Combining Scatter with Coatings

Transcription

1 Combining Scatter with Coatings INTRODUCTION During a raytracing process, rays encounter surfaces that might have a combination of reflection, transmission, absorption and scatter properties that split the rays into various components. FRED allocates flux values to each ray by looking at these surface properties in a specific order. The user needs to understand this order to be certain that the actual flux values created during the raytrace are as expected. This is demonstrated by considering a surface that has Lambertian scatter properties along with a userdefined specular reflection coefficient. EXPLANATION Depending on the assigned models, a ray incident on a surface could be split into specular reflected rays, specular transmitted rays, back scattered rays, forward scattered rays and absorbed rays. During this process, conservation of energy dictates that the sum of these transmitted, reflected and absorbed components is equal to the incident power flux. F trans + F fwdscat + F refl + F backscat + F abs = F inc FRED assigns the flux for each component of the above equation in a specific sequence. When a user wishes to define surfaces that have both scatter properties and reflection / transmission coatings assigned, knowing this order is critical to correctly defining the power coefficients for the individual components. The order that FRED follows during this power allocation is as follows: 1. FRED determines the flux in the back scattered rays: F backscat = TIS back * F inc (a) 2. FRED determines the flux in the forward scattered rays: F fwdscat = TIS fwd * F inc (b) 3. FRED determines the flux in the reflected specular rays: F refl = (1 TIS backscat TIS fwdscat )*R*F inc (c) 4. FRED determines the flux in the transmitted specular rays:

2 F trans = (1 TIS backscat TIS fwdscat )*T*F inc (d) 5. FRED attributes any remaining flux to be absorbed : F abs = F inc TIS backscat TIS fwdscat F refl F trans (e) Note: TIS backscat and TIS fwdscat are the Total Integrated Scatter values of the back and forward scattering respectively. EXAMPLE The significance of this sequence is shown in a simple example where the aim is to define a surface that has the following properties: a) a simple scatter model that defines 15% reflectance in a Lambertian profile. b) and a reflection coating that defines 55% specular reflection. (It is assumed that the remaining 30% power is absorbed.) Specular Reflected (55%) Back Scattered (15%) Fig 1. Schematic of example surface Assigning a new Lambertian scatter model and defining the TIS is straightforward. Fig 2. The Lambertian Scatter Model settings dialog

3 In this case the Refl coefficient is set to be 0.15 I.e. 15% of incident power. This is the TIS backscat component used in equations above. Defining the reflected flux takes a little more care. Since the aim is to define a surface that reflects 55% of the incident power in the specular direction it might be assumed that setting the reflection coefficient (R) of the coating to be 0.55 would be sufficient. However this is not correct and will actually define a model that has a specular reflection value 46.75%. This is because FRED has already allocated 15% of the incident flux to the scatter model. The reflection coefficient of 0.55 is actually applied to the remaining power after the scattering is taken into account. 55% * (1 0.15) = 46.75% To obtain a reflected scatter flux of 55% * F inc the reflection coefficient (R) of the coating is determined by equation (c) above and in this case needs to be: Thus R needs to be F refl = (1 TIS backscat )*R* F inc 0.55 = (1 0.15) *R Fig 3. The Sampled Coating settings dialog

4 VALIDATING It is quite simple to test the set up by defining a simple model that consists of a source, a plane surface with the desired coating and scatter properties, the Allow All Raytrace Control (with all Allowed Ray Operations checked), and DAE Analysis surfaces with the appropriate ray filters. Fig 4. FRED model including the DAE Analysis surface. The DAE filters allow the user to determine the contributions of the specular reflected power and the back scattered power individually. This can be done by looking at the integrated power automatically displayed in the output window when FRED calculates the Intensity on a Polar Grid. Fig 5.Ray filters for the DAE that will (left) only consider the specular reflected rays, (center) only consider the scattered rays and (right) only consider the absorbed rays. The figures below show the integrated power for these three ray filter settings.

5 Fig 6a. Total Integrated power when considering only the specular reflected rays Fig 6b. Total Integrated power when considering only the back scattered rays Fig 6c. Total Integrated power when considering only the absorbed rays It should be noted that the sum is equal to unity as these are the only operations defined in this model and therefore energy is conserved between these components. CLOSING REMARKS The above example considers the simple case of a surface that has backscatter properties sitting alongside coating properties that define a specular reflection coefficient. Models that also include transmission, forward scatter and absorption properties can also be defined without too much trouble if care is taken regarding the recipe (equations a e above) that FRED follows when assigning flux values.