# A New Diffuse Optics Emitter for High Visual Diffuse Transmission Density Measurement
## 2 Materials and Methods  
The diffuse optics emitter is designed as a hemisphere structure with 235 optical fibers, as shown in Figure 1. The main component of DOE is a hemisphere (diameter is 25 mm), and there are 235 optical fibers connecting to the back surface of the hemisphere. One end of these 235 optical fibers is inserted in the hemisphere. The distance, in terms of solid angles, between adjacent optical connection fibers is constant. The other end of these optical fibers is combined in one point to generate a plane called the \"incident plane of DOE\". An idea diffuse transmit glass named \"opal\" is attached at the hemisphere center. That means the hemisphere center is in the upper surface of opal. When the light is emitted at the bottom surface, the light is diffused twice. The whole device is shown in Figure 1b. This diffuse optics emitter corresponds with the geometric conditions of ISO 5, and it can improve the light flux and diffuse property all in the visual spectrum range. In detail, the output ends of the optical fibers are arranged on the hemisphere in an equal solid angle, and the end planes of each optical fiber are on the same surface with the hemisphere's inner surface. The geometric extension lines of all optical fibers exit and intersect at the hemisphere center, and the upper surface center of the opal coincides with the hemisphere center. According to these conditions, the number of these optical fibers \(n\) is decided by Equation (2), where \(k\) is the attenuation coefficient, \(M\) is the radius of the hemisphere, \(m\) is the diameter of the optical fiber, and \(u\) is the spectrum attenuation coefficient of the optical fiber. _Trunk_ means taking the integer of the result. Figure 1: The diffuse optics emitter (DOE). (**a**) The prototype of DOE; (**b**) the structure diagram of DOE (cross-section), where 1 is the hemi-sphere, 2 are the fiber heads (235 in total), 3 are the light rays, 4 is the opal, and 5 is the light emitting surface. \[n=trunk(k\frac{M}{m}\sqrt{u}) \tag{2}\]  
In this work, \(M\) is 25 mm, \(k\) is 14.5 dB, \(m\) is 8.1 mm, and \(u\) is 0.1 dB in 380 nm-780 nm. Thus, the result is 235. Under these conditions, the parameters of these optical fiber are numerical aperture (NA): 0.15, core diameter: 0.1 mm, outer diameter: 2.5 mm, disperse angle: less than 100 mrad, and materials: quartz. Furthermore, this diffuse optics emitter is used in the new national reference densitometer of NIM. The diffuse light source of this reference based on DOE is shown in Figure 2. A compressed air channel is attached in this device. So that the sample can be placed on the surface of the opal closely and moved harmlessly. In this structure, 1 is DOE, 2 is opal, 3 is the mechanical components, 4 is the compressed air channel, and 5 is the sample for measurement. The compressed air is used to fix the sample on the opal; thus, the measurement is precise. The whole structure of the new densitometer is shown in Figure 3. All components in the figure are not to strict size relation. Label 1 is the diffuse light source based on DOE, 2 is the sample, 3 is the light lamp, 4 is an off-axis elliptical reflector, 5 is a bandpass filter, 6 is a flat reflect mirror, 7 is the optical fiber bundle, 8 is an imaging optics system, and 9 is the detector. Figure 3: Full diagram of the new densitometer. Figure 2: The structure diagram of the diffuse light source based on DOE. The off-axis elliptical reflector 4 has two focuses at the light axis, and the lamp 3 is placed on the first focus. The bandpass filter 5 selects the visual spectrum of the light. The flat reflecting mirror rotates the light to the vertical axis. The incident plane of DOE is on the second focus of the off-axis elliptical reflector 4. It must be pointed out that this focus is on the vertical axis, relatively. The detector system collects the flux from the sample or the opal (when there is no sample). The system is an imaging optics system. When the measurement starts, the sample is moved by a movement component to the measurement point.