Optical System Designs for Star Trackers

Key Takeaways

• This technical note explores optical system design for wide-spectrum star trackers, a key technology for spacecraft attitude determination.
• It addresses reflective, catadioptric, and transmissive types, outlining their advantages in space applications.
• A compact, athermalized f/2.8 star tracker lens design example optimized for 450-1000 nm and 2048×2048 sensors is presented, delivering stable, high-performance star identification across extreme temperatures, crucial for dependable space navigation.

Optical System Types for Star Tracker Applications

A star tracker (also known as a star sensor) is an important device used to determine a spacecraft's attitude. These sensors typically include an optical system, image sensor, processor, memory card, and housing.

Star trackers capture images of star fields and compare the observed star positions to an onboard star catalog. Spacecraft attitude can be determined with high precision by using star sensors to identify and match star patterns with known positions.

The optical system is central to a star sensor, focusing starlight onto the image sensor. The tracker's reliability and precision are directly dependent on the performance of the optical system. Inadequate optical design results in blurred or distorted star images, reducing attitude determination accuracy.

Star sensor optical systems, used in spacecraft attitude determination, are generally classified into three main types based on their optical design: reflective, catadioptric, and transmissive systems.

Star Trackers. Image Credit: Avantier Inc.

1. Reflective Systems

Reflective optical systems use mirrors to create images. They are inherently free of chromatic aberration, making them suitable for wide-spectrum imaging.

2. Catadioptric Systems

Catadioptric systems combine refractive and reflective elements, using the advantages of both. These systems provide effective chromatic aberration correction, structural simplicity, and durable environmental adaptability, features that make them reliable even under the demanding conditions of space.

3. Transmissive Systems

Transmissive systems depend solely on lenses and are especially beneficial for designs that demand a wide field of view and high relative aperture. Their structural versatility supports various configurations, including double-Gauss, Petzval, and telephoto types.

Key Features of a Star Tracker Optical Design

1. High Optical Quality

• • High resolution with minimal aberrations.
  • For precise star measurements, clear, low-distortion image generation is required.

2. Large Field of View (FoV)

• • Typically, it ranges from 5 ° to 20 °, depending on mission requirements.
  • A larger FoV allows for increased star capture per image, which boosts precision and durability.

3. Large Aperture

• • Stars are hard to capture as they are not particularly bright, so the lens must contain a large aperture (low f-number) to maximize light collection.
  • Frequently coupled with highly sensitive image sensors and extended exposure durations.

4. Radiation-Resistant and Space-Qualified Materials

• • Lenses must withstand the radiation, thermal extremes, and vacuum conditions of space.

5. Thermal Stability

• • Lens materials and mounts must be able to preserve optical stability across temperature fluctuations to prevent focus shifts.

6. Mechanical Structure

• • Use compact lens holders for alignment and vibration resistance
  • Include athermalized lens mount designs to compensate for thermal expansion
  • Use lightweight metals such as aluminum 6061-T6 or carbon composites for housing

Wide-Spectrum Star Tracker Lens Design Example

• Lens Design Parameters

Source: Avantier Inc.

Note: lens parameters created to match a star sensor with a resolution of 2048 x 2048 pixels and a pixel size of 6.5 µm. 

• Lens Optical Configuration

Minimizing lens size and mass is crucial in space applications. Positioning the aperture stop at the front surface significantly reduces lens diameter and overall volume.

Excluding the radiation-shielding quartz window, the optical system contains eight lens components, weighing a total of 22 g. The back focal distance measures 10 mm, and the optical track length is 48 mm.

The optical system achieves a telecentric optical path design, maintaining telecentricity within 0.5 ° across the whole field of view. This ensures the active detection area is uniformly illuminated.

The telecentric lens configuration also helps to minimize the effects of mechanical shock and vibration experienced during satellite launch, preserving measurement precision, an important factor for dependable performance of the star sensor system.

Star Tracker Lens Configuration. Image Credit: Avantier Inc.

• Lens Modulation Transfer Function (MTF)

The Modulation Transfer Function (MTF) is an essential metric for evaluating an optical system’s imaging performance, providing a quantitative and intuitive measure of image quality. In this system, the detector has a 6.5 μm pixel size, corresponding to a Nyquist frequency of 77 lp/mm.

As demonstrated in the figures below, the MTF design results at 20 °C room temperature exhibit outstanding imaging performance, with values exceeding 0.46 at 77 lp/mm across the entire field of view. The optical system is designed for passive athermalization, maintaining stable performance over a - 40 °C to + 60 °C operational temperature range.

The corresponding MTF performance under these thermal extremes confirms minimal degradation and consistent image quality throughout the specified temperature range

Image Credit: Avantier Inc.

High-Performance Star Tracker Lens Product with a Wide Spectrum

This lightweight, compact star sensor lens has been designed to meet the stringent optical, mechanical, and environmental criteria for space missions. Equipped with a 40 mm focal length, 26.4 ° field of view, and rapid f/2.8 aperture, it offers excellent imaging performance across a wide spectral range of 450 nm to 1000 nm.

Star Tracker Lens. Image Credit: Avantier Inc.

Optimized for use with a 2048 × 2048 resolution sensor featuring 6.5 µm pixel size, the lens is able to concentrate over 85 % of incoming optical energy within a 3-pixel radius. This high energy concentration substantially improves star identification capabilities and boosts attitude determination precision, which are crucial parameters for spacecraft navigation and control.

The athermalized optical design maintains consistent focal performance across extreme temperature shifts, ensuring imaging accuracy and system dependability in demanding space settings.

Additionally, the lens features a telecentric optical path and a significantly low distortion profile, essential to high imaging fidelity across the whole field of view. The front and middle lens groups use a low optical power configuration, similar to that of a low-magnification Galilean telescope, and conventional glass types to correct chromatic aberrations effectively.

These properties and the lens's compact structure make it ideal for high-precision star trackers and celestial navigation systems in micro- and nano-satellite applications.

Product specifications. Source: Avantier Inc.

This lens is ideal for star trackers and celestial navigation systems requiring compact, high precision optical solutions.

Optical Design for Space Applications

Avantier offers support for optical component and assembly design tailored to specific applications.

This information has been sourced, reviewed, and adapted from materials provided by Avantier Inc.

For more information on this source, please visit Avantier Inc.