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Proper Positioning of a Focal Reducer
on a Ritchey-Chrétien Cassegrain Telescope

Russell Croman

Introduction

The Ritchey-Chrétien optical system provides superior optical performance over a very wide field of view compared to other, more easily manufactured designs. While focusing an RC telescope can be done in the usual way using a draw-tube focuser at the back of the telescope, many current designs also employ an electronically-controlled secondary mirror positioning system for fine focus. This enables automatic focus when doing electronic imaging. Also, the standard focuser can then be replaced by a more rigid system to directly attach instruments to the telescope, eliminating flexure from the system.

A consequence of the Richey-Chrétien design is that the spacing between the primary and secondary mirror must be kept very near the value intended by the optician who figured the mirrors. If this spacing is allowed to deviate much more than a few millimeters, significant deterioration of performance will result due to spherical aberration.

The method of focusing by moving the secondary mirror is thus at odds with maintaining the performance of the system. The solution is to locate the instrument, be it a CCD camera, an eyepiece or what have you, close to the focal point of the telescope with the secondary mirror at its proper distance from the primary. The secondary focuser can then be moved only for fine adjustment of the focus.

Adding a focal reducer into the mix complicates matters. With the reducer in place, where is the new focal point of the system? How does one determine the correct position of the reducer such that the system will be nearly in focus without having to move the secondary mirror from its optimum position?

This paper is an analysis of how to do this.

Focal Ratio and the Angle of the Light Cone

To start the analysis of how to properly position the focal reducer, we need the concept of the “light cone” and how it relates to the telescope’s focal ratio. A telescope receives a circular section of the incident light, and focuses it to a point at some distance, the effective focal length, from the front aperture. Incoming light rays are formed into a converging cone, with the apex being at the focal point. A simplified diagram illustrates this:

 

 

The angle of the light cone for a telescope of a given focal length and aperture is easily found by trigonometry:

where A is the aperture diameter, and F is the focal length. This can be re-written in terms of the focal ratio, :

For example, an f/10 telescope will have a light cone that converges at an angle of 2.86o.

The Reduction Factor and Working Distance

The amount of reduction (R) produced by a focal reducer is a function of the focal length (FR) of the reducer and its distance (D) from the camera’s focal plane:

For example the Astro-Physics 0.75x focal reducer has a focal length of 700mm. Thus the correct working distance to yield a 0.75x reduction is

Note: the AP web page for the 0.75x reducer states that the distance from the edge of the 2” adapter should be about 65mm for 0.75x reduction. However, measurement of the reducer and 2” adapter combination yields a distance of about 60mm from the back of the optics to the back edge of the 2” adapter. Thus, according to the above computation, an additional 115mm is needed to achieve 0.75x. Using a 65mm spacing from the adapter to the focal plane will yield approximately 0.82x reduction.

Focal Reduction Steepens the Light Cone

The action of the focal reducer is to cause the incoming light rays to converge at a greater angle than they were before entering the reducer. In other words, it steepens the angle of the light cone.

The new angle is simply a function of the new focal ratio, which is the product of the telescope’s native focal ratio and the reduction factor:

To avoid needing to move the telescope’s secondary mirror to achieve focus, the focal reducer must be placed at a position such that its light cone intersects with the native light cone of the telescope. In other words, the diameter of the new light cone must equal that of the original light cone at the position of the focal reducer. This diameter is labeled X in the above diagram. D is the reducer’s working distance, and Y is the distance from the reducer to the original native focal point of the telescope.

We can write an equation for X for each light cone. First, for the focal reducer’s light cone:

Then for the native light cone:

As stated above, X must equal XR for proper positioning. Thus

or

Recalling that and, the above reduces to

The focal reducer must be placed a distance Y in front of the native focal point of the telescope. This distance is simply the ratio of the working distance of the reducer to the reduction factor.

For the AP 0.75x reducer at a 175mm working distance, Y is approximately 233mm, or about 9.2 inches. On my 14” f/10 telescope, the native focal point is only 8.54” behind the back plate. Thus the reducer optics must be located ahead of the back plate, inside the telescope! Fortunately, the AP 0.75x reducer is designed such that this will be the case if it is mounted directly to the back plate using RC Optical Systems’ fixed-instruments adapter.

Actual Working Distance

In practice it is difficult to achieve the exact working distance needed to yield the specified reduction factor. A more practical approach may be to try to get close, and then use the achieved working distance in the above formulation to compute the proper reducer position. Various spacers included with RC Optical Systems’ fixed-instruments adapter, for example, can then be used to try to achieve this position.

Recalling that the reduction factor is just , the above equation for Y can be rewritten as:

For example, here is the calculation of the working distance for my setup:

Then:

or about 9.33”.

Thus the reducer optics must be 9.33” in front of the native focal point of the telescope, or about 0.79” in front of the back plate.

The distance from the front flange of the reducer to the center of the reducer’s optics is about 1.25”. The fixed-instrument adapter plate adds about 0.30”. So I need an additional 0.16” (4mm) spacer in front of the reducer (between the reducer and the fixed-instrument adapter plate) to get the proper positioning.

The working distance just happens to be almost exactly what is needed for 0.75x reduction:

Conclusions

The above analysis provides the formulas needed to compute the correct position of a focal reducer relative to the native focal point of a Richey-Chrétien Cassegrain telescope. Using these formulas, one can determine for a particular telescope and instrument setup how to position the reducer such that the system can reach focus with only minor adjustment of the secondary mirror position. The performance of the system will thereby be optimized.

John Smith has developed an excellent spreadsheet for performing the calculations involved in properly positioning a focal reducer. It appears at the following page, along with handy tables of the space introduced by various camera elements: