1 Introduction

Over the past decades, space research in the form of earth observation has required for a compact and lightweight optical system with a large field of view, and also generated stringent stray light control requirements, that makes the off-axis catadioptric optical system (OCOS) get greatly improvement. The OCOS has the following features: unobscured; easy to be lightweight; has better tolerance in the heat deformation; more design freedom; and can install field stop and multiple Lyot stop to restrain the stray light^[1-4].

Stray light is the unwanted light reaching the focal plane array (FPA) during the operation of the infrared optical system, namely, it will create additional signal which can decrease the system's sensitivity, and will reduce the contrast of image, Modulation Transfer Function (MTF) and the Signal Noise Ratio (SNR)^[5]. Hence, the suppression of stray light has become the key factor in the space optical system. In the 19th century, some institutions have developed a vast variety of software to model and simulate the stray light, such as GUERAPⅢ, APART/PADE, LightTools, TracePro, OptiCAD and so on^[6-7]. At present, the main method of analyzing stray light is the method of modeling and simulating. This method is prevalently adopted to analyze the stray light, and with this method, it cannot only get the numerical value of the stray light, but also can render a visualized information of critical surfaces^[8]. As a result, this method has become the main approach to study the stray light, moreover, the results of the simulation are taken as a guideline to design the suppressive structure of the optical system.

2 Optical Design

There are several types of configuration for realization of an infrared observation in the space. The different types can be divided into two main categories, namely, coaxial and non-coaxial systems. This article chooses non-coaxial system as the optical configuration of the system due to the following reasons: (1) without a central obstruction caused by its secondary mirror it will get a smaller diffraction pattern; (2) get a smaller size of baffle; (3) it is easy to get a larger FOV in the sagittal plane; (4) get a better image contrast and quality^[9-12].

Fig. 1 shows the system configuration of the optical system, which consists of a Cook type off-axis three-mirror-anastigmatic system (TMAS), a folding mirror, a lens group and a flat FPA. The layout of the system is shown in Fig. 1, and its main specification is listed in Table 1.

The TMAS provides an obstruction-free aperture, high spatial resolution over a wide FOV and free of chromatic aberrations^[13-15]. It consists of a concave primary mirror, a convex secondary mirror, a concave tertiary mirror and the aperture stop is located 60 mm before the primary mirror. All reflective mirrors share a common optical axis, although their mechanical axes are different from each other. The primary and tertiary mirror are ellipsoid, and the secondary mirror is a hyperboloid. The re-imaging plane is located between the the secondary and tertiary mirror. Table 2 summarizes the fundamental parameters of the TMAS.

The illustration of the relay lens group with the superimposed optical ray-trace is shown in Fig. 2. The material of the third lens is ZnSe, and the others are Germanium. The whole relay lens group has a 6° tilt about X axis, and a -117.6 mm decenter about Y axis. This is for connecting between the relay lens group and real exit pupil of the system. And it provides obstruction free aperture with one hundred percent cold stop efficiency to suppress shading of the infrared image.

After optimization, the image quality of the optical system almost approach to the diffraction-limits in all FOV. The MTF and the spot diagram are shown in Fig. 3.

Optical design and optimization is substantial, but it is far from having a practicable infrared optical system. Therefore, the stray light must be analyzed and the suppressive structure must be designed to satisfy the requirements of image quality.

3 Evaluation Criterion of Stray Light 3.1 Stray Light Analysis

The power of the stray light which is received by the FPA depends on the following equation^[16-18]:

$ {\mathit{\Phi }_{{\rm{FPA}}}} = {\mathit{\Phi }_{{\rm{source}}}} \times {f_{{\rm{GCF}}}}\left( {S,F} \right) \times {f_{{\rm{BRDF}}}} \times \pi $

(1)

where Φ_FPA is the stray light power received by the FPA; Φ_source is the power of the source; f_GCF(S, F) is the geometrical configuration factor, which represents the geometrical nexus between the source and the FPA; f_BRDF is the bidirectional distribution function, which represents the surface scattering characteristics. According to Eq.(1), the ways to reduce the energy of stray light is to decrease f_GCF(S, F) of the system.

3.2 Mathematical Models of Stray Light

In general, the stray light contamination at a pixel is required to be less than 10% of the target irradiance to make sure that the SNR satisfies the requirement of image quality. For the earth observation space-borne infrared telescope, the useful signal is mainly from a narrow wavelength spectrum of thermal emission from the target. The infrared telescope that involved in this context, which has an extraordinarily small angle between optical axis and the earth's horizon, thus the external stray light is mainly from the out-of-field radiation of the earth.

This article uses Point Source Transmission (PST) as the evaluation criterion of the stray light, it represents the capability of the optical system to restrain the stray light^[8-9]. The expression of PST is as Eq.(2):

$ {S_{{\rm{PST}}}} = \frac{{{E_d}\left( \theta \right)}}{{{E_i}\left( \theta \right)}} $

(2)

where E_d(θ) is the irradiance at the FPA; E_i(θ) is the irradiance at the entrance pupil, and θ is the off-field angle.

The average irradiance at the entrance pupil can be obtained by Eq.(3):

$ {E_i}\left( \theta \right) = {L_e}{\mathit{\Omega }_e}\cos {\theta _e} $

(3)

where E_i(θ) is the average irradiance at the entrance pupil; L_e is the earth's radiance in the specified wavelength; Ω_e is the solid angle between the earth and the entrance pupil; θ_e is the angle between the earth and the entrance pupil.

The radiant of the target at the FPA, namely, φ_td can be expressed by Eq.(4):

$ {\varphi _{{\rm{td}}}} = \frac{{\rm{ \mathsf{ π} }}}{4}{L_e}A{\Omega _t}{\tau _0}\cos \left( {{\theta _t}} \right){\left( {\frac{D}{f}} \right)^2} $

(4)

where A is the area of the target; Ω_t is the solid angle between the target and the entrance pupil; τ₀ is the total transmittance of optical system; θ_t is the angle between the optical axis and the line that connecting the center of the target and the entrance pupil (θ_t is extremely small, so cos (θ_t) is approximately equal to 1); D is the diameter of the entrance pupil; f is the effective focal length.

Considering the actual image process, as the center of the image spot hardly coincides with one single pixel, therefore, an area of 2×2 pixels is regularly taken into account during the calculation. So the irradiance of the target at the FPA is as Eq.(5):

$ {E_{{\rm{td}}}} = \frac{{{\varphi _{{\rm{td}}}}}}{{4\alpha }} $

(5)

where E_td is the irradiance of the target at the FPA; α is the area of one single pixel. Through the above analysis, it can be obtained that E_d(θ)≤0.1E_td.

4 Stray Light Analyzing 4.1 Suppressive Structure Design

The suppressive structure includes baffles, vanes and stops.These are mechanical structures which can block the propagating path of the unwanted light.

The function of the baffle is to minimize stray light which has a large field angle. Vanes are the structure which are used to weaken the power of stray light, and force the stray light reflect several times before leaving the baffle^[3]. Due to the strip FOV of the system, the shape of the vane is similar to rectangular as presented in Fig. 4(a), and the depth of the first vane is 118 mm, the width of the vane is 220 mm, and the bevel angle of the vane is 45°, which is shown in Fig. 4(b).

Stop is one of the most effective methods to restrain the stray light. In the optical system designed above, there are four types of stop which can be adopted, namely, aperture stop, field stop, Lyot stop and cold stop (coinciding with real exit pupil, and locating among the lens group). The folding mirror is behind the optical aperture which is on the supportive structure of the primary mirror, some stray light have direct view from the entrance pupil to the folding mirror. To avoid this stray light, four internal occulters are placed inside the optical system. More details is shown in Fig. 5.

4.2 Stray Light Analysis

In order to analyze the stray light and the suppressive structure designed, two detailed models are established in TracePro. One is the model ofoptical system with whole suppressive structure, and the other is the model of optical system with merely the supportive structure of the primary mirror. The surface in TracePro is defined by ABg model of the BRDF^[18-20]:

1) Reflective mirror surface (SiC): λ=10 μm, r≥95%, in BRDF model A=0.001 5, B=0.001 4, g=1.8;

2) Refractive mirror surface: λ=10 μm, τ≥95%, in BRDF model A=1E-5, B=0.015, g=2, in BTDF model A=0.000 1, B=0.015, g=2;

3) Mechanical surface (coating with black paint Z-306): α=93%, r≥2%, in BRDF model A=0.636 6, B=0.015, g=2.

4) Focal plane: α=100%. where r is the reflectivity; τ is the transmittance and α is the absorptivity.

This article analyzes and contrasts the PSTs of the two models. The detailed PSTs for different incident angles are calculated, and the PST curves as shown in Fig. 6.

According to Figs. 6(a) and 6(b), with the increase of off-field angle, the PST of the optical system decreases. In the X direction, the structure and the FOV of the system is symmetric, the PST curve decreases in both directions, between 10° and 40° the PST decreases quickly, at off-field angle 3°, the PST of the first model arrives at 10^-5, while the first is 1-4 order higher than the second model. In the Y direction, the system is asymmetric, and between the off-field angle of 10°-30° the PST curve of -Y direction is higher than +Y direction, which is caused by the configuration of the system, and it is evident that the first model is 1-4 order higher than the second. In Fig. 5, the fluctuations between off-angle 15° and 40° are obvious which are caused by the stray light incidence onto the FPA after several reflections between the baffle and vanes. The analysis of the two models demonstrates that the stray light simulation and analysis is an effective approach to guide the suppressive structure design of the infrared optical system.

5 Conclusions

This article presents the design of a re-imaging off-axis catadioptric optical system, and the image quality of the system almost approaches to diffraction limits in all fields of view. Due to its unique features, the system has been widely used in the space telescopes. Then the mathematical models of stray light is built, and the suppressive structure is established to eliminate the effect of stray light. And based on optical simulations by the stray light analysis software TracePro, which can fully describe the geometries and surface's properties of the system, the results indicate that the suppressive structure of the optical system has excellent ability to restrain the stray light, and decreases the PST of the optical system approximately 1 to 4 orders. At the same time, the calculated and simulated results can be a reference for system design.