Measuring a secondary mirror, particularly for sizing purposes in telescope design, often involves a straightforward calculation based on the primary mirror's dimensions and focal ratio. A commonly used method simplifies this process to determine the necessary minor axis of the secondary, which is its diameter.
Understanding the Calculation Method
The core of this practical measurement involves determining the "intercept distance" – the point where the light cone from the primary mirror has expanded to a certain size before hitting the secondary.
Here's the step-by-step process:
- Calculate Half the Primary Mirror's Diameter: Begin by taking half of your telescope's primary mirror diameter.
- Add a Fixed Value: Add a fixed value of 4 inches to this half-diameter. This addition accounts for the light cone's expansion and ensures the secondary mirror is large enough to capture all incoming light. The result is what is referred to as the "intercept distance."
- Divide by the Focal Ratio (f/#): Divide the intercept distance by the telescope's focal ratio (f/#). This final division gives you the approximate required size for your secondary mirror's minor axis.
- Adjust to Standard Flat Sizes: After performing the calculation, if the resulting size is close to a standard available flat (secondary mirror) size, it is recommended to go up one flat size. This provides a margin for error and ensures optimal illumination of the focal plane.
Practical Example
Let's illustrate this with the provided example of a 16-inch f/4 telescope:
- Primary Mirror Diameter: 16 inches
- Focal Ratio (f/#): 4
| Step | Calculation | Result (Inches) |
|---|---|---|
| 1. Half the Mirror's Diameter | 16" / 2 | 8" |
| 2. Add 4 inches (Intercept Distance) | 8" + 4" | 12" |
| 3. Divide by f/# | 12" / 4 | 3" |
| 4. Adjust to Standard Size | If 3" is close to a standard size (e.g., a standard size is 2.8" or 3.1"), consider going up. | Approx. 3" |
Therefore, for a 16-inch f/4 telescope, a secondary mirror with a minor axis of approximately 3 inches would be indicated by this method. Depending on available standard sizes, you might select a 3.0-inch, 3.1-inch, or even a slightly larger secondary for optimal performance.
Key Considerations for Secondary Mirror Sizing
While this method provides a quick and practical way to size a secondary, it's important to remember that precise optical design can involve more detailed ray tracing to optimize secondary obstruction and illumination. However, for most amateur telescope builders, this formula serves as an excellent starting point.
- Obstruction: The secondary mirror inherently obstructs a portion of the incoming light. A larger secondary means more obstruction, which can slightly reduce contrast. This method aims to balance full illumination with minimal necessary size.
- Illumination: The goal is to fully illuminate the field of view at the focal plane. Undersized secondaries can lead to vignetting (darkening at the edges of the image).
- Standard Sizes: Secondary mirrors are typically manufactured in standard sizes (e.g., 1.5", 1.83", 2.14", 2.60", 3.10", etc.). The "go up one flat size" rule helps align your calculated size with readily available options.
For further exploration of telescope optics, you might refer to resources on telescope design principles or Newtonian optics. (Note: These are placeholder links; real links to reputable sources would be used in a live context).
