Design Method of Solar Radiation Simulation Optical System with High Energy Utilization Rate

Fanlin MENG; Shi SU; Guoyu ZHANG; Jian ZHANG; Shi LIU; Gaofei SUN; Haowen PENG

doi:10.3788/gzxb20215012.1222003

Abstract

Aiming at the disadvantages of large-scale solar simulators in the past, such as complex structure, low energy utilization rate and poor uniformity, a design method of solar radiation simulation optical system with high energy utilization rate was proposed. The ellipsoid condenser was designed based on the luminous characteristics of the real xenon lamp. By adding a spherical reflector, the combined condenser system was used to improve the energy utilization rate. The optical integrator was designed according to the principle of pupil matching. The irradiation uniformity was improved by the edge elimination method. The simulation results suggest that the energy utilization rate of the combined condenser system is 21.2% higher than that of the single ellipsoid condenser. The irradiation uniformity of the edge elimination method is 4% higher than that of the edge compensation method. The experimental results suggest that the working distance is 20 m, irradiation surface diameter is Φ2 m, maximum irradiance is 1 363.1 W·m^-2, non-uniformity is ±4.5%. It has realized large-area, high-energy utilization rate solar radiation simulation, which provided an advanced means for semi-physical simulation and testing of solar sensors in space field.

Keywords

Combined condenser system Edge elimination method High energy utilization rate Large area Solar radiation simulation

0 Introduction

Solar simulator is a kind of test equipment and calibration equipment that simulates solar radiation with artificial light source^［1-2］. It has been widely used in the field of space semi-physical simulation and testing of solar sensors on the ground， attitude control of satellite space flight， thermal balance test of spacecraft， and probe test in lunar exploration project^［3-5］.

In order to realize the simulation of solar irradiation with large area spots， most of the large-scale solar simulators currently use off-axis optical system， and several xenon lamps are used as the array of light sources^［6-9］. However， off-axis solar simulator has large volume， complex structure， high difficulty in installation and adjustment， and high manufacturing cost. In addition， the use of multiple xenon lamp arrays can improve the irradiation intensity， but the energy utilization rate is low， and the irradiation uniformity is poor. Therefore， in order to meet the continuous development of aerospace engineering， on the basis of low cost and high uniformity， it is imperative to research a kind of optical system which can achieve long-distance， large area and high energy utilization of solar irradiation simulation.

In addition， the current research on solar simulator is mostly focused on how to improve the irradiation uniformity， and there are few studies on how to improve the energy utilization rate. For example， PARUPUDIA R V and others designed parabolic mirrors to effectively improve the irradiation uniformity of the solar simulator^［10］. To improve the spatial uniformity of the concentrating solar simulators， XIAO Jun and others introduced a concept of non-coaxial deflection angle to the typical ellipsoidal reflectors^［11］. LV Tao and others studied the ellipsoid converging lens with variable curvature^［12］ and optical integrator for the number and shape of the element lens^［13］ to improve irradiation uniformity.

In some fields， combined condenser systems are used to improve the energy utilization rate. For example， MENG Xiangxiang and others designed a trapezoidal secondary concentrator to improve the conversion efficiency of laser cells^［14］. GUO Qibo designed a combined LED condenser that includes a reflective cup to improve the efficiency of light use^［15］. YANG Chen designed a combined face concentrating device to achieve a high flux of concentrated light at a small aperture outlet^［16］. WU Qing and others designed a kind of high reflectivity light distribution bulb with the combination of ellipse and multi-curved surface， which can effectively improve the focusing effect and make full use of energy^［17］. Based on the above experience， the combined condenser system is considered to be applied to the solar simulator to improve the energy utilization rate of the solar simulator.

Aiming at the problems of high cost， complex structure， low energy utilization rate and poor irradiation uniformity of the current large-scale solar simulator， a solar radiation simulation optical system with high energy utilization rate is designed. The combined condenser system is adopted to improve the energy utilization rate and the edge compensation method is used to improve the irradiation uniformity. The simulation of solar irradiation with high energy utilization rate and high uniformity is realized.

1 General layout of a solar radiation simulation optical system with high energy utilization rate

The solar radiation simulation optical system with high energy utilization rate consists of a high-power xenon lamp light source， a concentrating system and a homogenizing system， as shown in Fig. 1.

Figure 1.Solar radiation simulation optical system

In order to improve the energy utilization rate， the concentrating system adopts the combined condenser system， which is composed of an ellipsoidal condenser and a spherical reflector. The homogenizing system uses the optical integrator to homogenize the convergent Gaussian radiation distribution and emit it at a certain divergence angle^［18］. The high-power xenon lamp is located at the first focus of the ellipsoid condenser. The light emitted by the light source is reflected and converged to the second focal plane by the combined condenser system， and then homogenized by the homogenizing system. Finally， a large area， high irradiance and high uniformity of solar irradiation simulation spot is formed.

2 Optical system design

2.1　Combined condenser system design

2.1.1　Ellipsoid condenser design

In previous designs， the xenon lamp was ideally used as a point light source and a single ellipsoid condenser was used to collect the light. However， the real xenon light source obeys a certain luminous intensity and angular distribution， limited by the containment angle， there will be a large amount of stray light that cannot be used. In order to avoid the energy loss beyond the containment angle， eliminate stray light and improve the energy utilization rate， a combined condenser system composed of ellipsoid condenser and spherical reflector is adopted^［19］.

The xenon arc is simplified to a cylindrical model with length l₀ and diameter d₀. The light path principle of the ellipsoid condenser is shown in Fig. 2. The light emitted by the light source at the first focus converges to the second focal plane after reflection by the ellipsoid condenser. Since the xenon arc has a certain volume， it will form a wide range of light spot.

Figure 2.The light path principle of the ellipsoid condenser

The x-axis is the optical axis， F₁ is the first focus， F₂ is the second focus， D₁ is the rear opening diameter of the condenser， D is the front opening diameter of the condenser， D₀ is the optical aperture of the optical integrator， angle u is the aperture angle of incident beam， angle u′ is the aperture angle of the outgoing beam， angle u₀ is the rear opening aperture angle corresponding to the luminous point on the shaft， angle u_m is the front opening aperture angle corresponding to the luminous point on the shaft， angle u_l is the aperture angle corresponding to the beam b emanating from the luminous point A（f₁-l，0） on the axis， l is the distance from point A to point F₁， beams a and c are the beams emitted from the rear opening and the front opening respectively.

Let the ellipsoid equation be

y^{2} = 4 \frac{f_{1} f_{2}}{f_{1} + f_{2}} x - (1 - {(\frac{f_{2} - f_{1}}{f_{2} + f_{1}})}^{2}) x^{2}

（1）

The range of the effective containment angle of the ellipsoid condenser should match the light distribution curve of the xenon lamp to maximize the energy utilization. The luminous range of the xenon lamp light distribution curve is 30°~135°. In order to make full use of the light energy， the reflection area of the ellipsoid condenser should contain this area. D₁ is determined by u₀， and D is determined by u_m. According to Eq. （2） and Eq. （3）， D₁ and D can be obtained，

{(\frac{D_{1}}{2})}^{2} = 4 \frac{f_{1} f_{2}}{f_{1} + f_{2}} (f_{1} + \frac{l_{0}}{2} - \frac{D_{1}}{2 t a n u_{0}}) - (1 - {(\frac{f_{2} - f_{1}}{f_{2} + f_{1}})}^{2}) {(f_{1} + \frac{l_{0}}{2} - \frac{D_{1}}{2 t a n u_{0}})}^{2}

（2）

{(\frac{D}{2})}^{2} = 4 \frac{f_{1} f_{2}}{f_{1} + f_{2}} (f_{1} - \frac{l_{0}}{2} - \frac{D}{2 t a n u_{m}}) - (1 - {(\frac{f_{2} - f_{1}}{f_{2} + f_{1}})}^{2}) {(f_{1} - \frac{l_{0}}{2} - \frac{D}{2 t a n u_{m}})}^{2}

（3）

After D is determined， the depth H of the ellipsoid condenser is calculated

H = \frac{f_{1} + f_{2}}{2} - \frac{f_{1} + f_{2}}{2 \sqrt[]{f_{1} f_{2}}} \sqrt[]{f_{1} f_{2} - {(\frac{D}{2})}^{2}}

（4）

In addition to the light emitted by the luminescent point at F₁ converging to F₂ for imaging， the light emitted by other luminescent points outside F₁ at different incident angles is reflected， and the position on the second focal plane is a function of the incident Angle. Only the actual calculation of the light can determine the accurate position of the image point. If the light from A（f₁-l，0） on the xenon arc axis intersects the ellipsoid at the point B（x₀，y₀）， when the aperture Angle u_l is given， the incident ray equation is，

y = t a n (π - u_{l}) [x - (f_{1} - l)]

（5）

B（x₀，y₀） can be obtained according to Eq. （1） and Eq. （4）. According to the law of reflection， the angle of reflection is equal to the angle of incidence， so we can figure out the slope of the reflected ray，

k = \frac{y_{0} [2 (x - (f_{1} - l)) t + t^{2} - y_{0}^{2}]}{2 t y_{0}^{2} - (x - (f_{1} - l)) t^{2} + (x - (f_{1} - l)) y_{0}^{2}}

（6）

where $t = 2 \frac{f_{1} f_{2}}{f_{1} + f_{2}} - (1 - {(\frac{f_{2} - f_{1}}{f_{2} + f_{1}})}^{2}) x_{0}$ ， then the reflected light equation is

y - y_{0} = k (x - x_{0})

（7）

When x=f₂， the intersection of the light emitted by A（f₁-l，0） with the second focal plane after being reflected by the ellipsoid can be calculated. When the light is incident at the aperture angle u_lm， the y value of the intersection point with the second focal plane after reflection from the ellipsoid condenser is the maximum， so that the spot diameter at the second focal plane can be determined. In order to ensure a high energy utilization rate， the optical aperture D₀ of the field lens set of the optical integrator is equal to the spot diameter at the second focal plane.

D_{0} = 2 k (f_{2} - x_{0}) + y_{0}

（8）

2.1.2　Spherical reflector design

In order to improve the energy utilization rate， the optical axes of the spherical reflector and the ellipsoid condenser coincide， and the light from the edge of the ellipsoid condenser can enter the spherical reflector， so that the light beyond the containment angle can be used for a second time. According to the optical principle of the sphere， the light emitted by the xenon lamp located at the center of the sphere is reflected by the spherical reflector， and the light will be reflected back to the center of the sphere without spherical aberration and loss. Using this principle， the center of the spherical reflector coincides with the first focus F₁ of the ellipsoid condenser. The direct light emitted by the xenon lamp is reflected back to F₁ through the spherical reflector， and then converged to F₂ through the ellipsoid condenser， which reduces the energy loss and improves the energy utilization rate.

The external dimensions of the spherical reflector are shown in Fig. 3.

Figure 3.The external dimensions of the spherical reflector

The spherical equation is

{(x - f_{1})}^{2} + y^{2} = {(\frac{f_{2} - f_{1}}{180 ° - θ - β} θ)}^{2}

（9）

The diameter D₂ of the back opening of the spherical mirror and the diameter D₃ of the front opening are

D_{2} = 2 \sqrt[]{r^{2} - {(f_{2} - f_{1} - \frac{D}{2 t a n θ})}^{2}}

（10）

D_{3} = 2 r s i n β

（11）

where β=α， α is the aperture angle of the rear opening corresponding to F₁， and θ is the aperture angle of the outgoing beam corresponding to the edge rays of the ellipsoid condenser.

2.2　Homogenizing system design

The homogenization system adopts an optical integrator to homogenize the Gaussian radiation distribution and emit it at a certain divergence angle. The optical integrator is composed of a field lens group L_F， a projection lens group L_P and two additional lenses （L₁ and L₂）， as shown in Fig. 4. The field lens group is placed at the second focal plane， and the light emitted by the light source is divided into multiple images by L₁ and L_F， and projected to the corresponding projection lens group respectively. The images are superimposed to the irradiation surface by L_P and L₂， and the irradiation uniformity is improved by the way of light segmentation， superposition and symmetric compensation.

Figure 4.The structure of optical integrator

The field lens group and the projection lens group are composed of multiple element lenses arranged symmetrically according to the center. The aperture and focal length of the two groups of element lenses are the same， and they are in the focal plane of each other. If the number of element lenses is too small， the evenness effect cannot be guaranteed. In excess， the uniformity is affected by machining errors. Considering the processing difficulty and the effect of uniform light， 19 regular hexagonal element lenses are selected. The diameter of the inner circle of the element lens d is

d = \frac{D_{0}}{N}

（12）

where N is the number of element lenses contained in the diameter of the outer tangential circle of the optical integrator.

In order to improve energy utilization rate and reduce stray radiation of optical system， it is necessary to consider the factor that the relative aperture of the condenser system matches the relative aperture of the element lens of optical integrator. According to the principle of pupil matching， the following relation is established to calculate the focal length f of the element lens，

\frac{D}{f_{2} - H} = \frac{d}{f}

（13）

The whole optical integrator system is represented by six matrices， the first matrix is incident matrix， the next four are field mirror matrix， projection mirror matrix， and the last one is additional mirror matrix. The incident angle of the rays is u′， and the exit angle is u′′. The focal length of the two groups of element lenses is the same， $f_{L_{F}} = f_{L_{P}} = f$ . According to Eq. （14）， the irradiation surface diameter D_af can be obtained.

(\begin{matrix} D_{a f} \\ u^{″} \end{matrix}) = (\begin{matrix} 1 & l \\ 0 & 1 \end{matrix}) (\begin{matrix} 1 & 0 \\ - \frac{1}{l} & 1 \end{matrix}) (\begin{matrix} 1 & 0 \\ - \frac{1}{f_{L_{P}}} & 1 \end{matrix}) (\begin{matrix} 1 & f \\ 0 & 1 \end{matrix}) (\begin{matrix} 1 & 0 \\ - \frac{1}{f_{L_{F}}} & 1 \end{matrix}) (\begin{matrix} d \\ u^{'} \end{matrix})

（14）

When the working distance l and divergence Angle α are given， the optical aperture $D_{0}^{'}$ of the projection lens group of the optical integrator can be calculated.

D_{0}^{'} = D_{a f} - l t a n α

（15）

The irradiance at the edge of the irradiation surface of the solar simulator is usually lower than the central irradiance. The edge compensation method is usually adopted， that is， several small triangular lenses are added to the edge of the optical integrator to improve the edge irradiance， so as to improve the irradiation uniformity. However， considering the processing cost， an edge elimination aperture is designed according to the element lens array to intercept the edge light and ensure that the light can only pass through the element lens to improve the irradiation uniformity. Edge compensation method and edge elimination method are shown in Fig. 5 and Fig. 6.

Figure 5.Edge compensation method

Figure 6.Edge elimination method

3 Simulation and experiment

3.1　Simulation analysis

The working distance of the solar radiation simulator optical system is 20 m， and the diameter of the irradiation surface is Φ2 m. The optical parameters are shown in Table 1.

Table Infomation Is Not Enable

3.1.1　Comparison of energy utilization rate between single ellipsoid condenser and combined condenser system

A single ellipsoid condenser and a combined condenser system were modeled and simulated by using LightTools software. The receiver was placed at the second focal plane， and the radiation flux was set as 20 000 W. The energy utilization rate of the two was compared. The simulation light path is shown in Fig. 7， and the energy utilization rate comparison is shown in Fig. 8.

Figure 7.Simulation light path diagram

Figure 8.Energy utilization rate comparison

As can be seen from Fig. 7 and Fig. 8， the single ellipsoid condenser has a large amount of stray light that cannot be utilized， and the combined condenser system eliminates the stray light. At the second focal plane， the single ellipsoid condenser receives 10 131 W of energy， and the energy utilization rate is 50.66%. The combined condenser system receives 14 372 W of energy， and the energy utilization rate is 71.86%. The energy utilization rate is increased by 21.2%.

3.1.2　Comparison of irradiation uniformity between uncompensated optical integrator, edge compensation method and edge elimination method

LightTools software was used to model and simulate the optical integrator， and the irradiation uniformity of uncompensated， edge compensation method and edge elimination method was compared. The simulation model is shown in Fig. 9， and the irradiation uniformity comparison is shown in Fig. 10.

Figure 9.Simulation model of optical integrator

Figure 10.Comparison of irradiation uniformity

As can be seen from Fig. 10， when the optical integrator is uncompensated， the irradiance of the edge is lower than that of the center. The edge irradiance is improved when the edge compensation method is used. The irradiation uniformity is improved obviously by using the edge elimination method. Compared with uncompensated method， the improvement is 8.4%， and the improvement is 4% compared with edge compensation method.

3.1.3　Integrated optical system simulation

LightTools software was used to simulate the integrated optical system by combining the modeling of the combined condenser system and optical integrator. The simulation model is shown in Fig. 11， and the simulation results of irradiation uniformity are shown in Fig. 12.

Figure 11.Optical system simulation model

Figure 12.Simulation results of irradiation uniformity

The calculation formula of irradiation non-uniformity is^［20］

ε = \pm \frac{E_{m a x} - E_{m i n}}{E_{m a x} + E_{m i n}} \times 100 %

（16）

where ε is the irradiation non-uniformity， E_max is the maximum irradiance and E_min is the minimum irradiance.

As can be seen from Fig. 12， the working distance is 20 m， the diameter of the irradiation surface is 2 m， the maximum irradiance is 1 372.6 W·m^-2， and the minimum irradiance is 1 258.5 W·m^-2. According to Eq. （16）， the simulation result of irradiation non-uniformity can be calculated as ±4.3%.

3.2　Experimental verification

The working distance and the diameter of the irradiation surface of the solar radiation simulator with high energy utilization rate were tested by using the laser anomaly calibration system. When the working distance is 20 m， the diameter of the irradiation surface is Φ2 m. The uniformity was measured and evaluated with FZ-A solar irradiance meter from Beijing Normal University Photoelectric Instrument Factory. The wavelength range of FZ-A solar irradiance meter is （400~1 000） nm， the minimum resolution is 10^-4 mW·cm^-2 and the upper limit of measurement is 199.9 mW·cm^-2.

The short-arc xenon lamp was lit， and the FZ-A solar irradiance meter was placed on the effective working irradiation surface of the solar simulator， with the photosensitive surface facing the mirror cylinder of the solar simulator. After the light source was stabilized， 41 sampling points were selected on the effective irradiation surface to conduct the irradiation non-uniformity test， and repeated measurements were made for several times to eliminate the errors caused by light intensity instability. The distribution of test sampling points is shown in Fig. 13， the test results of irradiation non-uniformity are shown in Fig. 14， and the experimental data of irradiance are shown in Table 2.

Figure 13.Distribution of test sampling points

Figure 14.Test results of irradiation non-uniformity

Table Infomation Is Not Enable

The maximum irradiance and minimum irradiance in the effective irradiation surface measured by the experiment are 1 363.1 W·m^-2 and 1 245.4 W·m^-2 respectively. According to Eq. （16）， the irradiation non-uniformity can be calculated to be ±4.5%.

4 Conclusion

A design method of solar radiation simulation optical system with high energy utilization rate using a single high power xenon lamp as light source was proposed. Based on the luminous characteristics of real xenon lamp， the ellipsoid condenser was designed. On this basis， the combined condenser system was used to improve the energy utilization rate by adding a spherical reflector. The optical integrator was designed according to the principle of pupil matching and the irradiation uniformity was improved by using the edge elimination method. The simulation results show that the energy utilization rate of the combined condenser system is increased by 21.2% compared with that of a single ellipsoid condenser. Compared with the edge compensation method， the irradiation uniformity is improved by 4% by using the edge elimination method of optical integrator. The experimental results show that the working distance is 20 m， the diameter of the irradiation surface is Φ2 m， the maximum irradiance is 1 363.1 W·m^-2， and the irradiation non-uniformity is ±4.5%. It has broken the shortcomings of the large size， complex structure， low energy utilization rate and poor uniformity of the previous large-scale solar simulator， and provided an advanced means for the ground semi-physical simulation and testing of the solar sensor in the field of space.

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