一个用于太阳与天空穹顶光照实验对比的框架
Joseph T. Kider Jr.
Daniel Knowlton
Jeremy Newlin
Yining Karl Li
Donald P. Greenberg
Program of Computer Graphics, Cornell University
图1：我们捕获太阳/天空穹顶的光谱辐射亮度，并比较最先进的模拟模型。(a) 我们定制的太阳天空穹顶扫描仪，(b) 最先进模拟模型与我们在半球上测量样本之间的相对差异，(c) 采样点和捕获的天空图像示例，以及(d) (c)中不同采样点的光谱辐射亮度曲线。
摘要
太阳/天空穹顶的照明和外观对于计算机图形学、计算机视觉和日光研究中的许多应用至关重要。不幸的是，对这种快速变化的光源进行物理精确的测量难以实现，但对于开发精确的基于物理的天空照明模型以及现有模拟模型的比较研究却是必需的。
为了获得这种随时间变化的各向异性光源的基线数据，我们设计了一种新颖的采集装置，以同时测量全面的光照属性。我们的硬件设计同时获取天空穹顶的光谱、空间和时间信息。为实现这一目标，我们使用定制的光谱辐射亮度测量扫描仪来测量方向光谱辐射亮度，使用总日射表测量整个半球的辐照度，并使用相机捕获天空的高动态范围图像。这些计算机控制的测量设备的组合提供了一种快速获取太阳/天空穹顶精确物理测量的方法。我们利用测量结果评估了多种太阳-天空模拟模型的优缺点。我们还提供了一个包含各种晴朗天空条件下天空光照数据的测量数据集，以及一个用于模型比较分析的交互式可视化工具，可在 http://www.graphics.cornell.edu/resources/clearsky/ 获取。
CR Categories: I.3.7 $$ Computing Methodologies
Keywords: skylight models, measurements, validation, spectral Links: DL PDF WEB DATA # 1 Introduction The sky’s highly varying appearance is critical for many applications. In the field of computer graphics, many sophisticated solar/skydome models have been developed primarily to create visually plausible images for the feature film and gaming segments of the entertainment industry $$ Sloup 2002 $$. Since the sky is certainly the most important light source for outdoor scenery, these models have also been used not only as backdrops, but as illumination sources to produce visually pleasing images. However, many of these existing skylight models target the creation of plausible images, but their physical accuracy has not been compared to measurements. 与生成美丽图像的目标不同，其他领域需要可靠且精确的辐射测量光照。计算机视觉领域需要了解光源的特性，以便在不同光照条件下准确确定物体的材质属性。建筑环境的设计与分析需要准确预测建筑物的日光行为。研究发现，自然日光的质量会显著影响建筑物居住者的感知舒适度，并缩短患者的康复时间。光源的两个最重要特性是其光谱分布以及随空间和时间变化的辐射亮度和亮度。迄今为止，尽管在模拟太阳/天空穹顶方面做了大量工作，但捕获、测量和比较太阳/天空穹顶不断变化的辐射亮度仍然是一个重大挑战。此类数据的缺失催生了对精确测量天空光照的采集方法的需求。 收集太阳和天空穹顶光照的辐射测量精确数据是一项重大挑战。在本研究中，我们开发了一种新系统，可同时扫描天空并测量光谱辐射亮度、总辐照度，并捕获高动态范围（HDR）图像。所得数据通过提供地面实况物理测量，可直接用于比较当前的天空光模型。一些现有的采集系统专注于捕获太阳/天空穹顶的辐照度或亮度。然而，大多数先前的方法并未捕获天空的光谱辐射亮度分布。这限制了这些方法的适用性，因为天空光的辐射亮度在光谱和方向上变化都非常快。 我们的测量数据能够对几种最先进的天空光模型与地面实况辐射亮度和辐照度测量进行全面比较。作为利用辐射光谱数据的附加应用，我们使用这些数据创建了一个数据驱动的插值太阳/天空光模型，该模型对于地面实况日光研究非常有用，并且比HDR摄影提供更多信息。 因此，我们的贡献包括： • 一种多设备采集技术，用于同时获取集成的太阳/天空穹顶辐射亮度、半球总辐照度以及天空的高动态范围图像。这包括设计一种新颖的太阳/天空穹顶光谱和空间辐射测量扫描仪，这是精确天空测量的基础技术。 • 一个公开可用的测量数据集，覆盖半球上81个等立体角，可从 http://www.graphics.cornell.edu/resources/clearsky/ 获取。该数据用于创建数据驱动的太阳/天空穹顶模型。 对几种最先进的太阳/天空模型进行比较，指出其优缺点，并以图形方式展示它们与测量结果的偏差。 • 一个交互式可视化界面，描绘太阳/天空穹顶的外观，包括光谱分布、辐射亮度、辐照度以及各种误差度量可视化。 精确测量和交互式可视化工具的可用性，为全面的比较分析提供了一个框架，从而改进基于物理的太阳/天空穹顶模拟，使其更贴近真实世界。 ## 2 先前工作 捕捉太阳/天空穹顶的照明以及对其进行建模，都是一个具有挑战性的多学科研究问题。该问题在计算机图形学、大气科学和物理学中得到了深入研究。虽然太阳是天空中最重要的光源，但其大部分光线在到达地表之前会在大气中散射。精确的照明模型必须同时考虑太阳和天空穹顶的贡献。尽管天光在直射阳光之后通常处于次要地位，但在清晨和傍晚时分，天空是主要的照明来源。我们认识到，许多现有的天空模型主要关注为电影和游戏行业生成视觉上可信的图像。尽管这种限制对于渲染来说是可以接受的，但对于存在大范围波长分布的日光模拟来说则不可接受。Radiance $$ Ward 1994 $$ is one popular physically-based rendering tool that calculates daylighting factors, irradiance, and luminance that is widely used outside of graphics, namely in building design. We provide a strong experimental foundation that helps quantitatively ground the accuracy of these methods. A process to more robustly capture the skylight opens the door for future comparisons and daylighting studies. Sky Capture Techniques. Many commercial systems for measuring various aspects of the sky have been developed, and are currently being used in meteorology and atmospheric science. They generally use a pyranometer $$ Abbot et al. 1916 $$ to measure total hemisphere radiation which measures the global horizontal irradiance. These devices measure spectral distributions or sum wavelengths to produce one irradiance measurement. The pyranometer has a rotating disc that blocks the direct solar component to enable the measurement of the diffuse sky radiation. Common models include Kipp-and-Zoen and Apogee. A pyrheliometer measures the direct sun energy by pointing the device at the sun. The device typically has a narrow field of view to block non-solar light, and the device tracks the sun automatically throughout the day $$ Myers 2013 $$. A spot luminance meter $$ Zotti et al. 2007 $$ measures the instantaneous luminance in the direction the device is pointed. Common models are available from Konica Minolta. Sky Radiometers measure direct solar radiation and diffuse sky radiation for 8-11 wavelength bands between 315nm to 2200nm. The most popular model is a Kipp Zonen POM-02. Stumpfel et al. $$ 2004 $$ proposed a technique to directly capture the sky and sun by high dynamic range photography using a series of meticulously set aperture and shutter settings, however their approach has a limited spectral range. Clear Skylight Models. One of the first simulation models used to describe luminance distributions in a clear sky was the Standard Clear Sky specified by the CIE (International Commission on Illumination). This model was originally intended to provide lighting designers with the ability to evaluate the luminance a building will receive. The model does not directly provide any spectral information, and the lack of color limited the model’s utility for both rendering and daylighting design. The Perez All-Weather model $$ 1993 $$ presented a better analytic solution for simulating clear skies and the CIE $$ 2004 $$ modified and adapted Perez’s formulation in their recent standard . The Perez and CIE equations adjust the luminance based on three non-intuitive and non-physical parameters. Perez $$ 1993 $$ suggested using tabulated values, and subsequently Preetham $$ 1999 $$ and his colleagues proposed solving the parameters analytically. Rendering realistic sky color typically involves both single scattering $$ Nishita et al. 1993 $$ and multiple scattering $$ Nishita et al. 1996 $$ methods. Nishita and his colleagues proposed the first ground breaking work, which included color information, and they created one of the first plausible sky images useful for movies and games. They ignored spatially-varying ground interreflections and spatially varying particles in the atmosphere. Haber et al. $$ 2005 $$ further developed a multiple scattering model in a physically-based, bruteforce numerical simulation of radiative transport in the sky. This model accounts for particles which vary spatially by altitude but not horizontally, which limits the model, for example, where smog above a city might locally skew atmospheric scattering in a given direction. Since, these brute-force simulation methods are computationally expensive, more recent techniques have been developed for approximating the clear sky. Several analytical models fit simulation data to the Perez Model equations rather than rely on tabulated data. These equations generally assume sky particle and scattering conditions are similar everywhere on the globe. Analytical methods such as the Preetham sky $$ 1999 $$, Hosek skydome $$ 2012 $$, and Hosek solar disc $$ 2013 $$ are extremely quick to compute, but these methods only approximate sky radiance. Dobashi et al. first proposed a GPU-based method to simulate atmospheric scattering utilizing a spherical volumetric rendering approach. Hoffman and Preetham $$ 2003 $$ proposed simplified scattering equations to simulate the sky in real-time. This computation can further be accelerated by precomputing the atmospheric properties, such as transmittance and in-scattering, as a series of lookup tables which has been done by Bruneton et al. $$ 2008 $$ and Elek and Kmoch $$ 2010 $$. GPU methods create plausible sky images for games that run in real-time for games, but sacrifice accuracy for efficiency. All of the models described above are restricted to visible wavelengths and are primarily used for graphic renderings. To conduct accurate energy and daylighting studies for the sustainable design of the built environment, the full range of wavelengths must be considered, both spectrally and spatially. 大气科学界在求解太阳辐射模拟的辐射传输方程方面也有着悠久的历史。大多数光谱辐射模型计算成本高昂。这些模型的一些例子包括 LOWTRAN $$ Kneizys et al. 1981 $$, LibRadTran $$ Mayer and Kylling 2005 $$, MODTRAN $$ Acharya et al. 2003 $$, SBDART $$ Ricchiazzi et al. 1998 $$, and SMARTS $$ Gueymard 1995 $$. These models are highly regarded in the atmospheric science community for their physical simulation abilities. Atmospheric science models are generally concerned with precisely solving a single wavelength at a single angle. These models sacrifice speed for accuracy, making it extremely expensive to compute an entire solar/skydome image or rendering. Karayel et al. $$ 1984 $$ and Soler and Gopinathan $$ 2000 $$ looked at sky luminance distributions for daylighting calculations. This work differs from work from Tominaga et al. $$ 2007 $$ which attempts to extend RGB signals to hyperspectral from priors. Our measuring device takes ground truth data and does not infer the spectral distribution. 天光比较研究。Zotti 等人 $$ 2007 $$ provided comparisons between the sky luminance of the Preetham $$ Preetham et al. 1999 $$ and CIE $$ Darula et al. 2002 $$ skylight model and measurements taken by a Minolta LS-110 Luminance Meter. These measurements were taken by hand on a tripod by manually rotating the device. Their major insight demonstrated where the Preetham model produced poor luminance patterns compared to measured data. Luminance, however, does not measure or validate the electromagnetic radiation wavelengths of light. Building science researchers have recently addressed the problem of measuring and validating irradiance to various sky models $$ Diez-Mediavilla et al. 2005; Loutzenhiser et al. 2007; Noorian et al. 2008; Ochoa et al. 2011 $$. These comparisons, however, only focus on total or diffuse irradiance and do not consider any directional radiance measurement or validation studies. Most Building Simulation studies $$ Grynberg 1989 $$ also focus on comparing measured results to sky models simulated in Radiance $$ Ward 1994 $$. Additional luminance and irradiance measurements and comparisons were done by Littlefair $$ 1994 $$ and Ineichen et al. $$ 1994 $$ which focused again on the CIE and Perez models. ## 3 框架概述 我们框架的目标是提供一种全面的测量太阳/天空穹顶的方法，该方法适用于实验性地比较当前最先进的天空模型。天空捕获过程测量辐射亮度、辐照度，并捕获天空穹顶的高动态范围图像。比较阶段使用这些测量数据来确定各种最先进的太阳/天空穹顶模型的准确性。我们开发了一个工具来帮助分析和可视化所有太阳/天空穹顶模型的各种优点和缺点。此外，我们进一步利用这些数据生成一个完全数据驱动的光谱天光模型，用于特定捕获时刻的采光研究。 数据采集设计。数据测量采集装置的目的是捕获太阳/天空穹顶的光谱照明。我们的测量过程分为三个阶段：辐射亮度测量、辐照度测量和 HDR 图像。图 2 展示了我们使用的三种设备：一个定制的天空辐射亮度扫描仪、一个用于捕获辐照度的总辐射表，以及一台配备鱼眼镜头的 Canon 5D 相机用于捕获 HDR 图像。第 4 节详细介绍了我们使用的硬件、捕获的数据以及数据存储方式的结构和基本操作。该数据集首次允许对天光进行更精确的光谱比较。这些测量数据集合构成了我们的天空外观数据库。  图 2：我们用于捕获天光的测量装置。定制的辐射亮度扫描仪（左）捕获天空的光谱样本。总辐射表（中）采样天空穹顶的辐照度，Canon 相机（右）捕获 HDR 图像。 比较分析。我们在第 5 节中比较了测量数据与几种最先进的太阳/天光模型的输出。我们选择了七种不同的方法，其中包括：六种天光模型：Nishita 单次散射模型 $$ 1993 $$, the Nishita multiple scattering Model $$ 1996 $$, the Preetham Model $$ 1999 $$, the Haber Model $$ 2005 $$, the Bruneton Model $$ 2008 $$, the Hosek Skydome Model $$ 2012 $$, and three solar models: the Preetham Solar Model$$ 1999 $$, the Bruneton Solar Model$$ 2008 $$, and the Hosek Solar Radiance Model $$ 2013 $$ to analyze. We compared the radiance (Section 5.1), irradiance (Section 5.2), and illumination (Section 5.3) of the various models. Section 7 provides insights we found while comparing the strengths and weaknesses of the various models, and describes when to use each approach. Data-driven Skylight Model. One application of the measured spectral radiance data is the creation of a data-driven spectral sky model. Normally, data-driven sky models only use HDR-imagery $$ Stumpfel et al. 2004 $$. However, this method is limited only to RGB and does not provide spectral varying data needed to illuminate spectrally varying BRDF, spectral varying phase functions, and daylighting studies. We introduce a new data-driven method for synthesizing spectral sky illumination. We spherically interpolate the discretized measured radiance samples from our custom-built sky scanning device. Section 6 describes the details for creating this spectral data-driven sky model. ## 3.1 色彩渲染与色调映射 对于本文中的视觉比较，我们在 sRGB 中渲染并色调映射图像。我们在 350nm 到 830nm 之间以 40 个光谱区间对所有图像进行光谱渲染。我们将这些图像转换到 CIE XYZ 空间，并映射到 sRGB。我们使用 Reinhard 等人 $$ 2002 $$ technique followed by gamma correction to tonemap recorded radiance values to the low dynamic range displayable for the paper. Please view the paper’s images on a color calibrated monitor. In the supplementary material, we provide high-dynamic range EXR files so the reader can view the full dynamic range of some of the results.  Figure 3: The custom-built radiance scanner which captures spectral samples of the sky. The device features interchangeable foreoptics lenses which send the light to a spectroradiometer which measures the spectral radiance between 350nm to 2500nm. The device is rotated to any angle by an arduino which controls 2 servo motors. # 4 Data Acquisition Design The important properties of daylight motivate the need to meticulously capture the spectral radiance, irradiance, and HDR imagery of the entire sky. We design a unique multi-device acquisition system to capture these features. # 4.1 Spectral Radiance Measurements To measure radiance our setup incorporates a spectroradiometer, which is rotated and tilted, with a single fore-optics lens and a fiber optic cable. Figure 3 shows a photograph of this sky-scanning radiance instrument. Spectroradiometers are the most accurate measuring devices for capturing the spectral energy distribution of any light source. We utilized an ASD Fieldspec Pro Hi-Res spectroradiometer for the spectral data collection. The device measures a spectral range from 350nm to 2500nm which includes some ultraviolet, some near infrared, and all of the visible spectrum wavelengths. The device scans at roughly a 1.4nm wavelength resolution in the visible range, and 3nm in the near infrared. The device is fitted with either one-degree or eight-degree fore-optics which subtends the field-of-view by capturing the light through the foreoptics down the fiber-optics. Most of the scans in our measurement database use the one degree fore-optics, but some scans include the eight degree fore-optics (One and eight-degree fore-optics were the two light collimators we had easily available. The spectroradiometer could be fitted with custom designed fore-optics if desired.) Each measurement sample contains the spectral distribution (nm) and the radiances. The measured radiance values have units of power (W ) per unit area $(m^{- 2})$ per steradian $(sr^{- 1})$ per unit wavelength $(nm^{\widehat{-}1})$ . Figure $4(a)$ shows a radiance measurement’s sample spectral distribution varying spatially across the sky. Figure 4(b) shows the same measurement angle sampled every 10 minutes for a few hours. These measurement readings illustrates how the sky’s spatial and temporal spectral distribution changes over the hemisphere and throughout the day.  Figure 4: (a) shows the measured output of the sky showing spatial variance of skylight with 9 spatial samples for one scan cycle, and (b) shows the temporal variance of skylight by showing how the spectral distribution changes for one spatial locations over 15 minute scan cycles.  Figure 5: This image demonstrates the general accuracy of the measurement device. (a) NASA solar radiance data - taken from Guey et al. (2003) (red) is plotted against our measurement(blue). The measurement is what we expect since light is attenuated through the atmosphere. (b) A published graphic that shows this effect by a satellite above the atmosphere. For each vector direction, the device takes 10 samples and averages the data to reduce measurement noise per measured wavelength. At the end of a full sky scan, we measure the dark current to further reduce noise in the spectroradiometer measurements ensuring more accurate data. Figure 5 (a) demonstrates the accuracy of the device itself - a spectral sample of the sun plotted against tabulated data obtained from NASA (measured at the top of the atmosphere.) Our measured graph is slightly lower since light is attenuated through the atmosphere as it reaches the Earth’s surface, and passes through different absorption bands. This follows other published data Figure 5 (b) which demonstrates this effect. Our measurements are repeatable across different measurement days and return the natural variation you would expect to find from different sky conditions. Our device uses two servo-motors to pan and tilt the device’s foreoptics to scan the sky. The motors are controlled by an Arduino controller which accepts a pan and tilt angle to move the device. These motors are accurate and repeatable. The rotational error of these devices is around 0.5 degrees. This is sufficiently accurate to capture skylight since the motors move the fore-optics to any position to scan the skydome. The device takes around three minutes to sample the entire hemisphere at 81 sample points. We noticed that spectral distribution measurements were more sensitive to elevation errors than to azimuthal errors.    Figure 6: The sky-scanner uses different fore-optics to scan the sky. We choose a pattern to scan 81 equal solid angles. The left image shows coverage at 1 degree fore-optics, the middle image shows 8-degree fore-optics, and the right image shows the plan view coverage of sample coverage on the hemisphere. We can program any custom scanning pattern to sample the skylight in the skydome. We selected a pattern based on the approach by Shirley and Chiu $$ 1997 $$ to divide the hemisphere into samples of equal solid angle, or equal area on the unit hemisphere. (We use the source to code for this concentric mapping directly from the Shirley-Chiu paper). The samples are evenly distributed across the sky, are symmetric from the zenith, and do not overlap due to the subtended angle of the fore-optics. Figure 6 illustrates the sampling pattern and fore-optics we used in our scans. Any pattern may be programmed and scanned by the device, including the one proposed by the CIE $$ 1994 $$. Once a sampling pattern is devised, the pattern is sent to the device as an array of angles. Care must be taken to ensure the fiber optics do not become twisted or tangled during the scanning procedure. Therefore at each elevation we unwind the pattern to ensure the fiber optic cable is not bent.    Figure 7: This image provides details of our pyranometer which measures the irradiance. (a) Shows the device we use: an Apogee pyranometer to measure the total irradiance, (b) Shows the cosine response of the device, (c) Shows sample data captured by the pyranometer for a typical clear day. # 4.2 Irradiance Measurements We use an Apogee pyranometer to measure the total hemisphere irradiance $(\widehat{W}/{\bar{m}}^{2})$ , also known as the global shortwave solar radiation ( Figure 7(a)). The pyranometer has a 180 degree field of view which measures light from the entire skydome. Figure 7(b) illustrates the cosine response for the device. Specifically, we use a silicon-cell pyranometer manufactured by Apogee with a diffuser. For our Apogee sensor, a conversion factor of 0.5 $W/(m^{2}$ ∗ mV ) is used to convert the sensor output to the final radiation value. The conversion factor is based on the output sensor voltage which is different per device. For our pyranmeter the sensor output is 2.2V , and the device is calibrated such that:2.2*\text{\ ConversionFactor\ } = \text{\ DirectSunlight\ }*\frac{W}{m^{2}}
The conversion factor from Equation 1 simply scales the raw output to irradiance. The device is wired to the Arduino controller and samples the irradiance once every time the sky-scanner takes radiance measurements. The voltage signal of the sensor is converted to radiation incident on a horizontal planar surface since the signal is exactly proportional. The sensor is calibrated directly to a clear sky conditions. Figure 7(c) provides sample output from the device over a clear day. The values are averaged and accumulated to determine the final total irradiance measured during the scan. We take a value every sample in case the sun is partially occluded and drastically changes the total irradiance, and thus we can account for any noise in the samples during the radiance scan.   Figure 8: This image provides details of our HDR imagery setup. (a) We use a Canon 5D camera with a 8mm fish-eye lens to acquire 8 photographs (b) which capture the wide dynamic range of the sky. # 4.3 High Dynamic Range Imagery To capture HDR imagery of the sun and sky, we follow the method outlined by Stumpfel et. al $$ 2004 $$. This method uses a Canon fullframe camera (5D), a fisheye lens (Sigma 8mm), a neutral density filter (Kodak Wratten 2 ND 3.0), and a laptop (Figure 8(a)). On a clear day, varying exposure times and aperture settings captures the full 17 stop dynamic range of the sky with eight photographs. Figure 8(b) shows the HDR sequence and camera settings which follow Stumpfel’s approach. The first four images (top) the solar disc, and the last four (bottom) capture the diffuse skylight. We use the library libgphoto which allowed us to tether the camera to a laptop and automatically capture and download the HDR sequence. The HDR sequence takes approximately 40 seconds to capture. The HDR images are useful to visualize the current sky conditions. We provide the RAW images captured; but the lens distortion, chromatic aberration, vignetting, and neutral density filter must be accounted for to produce a properly calibrated HDR stack.   图9：该图像可视化天气数据。(a) 显示了东海岸的能见度数据。(b) 显示了地面反照率。 ## 4.4 大气天气数据 天气数据提供了测量地点主要大气条件的详细分类。大气条件包含复杂的结构和气溶胶变化。我们使用了三种数据源来评定当前天空。快速刷新 (RAP) 同化了来自地面雷达、常规气象站和卫星数据的数据。该数据（见图9）提供了能见度和反照率的二维网格 (http://rapidrefresh.noaa.gov/)。RAP 还提供了 13km 的三维网格，涵盖广泛的大气条件，包括：温度、气压和湿度。该数据每小时更新一次。SYNOP 和 METAR 是由有人值守和自动气象站（通常位于机场附近）提供的两个地面常规天气观测点。这些     Measurement –Bruneton ★Haber Hosek2012 -Hosek2013 →Nishita93 Nishita96 ←Preetham 图10：左：该图显示了测量数据与7个最先进的太阳/天空穹顶模型在四个空间角度上的辐射率光谱差异。测量的辐射率（W/m2/sr1）以红色显示。 也提供能见度和天空晴朗度的测量。SYNOP 每六小时更新一次，METAR 每小时更新一次。 必须注意确保 RAP 报告的能见度与 Preetham 和 Hosek 定义的浑浊度一致。这里浑浊度衡量空气中的气溶胶含量。以下方程将该值转换为预期的浑浊度项：turbidity = 2^{( - 2.3*\log(0.26*\frac{\log_{10}(\text{\ visibility\ } + 0.5)}{\log_{10}(4)})}
## 4.5 太阳/天空穹顶测量数据集 利用我们设备进行的测量，我们随后为社区创建了一个精确的测量数据集。其结果是获取了一个由整个天空穹顶上基于波长的辐射率定义的半球照明源。这些测量定义了天空的照明。我们捕获了来自不同春、夏、秋日的许多晴天数据样本。数据按每个时间片组织，每个时间片存在于一个以 GMT 捕获时间命名的文件夹中。该文件夹包含两个文本文件，分别记录辐射率和辐照度，以及该扫描周期的八张 HDR 照片。我们还提供了一种收集天气数据的方法，以明确分类当前的天空状况。该数据集允许对天光与各种模拟模型进行更精确的光谱比较。每个时间片的数据是同时捕获的。数据本身以原始格式提供，直到在各种应用中使用时才进行积分。 ## 5 比较分析 在过去的二十年中，人们提出了各种日益复杂的天光模型。我们选择了七个经常被使用和引用的太阳/天空穹顶模型，并比较了每个模型产生的照明的辐射率、辐照度和可视化效果。这七篇出版物中有六篇提出了天空穹顶模型，其中三篇包含太阳模型。我们比较的天空穹顶模型是 Nishita 等人 $$ 1993 $$ single scattering Model , the Nishita et al. $$ 1996 $$ multiple scattering Model, the Preetham Model $$ 1999 $$, the Haber Model $$ 2005 $$, the Bruneton Model $$ 2008 $$, the Hosek Skydome Model $$ 2012 $$. The three solar models are the Preetham Model $$ 1999 $$, the Bruneton Model $$ 2008 $$, the Hosek Solar Radiance Model $$ 2013 $$. We develop and present an interactive interface tool which can load any sky model’s radiance, irradiance, and imagery data for the skydome hemisphere. We have open sourced this tool so other researchers can run similar comparisons. Though we only choose 7 models to compare, any model can be easily loaded under this tool. The graphic interface features a wide range of comparison tools that compared the different model’s strengths and weaknesses when compared to our measured data. We plot a variety of data, difference information, and imagery. The solar/skylight models are all implemented in the Mitsuba framework $$ Jakob 2010 $$ to ensure the comparison analysis experiment is consistent. Most models are formulated on a wavelength basis and were run spectrally. Model comparisons span a spectral distribution between 360nm to 830nm with 40 spectral bins. Our results only show data between 360nm to 720 nm since some models do not have data beyond that range. We use this spectral range since most skylight models were primarily designed for the visible range to make images. To run the models spectrally, we use the same solar table, and the same Rayleigh, and Mie constants across all models. We replaced the RGB triplets for these constants with discretized spectra between 360nm and 830nm in 5nm bins. These spectra were interpolated and sampled at each of the 40 bins. We simulate all models with the same parameters (when applicable in the model), such as turbidity and ground albedo. The turbidity for the clear sky was found from the closest weather station for that day. Wherever possible, we directly integrate the author’s source code into their own Mitsuba plug-ins $$ Preetham et al. 1999; Bruneton and Neyret 2008; Hosek and Wilkie 2012; Hosek and Wilkie 2013 $$. The other models ($$ Nishita et al. 1993; Nishita et al. 1996; Haber et al. 2005 $$ were carefully implemented from their respective papers to the best of our ability. Additional simulation data can be easily added both to Mitsuba and to the interactive framework. 用于驱动分析模型和路径追踪模型的参数选择，直接源自第 4.4 节讨论的测量数据。Rapid Refresh 数据提供了当前地面反照率的颜色和强度，我们使用公式 2 推导出浑浊度。这些数据也显式地驱动 Haber 模型的输入。我们将每层的湿度输入到 OPAC $$ Hess et al. 1998 $$, which is used by Haber’s model. # 5.1 Spectral Radiance Comparisons We compare the spectral radiance in two groups: six skydome models and three solar light models. For the skydome radiance comparison we use time-slices where the solar disc did not cross one of the 81 measured points. For the solar light comparison, we directly measure the solar region with the sky scanner and compare the solar model simulation data at that specific angle. This ensured that we are only comparing skydome to skydomes and solar region to solar region. (Our device scans the entire solar/skydome. This grouping was only done to consistently compare various simulation models.) Figure 10 plots the spectral radiance of the six skylight models with the measured data from the spectral sky-scanner for a four different angles. We graph absolute radiance at each wavelength. In the supplementary material, we provide a complete and detailed analysis of the skydome for all 81 sample points for a few timeslices. We provide other visualizations of the differences. We calculate the R2 difference between the sample points per wavelength and the measured data, the total $R^{2}$ difference summed over wavelengths, and the relative difference. Figure 11 plots the spectral radiance of the three solar models with the measured solar data.  Figure 11: This figure shows the spectral plots of radiance between measured data and the 3 state-of-the-art solar models for one scan cycle. The measured radiance is shown in red. # 5.2 Irradiance Comparisons We calculate the total irradiance from the seven solar/skylight models. Here we made an assumption about combining the solar/skydome models. We added the Preetham solar model to every model except the Bruneton2008 and Hosek2013 models. Those models use their respective solar models and skydomes. Up until the publication of the Hosek2013 solar model, this was an acceptable practice in many renderers. This combination exists in Mitsuba, V-Ray, and other popular renderers as a default solar/skydome model. The evaluation results are summarized in Figure 12 in which we compare a five hour block (20 different measurements) of clear sky conditions. We compare the total irradiance simulated to the total irradiance measured by the pyranometer. These graphs capture how the models perform over all the angles in the hemisphere. We compare the measurements to the pyranometer since the spectroradiometer only samples discretized points and not the whole sky, and the HDR-imagery texel size varies across the image. The pyranometer provides an effective way to measure the irradiance without having to discretize the integration across the hemisphere from the other measuring techniques. Figure 12 shows that the Hosek solar model and the Bruneton solar/skydome produce an unnatural bump in irradiance at high solar angles. This was a surprising result. The Hosek skydome (with the Preetham solar model) significantly corrected the sky’s irradiance compared to the Preetham skydome. The two Nishita models tend to best follow the measured irradiance curves.  Figure 12: This figure shows the difference of total irradiance between measured data and 7 skylight models for part of the day. (We provide a comparison of full day irradiance in the supplementary documentation.) # 5.3 Illumination Comparisons Many graphics applications need scenes lit by these solar/skydome models to produce physically accurate renderings. We rendered fisheye views of all the skydomes and compared them to tonemapped HDR-imagery in Figure 13 using the tone mapping approach discussed in Section 3.1. This figure shows the seven solar/skydome models at four different times of day on May 26 and 27, 2013 in the United States. This result provides a visualization of how the illumination color varies between the different models over various times of a day. In the supplementary material, we provide more time comparisons of the color differences of the various models and a dynamic sequence over a whole day. The change in color occurs due to the different methods each simulation uses to simulate the skydome. In Figure 18(top), we illuminated a kitchen scene with a few of the solar/skydome models. This demonstrates the impact the different models have on indoor scenes. Both the colors and intensity vary throughout the day between the models. This is potentially important for situations where the color and appearance of objects matter. The final illumination could vary depending on which model is used. Figure 18(bottom) show the luminance and intensity curves commonly used in daylighting studies.  Figure 13: This image shows the seven simulation models compared with their tone-mapped fisheye images. (Note: The fisheye images use the same tone-mapping technique as the simulation figures.) # 6 Data-Driven Spectral Skylight Using the method for capturing spectral radiance data described above, we are able to reconstruct realistic spectral illumination for outdoor scenes across the entire visual spectrum, and not only RGB. We start by projecting the 81 measured data points with positions represented in spherical coordinates onto the unit hemisphere. Bicubic spherical interpolation is used to reconstruct radiance values for positions on the hemisphere that lie in between measured radiance samples. For the solar disc, we sample the sun directly in our capture process, and use that spectral information to drive the solar model directly. Depending on the user’s requirements, the sky can be sampled with any pattern providing even better results. This model produces more accurate spectral information than HDR-imagery.    Figure 14: This image shows the results of our data-driven spectral skylight. (A) shows a scene illuminated with the data driven skylight shown as a fisheye image in (B). (C) shows the samples points and their corresponding RGB color. A CIE XYZ fitting can also be done for applications where the full spectral model is not needed. Figure 14 shows a sample scene with the illumination derived from the data-driven method. Figure 14(B) shows a fisheye view of the constructed skydome in sRGB. Figure 14(C) shows the conversion of just the sample point themselves. This approach provides full spectral data for illumination which could be used for spectrally varying BSDFs, daylighting, and thermal studies that could not be simulated directly with Stumpfel et als. $$ 2004 $$ proposed technique. Daylighting studies specifically can take advantage of having a fully spectral sky. The data-driven model differs from HDR-imagery techniques since it explicitly provides the full spectral sky. HDR-imagery $$ Debevec 1998; Inanici and Galvin 2004 $$ tries to use machine learning to predict the spectral radiance, but does not provide explicit measurements. The measurements provide the exact radiance at a particular angle and does not worry about an HDR camera’s response curve and lens issues (chromatic aberration, distortion, vignetting, etc.) # 7 Discussion We have presented a unique method to capture the physical daylight of the solar/skydome. By using our custom-built sky-scanning device, we gather ground-truth data that measures incoming light spectrally, spatially, and temporally. Our analysis of the captured data currently only considers clear sky days without any clouds. We choose to omit cloudy skies from this study due to the rapid atmospheric changes that clouds produce and limitations associated with our capture method. More precisely, our sky-scanning device takes three minutes to scan and capture the entire skydome. While this length of time is insignificant for the gradual atmospheric changes on clear sky days, the presence of clouds introduces rapid changes to the atmosphere that prevent consistent measurements across the full skydome. We provide a comparison of current state-of-the-art solar/skydome simulation methods with our ground-truth data scanned by our approach. Analyzing these comparisons show interesting insights in the current state-of-the-art of sky rendering. Analytical models are optimized to satisfy speed and ease of rendering while minimizing any expensive path-tracing steps. The seed images for the nonlinear optimization step are path traced, usually at a single location, but simplify down to a few formulas for generalized rendering. Through comparisons to our measured data, we show that most analytical models produce plausible results but vary significantly in various regions of the skydome.  Figure 15: This figure plots the radiance difference over the skydome. We have interpolated the difference between the measurement and simulation for this visualization to better illustrate where the models differ. It should be noted that our comparison methodology of measurements to the various sky models is driven from the best data we were able to find, however it is difficult to remote sense the exact atmospheric conditions at a particular time. 3D aerosol distribution data is not currently accurate enough to drive a highly authoritative reference simulation. RapidRefresh data only provides 13km regions which blur the aerosol distributions and does not provide the required granularity for accurate atmospheric composition data for the measurement locations. In the past, this granularity was not needed and our work demonstrates a clear need to have fine-grained altitude dependent variability of 3D aerosol distributions. The major differences between the measurement data and most of the simulation models occur around two regions. The first major difference region is located around the current position of the solar disc. Figure 15 plots the relative radiance error (summed equally across all wavelengths and interpolated over the skydome). This graph illustrates how the difference is significant near the solar disc. Specifically, the models undershoot the radiance in this region. The second major difference region is the area near the horizon. A variety of the models produce vastly different spectral distributions around the horizon (Nishita single scattering and Preetham). Visually these models have a red saturation around this region which the Hosek skydome fixed for high solar angles. Figure 15 percentage difference plots would improve by driving the initial simulations with better 3D aerosol distribution data and this should be considered when viewing these plots.  Figure 16: This image directly shows the total radiance error plots for the Preetham and Hosek skydome. This figure illustrates how the Hosek skydome significantly improved the Preetham model across a large portion of the skydome. Our comparisons also demonstrate how and where the Hosek skydome improved the Preetham model both spatially and spectrally. Since we have a ground-truth data-set, we are able to quantify improvements. Figure 16 illustrates this difference and highlights specific areas of improvement for the Hosek skydome. The error plots show how much better the Hosek model performs.  Figure 17: This image shows total radiance error graphs for both the the Nishita single scattering Model and the Nishita multiple scattering Model. We also provide the difference image (between single and multiple scattering), where the areas in dark blue show the primary areas where multiple scattering has a direct effect. Our data reinforces the importance and accuracy improvements associated with using a fully path-trace-based method when rendering the solar/skydome. The path-traced models more accurately predict the scattering effects at a particular point in time. Examples of this are the path-traced methods of Nishita et al. $$ 1993 $$ and Nishita et al. $$ 1996 $$. The Hosek model is also initially brute force path traced, it is important that the atmospheric layering and composition used for the reference simulations are similar. Our comparisons have only analyzed the analytical results of the Hosek model, however reinitializing the model with new path traced results with the exact atmospheric conditions should change the model’s accuracy. Furthermore, the importance of the multiple scattering from Nishita $$ 1996 $$ increases as the solar elevation decreases due to the increased amount of the atmospheric light rays must traverse. At high solar elevations on clear days, single scattering dominates. In addition, as atmospheric turbidity increases, the effects of multiple scattering are more pronounced. This follows the results of Bary and Eshelbach $$ 1974 $$ who studied the ratios of primary scattering to total scattering of sky radiance. Figure 17 illustrates where multiple scattering has a direct effect on the skydome. The difference between the measurements and models occurs for a variety of reasons. The majority of the models assume aerosol properties are constant at every location (Haber is the only model to account for aerosol changes, but only in layers). Aerosols are not constant in the atmosphere, especially for cities such as Los Angeles and Shanghai, where dense areas of particles in the air show the anisotropic nature of atmospheric conditions which vary both vertically and horizontally at a fine scale. Additionally, the distribution of haze in the lower atmosphere is typically fairly different across climate zones. Some models also assume you are at ground level, so it becomes harder to accurately simulate a sky in a city such as Denver, CO (which is one mile above sea level). There is also a unique impact of light’s attenuation per global position. All the models account for the sun location change since all allow the latitude and longitude to account for the proper solar position, but not the change in the cycle of the sun’s power. Many of the models also approximate Mie scattering by using a Henyey-Greenstein scattering function. These functions are poor approximations for atmospheric scattering as turbidity increases. In our simulations, we drove the Haber model two ways: from synthetic data which assumed a data inspired starting point and an exponential falloff for atmospheric properties, such as humidity, and directly from RapidRefresh data which explicitly defined those properties per layer for the given time-slice. The RapidRefresh data driven approach tended to underestimate the radiance, while the synthetic data overshoots. We noticed that properties such as humidity did not exhibit a linear falloff in measurements and many layers had little to no humidity on clear days. (In the supplemental document, we provide a side-by-side illustration of the Haber model using both techniques).  Figure 18: The top row shows the results of lighting a test kitchen scene with various models. The bottom row shows the differing daylight illumination between the various models. The times are shown in GMT for a location on the East coast. We manually tested the choice of parameters by hand to see if there was a better fit to the measured data. Specifically, this was done by adjusting the inputs for the Haber model and the Hosek skydome. For the Haber Model, we tried both the exponential falloffs and varying the atmospheric properties. For the Hosek skydome, we discretized ten turbidities by ten ground albedos and ran 100 simulations. This manual search through the space did not produce better fits to the measured data. After analyzing the data, we evaluated the different simulation models’ strengths and weaknesses. The Nishita models are excellent in accounting for the direct solar and scattering parameters since they in essence run a brute force path-trace on the scene. The major concern is that brute force path trace is not applicable for real-time applications. The Haber model is designed for more plausible sunrise and sunset images since the model accounts for twilight phenomena, but significantly underestimates the radiance at other times of day. The model accounts for optical changes in the density of the atmospheric layers which we drive directly from RapidRefresh data. Haber, however, also requires a brute force path-trace which is slow. If execution time is not a constraint, path-traced models will produce the best results. The analytic models (Hosek and Preetham) and the Bruneton real-time model produce very fast results which balance accuracy with usability. Preetham had an unnatural spectral distribution near the horizon that the Hosek skydome corrected to produce much more natural and realistic looking images. Hosek also performs better spectrally. These models should be used when speed is a major concern. To amplify the importance of physically correct solar/skydome illumination models, we illustrate their impact on daylighting studies for a known kitchen environment. Figure 18(bottom) illustrates this daylighting study and how the various models produce different results. This is important for accurate physical modeling, but necessary for building code compliance with respect to luminance on pre-defined surfaces. Since our approach measures all light incident on our sensor, we measure the light from the current atmospheric conditions. We currently do not measure skylight polarization. Polarization influences the appearance of reflections with highly specular surfaces $$ Wilkie et al. 2004 $$. Stumpfel $$ 2004 $$ provides a simple technique to begin to quantify this parameter with HDR-imagery, and Pust et al. $$ 2007 $$ suggests a more accurate technique using liquid crystal variable retarders. As more simulations, renderers, and BRDFs support polarization, this would be an interesting feature to measure next. ## 8 结论与未来工作 我们提出了一种采集太阳与天空穹顶物理光照的获取方法。我们还提供了一个天空测量数据集，涵盖春季、夏季和秋季不同时间、不同日期的多种晴空条件。目前该数据集已包含超过 100 个样本。该方法捕获了太阳和天空穹顶的光谱辐射率 (spectral radiance)、辐照度 (irradiance) 以及 HDR 图像。我们采集的数据有助于比较各种模型的优缺点，并利用它对七种太阳/天光模型进行了比较。我们计划将天光数据集和可视化界面一同发布给社区。此外，我们利用采集的数据，基于测量样本构建了一个光谱数据驱动的天空模型。由此产生的光照模型可用于渲染、日光研究或热评估，因为光照信息覆盖了从 350nm 到 2500nm 的更宽光谱范围，而非仅限于 HDR 图像。 我们选择专注于构建一个系统，以捕获给定太阳/天空穹顶的光谱和空间数据。我们进一步比较并验证了过去 25 年天空渲染研究中提出的许多假设和理论。一个自然的延伸是研究我们的数据能否与当前的分析方法和路径追踪方法相结合，以提高其精度，特别是在那些通常与测量结果存在显著差异的区域。最后，一个令人兴奋的未来工作方向是创建一种直接受捕获的天空辐射率数据启发的新型天空渲染技术。我们采集的数据提供了比以往计算机图形学应用中模拟的辐射光谱范围大得多的数据，并且提供了精确的地面实况测量来驱动该模型。这将为进行光谱精确的日光和能量研究开辟新的机会， 否则将不可能实现。 未来，我们希望利用从测量数据中获得的信息，生成一个更精确的太阳/天空穹顶仿真模型，以再现各种天空条件。该采集方法为未来关注的重点方向提供了新颖的见解。在当前模型中，太阳盘面周围的区域往往与实际测量结果差异最大。该区域无论是在光谱上还是在辐射率大小上，变化率都是最大的。另一个感兴趣的区域是地平线附近低方位角处，那里的光谱和辐射率值与我们的测量数据存在显著差异。该区域也往往与我们的测量数据不一致。这有几个原因：要么是大气中的气溶胶没有被准确考虑，要么是 Henyey-Greenstein 散射近似不够鲁棒，无法捕捉这些独特的 Mie 散射效应。 虽然我们提出了一种可能的扫描配置，但我们的系统可以通过定制扫描模式来满足特定应用的需求，从而得到改进。例如，CIE 已经为亮度分布设定了多种天空采样模式。这些相同的模式可以编程到我们的设备中。该设备仅限于扫描一度或八度的窄视场辐射率。可以尝试使用其他前置光学镜头来执行不同的天空辐射率扫描。此外，可以使用光谱日射强度计 (spectral pyranometer) 来比较各种太阳/天空穹顶模型的光谱辐照度输出。尽管我们的数据目前仅包含一个地理位置，但我们希望不久的将来能扫描不同的区域。 扫描设备当前的一个局限性与光谱辐射计有关。该设备本身并非专门为捕获天光而设计，因此光谱辐射计在清晨和黄昏时难以捕获准确的测量值。没有足够的光线让设备可靠地工作。快门时间受到限制，而增加快门时间会随之增加整个天空的扫描时间。此外，黄昏和黎明时光线的扫描需要更快，而不是更慢。黄昏和黎明有着最剧烈、最快速的变化，尤其是在天空的光谱分布方面。我们使用的是 ASD Fieldspec Pro（大约已有 10 年历史）。一款速度更快、灵敏度更高的新型光谱辐射计将缓解这一限制。我们面临的另一个局限是，难以找到比 RapidRefresh 数据更精细的、依赖三维海拔的气溶胶分布。 我们的采集方法是一种直接为比较各种天光模型提供基础的直接方式。由于这些天光模型被用于多种应用，比较这些模型的精度非常重要。未来，我们计划捕获更广泛的天空条件以进行比较和验证。这将有助于对所有天气条件下的所有天空光照模型进行类似的研究。随着计算机图形学界不断向基于物理的测量和模拟（例如，在测量声音、材料属性和力学方面）迈进，使用这种实验比较框架将推动光照模型的改进。 ## 致谢 本工作由 Autodesk 支持，用于能源与 daylighting simulation 研究。所有 renderings 均使用 Mitsuba。作者感谢 Bruce Walter、Kavita Bala、Steve Marshner、William Philpot 和 Adam Arbree，他们总是乐于提供反馈与指导。我们特别感谢 Kevin Pratt、Lars Schumann 和 Hurf Sheldon，他们协助搭建了该设备。