Want to take a selfie on Mars? Unless you have the same selfie gadget as the Tianwen-1 rover

On May 15, 2021, the Tianwen-1 probe successfully landed on Mars, taking an important step in my country's interstellar exploration journey. In a flash, this wanderer has arrived on Mars for more than a year.

During this year, Tianwen-1 can be called a "selfie master". From National Day to New Year's Day to the Year of the Tiger, every time there is a major event, it will take a "beautiful photo" and send it to Earth to express its thoughts and blessings to everyone. Don't think that "selfies" are very easy. If you want to "take a good selfie" in space, it is a very challenging thing.

The first image of Mars obtained by Tianwen-1

Image source: CCTV News

Today, let’s take a look at the selfie artifact of the “selfie master” Tianwen-1 - the off-axis three-mirror optical system, and uncover the secret of its high-resolution image capture.

High-resolution images of Mars taken by Tianwen-1's high-resolution camera

Image source: CCTV News

To take clear photos, ground coverage and resolution are essential

From the initial film-type return space camera to the current CCD sensor camera, people have never stopped exploring space cameras. Among them, CCD sensor cameras have gradually become the mainstream of space cameras due to their small size, high image quality, strong vibration resistance and anti-interference performance.

CCD array used in the Sloan Digital Sky Survey imaging system

Image source: wikipedia

So how do we calculate the resolution of images taken by space cameras? We only need to mount a CCD space camera on an aircraft, and assume that the imaging angle of the space camera is parallel to the ground. At this time, let the distance between the aircraft and the ground be H, the focal length of the space camera's optical system be f, the length of the pixel be d, the number of pixels in the focal plane be n, and the ground width W covered by each pixel is the ground pixel resolution of the camera. The smaller its value, the higher the resolution.

Working principle diagram of linear array CCD image sensor

Image source: Reference [1]

In this way, we can get the expression of ground pixel resolution (GSD) of CCD space camera by the similarity principle of triangles:

The width of ground cover is proportional to the number of pixels of the image sensor, and the expression of W is:

If you want to improve the observation range and clarity of aerospace cameras, you need to improve the camera's ground coverage and resolution.

From the above, we can see that lowering the orbit altitude, increasing the focal length of the camera's optical lens and reducing the pixel size of the image sensor can improve the ground pixel resolution of the space camera, while the ground coverage width of the space camera depends on its flight altitude, the camera's focal length, field of view angle, pixel size and number of pixels.

When the satellite altitude is constant, increasing the camera's field of view (simply put, the camera's field of view) can expand the camera's ground coverage, while increasing the angular resolution of the camera's optical system can effectively improve the ground resolution.

The former requires a telescope system with a long focal length and a large field of view, while the latter requires increasing the focal length while maintaining a certain relative aperture. This will increase the entrance pupil diameter accordingly, improve the angular resolution, and thus improve the ground resolution.

Generally speaking, field of view and resolution are a pair of contradictory parameters, that is, it is impossible to improve the field of view and resolution of an optical system at the same time (in other words, it requires to see many objects at the same time, and each object must be seen clearly), but practical applications require us to do "both". In this case, the off-axis three-mirror system came onto the historical stage.

How does “off-axis three-mirror” work?

Before understanding what “off-axis three-mirror” is, we need to first know what “co-axial” is?

"Coaxial" is the basis of "off-axis", which means that the optical system uses the optical axis as the symmetry axis, and the optical axis refers to a straight line where the centers of curvature of each mirror surface in the optical system are co-located. In an optical system, each curved surface is an axisymmetric rotational curved surface, and the symmetry axis coincides with the optical axis. This optical system is called a coaxial optical system.

The off-axis optical system is based on the coaxial optical system, and the aperture of the optical system is off-axis, the field of view is off-axis, or the mirror is tilted to achieve the purpose of "off-axis".

Off-Axis System Schematic

Image source: Reference [2]

The entity that limits the light beam in an optical system is the aperture, which can be the edge of a lens, a frame, or a specially designed screen with holes.

The function of the aperture can be divided into two aspects: limiting the light beam or limiting the size of the field of view (imaging range). The former is called the aperture aperture, which can limit the solid angle of the imaging beam and control the amount of light entering. From the meridian plane, it limits the maximum inclination angle of the edge light in the imaging beam, that is, the beam aperture angle; the latter is called the field aperture, which can limit the size of the imaging range of the object. For example, the film frame and reticle frame that overlap with the film in the camera are the field aperture.

Schematic diagram of aperture diaphragm and field diaphragm. This is a typical coaxial optical system, where the objective lens, eyepiece, and photosensitive element are all located on the same straight line.

Image source: Homemade

After clarifying the above concepts, we can roughly divide the off-axis system into three types: aperture off-axis, field of view bias, and a combination of aperture off-axis and field of view bias.

First, let's look at the aperture off-axis. As shown in the figure below, the incident light is limited by the aperture stop. At this time, although the incident light is still parallel to the optical axis, it is limited by the aperture and only a part that deviates from the optical axis is allowed to enter the system. This can make the system structure compact, but in the case of a larger field of view, the imaging quality will be reduced.

Aperture Stop Offset

Image source: Reference [3]

Next is the field of view bias. At this time, the incident light does not enter the system parallel to the optical axis, as shown in the figure below. CCD is a sensor, and we can regard it as the image field. There is an angle between the imaging light and the optical axis, which deviates from the optical axis, so it is called "off-axis", which is more suitable for the requirements of large field of view and large relative aperture.

Field of view bias

Image source: Reference [4]

Different from the situation in the coaxial system where the secondary reflector will cause aperture obstruction to the primary reflector, the off-axis system can eliminate the center obstruction problem existing in the coaxial optical system. Not only that, the off-axis system also increases the field of view, and to a certain extent can simultaneously achieve high resolution and wide coverage area, which are a pair of indicators that are difficult to balance. It is an asymmetric optical system with better performance.

After talking about "off-axis", let's talk about "three antis".

"Three mirrors" refers to the three mirrors in the optical system. This type of mirror is affected by many factors such as curvature radius, thickness, cone coefficient, and material, which increases the design freedom and improves the ability to adjust aberrations.

Off-axis three-mirror optical system

Image source: Reference [5]

The reason for adding a reflector is that, on the one hand, the reflective optical system is significantly superior to the refractive system in terms of lightweight, and has no chromatic aberration. It can increase the field aperture to improve the field of view and expand the observation range of the camera.

On the other hand, if the spatial distance is too far, if you want to improve the resolution of the observation, the focal length must be very high. The use of reflectors can fold the light path, make the structure compact, and enable the use of optical systems with larger focal lengths, increasing the entrance pupil diameter, thereby improving the ground resolution.

The popular off-axis three-mirror camera

As early as 1975, foreign countries proposed an unobstructed three-mirror type, namely the off-axis three-mirror system. The inherent characteristics of this optical system enable it to be applied to systems with low relative aperture, unobstructed, large field of view and high resolution. To date, a large number of unobstructed reflection systems have been developed.

By the end of the 20th century, there were many applications of off-axis three-mirror systems abroad, but there were few studies on off-axis reflective optical systems in China, and there was no systematic reflective optical theory. The aberration theory, design method, structural characteristics, and the relationship between various structural parameters of off-axis optical systems all need to be explored continuously.

During the exploration process, researchers also encountered many difficulties. For example, the mathematical expression of the off-axis telescope is very complex, which makes the design process very complicated; high-performance design requires the use of precise off-axis aspheric mirrors, and the manufacturing technology of such aspheric mirrors is still blank; and the optical elements in the system have a high degree of freedom, which makes its detection and assembly more difficult than design. The assembly accuracy is very high, and it is necessary to consider controlling its thermal stability in space.

Under such circumstances, in order to achieve the goal of national self-reliance in science and technology, the Changchun Institute of Optics, Fine Mechanics and Physics rose to the challenge and began to tackle the advanced manufacturing technology of off-axis three-mirror optical systems.

After ten years of hard work and efforts, the Changchun Institute of Optics, Fine Mechanics and Physics has made a number of breakthroughs in the off-axis three-mirror optical system, laying a solid foundation for the leapfrog development of my country's space optical remote sensors.

The high-resolution camera of Tianwen-1 was exhibited at the Northeast Asia Expo

Image source: China Jilin Network

It is precisely because of the off-axis three-mirror optical system that the high-resolution camera, which serves as the eyes of Tianwen-1, can achieve optical imaging with a resolution of 0.5 meters at a distance of 265 kilometers from the target. It also allows us to see the clearly visible iconic landforms of Mars, such as Acidalia Planitia, Chryse Planitia, Meridiani Planum, Schiaparelli Crater and the longest canyon, Valles Marineris, through the photos sent back by Tianwen-1.

The Martian landforms photographed by Tianwen-1

Image source: CCTV News

Captions: ① Acidalia Planitia; ② Chryse Planitia; ③ Meridiani Planum; ④ Schiaparelli Crater; ⑤ Valles Marineris.

Generation after generation of scientific researchers exploring science and technology will not stop. We look forward to them and Tianwen-1's "eyes" taking us to see more space scenery.

References:

[1] Zhang Mingyu. Research on TDI CCD camera image acquisition and processing system[D]. Graduate School of the Chinese Academy of Sciences (Changchun Institute of Optics, Fine Mechanics and Physics), 2011.

[2] Zhang Xuemin, Song Xing, Hou Xiaohua, Li Hua. Adjustment of off-axis three-mirror optical system with adjustable focus[J]. Optics and Precision Engineering, 2017, 25(06):1458-1463.

[3] Zhao Liang. Design of off-axis three-reflection optical system[J]. Optoelectronic Technology Application, 2014, 29(04): 1-4+29.

[4] Li Xinghua, Zhang Dong, Gao Lingyu, et al. Method for improving the imaging quality of off-axis three-mirror optical system:, CN107505694A[P]. 2017.

[5] Zhang Xuejun, Wang Xiaokun, Xue Donglin, et al. A common reference detection and processing method for off-axis three-mirror aspheric optical system:, CN106225712A[P].

Produced by: Science Popularization China

Produced by: May (Changchun Institute of Optics, Fine Mechanics and Physics, University of Chinese Academy of Sciences)

Producer: China Science Expo