Interferograms of surfaces contain information on irregularity, including Rotationally Symmetric Irregularity (RSI), slope errors that determine the middle spatial frequencies, and other manufacturing surface figure errors. These manufacturing errors depend on the type of polishing performed on spherical or aspheric surfaces, which can be conventional pitch polishing, high speed polishing, as well as polishing using magnetorheological fluid, a polishing method known as MRF. As it is difficult to model all these types of surface figure effects using Zernike terms, the best and fastest way to determine how surface errors can affect the overall system level performance is to attach the measured interferograms directly to the optical surfaces in OpticStudio. In this article, we demonstrate how to import interferometry measurement data to OpticStudio depending on the surface shape and orientation.

Authored By Apostolos Deslis, Dan Sykora (JENOPTIK Optical Systems LLC) and Csilla Timar-Fulep

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Introduction

Interferogram data in an .INT file format can be converted into .DAT file format and attached to the Grid Sag surface type in OpticStudio. However, users may need to adjust the orientation of the interferogram through rotations, flips, or inversions before the data import. How the data needs to be oriented depends on the surface shape and which lens face the data was measured from.

To understand the complete workflow, we shall perform a gedanken (thought) experiment. Let us assume that we have an equi-concave, or equi-convex lens. In addition, let us assume that the interferograms from each of the surfaces are identical to each other. This is highly unlikely in real life, but we shall make the assumption for this exercise.

The question is the following: Can we attach the same interferogram, since both are identical, to both the left and right side of a lens model in OpticStudio to simulate its measured performance? The answer is no, we cannot, we need to adjust the orientation as we shall see in the discussion later.

Interferometer File Formats

Zygo uses the native XXX.DAT file format as its internal representation, however it exports measurement results into the widely used XXX.INT interferometric file format, shared by other interferometer manufacturers too. In order to base our model off of real measurement data, we must have a Zygo or another interferometer generated XXX.INT file.

Then, the XXX.INT interferometric file needs to be converted to OpticStudio’s YYY.DAT file format, to be attached to a Grid Sag surface. The INT Grid to OpticStudio DAT tool under the File > Convert > Convert File Formats menu provides a built-in solution for this data conversion from interferometer manufacturers to OpticStudio. Further details about the OpticStudio Grid Sag YYY.DAT file format and its programmatic creation can be found in the following knowledgebase articles:

How to use the Grid Sag surface type

How to write a Grid Sag DAT file programmatically

At the file conversion stage, care must be taken with the file nomenclature, to prevent the OpticStudio YYY.DAT file to overwrite the original internal Zygo XXX.DAT file.

Interferogram Data Orientation on Optical Surfaces

To understand the required adjustments before attaching interferogram data files to optical surfaces in OpticStudio, let’s review the orientations and the mapping between the measurement data and the OpticStudio convention. In this section, we discuss how to prepare the measurement data depending on the shape of the lens, i.e. convex or concave, and on the surface orientation.

Convex Surface

First, let’s review the data orientation in case of convex optical elements. The figure below explains the mapping relationship between a convex surface and the generated interferogram file. Fiducials on the surface under test have the same orientation in the interferogram.

Based on this, the following adjustment steps are required as preparation before attaching the measured interferogram data to the surfaces in OpticStudio, depending on whether the surface is reflective or refractive, and whether it is the front (left) or rear (right) surface of a refractive element.

• Reflective surface: Attach the OpticStudio generated YYY.DAT file directly to the surface.
• Front (left) surface of refractive element: Attach the OpticStudio generated YYY.DAT file directly to the surface.
• Rear (right) surface of refractive element: Prior to attaching the YYY.DAT file to the surface, its orientation needs to be adjusted. Since the Z-axis orientation is the same for both the front and back surfaces of the lens in OpticStudio, which means that the local errors change sign, the measured interferogram data has to be inverted. Besides, as the X-axis orientation is the same for the front and back surfaces of the lens in OpticStudio, which means left-right flipping for the local errors, the data also needs to be flipped about the X-axis.
  

There are a couple of ways to do the adjustments required for the rear surface of the lens. The first option is to use the Zygo software if one has in-house access to a Zygo interferometer. The second way is to use the Python script attached to this article, which inverts the interferogram, i.e. changes the sign of the Z values in the .DAT file, and also flips the sag map about the X-axis. In order to use the script, Python has to be installed on the computer. Further references about the Python installation process, available Integrated Development Environments, and connection options to OpticStudio via the ZOS-API interface can be found in these knowledgebase articles:

Getting started with Python

ZOS-API using Python.NET

Using the attached flipGridSag.py script, the OpticsStudio-compatible YYY.DAT file can be selected, and then the data can be inverted and flipped about the X-axis. The generated output file is created in the same folder as the original OpticStudio YYY.DAT file with the extension _INV_FLIPX.DAT added to the original file name.

Concave surface

Similarly, let’s look at the data orientation in the case of concave optical elements. The figure below explains the mapping relationship between a concave surface and the generated interferogram data. Fiducials on the concave surface under test are flipped in the interferogram in both X and Y directions, due to the intermediate focus in front of the surface. This operation is equivalent to a 180 degrees rotation about the Z-axis, which can be easily accomplished in OpticStudio either by defining the Tilt Z parameter under the Surface Tilt/Decenter properties or by using Coordinate Breaks and defining the Tilt About Z parameter there. For further discussion about using Coordinate Breaks, please take a look at this knowledgebase article:

How to tilt and decenter a sequential optical component

Based on this, the following preparation steps are required before attaching the measured interferogram data to the surfaces in OpticStudio, depending on whether the surface is reflective or refractive, and whether it is the front (left) or rear (right) surface of a refractive element.

• Reflective surface: Attach the OpticStudio generated YYY.DAT file to the surface and rotate it by 180 degrees about the Z-axis.
• Front (left) surface of refractive element: Attach the OpticStudio generated YYY.DAT file to the surface and rotate it by 180 degrees about the Z-axis.
• Rear (right) surface of refractive element: Invert the YYY.DAT file and flip about the X-axis prior to attaching to the surface, then also rotate by 180 degrees about the Z-axis. The interferometry data file can easily be inverted and flipped by running the attached flipGridSag.py script.
  

Importing interferograms to OpticStudio

Based on the theoretical considerations discussed in the previous section, let’s study real use cases. Import measured interferogram data into OpticStudio, and then verify that the simulation results are in good agreement with the measurement results if the preparation steps suggested above are followed.

Convex mirror

As a first case, let’s use a double-pass system with a convex mirror with the following specifications:

• Clear Semi-Diameter: 25.85 mm
• Radius: 111.9837 mm [Note: the radius is indicated in the XXX.DAT data file generated by Zygo]

The picture below shows the Zygo interferogram of the convex surface, with an aperture diameter of 51.7 mm. Based on the interferometry measurement results of the surface the Peak to Valley wavefront error equals 0.433 waves and the RMS wavefront error equals 0.084 waves at the 632.8 nm measurement wavelength.

From Zygo the measured interferogram can be exported to a .INT file. To convert the .INT file into an OpticStudio compatible .DAT file, which can be directly imported to a Grid Sag surface, we can use the INT Grid to OpticsStudio DAT converter under File > Convert > Convert File Formats, as shown below.

In the Convert File Format tool, we can select the XXX.INT file from Zygo to convert, and we can define the aperture diameter used in the original interferogram which in this case is 51.7 mm.

In order to verify that we can attach the YYY.DAT file generated by OpticStudio to the mirror surface directly, we create a double-pass system with Paraxial lenses, where the Paraxial lens refracts the collimated incoming beam in such a way that all rays hit the mirror surface perpendicularly. This setup exactly mimics how interferometers measure the surface shape.

First, in the System Explorer, under the Aperture tab, set the Aperture Type to Float By Stop Size. Then in the Lens Data Editor, set the STOP surface to be located on the mirror surface, and set its Semi-Diameter to 25.85 mm, and its Radius to 111.9837 mm according to the measurement results.

Next, in the System Explorer, under the Wavelengths tab, set the Wavelength to 632.8 nm, which is the wavelength used in the interferometry measurement.

As a next step, add a Paraxial surface before the mirror surface with a 38.0163 mm Thickness, and a 150 mm Focal Length to imitate a transmission sphere. Then, use the Make Double Pass tool to create a second pass through the previously specified surfaces, which represents the reflection propagating back through the system. As in this case the paraxial lens is used at infinite conjugates with a collimated incoming beam, its OPD Mode parameter should be set to 2. Further references about the Paraxial surface type can be found here:

How to parametrize a "Paraxial lens" ?

Finally, change the mirror surface type to Grid Sag surface, and then the OpticsStudio generated YYY.DAT file can be imported to surface under the Surface Properties > Import tab as shown below:

At this point, the double-pass system modeling the measurement of a convex surface via interferometry should look like the following.

Now, we can inspect the Surface Sag plot, to verify the shape of the mirror. In order to best visualize the small manufacturing errors, set the Remove option to Base Radius, to subtract the base radius of curvature from the current sag and report only the difference. As expected, based on the measurement results, the Surface Sag map shows a peak at the center of the surface. This means that from a qualitative perspective, the data matches between the Zygo measurement and the OpticStudio simulation methods. 

In order to numerically verify the results as well, besides the qualitative analysis, we can use the Wavefront Map tool. As this is a double-pass model simulating how interferometers measure the surface shape, we expect the Peak to Valley (0.433 waves) and RMS (0.084 waves) wavefront errors to double compared to the measured values, since the measurement results are reported as in transmission. Let’s double-check this on the Wavefront Map.

As expected, the numerical values of the Peak to Valley (0.8686 waves) and RMS (0.1617 waves) wavefront errors are twice as large in the double-pass simulation setup as reported in case of the measurement. The reason why the shape of the Wavefront Map seems to be inverted, showing a valley in the center and not a peak, is because in OpticStudio the wavefront error is defined as the Optical Path Difference between the chief ray and the pupil ray. This can be interpreted as viewing the wavefront in the direction of the ray propagation, so in this case looking from the mirror towards the Image plane. This is opposite of how Zygo looks at it, from the source to the mirror, so this explains the flip in the wavefront shape.

Based on this first experiment with the convex mirror, we can conclude that the OpticStudio generated YYY.DAT data file can be directly attached to the surface model, and both the qualitative and quantitative results are in good agreement with the expectations.

Bi-Convex lens

As a next use case, let’s model a bi-convex lens with the same specifications as before:

• Clear Semi-Diameter: 25.85 mm
• Radius: 111.9837 mm [Note: the radius is indicated in the XXX.DAT data file generated by Zygo]
• Peak to Valley wavefront error: 0.433 waves, RMS wavefront error: 0.084 waves at 632.8 nm

To verify that we can attach the OpticStudio generated YYY.DAT file directly to the front surface of the lens and use the inverted and flipped data file on the rear surface of the lens, we create a lens system, where the nominal bi-convex lens together with an optimal additional lens perfectly focuses the collimated incoming beam without residual wavefront error. We use a multi-configuration setup, where the first configuration contains the nominal bi-convex lens, while the second configuration adds the interferometry results too.

Similarly as before, the Aperture Type is set to Float By Stop Size, but the STOP surface is a dummy surface with 25.85 mm Semi-Diameter, located 5 mm in front of the bi-convex lens.

The radii and back Conic constant of the extra lens after the tested bi-convex lens is optimized for the smallest RMS Wavefront error in the nominal setup. As a consequence, the nominal configuration has essentially 0 wavefront error (RMS wavefront error: 0.0001 waves).

After importing the OpticsStudio generated YYY.DAT file to the front surface of the lens, and importing the flipped and inverted data file to the rear surface of the lens, the multi-configuration OpticStudio model, looks like the following.

We can verify the shape of the lens on the Surface Sag plots. As expected, the shape of the rear surface is inverted compared to the front surface, since the Z-axis orientation is the same, which means that the local features are reversed. This shows the same behavior as the Radius sign convention in OpticStudio.

Compared to the previous scenario, in this case the Wavefront Map analysis can only be used as a qualitative check as well, since the exact wavefront error value depends on the thickness of the lens and on the rays incident angle too. As expected, in this case the Wavefront Map shows a peak at the center, similarly as the Zygo measurement shown in the Convex Mirror section of the article, as both look the wavefront in the same direction, from the object to the image plane.

Based on this experiment with the bi-convex lens, we can conclude that the OpticStudio generated YYY.DAT data file can be directly attached to the front surface of the lens, while the inverted and flipped data file can be used for the rear surface of the lens. The qualitative results are in good agreement with the measured Zygo data.

Concave mirror

Next, let’s use a double-pass system with a concave mirror with the following specifications:

• Clear Semi-Diameter: 21.1 mm
• Radius: 78.587 mm [Note: the radius is indicated in the XXX.DAT data file generated by Zygo]

The picture below shows the Zygo interferogram of the concave surface, with an aperture diameter of 42.2 mm. Based on the interferometry results, the Peak to Valley wavefront error equals 0.306 waves and the RMS wavefront error equals 0.063 waves at 632.8 nm.

Similarly, as for the convex case, the measured interferogram can be exported to a .INT file, which can be converted to an OpticStudio compatible .DAT file, using the INT Grid to OpticStudio DAT converter tool. In the Convert File Format tool, we can select the XXX.INT file from Zygo, and we can define the aperture diameter, which is 42.2 mm in this case. The converted the .DAT file then can be directly imported to a Grid Sag surface in Opticstudio.

After the file conversion, we can set up a double-pass system as in case of the convex mirror, to verify that we can attach the generated YYY.DAT file to the mirror surface directly. Again, in order to accurately mimic Zygo interferometry measurements, we use Paraxial lenses in the setup to refract the collimated incoming beam in such a way that all rays hit the mirror surface perpendicularly.

As in case of the convex mirror, the Aperture Type is set to Float By Stop Size, and the STOP is located on the reflective surface. The mirror Semi-Diameter is set to 21.1 mm, and its Radius is set to -78.587 mm according to the measurement results. The Wavelength is set to the 632.8 nm measurement wavelength.

In this case we use a Paraxial surface with a 100 mm Thickness and Focal Length to mimic transmission sphere and the intermediate focus in front of the concave mirror. The Thickness from the intermediate focus to the mirror equals the Radius of the mirror to ensure normal incident.

Finally, a pair of Coordinate Breaks is used surrounding the Grid Sag mirror surface with a Tilt About Z parameter set to 180 degrees, to account for the proper orientation of the surface. At this point, the double-pass system modeling the measurement of a concave surface via interferometry should look like the following.

We can verify the shape of the mirror based on the Surface Sag plot. Similar to the Convex Mirror case, for analyzing the Surface Sag shape the Base Radius is removed from the current sag profile to focus only the small manufacturing errors. As expected, based on the measurements, the Surface Sag map shows a valley at the center of the surface.

To double-check the numerical results as well, we can use the Wavefront Map analysis. Since it is a double-pass model, we expect the Peak to Valley (0.306 waves) and RMS (0.063 waves) wavefront error values to double compared to the measurement results reported as in transmission.

As expected, the numerical values of the Peak to Valley (0.6106 waves) and RMS (0.1250 waves) wavefront errors are twice as large in the double-pass simulation setup as in case of the interferometry measurements, where the results are reported in transmission. In this mirror case again, the Wavefront Map seems to be inverted compared to the Zygo results, however this inversion is expected due to the wavefront error definition in OpticStudio, using the Optical Path Difference between the chief ray and the pupil ray.

Based on this experiment with the concave mirror, we can conclude that the OpticStudio generated YYY.DAT data file can be directly attached to the surface model, however in order to properly render the data on the plots, the mirror surface needs to be rotated by 180 degrees about the Z-axis. Once it is completed, both the qualitative and quantitative results are in good agreement with the measured data.

Bi-Concave lens

Finally, let’s model a bi-concave lens with the same specifications as before:

• Clear Semi-Diameter: 21.1 mm
• Radius: 78.587 mm [Note: the radius is indicated in the XXX.DAT data file generated by Zygo]
• Peak to Valley wavefront error: 0.306 waves, RMS wavefront error: 0.063 waves at 632.8 nm

In order to verify that we can attach the OpticStudio generated YYY.DAT file to the front surface of the lens and use the inverted and flipped data file on the rear surface of the lens, we create a multi-configuration system, where the nominal bi-concave lens surrounded by two additional optimal lenses perfectly focuses the collimated incoming beam without residual wavefront error. In the setup, the first configuration contains the nominal bi-concave lens, while the second configuration adds the interferometry data as well.

Similarly as in case of the bi-convex lens, the Aperture Type is set to Float By Stop Size, but the STOP surface is a dummy surface with 21 mm Semi-Diameter, located 15 mm in front of the first lens.
The radii and thicknesses of the extra lenses are optimized for the smallest RMS Wavefront error in the nominal setup. Consequently, the nominal configuration has essentially zero wavefront error (RMS wavefront error: 0.0005 waves).

After importing the OpticsStudio generated YYY.DAT file to the front surface of the lens, and importing the flipped and inverted data file to the rear surface of the lens, the multi-configuration setup looks like the following. Please note, that Coordinate Breaks are used again surrounding the lens surfaces with the Tilt About Z parameter set to 180 degrees, to adjust the surfaces to the proper orientation.

We can use the Surface Sag maps to verify the shape of the lens. As expected, the rear surface is inverted compared to the front surface of the lens, similarly as in case of the bi-convex lens.

Again, in this case, the Wavefront Map analysis can only be used as a qualitative check. As expected, the Wavefront Map shows a valley at the center, similarly as the Zygo measurement shown in the Concave Mirror section of the article, as both look at the wavefront in the same direction, from the object to the image plane.

Based on this last experiment with the bi-concave lens, we can conclude that the OpticStudio generated YYY.DAT data file can be attached to the front surface of the lens, while the inverted and flipped data file can be used for the rear surface of the lens. Again, due to the concave surface shape, extra Coordinate Breaks are used around the surface to properly orient the interferometric data. The qualitative results are in good agreement with the measured data.

Summary

In this article, we have discussed how the measured interferogram data needs to be adjusted in orientation through rotations, flips, and inversions before the data import to OpticStudio, depending on the shape of the surface and whether it is the front or rear face of the lens. Based on the test results, the required preparation steps can be summarized as below.

Convex Surface

• Reflective surface: Attach the OpticStudio generated YYY.DAT file directly to the surface.
• Front (left) surface of refractive element: Attach the OpticStudio generated YYY.DAT file directly to the surface.
• Rear (right) surface of refractive element: Invert the YYY.DAT file and flip about the X-axis prior to attaching to the surface. This can be easily accomplished by running the attached flipGridSag.py Python script.

Concave Surface

• Reflective surface: Attach the OpticStudio generated YYY.DAT file directly to the surface, and then rotate the surface by 180 degrees about the Z-axis.
• Front (left) surface of refractive element: Attach the OpticStudio generated YYY.DAT file directly to the surface, and then rotate the surface by 180 degrees about the Z-axis.
• Rear (right) surface of refractive element: Invert the YYY.DAT file and flip about the X-axis prior to attaching to the surface. This orientation adjustment can be accomplished by running the attached flipGridSag.py Python script. Once the data is imported, then also rotate the surface by 180 degrees about the Z-axis.
  

For further reference, an OpticStudio file is included in the Article Attachments for each of the above discussed scenarios.