Stray Light Analysis and Elimination of an Optical System Based on the Structural Optimization Design of an Airborne Camera

Abstract

An aspherical airborne camera has excellent performance in the field of photoelectric reconnaissance equipment. However, the image plane contrast of the optical system will be reduced by stray light originating from inside or outside of the optical system. In the present work, the self-designed aspheric airborne camera is manufactured with a baffle and vanes to reduce the impact of stray light on the camera imaging quality. TracePro software is used to analyze the stray light and establish an ABg mathematical model based on the scattering intensity measurement. The incident angle of the light parallel to the optical axis is set, and ray tracing is performed on the optical machine model to verify whether it conforms to the optical system design. The results showed that when the incident angle of the light source is greater than 0.5°, the point source transmittance (PST) value drops rapidly, and when the incident angle is 30°, the PST value of the system is in the order of 10⁻⁸. Stray light analysis verifies that the self-designed aspheric surface-based camera optomechanical structure has the ability to suppress stray light. The design of the baffle and vanes further enhances the ability of the optical system to suppress stray light, which can provide a reference for the design of a stray light elimination structure.

1. Introduction

As a main way to obtain important ground information, aerial photography technology has the advantages of good maneuverability, high timeliness, low investment, etc. In addition to observing geomorphology, resources, environment, weather, and natural disasters of the earth, aerial photography technology has also made significant contributions to the safety and progress of human society, such as accurate and targeted reconnaissance of sensitive military targets to obtain target data [1,2,3].

Aerial camera performance depends largely on the aerial camera optical system. Imaging quality is an important standard to measure the performance of aerial cameras, which is mainly affected by the performance of the optical system and imaging system. At present, various methods to improve the image quality of the optical performance have been used, while the environmental factors are still unavoidable [4,5,6]. Aspheric lenses have a more suitable curvature, and their performance can be improved by correcting aberrations [7]. The current aspheric design can correct images, solve problems such as visual distortion, and has excellent clarity and higher resolution [8]. Lens miniaturization can also be achieved with aspheric lenses. With the continuous breakthrough of aspheric lens manufacturing inspection technology, the manufacturing cost of aspheric lenses has gradually decreased, which is conducive to improve the utilization and manufacturing accuracy of lenses. Therefore, the development of aspheric manufacturing technology makes the application of aspheric surfaces in aerial cameras possible [9,10,11,12].

In the development and design of optical systems of aerial cameras, the presence of stray light is an obstacle to the improvement of the imaging performance of some high-end precision optical systems [13,14,15]. Therefore, the design of stray light suppression is an important task [16,17]. In addition, stray light evaluation has always been an important link in the development of optical instruments. The research methods generally include theoretical simulation, stray light testing, and correction [18,19,20,21]. General evaluation functions of stray light are source transmission, stray light coefficient, etc. Different evaluation methods are related to the characteristics of the instrument and the means of stray light suppression. Sholl et al. [22] analyzed the stray light situation of an SNAP telescope. The stray light was suppressed by means such as an outer baffle and vanes, and the model was established and analyzed using ASAP software. Mazzoli et al. [23] conducted an in-depth study of the stray light of the ASPIICS corona observer. They analyzed the sources of stray light, designed an outer baffle and built-in baffle structure to eliminate stray light, and simulated the distribution of diffraction spots formed on the edge of the outer baffle. Lahenrere et al. [24] tested and corrected the stray light of a polarized multi-angle sensor and divided the stray light on the image surface into one type of stray light and two types of stray light. At the same time, the algorithm was used to correct the stray light, but no quantitative theoretical analysis results were given. Although some scholars have studied the stray light suppression of aspheric optical systems, the structure of optical mechanical systems will also affect the effect of stray light suppression [18,25]. The existence of stray light will reduce the image plane contrast of the optical system, optical transfer function, and signal-to-noise ratio. Therefore, it is necessary to analyze the stray light to improve the performance of different aspherical camera optical systems.

This article contains the following sections: the second part mainly introduces the theoretical basis of stray light and the structural design of the optomechanical system. In order to eliminate stray light, extinction coating and structural factors were comprehensively considered and the design of baffle and vanes was optimized based on the camera structure. The third part uses TracePro optical analysis software to analyze the stray light of the optomechanical system based on the optimized structure. Finally, the conclusion is presented in the fourth part.

2. Theory and Methods

2.1. Theoretical Basis of Stray Light Analysis

In addition to the imaging rays in the optical system, other non-imaging rays distributed on the imaging surface and rays reaching the imaging surface via the abnormal optical path are called stray light. Stray light usually reduces the image plane contrast of the optical system, thereby reducing the optical transfer function and signal-to-noise ratio. In addition, the stray light formed by the abnormal light transmitted to the imaging surface through the lens and light shield is the main source of external stray light for the aerial camera system. Stray light caused by scratches, bubbles on the outer surface of the lens, notches around the outer edge of the lens, and unintentional fine fragments during the assembly of the camera lens are the main sources of external stray light in the aerial camera system.

The basic energy transfer equation in radiant heat transfer theory is to transfer energy between any two surface elements in the optical system, which is the physical basis of the stray light analysis. Then, the related physical quantities in the transfer equation are connected to analyze the stray light in different ways.

As shown in Figure 1, $d{A}_s$ and $d{A}_c$ represent the two arbitrary facets in the optical system. r represents the center distance. ${\theta }_s$ and ${\theta }_c$ represent the angle between the connection of the normal of any two facets and the center of the two facets, respectively. $L_s({\varphi }_0,{\theta }_0)$ represents the amplitude of $d{A}_s$. The radiant flux received by $d{A}_c$ and the radiant flux emitted from $d{A}_s$ are given by Equation (1):

$$\begin{array}{ll}d{\varphi }_c& =L_s({\varphi }_0,{\theta }_0)\cos {\theta }_{s}d{A}_{s}d{\mathsf{\Omega }}_s\\ & =\frac{L_s({\varphi }_0,{\theta }_0)\cos {\theta }_{s}d{A}_s\cos {\theta }_{c}d{A}_c}{r^2}\\ & =BRDF({\varphi }_i,{\theta }_i,{\varphi }_0,{\theta }_0,\lambda )d{\varphi }_{0}GCF({\theta }_s,{\theta }_c)\end{array}$$

(1)

where $BRDF({\varphi }_i,{\theta }_i,{\varphi }_0,{\theta }_0,\lambda )$ represents the bidirectional reflection distribution function of the diffuse reflection characteristics. It is the ratio of the surface reflection amplitude brightness $L_s({\varphi }_0,{\theta }_0,\lambda )$ and the incident amplitude brightness $E_s({\varphi }_i,{\theta }_i,\lambda )$, as shown in the equation below:

$$BRDF({\varphi }_i,{\theta }_i,{\varphi }_0,{\theta }_0,\lambda )=\frac{L_s({\varphi }_0,{\theta }_0,\lambda )}{E_s({\varphi }_i,{\theta }_i,\lambda )}$$

(2)

$GCF({\theta }_s,{\theta }_c)$ reflects the projection angle of $d{A}_s$ to $d{A}_c$ stereo, which can be obtained by:

$$GCF({\theta }_s,{\theta }_c)=\frac{\cos {\theta }_{s}d{A}_c\cos {\theta }_c}{r^2}$$

(3)

It is clear that the luminous flux received by $d{A}_c$ is directly related to $d{\varphi }_s$, BRDF, and $GCF({\theta }_s,{\theta }_c)$ by Equation (3). Therefore, three methods are commonly used to reduce the stray light flux received by reducing the bidirectional reflection distribution function (BRDF) on the surface of the material, the incident light energy of stray light or the outgoing radiation flux $d{\theta }_s$ of the upper surface, and the projection solid angle of the surface source $d{A}_s$ and the receiving surface $d{A}_c$.

2.2. Model of the Optomechanical System

2.2.1. Optical System Design

In order to satisfy the performance parameter and the structure types of the optical system, the optical system was designed and optimized based on ZEMAX optical design software in our previous studies [8], as shown in Figure 2.

For imaging systems, the modulation transfer function (MTF) is the most comprehensive standard among all optical system performance standards. Figure 3 shows the image intensity map, starting from a periodic target, its intensity changes in the form of a sine curve, and finally through the lens imaging. Due to factors such as aberration, diffraction, assembly, and calibration errors, the image quality declines. Definition terms are shown in Equation (4):

$$\{\begin{array}{l}\mathrm{Modulation}=\frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }}\\ MTF=\frac{\mathrm{Modulation}\mathrm{of}\mathrm{the}\mathrm{image}}{\mathrm{Modulation}\mathrm{of}\mathrm{the}\mathrm{object}}\end{array}$$

(4)

where MTF represents a function of spatial frequency, and the unit is lp/mm. Therefore, MTF represents the relationship between the modulation transfer from the object through the lens to the image and the spatial frequency.

In addition to evaluating whether the image quality and other indicators of the system meet the required standards, tolerance should also be considered during the evaluation process. For general equipment, structures with larger tolerances are easier to install. For instruments that require higher precision, the required tolerances are smaller, often exceeding the capabilities of current processes, and it is difficult to successfully process and assemble.

The precision of the lens aperture radius of curvature is 1 mm, the element thickness and the air interval are 0.01 mm, the element eccentricity is 0.02 mm, and the element assembly tilt is 0.02°. Modify the default tolerance function, select the sensitivity analysis method, and finally perform the tolerance analysis. The average MTF value is used as the evaluation standard, and the tolerance analysis of the aspheric camera optical system is performed. The analysis results are shown in Figure 3.

After setting the tolerance of the optical system, the optical system has a 50% probability of reaching 0.43 at the cut-off frequency of 63 lp/mm and a 90% probability of reaching 0.36, which can meet the imaging requirements of aerial cameras. The aerial camera lens consists of a lens, a press ring, a spacer ring, a lens barrel, and a flange. Figure 4 shows the two-dimensional structure of the camera.

2.2.2. Baffle and Vane Design

For refraction-type optical systems, the usual method to eliminate stray light is to add a baffle and a light-blocking ring. The design of the baffle can effectively suppress the stray light entering the camera lens and block the incident stray light larger than the critical blocking angle. When the scattered and reflected light reaches the inner surface of the baffle, the stray light will generate a halo when it reaches the image surface. In order to prevent non-imaging light from reaching the inner surface of the baffle, a light-blocking ring needs to be added at this time.

The optomechanical structure’s ability to suppress stray light increases with the length of the designed baffle. However, in actual engineering applications, the size and weight of the optomechanical system have a certain impact on camera performance. Therefore, the design of the optomechanical structure also needs to be considered. The final design of the baffle needs to be able to block non-imaging light from reaching the detector and at the same time make the effective imaging light smooth enter the imaging surface.

The three-dimensional model of the camera lens is shown in Figure 4. When the clear aperture of the optical system $D_1=20 \mathrm{mm}$, the length of the optical system $L_s=36.76 \mathrm{mm}$, the angle of view $2\beta =28°$, the solar evasion angle $\alpha =30°$, and the entrance pupil diameter $D_1=20 \mathrm{mm}$ are known, the size of the length L and diameter D₂ of the baffle can be calculated by:

$$\{\begin{array}{l}{D}_2=D_1+2L\tan \beta \\ L\tan \alpha =D_1+L\tan \beta \end{array}$$

(5)

Based on the above equations, $D_2=50.418 \mathrm{mm}$, $L=60.97 \mathrm{mm}$, take $D_2=51 \mathrm{mm}$, $L=61 \mathrm{mm}$, $D_1=20 \mathrm{mm}$, as shown in Figure 5.

When designing the vanes, the interval between adjacent vanes must be accurately calculated. The designed vanes will not block the imaging light in the field of view of the system, so that the vanes can effectively reduce stray light. As shown in Figure 6, first connect point A and edge point C of the baffle with the wall thickness at E₀, which is the first vane; connect point D at the edge with the first vane’s edge point E_0. Intersect the outer baffle at point E₁, connect point A and point E₁ at the edge of the baffle and the wall thickness at point E₂ to determine the next vanes, and design the vanes in this way.

Calculate the position and height of the vanes in the two-dimensional drawing software, and the number n of the vanes and the interval ‘1′ between each vanes satisfy the Equation (6):

$$(n-1)l=L$$

(6)

The length of the camera baffle L = 61 mm according to the design index requirements to set 4-level vanes; from Equations (5) and (6), l = 20 mm; set the thickness of the vanes to 0.25 mm.

3. Calculation and Results

3.1. Analysis of Stray Light

During analysis of the stray light, the three-dimensional model of the camera optical system and the field of view were exported from the optical software Zemax in the IGES format. The exported file was imported into UG, and the baffle and vanes were designed and exported in STEP format. Finally, import the file into TracePro optical analysis software to assign material properties of each component and perform stray light analysis of the optical system.

At present, the Monte Carlo algorithm is commonly used to analyze the stray light in Tracepro software. Based on mathematical statistics and probability analysis, the Monte Carlo algorithm can track the incident light to analyze the ability to suppress stray light in the optomechanical system.

In the process of stray light analysis, the material properties of optical and mechanical structures are defined as reflection, transmission, absorption, and surface scattering. The surface scattering properties of the optomechanical parts need to be set before ray tracing. The scattering intensity measurement on the surface of the parts is usually defined by the bidirectional scattering distribution function (BSDF), which can be expressed as:

$$BSDF({\theta }_i,{\varphi }_i,{\theta }_s,{\varphi }_s)=\frac{d{L}_s({\theta }_s,{\varphi }_s)}{d{E}_s({\theta }_i,{\varphi }_i)}$$

(7)

where ${\phi }_S$ and ${\theta }_S$ represent the azimuth and incident angle of reflected light. ${\phi }_i$ and ${\theta }_i$ represent the azimuth and incident angle of incident light. In the BSDF model of the surface of the optical mechanism, a relatively stable quasi-power reciprocal ABg model is selected, as shown in Figure 7. The scattering distribution function is as shown in Equation (8):

$$BSDF(\overrightarrow{x})=\frac{A}{\left(B+{\left|\overrightarrow{x}\right|}^g\right)}$$

(8)

where $\left|\overrightarrow{x}\right|=\left|\overrightarrow{\beta }-{\overrightarrow{\beta }}_0\right|$ and $\overrightarrow{\beta }$ are unit vectors in the scattering direction. $\overrightarrow{r}$ is the projection on the surface, ${\overrightarrow{\beta }}_0$ is the unit vector in the mirror direction, and ${\overrightarrow{r}}_0$ is the projection on the surface. Because the lengths of $\overrightarrow{\beta }$ and ${\overrightarrow{\beta }}_0$ are less than or equal to 1, $\left|\overrightarrow{x}\right|\le 2$. A, B, and g are three undetermined parameters of the ABg model. The parameters of the ABg model are defined as $B\ge 0$, $g\ne 0$. If $g=0$, it will become a Lambertian BSDF with a value of $A/(B+1)$ and a total scattering of $A/(B+1)$. If $g<0$, the BSDF will increase with $\left|\overrightarrow{\beta }-{\overrightarrow{\beta }}_0\right|$.

UG 3D software was used to model the camera as a whole and export it as a STEP file. This file was imported into TracePro software. The ray tracing model is shown in Figure 8.

The surface properties and material properties of the light source and parts need to be set strictly according to the actual working conditions. The working band of the camera is in the range of 400–760 nm, so the center wavelength of the light source is set to λ = 580 nm. The environment temperature is 20 °C, the lens surface transmittance is 96%, the absorption rate is 0.1%, and the scattering ABg model parameter are set as A = 0.01, B = 0.0001, and g = 1. The window is made of germanium material; the surface transmittance is set to 1. The material of the lens barrel, pressure ring, baffle, and vanes is aluminum, and the material of the machined parts is black anodized material, so the surface absorption rate is set to 97%, with a transmittance of 0, and the scattering ABg mathematical model parameters are A = 0.001, e = 0.01, and g = 3.5. The focal plane surface property is set to completely absorb.

After setting the material properties and surface properties of the optomechanical structure, perform ray tracing on the optomechanical model to check whether it conforms to the design scheme of the optical system. Set the incident angle of light parallel to the optical axis. After passing through the optomechanical model, the main purpose is to determine whether the parallel light converges on the center of the imaging surface. Therefore, there is no need to set an excessive number of rays, and the light threshold does not need to be too small. The ray tracing of the 0 ° field of view is shown in Figure 9, which verifies the correctness of optomechanical modeling.

3.2. Ray Tracing and Result Analysis

After verification of the correctness of the optical machine modeling, the optical machine system is applied to ray tracing. The more ray tracing is set, the more accurate the simulation results, and the simulation workload will be increased. Simulated light rays are incident at different off-axis angles, tracing the incident light rays in different directions from 0 to 80°, with 5° as a step; a total of 15 incident directions are used for corresponding ray tracing, and the corresponding point source transmittance (PST) of off-axis angles are calculated.

PST is one of the important indicators to verify the suppression ability of stray light in the optical system. The PST is the ratio of the irradiance $E(\theta )$ generated when a point light source with an incident angle of $\theta$ is imaged by the optical system, and the irradiance $E_0(\theta )$ generated when the point light source irradiates the image system perpendicular to the optical system; the value of PST are given by Equation (9):

$$PST=\frac{E(\theta )}{E_0(\theta )}$$

(9)

The value of PST represents the suppression ability of stray light in the optical system and is not related to the stray light radiation intensity outside the optomechanical system. The smaller the PST value, the stronger the ability of the optomechanical system to suppress stray light. After setting the PST threshold, use Trace pro software to simulate the irradiance value of each incident angle outside the tracking field of view and bring it into Equation (9) together with the irradiance of the on-axis point light source after passing through the optomechanical system. The suppression ability of stray light in the optical system can be calculated.

The light from the point light source at infinity can be regarded as 0° field of view light. A surface light source is placed in front of the optical system, and the light emission direction is perpendicular to the light source surface. The incident light fills the entire entrance pupil, the total light flux of the light source is 1 W, and the number of light traces is set to 1 million. As the off-axis angle increases, the energy threshold gradually reduced from 10⁻⁴ to 10⁻⁸.

Ray tracing is performed on 15 rays with different incident directions between 0° and 80°, and the PST value curve analysis chart at 0° azimuth is shown in Figure 10.

As shown in Figure 10, with the incident angle increases, the PST value of the aerial camera optical system gradually decreases, and the stray light radiation entering the optical system also decreases. When the incident angle of the light source is greater than 0.5°, the PST value drops rapidly. When the incident angle is 30°, the PST value of the system is in the order of 10⁻⁸. The aspherical aerial camera optical system’s ability to suppress stray light meets the design requirements.

4. Conclusions

In this paper, the optical system, baffle, and vanes of the aspherical camera are designed. At the same time, the stray light analysis of the designed optomechanical structure is carried out, and the following conclusions are drawn:

(1) The MTF value of the optical system is greater than 0.4 (63 lp/mm), the maximum diameter of the airy disk is less than 10 μm, and the total field distortion is less than 0.4%, which verify the imaging performance of the optical system.

(2) By combining the mechanical structure design of the camera and stray light analysis, the camera lens is optimized for the lens baffle and shading ring. The PST value of the point light source transmittance is calculated under different incident angles. When the light source’s incident angle is greater than 0.5°, the PST value will drop rapidly. When the incident angle is 30°, the PST value of the system is about 10⁻⁸. The aspherical aerial optical system has the ability to suppress stray light.

(3) The results show that the designed baffle and shading ring can effectively suppress the stray light of the optical system, which can provide a reference for the structure design of other lenses. As the angle of incidence increases, the PST value of the aspheric optical system gradually decreases, and the stray light entering the optical system also decreases.

In future research, the effect of improving the imaging quality of the camera system will be evaluated, and the stray light suppression ability also be quantitatively analyzed.