Stray light refers to any unintended light that reaches the detector in an imaging system [1–3]. This phenomenon typically occurs when bright sources, such as the sun, are near the observed object, or when the object itself is very dim. Stray light can degrade image quality by causing glare, reducing contrast, and introducing unwanted artifacts. As a result, it is crucial to analyze and mitigate stray light in various optical systems used in applications such as astronomy, Earth observation satellites, telescopes, and aircraft [4].

Stray light can be classified as either external or internal, based on its source [5, 6]. External stray light arises when light from an external source, such as sunlight or cloud reflections, enters the optical system through lenses or windows and reaches the detector after undergoing reflections, refractions, or diffractions within lenses, mirrors, or frames. Internal stray light, however, originates from thermal emissions within the optical components themselves. This is particularly significant in longwave infrared (LWIR) imaging systems, such as the LWIR optical payload under development shown in Fig. 1, where internal stray light acts as noise that reduces image consistency and accuracy.

Figure 1. Three-dimensional model of long-wavelength infrared (LWIR) optical payload.

Figure 2 illustrates the paths of external and internal stray light in the optical payload. In Fig. 2(a), the green rays represent the normal light path, while the red rays indicate external stray light entering from outside the field of view (FOV). In Fig. 2(b), the red rays represent the path of internal stray light emitted from the secondary mirror that reaches the sensor. In addition to the secondary mirror, all structures inside the optical system act as light sources emitting internal stray light. In standard optical systems, internal stray light has minimal impact, so external stray light is typically mitigated using sunshades, baffles, or vanes [7–9]. However, in the LWIR range, these mechanical structures can themselves become sources of stray light, necessitating the simultaneous consideration of both external and internal stray light in the optimal design of baffles.

Figure 2. Layout of stray light paths: (a) External stray light path showing green rays as the normal path and red rays as stray light entering from outside the field of view. (b) Internal stray light path with red rays representing thermal emission from the secondary mirror reaching the sensor.

Pravdivtsev and Akram [10] proposed an evaluation method for both external and internal stray light using a non-sequential ray tracing technique, while Chunlei and Xiaoping [11] presented an approach for analyzing external stray light in the LWIR range and calculating noise caused by internal stray light. Wang et al. [12] suggested a baffle structure to suppress internal stray light in space-based infrared optical systems, and Zhu et al. [13] proposed an integrated suppression process for both internal and external stray light in LWIR catadioptric telescopes. However, most studies, including these, focus primarily on optimizing the suppression of external stray light, while reducing internal stray light either by using materials with low emissivity for the lenses or by cooling the system. Although material substitution and cooling methods are commonly used to reduce internal stray light, these approaches often require complex designs and incur significant costs for the installation and maintenance of cooling systems.

In this study, we defined the conditions for completely blocking external stray light in the LWIR Cassegrain payload based on geometrically related parameters and results derived from optical design software. Subsequently, we conducted a parametric search to identify the parameters that minimize internal stray light for the primary and secondary baffles that meet these conditions, and proposed an optimized design. This approach enables the simultaneous suppression of both external and internal stray light, and the optimization is aimed at reducing the need for additional cooling systems, thereby minimizing installation work and related costs.

Section 2 describes the optical model used for analysis, along with the conditions for external stray light suppression. Section 3 details the methods employed for parametric optimization, including the reduction of the solution space by applying the direct-shot blocking condition while maintaining the central obstruction ratio. In Section 4, we present an optimized baffle design and investigate the point transmittance function of the payload with the optimized baffles, accompanied by a forward-backward-forward method [14, 15]. Finally, Section 5 concludes the study.

2.1. Optics Overview

The optics under study is an imaging payload designed for Earth remote sensing in the LWIR range of 7.4 to 9.4 μm, with a FOV of ±1.2°. This payload includes an f/1.4 Cassegrain telescope comprising a primary mirror (PM), a secondary mirror (SM), four sequential field correction lenses (Lens 1, Lens 2, Lens 3, and Lens 4), a window, and an LWIR spectral bandpass filter. A cooled LWIR imaging detector with a resolution of 512 × 512 pixels and a pixel size of 15 μm is integrated into the system through an f/1.4 cold stop, positioned 16 mm from the sensor plane, where the window and spectral filter are also located.

Figure 3 provides a detailed optical layout with labeled components, where the cold shield, indicated by Ⓗ, is cooled to 50–80 K, while other structures are uncooled, making them potential sources of internal stray light. Major dimensions and their symbols are shown in Fig. 4, and Table 1 lists key values of these dimensions, which were compactly designed to meet volume and mass constraints.

Figure 3. Layout of the long-wavelength infrared (LWIR) optical payload with major components labeled.

Figure 4. Major dimensions with their symbols.

TABLE 1. Major dimensions of the payload.

Component	Parameter	Symbol	Value (mm)
Outer Baffle (Optical Tube)	Diameter	DOB	181.2
	Distance from PM	lOB	113.0
	Distance from Lens Barrel	l1	65.2
Primary Mirror	Diameter	DPM	142.2
Secondary Mirror	Diameter	DSM	47.0
	Distance from Lens Barrel	l2	47.5
	Distance from PM Baffle	l3	41.1
Lens Barrel	Diameter	DLT	9.0

This study does not focus on the optical design itself; However, it is important to note that the optics are compactly designed, with the length of the outer baffle being approximately equal to the distance between the primary and secondary mirrors. While a longer tube length would be ideal for blocking external stray light, this compact design necessitates a more effective baffle design to ensure sufficient suppression of external stray light. We still retain some design flexibility in the inner baffle, specifically, the primary and secondary mirror baffles defined by their lengths and slopes (l_SB, l_PB, θ_SB, θ_PB). These baffles should block residual direct shots while minimizing IR irradiance from self-heating.

2.2. Analysis Modeling

Stray light analysis for the optimized baffle design was conducted with LightTools software using two models based on the geometry shown in Figs. 3 and 4 and dimensions listed in Table 1. Each model employed distinct light source configurations to address external and internal stray light within the LWIR catadioptric optical payload. Figure 5 provides schematic diagrams for each analysis method, and relevant parameters are summarized in Table 2.

Figure 5. Schematic diagrams of the two analysis models: (a) External stray light analysis model, (b) internal stray light analysis model.

TABLE 2. Parameters of the analysis models.

Parameter		Internal Stray Light Analysis Model	External Stray Light Analysis Model
Source	Location	Each Surface	Far Field
	Shape	Surface-dependent	Circular (ф 71 mm)
	NA	Diverging (NA 1.0)	Collimated (NA 0)
	Aiming	None	Entrance Pupil
	Spectrum (nm)	7,400–9,400
	No. of Rays	108
Detector	Format	64 × 64	512 × 512
	Shape	Rectangular (7.68 × 7.68 mm2)
	Type	Irradiance

For external stray light, external sources like the sun were simulated using forward ray tracing, with parallel rays entering the system and interacting with baffles, mirrors, and lenses before reaching the detector plane. The detector was configured to match the intended sensor’s specifications for realistic results.

For internal stray light, all optical and mechanical surfaces were modeled as surface light sources to simulate thermal radiation, and the shape and position of each source was tailored to its specific structure. Emittance was set to match the absorptance of each surface, as shown in Table 3. The detector configuration was consistent with external stray light analysis, but the 8 × 8 sensor pixels were merged into a single unit to simplify analysis, since the irradiance pattern from internal stray light lacks the high spatial frequency seen in external stray light.

TABLE 3. Average surface properties of the payload across the long-wavelength infrared (LWIR) spectrum.

Parts	Material/Coating	Transmittance(%)	Reflectance(%)	Absorption(%)
L1	IRG 26/ARa)	98	1.46	0.54
L2	ZnS/AR	98	1.36	0.64
L3	IRG 26/AR	98	1.58	0.42
L4	IRG 26/AR	98	1.40	0.60
PM, SM	SiC/HRb)	0	99	1
Window	Ge/AR	97	2.75	0.25
Filter	Ge/AR	93	6.87	0.13
Housing	Black Paint	0	2	98

^a)AR, anti-reflection; ^b)HR, high reflection..

In both models, surface characteristics including partial reflection, transmission, and scattering were incorporated as listed in Table 3, as they significantly affect stray light behavior. To reduce external stray light, a black coating with high absorptance (98%) across the LWIR spectrum was applied to all mechanical housing components. This high absorptance effectively minimizes reflected external stray light, but on the other hand, increases internal stray light due to high thermal emittance. Optical components such as mirrors and lenses have low absorption and emittance, which suggests that internal stray light is primarily influenced by mechanical surfaces, including the inner baffles.

3.1. Overview

The objective of the parametric optimization was to refine the inner baffle configurations for simultaneous suppression of external stray light (e.g., sunlight) and internal stray light from thermal emissions. Key parameters of the inner baffles, represented by the lengths and slopes of the primary and secondary mirror baffles (l_SB, l_PB, θ_SB, θ_PB), were optimized to block unwanted rays while minimizing thermal emission interference.

This approach involved a parametric search across the solution space defined by the four variables, as outlined in Table 4. To streamline the process, the direct shot blocking conditions, detailed in the following section were applied to reduce the solution space by eliminating 0^th and 1^st order external stray light paths. The analysis of extensive external stray light, including multiple reflections and scattering, is reported in another paper [14, 15].

TABLE 4. Solution space for inner baffle design parameters.

Component	Parameter	Symbol	Min	Max	Δ
Secondary Mirror Baffle	Length (mm)	lSB	4	9	1
	Slope (deg)	θSB	10	20	1
Primary Mirror Baffle	Length (mm)	lPB	10	20	1
	Slope (deg)	θPB	10	20	1

For each configuration in the reduced space, we recorded the maximum thermal irradiance on the detector from the internal stray light model and selected the optimal design by minimizing this value. We then assessed point source transmittance (PST) from the external stray light model, a key metric for evaluating external stray light suppression. PST indicates the fraction of light from an external point source that reaches the detector, effectively measuring the system’s ability to block unwanted light.

3.2. Direct-shot Blocking Conditions for Inner Baffles

The outer baffle, a cylindrical tube, suppresses stray light by setting the field angle θ_D, where rays bypass the mirrors and enter the lens directly as 0^th or 1^st order stray light, termed direct shot [Fig. 6(a)]. The direct shot angle θ_D ranges as follows:

Figure 6. Direct shot layout: (a) Direct shot without inner baffles and (b) direct shot blocking using inner baffles.

with

As listed in Table 1, the payload design without inner baffles leaves a direct shot range of 17.6° to 56.1°. As shown in Fig. 6(b), the inner baffles effectively block direct shots that would otherwise reach the detector.

To ensure effective blocking without excessive obstruction, the ends of the primary and secondary baffles (x_SB, x_PB and y_SB, y_PB) are aligned as follows:

In addition to satisfying the direct shot blocking condition, the inner baffles must maintain the central obstruction ratio, the ratio of the diameter of the obstructed area (caused by the secondary mirror and baffles) to the diameter of the primary mirror aperture, to achieve an optical resolution, represented by the modulation transfer function (MTF), above a certain threshold. To preserve this ratio, the ends of the inner baffles, specifically, should be positioned within the triangle formed by rays from the center and edge of the field, as shown in Fig. 7.

Figure 7. Placement of inner baffles to maintain the central obstruction ratio. Inner baffles should be positioned within the triangle formed by rays from the center (orange) and edge (green) of the field to preserve this ratio.

4.1. Solution Space Reduction

As shown in Table 4, the starting solution space consists of 6 × 11³, or 7,986 cases, which is impractical to fully survey. By applying the direct-shot blocking condition along with the central obstruction ratio constraint, the potential solution space is reduced to 224 cases. This reduction was achieved by applying the conditions described above to the primary mirror baffle end while varying the positions of the secondary mirror baffle end. Table 5 details the distribution of the reduced solution space, totaling 224 cases.

TABLE 5. Distribution of reduced solution space for inner baffle configurations, totaling 224 cases.

Secondary Mirror Baffle Slope (θSB (°))	Secondary Mirror Baffle Length (lSB (mm))
	4	5	6	7	8	9
10	1	0	0	0	0	0
11	1	0	0	0	0	0
12	1	0	0	0	0	0
13	1	5	0	0	0	0
14	2	5	0	0	0	0
15	2	8	11	0	0	0
16	2	8	11	0	0	0
17	2	8	11	11	0	0
18	3	8	11	11	0	0
19	3	8	11	11	11	0
20	5	8	11	11	11	11

4.2. Parametric Optimum Design for Inner Stray Light

Internal stray light analysis was conducted across the entire reduced space of 234 combinations by recording the number of photons per cell (an 8 × 8 pixel combination) reaching the SWIR detector as thermal irradiance noise. During the analysis, the payload was assumed to maintain a uniform temperature of 300 K (27 ℃) except for the cooled detector and cold shield, representing a median condition.

Notably, the analysis shows that irradiance across the detector plane is mostly uniform in all cases, as expected due to the use of a cold stop and shield on the short wavelength infrared (SWIR) detector, along with the low emissivity of lenses/mirors and high emissivity of the mechanical housing. Slight randomness in the irradiance pattern is attributed to quantum effects.

From the recorded data, we first identified the local parametric optimum solutions, as shown in Table 6. The overall optimum parameters for the inner baffles were found to be l_SB = 8 mm, θ_SB = 19°, l_PB = 14, and θ_PB = 14° mm, which are underlined in Table 6.

TABLE 6. Local parametric optimum inner baffle designs as the secondary baffle length varies.

Local Optimum Variables	Secondary Mirror BaffleLength (lSB (mm))
	4	5	6	7	8	9
Secondary Mirror Baffle Slope (θSB (°))	10	14	18	19	19	20
Primary Mirror Baffle Length (lPB (mm))	16	15	15	14	14	13
Primary Mirror Baffle Slope (θPB (°))	15	16	14	16	14	14
No. of Photons/Cell at the Detector (×106)	3.36	2.85	2.16	2.11	1.93	2.22

4.3. Confirmation of External Stray Light Suppression

First, prior to this optimization, a comprehensive investigation of the payload model with the initial inner baffles was conducted using a forward-backward-forward approach [14] as shown in Fig. 8, and the results will be published in another paper [15].

Figure 8. Relative illuminance of ghost images in the payload with initial inner baffles. Down arrow symbols (↓) indicates local peaks. Reprinted with permission from Copyright © 2025, Optical Society of Korea [15].

The payload with the initial baffle design exhibited a relatively high ghost image ratio (relative illumination) of a few 10⁻³ within its FOV (1.2°). Outside the field angle >2°, the ghost ratio remained very low at 10⁻⁷, with two noticeable peaks around 7° and 12° field angles, though these peaks are minor— approximately 10⁻⁸–10⁻⁷.

Since the LWIR payload primarily images the Earth near the horizon, it is particularly vulnerable to sun exposure. Therefore, external light sources outside the FOV are a primary concern when establishing a sun-avoidance angle. A prior investigation suggested that the PST from the sun should be below 10⁻⁹ to safely observe the Earth’s horizon without risking detector damage. This requirement would limit the payload’s operational angle to within 5°, resulting in an impractical sun-avoidance angle of 85°.

Figure 9 shows the PST of the payload before and after baffle optimization. The optimized design reduces external stray light, including those from the two peaks, to below 10⁻⁹ for all field angles >10°, allowing for a practical sun-avoidance angle.

Figure 9. Point source transmittance (PST) as a function of angle of incidence, shown before and after baffle optimization.

In this paper, we designed a baffle to simultaneously suppress external and internal stray light in an LWIR catadioptric optical system. A parametric approach was used to optimize baffle configurations, focusing on direct shot blocking angles derived through geometric relationships to effectively reduce external stray light. Point source transmittance was also evaluated to ensure that stray light suppression met required thresholds. Additionally, we analyzed the increase in internal stray light based on baffle length and slope angle. As a result of the optimization, the sun-avoidance angle for external stray light was reduced from 55° to 10°, and internal stray light was decreased by more than 2.7 times compared to the pre-optimized baffle.

This research was supported by the Agency for Defense Development and funded by the government (Defense Acquisition Program Administration) in 2024 as part of the Defense Research and Development Program (Grant no. 912984301).

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at this time, but may be obtained from the authors upon reasonable request.