- How to analyze stray light in Non-Sequential ZEMAX via use of the Filter String
- What Filter Strings are and how to write them.
- How to locate rays with specific properties via the Filter String.
- How to use Filter Strings with the Layout plots, Detector Viewer, and Ray Database Viewer.
This article is accompanied by a sample file which is used to demonstrate some of the powerful uses of the Filter String. The file is available via download from the very last page of the article.
ZEMAX's Non-Sequential ray tracing capabilties can further be extended to finding rays which have specific characteristcs or properties. For example, imagine you are studying the stray light in a telescope:
- How significant are rays which "ghost" reflect off of various surfaces (both mechanical and optical)?
- Rays which are experience multiple reflections may be important, but how signficant are those which experience more than four reflections?
- How effective is a strategically placed baffle in terms of limiting the amount of stray light on the detector?
Each of these, and many similar questions, may be answered conveniently using what are known as Filter Strings in ZEMAX. Filter strings are a means of defining a specific "test" that each ray must pass before it is displayed (on the Layouts or Detector Viewer) or reported in the Ray Database.
It is important to note that filter strings can be used to perform a full Opto-Mechanical assessment of stray light. Therefore, ZEMAX will consider partial reflections from optics, reflections from mechanical components, and scattering from both optics and mechanics.
The filter string syntax consists of logical operations between flags that indicate if one segment within a ray hit, missed, reflected, refracted, scattered, diffracted, or ghost reflected from an object within an NSC group. A complete listing of the availabe filter string flags and discussion may be found in "The filter string" section of Chapter 12 in the ZEMAX Users's Guide.
In this article, we will demonstrate where filter strings are entered, how they are applied, and how they may be used to analyze rays with certain optical properties. To do so, we will evaluate the amount of "moon" light that gets into the image area of a Cassegrain-type telescope when viewing a distant star. The basic concept? A large number of rays will be traced and saved to a database. We will then "dig" through this ray database to find rays which have explicit properties.
Imagine viewing a star with a telescope during a full moon. Some of the light from the moon, though off-axis (where the axis is described as the distance from the star to the vertex of the telescope barrell), reaches the detector plane (camera) of the telescope. We need to determine exactly how much stray light from the moon is reaching the detector.
This scenario is simulated using the following purely Non-Sequential (NS) ZEMAX lens file. Download the file attached to this article and open it from within ZEMAX.
 | FILE: "Stray Light_Telescope.ZMX" |
Note: For the purposes of demonstrating filter strings in ZEMAX, it is assumed that you are familiar with the standard procedure of performing a Non-Sequential (NS) Ray Trace and viewing the results on the Detector Viewer. If you are unfamiliar with these concepts, please refer to the article on Creating a Basic Non-Sequential System.
The moon in the telescope model is represented by an off-axis Source Ellipse. The moon is approximated as a collimated source, so rays from the moon (in green above) are parallel to one another. Similarly, the object of interest is represented by an on-axis collimated Source Ellipse. As in a typical Cassegrain-like telescope design, collimated rays (the blue rays in the layout above) from an on axis field focus to a well-corrected spot at the image plane. However, some of the rays(from both the moon and the star) do not follow the desired sequence of optical surfaces, yet still reach the detector.
Perform an initial NS ray trace with Use Polarization, Ignore Errors, Split Rays, Scatter Rays, and Save Rays all checked. Save the rays with any desired file name. Note that rays MUST be saved first before filter strings can be applied to the Ray Database and Detector Viewers! For the time being, we will leave the "Filter" entry blank since filters may also be applied later on in the settings of individual analysis features.
Note that the "Lost Energy" values due to thresholds and errors are very important, and should be reviewed with great care to ensure accurate evaluation of the current ray sample. If a ray falls below the minimum energy threshold for tracing, the ray will be terminated. The minimum relative and absolute energy thesholds are defined by the "Minimum Relative Ray Intensity" and "Minimum Absolute Ray Intensity" entries under the Non-Sequential tab of the System General dialog. To reduce the caluclation times in the current example, the Minimum Relative Ray Intensity is set to 1.00E-007. This value may need to be reduced in some applications in order to reduce the lost energy due to thresholds.
Energy loss due to errors is extremely important, and it is imperative that the magnitude of these errors are made as small as possible. There are several reasons why these errors occur, which are thoroughly discussed in an article entitled How To Locate Geometry Errors.
If the reported energy loss due to errors is significant, it is sometimes useful to review the propagation of the ray in great detail to locate the probable cause of error. This can be done via filter strings in the Ray Database Viewer. The Ray Database Viewer may be opened by selecting "Analysis > Database > Ray Database Viewer" or by pressing the "Rdb" button on the button bar. In the settings of the Ray Database Viewer, select the previously saved database file from the "File" pull down menu. Now, the Ray Database settings allow the option to apply a filter. The filter string, "Z", will only display those rays which have fatal errors. To apply this filter string, first check the "Apply Filter" box and type the string into the appropriate entry.
The filter may be applied to a small portion of the saved database by adjusting the "First Ray" and "Last Ray" field appropriately. Or, alternatively, the entire database may be processed if the "Last Ray" is set to the total number of rays launched in the initial ray trace.
In this example, the energy loss due to errors was zero, so not a single ray is displayed in the Ray Database Viewer once the error filter is applied. However, the filter capability in the Ray Database Viewer is not limited to displaying rays with errors. Any single filter, or any combination of filters, may be applied to the saved ray database; only those rays which "pass" the test will be displayed for more in-depth analysis.
From the Detector Viewer, it is clearly visible that the majority of the energy is at the centermost pixels of the detector. However, even on a log scale, it is very difficult to discern how much total power is associated with the rays which fall outside this central region.
To determine the fraction of total power which is associated with the moonlight, let's first isolate the rays from the moon. To do so, we may set the "# Analysis Rays" for Source Object 1 to zero and re-run the Ray Trace, or we may utilize the filter string to only display those rays which originated from a specific source. For the purposes of demonstrating the effectiveness of the filter strings, we will choose the latter of the two.
Filter strings may be applied to 3D Layouts, Detector Viewers, and (as we have already seen) within the Ray Database Viewer. Within the settings of each of these analysis tools, the desired filter string may be typed into the "Filter" entry. We may further demonstrate some of these capabilities using the current example file.
Within the settings of the Detector Viewer, select the previously saved .ZRD file from the "Ray Database" pull down menu. Once the desired Ray Database is selected, the "Filter" entry becomes enabled.
The "On" filter string flag will filter the database for only those rays which originated from source number n. Since we wish to only display those rays which originate from the moon (Source Object 2), the filter string "O2" can be applied. Note that the "O" is the letter O, not the number 0.
Depending upon the size of the saved ray database and the complexity of the string, it may take ZEMAX some time to process the data. Once complete, the Detector Viewer should show the filtered ray data.
Note that the data in the bottom portion of the Detector Viewer displays both the chosen ray database file and the filter string applied. Therefore, the settings need not be re-opened to verify which filter has been applied to the data you are viewing.
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From the filtered Detector Viewer in the present example, the "hot spot" is no longer present, which was undoubtedly the image of the star (rays originating from Source 1)
For the current ray trace, roughly 8.531E-006 Watts of the Moon's initial total power reaches the camera. But, as the moon is much brighter than the star, 10-5 rejection against stray moonlight may be inadequate, so it may be desirable to reduce the amount of stray moonlight to achieve better resolution of the image of the star. There are many methods which could be used in attempt to reduce the stray light from the moon. However, these topics go beyond the scope of this article, and will not be covered: we will concentrate on identifying the sources of the stray light in this article.
(Q2) Do stray rays come from a preferential region of the moon?
Detector Object 11, as you might imagine, is not well suited to answer this question. However, as was mentioned earlier, filter strings may also be applied to Layouts. In the current example, open the settings of the NSC 3D Layout, and once again select the previously saved .ZRD file from the "Ray Database" pull down menu. Displaying the entire ray database on the layout would become too crowded to perform any substantial analysis, so we will apply an appropriate filter in a moment.
It is important to note that filter string flags may be used alone, or they may be combined using logical operands. Some of the more common logical operands include: "&" (Logical AND), "|" (Logical OR), "^" (Exclusive OR), and "!" (Logical NOT). This is extremely useful when filtering for rays with multiple specific properties.
To demonstrate, let's filter for rays which still originate from the moon AND which reach the camera. Note that although the second portion of the string was not necssary when viewing the results from the Detector Viewer, we must explicitly add this flag to the string in the layout. Otherwise, all rays from the moon will be displayed, whether they reach the detector or not. To represent the second argument, the "Hn" flag may be used. The "Hn" flag represents rays which hit object n.
The filtered NSC 3D Layout in this case does not really indicate that rays come from a preferential region of the moon. As expected, rays within the center region of the Source Ellipse do not make it to the detector since they are blocked by the secondary mirror and the baffle surrounding this secondary. Since the number of rays which "pass" the filter is so large, and since ZEMAX must re-evaluate the filter each time the plot is rotated, it is difficult to glean any productive, additional information from the layout in the current sample file. Nevertheless, this methodology can certainly prove to be useful in other circumstances.
Y Position: 1.0
Z Position: -9.0
Tilt About X: 5.0
X Half Width: 6.1
Y Half Width: 6.1
# X Pixels: 50
# Y Pixels: 50
Leave all other parameters as the defualt. Note that this Detector Rectangle is placed directly in front of the moon. This way, using the filter string capabilities once again, we can better visualize the distribution of those rays which originate from the moon and hit the camera. Once the new Detector Rectangle is defined, open a new Detector Viewer to view Detector Object 12 (remember, the settings must be set correctly to show this).
If we perform a new ray trace and save the rays to a new database name, such as "Stray Light_Telescope_1A.ZRD," we can see the initial ray distribution on the newly defined detector:
Since no current filter is applied, the irradiance distribution on this detector includes rays from both sources. Again, we are only concerned with rays which originate from the moon AND reach the detector. Therefore, let's apply the following filter to Detector Object 12:
Once the filtered data is processed and displayed, it is much easier to observe the distribution of rays from the moon which actually reach the detector plane. It is apparent that undesired, stray rays at the detector plane, do indeed originate from "preferential" regions of the moon. These regions are highlighted in the Detector Viewer below. This information may be useful in determining which of the various stray light reduction techniques could be used to reduce the undesired light from the moon.
As you may recall from the initial ray trace, a definitive, rotationally symmetric ring surrounded the hot spot of the detector.
It is possible that this ring of rays is due to multiple reflections off of the currently uncoated, FIRST CORRECTOR lens (Object 3). To confirm this, we may again use the filter string capabilities.
(Q3) How are stray rays caused by multiple reflection in the first reflector affecting the total power at the camera?
The flag "Gn" refers to rays which are ghost reflected from parent segment's object n. This flag only gets set for ray segments reflected from refractive objects when ray splitting is activated. Let's observe the ray distribution at the camera from those rays (from both the star and the moon) which have ghost reflected from the first correcting lens. 
The "ring" of rays are undoubtedly due to ghost reflections from the corrector lens, and accounts for a small, but measurable fraction (5.780E-006) of the total power on the detector plane. To reduce the significance of these undesired rays on the camera, we may coat the corrector lens with an anti-reflective coating.
Open the Object Properties dialog for Object 3 and place an AR coating on both the front and back faces of the corrector. This is a single-layer MgF2 coatings optimized for the current primary wavelength.
When the coatings have been applied, re-run a NS ray trace and save the rays to a different file name.
Once the ray trace is complete, make sure that the appropriate .ZRD file is selected in the Detector Viewer and apply the same ghost filter, G3. By coating the corrector lens, we have effectively eliminated the spurious "ring" of rays and reduced the total "ghosted" energy by an order of magnitude.
Filter strings can be used to perform a full-optomechanical assessment of stray light, and will consider reflections, scattering, coatings; etc to both mechanical and optical components.
Filter strings may be applied to the initial Ray Trace/Detector Control dialog, Layouts, Detector Viewers, and within the Ray Database Viewer. Each of these analysis tools, in conjunction with the filter string, may be used in many different ways to isolate rays with specific properties. There are many filter string flags which are built into ZEMAX, and with the support of logical flags, the possibilities are endless.
REFERENCES
ZEMAX Optical Design Program User's Guide, ZEMAX Development Corporation