The models we have discussed in the last few sections rely on geometrical optics,which treats light as propagating in rays rather than waves. As discussed on page 303,geometrical optics is based on the assumption that any surface irregularities are either smaller than a wavelength or larger than about 100 wavelengths.
我们在最后几节中讨论的模型依赖于几何光学，它将光视为以射线而不是波的形式传播。如第303页所述，几何光学是基于任何表面不规则性小于一个波长或大于约100个波长的假设。
Real-world surfaces are not so obliging. They tend to have irregularities at all scales, including the 1–100 wavelength range. We refer to irregularities with such sizes as nanogeometry to distinguish them from the microgeometry irregularities discussed in earlier sections, which are too small to be individually rendered but larger than 100 light wavelengths. The effects of nanogeometry on reflectance cannot be modeled by geometrical optics. These effects depend on the wave nature of light and wave optics (also called physical optics) is required to model them.
现实世界的表面并不那么友好。它们在所有尺度上都有不规则性，包括1-100波长范围。我们将这种大小的不规则体称为纳米几何不规则体，以区别于前面讨论的微几何不规则体，后者太小而不能单独渲染，但大于100个光波长。纳米几何对反射率的影响不能用几何光学来模拟。这些效果取决于光的波动性质，需要波动光学(也称为物理光学)来模拟它们。
Surface layers, or films, with thicknesses close to a light wavelength also produce optical phenomena related to the wave nature of light.
厚度接近光波长的表层或薄膜也会产生与光的波动性质相关的光学现象。
In this section we touch upon wave optics phenomena such as diffraction and thinfilm interference, discussing their (sometimes surprising) importance in realistically rendering what otherwise can seem to be relatively mundane materials.
在这一节中，我们将触及波动光学现象，如衍射和薄膜干涉，讨论它们在真实渲染看起来相对平凡的材质时的重要性(有时令人惊讶)。
Nanogeometry causes a phenomenon called diffraction. To explain it we make use of the Huygens-Fresnel principle, which states that every point on a wavefront (the set of points that have the same wave phase) can be treated as the source of a new spherical wave. See Figure 9.44. When waves encounter an obstacle, the Huygens-Fresnel principle shows that they will bend slightly around corners, which is an example of diffraction. This phenomenon cannot be predicted by geometrical optics. In the case of light incident on a planar surface, geometrical optics does correctly predict that light will be reflected in a single direction. That said, the Fresnel-Huygens principle provides additional insight. It shows that the spherical waves on the surface line up just right to create the reflected wavefront, with waves in all other directions being eliminated through destructive interference. This insight becomes important when we look at a surface with nanometer irregularities. Due to the different heights of the surface points, the spherical waves on the surface no longer line up so neatly. See Figure 9.45.
纳米几何导致了一种叫做衍射的现象。为了解释它，我们利用惠更斯-菲涅耳原理，该原理指出波前上的每一点(具有相同波相位的点的集合)都可以被视为新球面波的源。参见图9.44。当波遇到障碍物时，惠更斯-菲涅耳原理表明，它们会在拐角处轻微弯曲，这就是衍射的一个例子。这种现象是几何光学无法预测的。在光入射到平面表面的情况下，几何光学确实正确地预测了光将在单一方向上反射。也就是说，菲涅耳-惠更斯原理提供了额外的见解。它表明，表面上的球面波排列得恰到好处，形成了反射波阵面，而所有其他方向的波都通过相消干涉被消除了。当我们观察具有纳米不规则性的表面时，这种见解变得很重要。由于表面点的高度不同，表面的球面波不再排列得那么整齐。参见图9.45。
Figure 9.44. To the left, we see a planar wavefront propagating in empty space. If each point on the wavefront is treated as the source of a new spherical wave, the new waves interfere destructively in all directions except forward, resulting in a planar wavefront again. In the center, the waves encounter an obstacle. The spherical waves at the edge of the obstacle have no waves to their right that destructively interfere with them, so some waves diffract or “leak” around the edge. To the right, a planar wavefront is reflected from a flat surface. The planar wavefront encounters surface points on the left earlier than points on the right, so the spherical waves emitting from surface points on the left have had more time to propagate and are therefore larger. The different sizes of spherical wavefronts interfere constructively along the edge of the reflected planar wavefront, and destructively in other directions.
图9.44。在左边，我们看到一个平面波前在真空中传播。如果波前上的每一点都被视为一个新的球面波的来源，这个新的球面波会在除了前进方向之外的所有方向上相消干涉，再次产生一个平面波前。在中心，波浪遇到一个障碍物。障碍物边缘的球面波右侧没有破坏性干扰它们的波，因此一些波在边缘周围衍射或“泄漏”。平面波阵面从平面反射到右边。平面波前遇到左侧表面点的时间比遇到右侧表面点的时间早，因此从左侧表面点发出的球面波有更多的时间传播，因此更大。不同大小的球面波前沿着反射平面波前的边缘相长干涉，而在其他方向相消干涉。
Figure 9.45. On the left we see planar wavefronts incident to a surface with rough nanogeometry. In the center we see the spherical waves formed on the surface according to the Fresnel-Huygens principle. On the right we see that after constructive and destructive interference has occurred, some of the resulting waves (in red) form a planar reflected wave. The remainder (in purple) are diffracted, with different amounts of light propagating in each direction, depending on wavelength.
图9.45。在左边，我们看到入射到粗糙纳米几何表面的平面波前。在中心，我们看到根据菲涅耳-惠更斯原理在表面上形成的球面波。在右边，我们看到在发生相长和相消干涉后，一些合成波(红色)形成了平面反射波。其余的(紫色)被衍射，根据波长的不同，在每个方向上传播的光量不同。
As the figure shows, light is scattered in different directions. Some portion of it is specularly reflected, i.e., adds up to a planar wavefront in the reflection direction. The remaining light is diffracted out in a directional pattern that depends on certain properties of the nanogeometry. The division between specularly reflected and diffracted light depends on the height of the nanogeometry bumps, or, more precisely, on the variance of the height distribution. The angular spread of diffracted light around the specular reflection direction depends on the width of the nanogeometry bumps relative to the light wavelength. Somewhat counter-intuitively, wider irregularities cause a smaller spread. If the irregularities are larger than 100 light wavelengths, the angle between the diffracted light and the specularly reflected light is so small as to be negligible. Irregularities of decreasing size cause a wider spread of diffracted light, until the irregularities become smaller than a light wavelength, at which point no diffraction occurs.
如图所示，光向不同的方向散射。它的一部分被镜面反射，即在反射方向上形成平面波前。剩余的光以定向模式衍射出去，这取决于纳米几何的某些特性。镜面反射光和衍射光之间的划分取决于纳米几何凸起的高度，或者更准确地说，取决于高度分布的变化。围绕镜面反射方向的衍射光的角展度取决于纳米几何凸起相对于光波长的宽度。有些与直觉相反，更大的不规则性会导致更小的价差。如果不规则性大于100个光波长，衍射光和镜面反射光之间的角度小到可以忽略不计。尺寸减小的不规则性导致衍射光的扩散更广，直到不规则性变得小于光波长，此时不发生衍射。
Diffraction is most clearly visible in surfaces with periodic nanogeometry, since the repeating patterns reinforce the diffracted light via constructive interference, causing a colorful iridescence. This phenomena can be observed in CD and DVD optical disks and certain insects. While diffraction also occurs in non-periodic surfaces, the computer graphics community has assumed for many years that the effect is slight. For this reason, with a handful of exceptions [89, 366, 686, 1688], the computer graphics literature has mostly ignored diffraction for many years.
在具有周期性纳米几何的表面上，衍射最为清晰可见，因为重复的图案通过相长干涉增强了衍射光，从而产生了彩色的彩虹色。这种现象可以在CD和DVD光盘以及某些昆虫身上观察到。虽然衍射也发生在非周期性表面，但计算机图形社区多年来一直认为这种影响很小。由于这个原因，除了少数例外[89，366，686，1688]，计算机图形学文献多年来大多忽略了衍射。
However, recent analysis of measured materials by Holzschuch and Pacanowski [762] has shown that significant diffraction effects are present in many materials,and may explain the continuing difficulty of fitting these materials with current models. Follow-up work by the same authors [763] introduced a model combining microfacet and diffraction theory, via the use of the general microfacet BRDF (Equation 9.26) with a micro-BRDF that accounts for diffraction. In parallel, Toisoul and Ghosh [1772, 1773] presented methods for capturing the iridescent diffraction effects resulting from periodic nanogeometry, and for rendering them in real time with point light sources as well as image-based lighting.
然而，Holzschuch和Pacanowski [762]最近对测量材料的分析表明，许多材料中存在显著的衍射效应，这可能解释了用当前模型拟合这些材料的持续困难。相同作者的后续工作[763]介绍了一种结合微法和衍射理论的模型，通过使用一般微法BRDF(方程9.26)和考虑衍射的微BRDF。与此同时，Toisoul和Ghosh [1772，1773]提出了捕捉周期性纳米几何产生的虹彩衍射效应的方法，以及使用点光源和基于图像的照明实时渲染这些效应的方法。
Thin-film interference is a wave optics phenomenon that occurs when light paths reflecting from the top and bottom of a thin dielectric layer interfere with each other.See Figure 9.46.
薄膜干涉是一种波动光学现象，当从薄电介质层的顶部和底部反射的光路相互干涉时就会发生这种现象。参见图9.46。
Figure 9.46. Light incident to a thin film on top of a reflective substrate. Besides the primary reflection, there are multiple paths of light refracting, reflecting from the substrate, and either reflecting from the inside of the top thin film surface or refracting through it. These paths are all copies of the same wave, but with short phase delays caused by difference in path length, so they interfere coherently with each other.
图9.46。光入射到反射衬底顶部的薄膜上。除了初级反射之外，还有多条路径的光从衬底折射、反射，或者从顶部薄膜表面的内部反射或者折射通过它。这些路径都是同一个波的副本，但由于路径长度不同，相位延迟较短，因此它们会相互相干干扰。
The different wavelengths of light either interfere constructively or destructively,depending on the relationship between the wavelength and the path length difference.Since the path length difference changes with angle, the end result is an iridescent color shift as different wavelengths transition between constructive and destructive interference.
不同波长的光相长干涉或相消干涉，这取决于波长和光程差之间的关系。由于光程差随角度变化，最终结果是不同波长在相长干涉和相消干涉之间转换时产生彩虹色偏移。
The reason that the film needs to be thin for this effect to occur is related to the concept of coherence length. This length is the maximum distance by which a copy of a light wave can be displaced and still interfere coherently with the original wave. This length is inversely proportional to the bandwidth of the light, which is the range of wavelengths over which its spectral power distribution (SPD) extends. Laser light, with its extremely narrow bandwidth, has an extremely long coherence length. It can be miles, depending on the type of laser. This relationship makes sense, since a simple sine wave displaced by many wavelengths will still interfere coherently with the original wave. If the laser was truly monochromatic, it would have an infinite coherence length, but in practice lasers have a nonzero bandwidth. Conversely, light with an extremely broad bandwidth will have a chaotic waveform. It makes sense that a copy of such a waveform needs to be displaced only a short distance before it stops interfering coherently with the original.
为了产生这种效果，薄膜需要很薄的原因与相干长度的概念有关。这个长度是一个光波的副本可以被移动但仍能与原波相干干涉的最大距离。这个长度与光的带宽成反比，光的带宽是其光谱功率分布(SPD)延伸的波长范围。带宽极窄的激光具有极长的相干长度。它可以是英里，取决于激光的类型。这种关系是有意义的，因为一个简单的正弦波被许多波长移位后，仍会与原始波相干干涉。如果雷射真的是单色的，那麽它的同调长度就会无限长，但实际上雷射的频宽并不为零。反之，带宽极宽的光会出现混沌波形。这种波形的拷贝只需移动一小段距离，就能停止与原始波形的相干干扰，这是有道理的。
In theory, ideal white light, which is a mixture of all wavelengths, would have a coherence length of zero. However, for the purposes of visible-light optics, the bandwidth of the human visual system (which senses light only in the 400–700 nm range) determines the coherence length, which is about 1 micrometer. So, in most cases the answer to the question “how thick can a film get before it no longer causes visible interference?” is “about 1 micrometer.”
理论上，理想的白光是所有波长的混合，其相干长度为零。然而，出于可见光光学的目的，人类视觉系统的带宽(仅感知400-700nm范围内的光)决定了相干长度，约为1微米。因此，在大多数情况下，对于“薄膜可以厚到什么程度才能不再产生可见的干涉”这个问题的答案是是“大约1微米”
Similarly to diffraction, for many years thin-film interference was thought of as a special case effect that occurs only in surfaces such as soap bubbles and oil stains. However, Akin [27] points out that thin-film interference does lend a subtle coloration to many everyday surfaces, and shows how modeling this effect can increase realism.See Figure 9.47. His article caused the level of interest in physically based thin-film interference to increase considerably, with various shading models including Render-Man’s PxrSurface [732] and the Imageworks shading model [947] incorporating support for this effect.
与衍射相似，多年来薄膜干涉被认为是一种特殊情况，只发生在表面，如肥皂泡和油渍。然而，Akin [27]指出，薄膜干涉确实给许多日常表面带来了微妙的色彩，并展示了如何模拟这种效果可以增加真实感。见图9.47。他的文章引起了人们对基于物理的薄膜干涉的兴趣，包括Render-Man的PxrSurface [732]和Imageworks着色模型[947]在内的各种着色模型都支持这种效果。
Figure 9.47. A leather material rendered without (on the left) and with (on the right) thin-film interference. The specular coloration caused by thin-film interference increases the realism of the image. (Image by Atilla Akin, Next Limit Technologies [27].)
图9.47。一种皮革材质，渲染时没有(左侧)和有(右侧)薄膜干涉。由薄膜干涉引起的镜面着色增加了图像的真实性。(图片由下一个极限技术公司Atilla Akin提供。)
Thin-film interference techniques suitable for real-time rendering have existed for some time. Smits and Meyer [1667] proposed an efficient method to account for thinfilm interference between the first- and second-order light paths. They observe that the resulting color is primarily a function of the path length difference, which can be efficiently computed from the film thickness, viewing angle, and index of refraction.Their implementation requires a one-dimensional lookup table with RGB colors. The contents of the table can be computed using dense spectral sampling and converted to RGB colors as a preprocess, which makes the technique quite fast. In the game Call of Duty: Infinite Warfare, a different fast thin-film approximation is used as part of a layered material system [386]. These techniques do not model multiple bounces of light in the thin film, as well as other physical phenomena. A more accurate and computationally expensive technique, yet still targeted at real-time implementation,is presented by Belcour and Barla [129].
适用于实时渲染的薄膜干涉技术已经存在了一段时间。Smits和Meyer [1667]提出了一种有效的方法来解释一阶和二阶光路之间的薄膜干涉。他们观察到，最终的颜色主要是光程差的函数，光程差可以通过薄膜厚度、视角和折射率有效地计算出来。它们的实现需要具有RGB颜色的一维查找表。该表的内容可以使用密集光谱采样来计算，并作为预处理转换为RGB颜色，这使得该技术非常快。在游戏《使命召唤:无限战争》中，一种不同的快速薄膜近似被用作分层材料系统的一部分[386]。这些技术没有模拟薄膜中的多次光反射以及其他物理现象。Belcour和Barla [129]提出了一种更精确且计算成本更高的技术，但仍以实时实施为目标。
