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How to Generate Cross-Section and Moment Data for an Extended Source using Geometric Image Analysis

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.
Sanjay Gangadhara
Analysis Features

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 < data>\Samples\Sequential\Objectives\ folder, and use the following settings in the GIA tool (located under the Analyze > Image Quality > Extended Scene Analysis > Geometric Image Analysis).

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

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 surface of interest.

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:

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

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 on the settings box for the GIA tool, once the desired settings have been specified:

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

The agreement 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:

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:

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

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, but thus 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:

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):

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:

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


The Geometric Image Analysis feature is a powerful tool for investigating the behavior of optical systems that are well-described by geometric optics. This feaure allows the performance of a system to be characterized for both a point source and an extended source. The corresponding IMAE merit function operand provides quantitative output from the tool, including fractional efficiency, intensity centroid, and intensity width. These data are available for any surface in the optical system.