Using both the scattering and coating capabilities in Non-Sequential ZEMAX, we can model a partially reflective (or optionally transmissive) surface which diffusely scatters only a fraction of the initial incident energy in a specific distribution. 

Assume that we wish to simulate a partially reflective (60% reflective) face of a rectangular volume which scatters 80% of this reflected light in a Lambertian distribution.  The other 20% is specularly reflected.  Using three Non-Sequential Objects, we may quickly and easily demonstrate how to apply Lambertian scattering and ideal coatings to produce the desired effects.

To avoid the redundancy of having to create the file from scratch, please download the attached Non-Sequential ZEMAX file on the very last page of this article.

FILE:  "Partial Reflection and Scattering.ZMX"

As the file currently exists, a single Source Ray is incident onto the front face of a Rectangular Volume made of material type MIRROR.  The ray from the source perfectly reflects back onto itself and is incident on the detector plane.  Currently, there are no coatings and/or scattering profiles defined on any single surface of the Rectangular Volume.

From a Monte Carlo Ray Trace without considering polarization, a single ray illuminates the centermost pixel of the detector with a total power of 1W.

Defining and Applying Coatings in ZEMAX is a topic unto itself, and is covered in detail in the “Defining coatings in ZEMAX” section of Chapter 20 in the ZEMAX User’s Guide.  ZEMAX can model any type of thin-film coating, including multilayer dielectric and metallic coatings.  However, we will limit our discussion in this article to constructing and applying simple, ideal coatings in ZEMAX. 

Like all coatings in ZEMAX, ideal coatings are created in a coating file consisting of sections of data defining materials, tapers, and coatings.  For one ideal coating, the syntax is simply:

IDEAL <name> <Transmitted Intensity> <Reflected Intensity>

IDEAL coatings are defined by only the intensity transmission and reflection coefficients, and are independent of ray wavelength or angle of incidence.  The absorption coefficient is computed automatically via A = 1.0 – R – T, to conserve energy.

IDEAL 60Reflect 40 60

will transmit 40% of the ray energy and reflect 60% of the energy, independent of the wavelength, incident angle; etc. 

The coatings made available in any single design in ZEMAX are defined in the “Coating File” as listed in the System General dialog.



The COATING.DAT file, which is the default coating file, is simply an ASCII text file which consists of sections of data relative to various types of coatings in ZEMAX.  This file may be modified to include other user-defined coatings.  If any additions or changes are made, it is always recommended that the file be saved under a different name.  Otherwise, updated installations of ZEMAX can overwrite the default coating file. 

Open the COATING.DAT file via a text editor/viewer (such as Notepad).  There are several simple ideal coatings which currently exist in the file, but none of which match the reflection/transmission ratio that we wish to model in this demonstration.



In the current example, we want 60% reflection from a mirrored surface.  Thus, the transmission is 40%.  We need to insert an ideal coating which represents these percentages:


Once the new ideal coating has been entered into the coating file, save the file under an appropriate filename, such as MYCOATING.DAT.  Note that the extension MUST end in .DAT and saved into the same directory as the COATING.DAT file.

For ZEMAX to recognize the newly created ideal coating, you must choose your new catalog from the “Coating File” field in the System General dialog.



To apply the coating the front face of the Rectangular Volume, open the Object Properties dialog for Object 2, and select the “Coating/Scattering” tab.  The first available menu under this tab is the “Coating/Scatter Group.”  Each object, depending upon its type, has different coating/scatter groups.  For the Rectangular Volume Object, there are three groups:  0, Side Faces; 1, Front Face; and 2, Back Face.



Because of this, different coatings and scattering profiles may be applied to different faces of the object.  For the current example, select the “Coating/Scatter Group” as 1, Front Face. 

By default, no coating is applied to any surface.  For the front face of the rectangular volume, the newly created ideal coating may be applied via the “Coating” pull-down menu just below the Coating/Scatter Group selection.



Once the appropriate coating is selected, press “OK” to accept the changes and exit the Object Properties dialog.  To verify that the coating is applied and is working properly, we can run a Monte Carlo Ray Trace with Use Polarization checked.



As expected, the total power of the ray reaching the detector has been reduced, and is exactly 60% of the initial power of the ray:

Just like coatings, scattering profiles can be selected for each Coating/Scatter Group on a particular object.  In the current example, re-open the Object Properties dialog for the Rectangular Volume.  Underneath the Coating/Scattering tab, make sure to re-select the 1, Front Face as the “Coating/Scatter Group.” 

There are various built-in scattering profiles in ZEMAX, one of which is Lambertian.  By default, “No Scattering” is selected.  Once the scattering is changed to “Lambertian,” there are two essential data entry fields which become activated: Scatter Fraction and Number of Rays.  The fraction must be between zero (no rays will be scattered) and 1.0 (every ray will be scattered).  How ZEMAX treats these values depends upon whether or not Ray Splitting is turned on (via each specific analysis feature).  For a complete discussion, please refer to the “Scattering” section in Chapter 12 of the ZEMAX User’s Guide.

For the current example, set the scattering to Lambertian and the Scatter Fraction and Number of Rays to 0.8 and 5 respectively.  Therefore, when splitting is turned on, then the scattered energy will be evenly divided amongst the five scattered rays.  The specular ray, on the other hand, will receive a fraction of the total reflected/scattered energy equal to 1.0 – Scatter Fraction.  In this case, the specular ray will receive 0.2W.



Select “OK” to make the applied changes.

In order to verify the changes made to the front face of the Rectangular Volume, choose Fletch Rays, Split Rays, Scatter Rays, and Use Polarization in the settings of the NSC 3D Layout.  Note that the initial source ray is scattered (with Lambertian probability) into 5 rays, for a total of 6 rays reaching the detector.



And, if we perform yet another Monte Carlo Ray Trace, the total power of these rays (provided that all 5 scattered rays hit the detector) is equivalent to 0.6 Watts, or 60% of the initial power.



And, tracing 2.5 million rays and increasing the detector resolution, we can observe that the highest radiant intensity is at normal incidence, which corresponds to the specular, reflected portion of the energy:



So, we have easily created a partially reflective scattering surface in ZEMAX.  The tools and concepts used in this example may be applied to much more complex systems, but the basis and fundamental approach to applying coatings and scattering profiles remains the same.

Let’s assume that we wanted to apply the same coating and scatter profiles to the back and side faces of the rectangular volume for further analysis.  Using the saved profile feature in the Coating/Scattering tab, these settings may be saved and quickly applied to other Coating/Scatter Groups, including those of other objects.

Once the desired settings have been applied, click the “Save” button near the upper-right hand corner of the Coating/Scattering tab of the Object Properties dialog.



In the Save New Profile dialog, you may choose to enter the desired Profile Name which will correspond to the saved coating and scattering settings:



This profile can then be chosen for the other coating/scattering groups of the Rectangular Volume:

A partially reflective scattering surface may be constructed in ZEMAX by applying an ideal coating in addition to a specific scattering profile.  Underneath the Coating/Scattering tab of the Object Properties dialog in Non-Sequential ZEMAX, various coatings and scattering profiles can be applied to different faces (known as Coating/Scatter Groups) of an object. 

By accounting for polarization, split rays, and scatter rays, the options for modeling different scattering type surfaces are virtually endless.

References

ZEMAX Optical Design Program User’s Guide, ZEMAX Development Corporation