.  The MAXfield is a very thick optical system.  Note that all measurements are slightly approximate since the the focal reducers are thick lenses and do not have their nodal point marked on the lens mount.  In this discussion, I am using the simple thin lens formulas so approximate locations for the lenses and images are sufficient.   Additionally, the 0.63 reducers have considerable variation allowed for their placement.  The 0.63 reducers work well from about 80 to 110 mm but with slightly different reduction ratios.

The focal reducers will give the specified focal reduction and the best optical performance when used at the design distance. They can be used at other distances to get slightly different reduction ratios. This property in not different from other optical systems such as the SCT itself which will give the best correction for objects at infinity and with the mirror toward the back of the optical tube.  This position of the mirror gives a real image quite near the back plate of the telescope.  As tubes, focusers and focal reducers are added, the mirror must generally be moved forward in the tube to extend the real image backward.  The maximum distance that the real image can be moved backward from the back plate is usually called the maximum back focus distance.  There is a design crunch caused by using focal reducers. When a relatively strong positive lens is placed in the optical path  of the telescope near the real image, it moves it forward significantly.  Thus, the original real image, without the reducer in place, needs to appear a considerable distance behind the back plate.

The approximate distances are easily calculated from thin lens formulas. The following two formulas are used for all calculations.  The assumption is that the telescope is to the right and the reducer and imaging surface to the left. Thus the light rays are moving right to left.

             Magnification = 1 - Fd / Fl

             and 1 / Fl  =  (1 / Fd) +  (1 / Ff)

Where  Fl  is the focal length of the reducer
          Fd  is the distance between the reducer and the CCD, film or imaging surface
          Ff  is the distance between the reducer and the original   image produced by the telescope with no reducer in place.
 

Optic drawing 1
Notice that for this lens system, since the initial image, that is, the real image produced by the telescope falls to the left of the reducer lens and so does that of the final image, the sign on the value of  Ff  is negative.  This diagram should be kept in mind since it shows that what really happens with a focal reducer is that the image is pulled forward, toward the telescope and is at the same time made smaller.

Examples: For the Meade 0.63 reducer, the distance between the rear of the reducer and the CCD should be 87 mm. (or about 96 mm from the lens pupil itself)  This means that the original real image produced by the telescope should be about 148 mm to the left of the reducer.  For the MAXfield 0.33 reducer, the distance from the rear or the lens structure to the chip should be about 29mm. For this reducer the real image produced by the telescope will be about 150 mm. to the left of the reducer.

The total distance that the original real image must be to the left of the back plate is the calculated distance plus the distance that the reducer is to the left of the back plate.  This considerations require the mirror to be moved toward the secondary enough to place the real image far enough to the left to satisfy the optical conditions for focus.  To meet this condition one needs to "have enough back focus."   For most SCTs the real image for a distant object can be moved from about 25 mm to about 250 mm behind the back plate of the telescope. These numbers depend upon the exact design of the SCT of course. Fortunately, this means that both the Meade 0.63 and the MAXfield 0.33 reducers can be focussed easily.

However, when too many focusers, filter wheels, flip mirrors and the like are used the required back focus may not be available. You can easily calculate your own optical situation using the formulas supplied above.  Note that using several reducers will not only cause back focus problems but may seriously deteriorate the image due to aberrations and non-optimal lens placement.  Additionally, a minimum amount of tubing (length) should be used in the optical path so that the primary mirror does not have to be moved more than necessary toward the secondary to attain focus.

Examples of three focal reducers are shown below.  The large, 82 mm, reducer is that from the Lumicon Giant OAG, the center one the standard Meade 0.63 reducer and on the right is the Optec 0.33 reducer.   The focal lengths of the Lumicon and Meade are about the same, 260 mm, while the Optec is a focal length of about 55 mm.  The Lumicon lens is a simple cemented doublet (two elements), the Meade a dual cemented doublet (four elements) and the Optec a more complex thick lens design.  While all field reducers have a limited field of illumination, designs like the Optec are very strong reducers and have a field, in this case, limited to the K 400 size chip.
 

Reducer set 1 Reducer set 2

 It should be noted that focal reducers with long focal lengths like the Meade and the Lumicon (260 mm)  can be used at reduction ratios that are somewhat different from their design centers without serious degradation of the image.  It has been reported that even at 0.4 reduction setting the images are quite good but may be best at the design center.  Lumicron allows for a generous adjustment of the distance settings.  On the other hand, the Lumicron is a much simpler lens design and may not have appropriate quality for the small imager chips where its size is not needed in any case.  It is designed primarily for the 35 mm film format, I believe.

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PART II Focal Magnifiers (Barlow lens)

Focal magnifiers are probably more familiar to most astronomers.  Their purpose is to increase (magnify) the size of the image.  This is most often done to squeeze higher power out of a telescope, often for planetary viewing.  The magnifier lens, which is in this case a strong negative lens,  is placed near focal plane and expands the cone of light thus expanding the image size.  It s placement seems to be not a critical as the placement of the focal reducer.  This is an illusion that must be tamed.  In fact, the exact same optical equations apply to the focal magnifier as to the focal reducer.

These equations are given once more for reference and a diagram of the focal magnifier is provided as well directly below.  The approximate distances are easily calculated from thin lens formulas. The following two formulas are used for all calculations.  The assumption is that the telescope is to the right and the magnifier and imaging surface to the left. Thus the light rays are moving right to left.

             Magnification = 1 - Fd / Fl

             and 1 / Fl  =  (1 / Fd) +  (1 / Ff)

Where  Fl  is the focal length of the reducer
          Fd  is the distance between the reducer and the CCD, film or imaging surface
          Ff  is the distance between the reducer and the original   image produced by the telescope with no reducer in place.
 

Optic drawing 2

Notice that for this lens system, since the initial image, that is, the real image produced by the telescope falls to the left of the reducer lens and so does that of the final image, the sign on the value of  Ff  is negative. Notice also that the sign of the focal length of the magnifier lens is also negative. This diagram should be kept in mind since it shows that what really happens with a focal magnifier is that the image is pushed backward, away form the telescope and is at the same time made larger.  This exactly the opposite of what the focal reducer does to the image.  When the formulas are used, with the appropriate signs for the distances and the lens, the magnification and the distances will be calculated correctly.

Thus it is clear that the amount of magnification that a given focal magnifier will give is dependent on the spacing between the magnifier element and the focal plane.  Magnifiers, like reducers, are designed to work at a specified magnification and thus a specified distance from the image focal plane, but their positioning is not as critical as that of reducers.   Magnifiers are most often used for added power when the eyepiece is not of short enough focal length.  The optical quality of the resultant image may suffer if too much magnification is demanded.

DISCUSSION:  Vignetting and Illumination

In the case of the image magnifier there is no problem with vignetting since the image is enlarged.  However it must be realized that the total illumination available is still confined to the cone of illumination striking the front surface of the magnifier and that this illumination is spread out over a larger surface thus reducing the intensity of illumination.  This makes the image dimmer and increases imager exposure as would be expected.

On the other hand, the focal reducer concentrates the light from the telescope and produces a brighter image thus shortening the exposure time required.  Reducers are used to image objects which are normally too large to fit on the surface of the imager, generally a CCD.  There is a problem with vignetting when a focal reducer is used.  Only those light rays which enter the front pupil of the reducer will reach the image plane.   Thus if the initial image, before reduction, is not uniformly illuminated over its full surface by the cone of light from the telescope, then neither will the reduced image.  This is usually not a severe problem with a focal reducer that is properly designed and used at its design distance.  But when using a larger field receptor like 35 mm film, the telescope will generally not illuminate the full initial image and will thus not illuminate the full reduced image.  For example, with a reduced image that is to fill a 35 mm frame, and a 0.63 reducer power, the initial image would have had to fill a frame 41 by 57 mm.  This is a circle of illumination of  71 mm.  (almost 3")  Small Cassegrain telescopes simply do not have a circle of illumination that large.  Thus some compromise may need to be made when using 35 mm cameras with a reducer.  Usually a square area the size of the short side of the frame is covered fairly well.   In a more flexible setup, one can adjust the distance of the reducer from the imaging surface to take slightly less reduction and obtain more uniform illumination of the film.

The size of the focal reducer and the size of the tubing used to attach it to the camera is also of some concern as described elsewhere on this web site.  Adapter tubes with "T" threads are generally not of sufficient size and will cause vignetting on 35 mm format film in almost all cases.

Focal Reducers Used With An Off Axis Guider

When using a focal reducer with an off axis guider, it is often the case that the focal reducer is used to reduce the desired image but not the guider image.  This arrangement is shown here.
 

Optic drawing 3

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