How to generate cross-section and moment data for an extended source using Geometric Image Analysis

Geometric Image Analysis is a powerful tool for investigating the behavior of optical systems that are well-described by geometric optics. This article describes how to use the Geometric Image Analysis feature to generate cross-section plots of and moment data (centroid, RMS width) for an extended source. This feature may also be used to generate results for a point source (in the limit where the source size is set to zero), allowing Geometric Image Analysis to supplement results provided by the Spot Diagram.

Authored By Sanjay Gangadhara


The Spot Diagram is one of the most useful analysis tools in OpticStudio. It traces bundles of rays through the system to the image plane and provides information on their patterns, RMS radius, and GEO radius. However, the Spot Diagram does not provide information on individual ray characteristics. In order to find the (x,y) coordinates of individual rays, or to view their cross-section distribution, the Geometric Image Analysis can be used. 

The Geometric Image Analysis tool can provide analysis on a point or extended source object for systems that are well-described by geometric optics. In this article, we will show how to use this tool to obtain the cross-section and moment data these sources.

Modeling a point source

Geometric Image Analysis is a very useful feature for characterizing the image quality of an aberrated beam on an arbitrary surface. This feature can be used to model the object as a point source (by setting the Field Size input equal to zero) or an extended source (non-zero for the Field Size). The size and pixelation of the detector used to record the image on the surface of interest may also be specified. More information on Geometric Image Analysis (GIA) may be found in the Help Files.

Open the file "Cooke 40 degree field.ZMX" located in the {Zemax}\Samples\Sequential\Objectives\ folder, and use the following settings in the Geometric Image Analysis tool (located under the Analyze...Image Quality...Extended Scene Analysis...Geometric Image Analysis).


geometric image analysis


The resultant image will look very similar to the Spot Diagram for the same field point:


geometric image analysis


This is expected since the GIA tool uses a zero input for the Field Size. One advantage of using GIA in this case is that when the "Show: " input is set to "Spot Diagram" the text listing of the GIA provides the (x,y) coordinates for each launched ray on the surface of interest.


geometric image analysis


Something which is not available with the Spot Diagram directly. Another feature of the GIA that is not available in the Spot Diagram is the ability to view cross-section data of the intensity:


geometric image analysis


For example, for the settings shown above, X cross-section of the intensity along the center row is:


geometric image analysis


Moment data using IMAE

The IMAE optimization operand can be used to obtain the fractional efficiency of the system for propagation of light from the object plane to a surface of interest. This operand may also be used to generate values for the centroid and width of the intensity pattern. To use this operand, you must first hit the Save button in the settings box for the GIA tool, once the desired settings have been specified:


geometric image analysis


Then the IMAE operand can be added to the Merit Funtion Editor:


merit function editor


Inputs to the operand are the surface number on which the results are evaluated (Surf), the field point from which rays are launched (Field), the size of the source (Field Size), and the type of data desired (Data).  If zeros are specified for the first three inputs, then the values given in the settings for the GIA tool when the settings box was saved will be used; otherwise those values are over-written by the inputs given in the operand. The IMAE operand can return six different values:


Data = 0: Fractional efficiency

Data = 1: Intensity X-Centroid

Data = 2: Intensity Y-Centroid

Data = 3: Intensity X-direction RMS width (i.e. X^2 intensity moment)

Data = 4: Intensity Y-direction RMS width (i.e. Y^2 intensity moment)

Data = 5: Intensity R-direction RMS width (i.e. R^2 intensity moment)


For our example, let's re-open the settings box and hit "Save" so that IMAE may be used (the settings used are shown in the above). Then add four IMAE operands to the merit function editor to calculate the fractional efficiency, intensity X- and Y-centroids, and the radial RMS width. For our example of a point source, the latter three values can be compared directly to other operands: CENX and CENY for the X- and Y-centroids and RSCE for the RMS width:


merit function editor


The agreement (shown in the Value column) is quite good, as expected. The difference between the values for the X- and Y-centroids is simply computational round-off associated with low ray sampling in the GIA calculation. Again, the nice feature of the IMAE operand is that we may now obtain results for other field points simply by changing the Field input. For example, to look at our edge field, simply set the Field input to 3:


merit function editor


There seems to be a discrepancy in the Y-centroids in this case. However, recall that the GIA calculation is being referenced to the chief ray at the moment. If we re-open the GIA and set the Reference to Vertex:


geometric image analysis


and then hit Save again, and then update the merit function we find excellent agreement:


merit function editor


Modeling an extended source

Of course, one of the main uses of the GIA tool is to model the performance of the system for an extended source. The source distribution is defined via an IMA or BIM file. Full details on these file types are provided in the Help Files (specifically under the sections entitled "The IMA format" and "The BIM format"). The distribution associated with any IMA or BIM file may be viewed using the IMA/BIM File Viewer tool (under Analyze...Image Quality...Extended Scene Analysis). As IMA files are text files, they may also be opened directly in any word editor (e.g. Notepad).

In our example, we have used the file CIRCLE.IMA as the input file. So far, this has not mattered since we've set the size of the source to zero. However, we can now view results for extended sources. If we are happy using the CIRCLE.IMA file as our input distribution, we can set the desired size of the source directly in the IMAE operand, e.g. for circle with 0.1 mm diameter:


merit function editor


There are no other operands to compare our results to in the case of an extended source.

Note that the IMAE operand always assumes that the GIA tool uses Spot Diagram for the "Show" input. Thus, the fractional efficiency remains at 100% even though light extends outside of the region defined by the "Image Size" in this case (still at 0.05 mm):

geometric image analysis


If we want to account for the vignetting of light that would occur due to the finite size of the detector, we would have to place an aperture on the IMA surface (or whatever surface the GIA is being used for) in this system. The "Image Size" input does define the region of emission viewed in the GIA, for both the 2D and cross-section plots. 

Just as with the point source, a cross-section plot of the intensity resulting from an extended source may be generated in either direction. For example, using the file named LINEPAIR.IMA with the following settings:




we find the following result in False Color:


geometric image analysis


and the following result for the X Cross-Section along the center row.


geometric image analysis



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