The article forms the second part of the aspheric lens article series. In the previous article we mainly focused on the importance of aspheres in aberration correction and spot size reduction in smaller systems like singlet, doublet and double gauss system. Here in the article, we apply our knowledge on a Schmidt Cassagrain telescope and use an aspheric surface to create a new design having more compactness and less aberration. 

• Aspheric Surfaces - Part 1: Introduction to Aspherical Surfaces in Optical Design

Authored By Akhil Dutt Vijayakumar

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• For full Compact Schmidt-Cassegrain system see Article Attachment at the end of the article. 

Introduction

The Schmidt-Cassegrain telescope, known for its versatility and high-quality image delivery, has been a mainstay for both astronomy enthusiasts and professionals. It combines a primary mirror, a secondary mirror, and a corrector plate to achieve a long focal length in a relatively compact design. However, its reliance on traditional spherical mirrors necessitates a bulky tube length, making it difficult to observe with and transport.

The main parts of the Schmidt-Cassegrain telescope include a spherical primary mirror, which gathers incoming light and focuses it onto a secondary mirror. The secondary mirror then reflects the beam through an aperture in the center of the primary mirror, directing it to the image plane. A corrector plate denoted as lens 1 is used in the design to correct spherical aberration in the incoming light before it reaches the primary mirror.

Initial Design

The initial design is shown here having a length of 198mm from the corrector plate to the primary mirror. The corrector plate is created using an even asphere which pre-compensates the spherical aberrations in the system. The starting system available here is having a good design with optimised performance and has relatively good aberration control. When we add mechanical mounting in this design the final telescope assembly will be bulky and difficult to carry.

Three field points are evaluated across the system for specific wavelengths. Analysis of the spot diagram and RMS spot radius versus field angle plot reveals diffraction-limited performance for all wavelengths up to a 0.7^o field angle.  A marginal increase in spot size is observed beyond this point, indicating good overall aberration control. These results suggest a promising starting design for further optimization.

Modified design

The initial telescope design is modified by incorporating additional optical surfaces. The thickness of surface 2 is reduced by half and designated as a variable for optimization during the design process. This parameter significantly impacts the overall telescope thickness, and the goal is to minimize it by roughly 50%. The newly added surfaces function as lenses to focus the light onto the image plane.

An initial optimization is performed, incorporating constraints on both glass types and air gaps within the system. Subsequently, analysis using an aspheric optimization tool identifies the 7th surface as the most suitable candidate for conversion into an asphere. This surface is then converted to an even asphere described by a 10th-order polynomial, with its relevant parameters designated as optimization variables. Within the merit function editor, operands such as MNCA and MXCA are employed to set minimum and maximum boundary values for the lens thickness, ensuring it remains within an acceptable range for the lens design.

After defining constraints for the remaining surfaces in the merit function editor, the optimization process is executed, resulting in the new optimized system, denoted in the LDE. Here in the design we added a single aspheric lens which helps to reduce the thickness of surface 2 from 198mm to 90mm.

System performance analysis

The new design exhibits excellent performance in the spot diagram. All field points achieve diffraction-limited spot sizes, confirmed by the RMS spot radius remaining consistently low across the field. This addresses the initial design's issue of increasing spot size at higher field angles, demonstrating a significant improvement.

While aspheric surfaces can enable designs with more lenses, incorporating just a single aspheric lens offers advantages in terms of complexity and manufacturability. This approach minimizes the number of additional optical elements needed to achieve the desired performance.

Compared to a design with multiple aspheric lenses, this single-lens solution simplifies both the mechanical design and assembly. The telescope requires only one additional mechanical mount for the lens, resulting in a more compact and less intricate overall system.

Conclusion

This article explored the effectiveness of incorporating an aspheric surface to achieve a compact and high-performing Schmidt-Cassegrain telescope design. The addition of this element successfully reduced the telescope size by roughly half compared to the initial design, while simultaneously improving the overall optical performance. Notably, the new design exhibits diffraction-limited spot sizes across a wider field of view, addressing the limitations of the original system.

References:

1. Schmidt-Cassegrain Telescopes - Cosmic Pursuits
2. Celestron Schmidt-Cassegrain telescope SC 127/1250 NexStar 5 SE GoTo (astroshop.eu)
3. vik dhillon: phy217 - catadioptric telescopes (shef.ac.uk)