BOG and the Ringo Challenge

Jim "Ringo" Perkins uploaded an SRB gem design, then issued the following challenge:

My results for face up and tilt brilliance follows:
Face up ISO=93.3% COS=87.6%
10 degrees tilt ISO=71.5% COS=65.6%
20 degrees tilt ISO= 62.9% COS=54.1%

My challenge is this. You must use the symmetry, I.R. and indicies I did. You can change angles and proportions to whatever you like. See if you can get better results.

This is exactly the kind of problem for which BOG is useful. In fact, optimization of an SRB for ISO brightness and tilt is the focus of the BOG online tutorial (click here to visit that tutorial).

Step 1 - Examine the Problem

Jim's "Optimizer" design is already very good, and his boast is justified - " Go ahead, make my day and take a shot at the gunslinger. :-)". I began by loading the .GEM file into BOG and entering the values shown at right. Note that I have selected the 42 degree pavilion angle and the 35.7 degree crown angle for reference.

Based on this tilt variation, I set up the Merit Function with the following weights: ISO -1 , Tilt - 30. For tilt, I set the Brightness Variation for Zero Magnitude (BVZM) to 15.

Step 2 - Examine the Landscape

Before proceeding to the optimization, I like to take a look at the Merit Function "landscape". From the main BOG window, click on the MF Map button and press Go. After a few minutes (about 5 minutes on my 4 year old PC), you should see the following. You can learn more about the Merit Function Mapper here.

This is a map of the stone performance (the Merit Function) for a range of Crown and Pavilion angles. Try clicking on various points. On the left, you will see the raytrace for that pair of angles, as well as the ISO/COS brightnesses and Merit Function values. Note the coloured bar - it indicates the total merit function value and the contributions due to ISO (red) and Tilt Performance (blue). Note that there is a "ridge" of good performance, ranging from upper left to lower right. In general, high crowns work well with low pavilions and vice versa.

A little exploration of this map can be quite instructive (click on Save to place a copy on disk for later study). For example, to the upper left (high crown, low pavilion), the tilt performance is very good - the MF bar shows lots of blue. Unfortunately, the ISO brightness is considerably worse, and the reflectance pattern in the raytrace is unappealing. To the lower right, the ISO is very high, but the tilt performance is poor. Jim's solution, although it does not have the absolute highest merit function value, represents a good compromise between better tilt and better ISO. I also like the reflectance pattern.

A hint of somewhat better performance lurks just to the lower left of Jim's solution. The "Better Solution?" highlighted above shows slightly higher ISO than Jim's, and qualitatively better tilt performance. Clearly, exploring near Jim's solution may be productive.

Incidentally, the aesthetic appeal of the reflectance pattern is a matter of taste, but I actually prefer Jim's to the "Better Solution" in this instance. The relative value placed on face-up ISO Brightness, Tilt Performance, and Reflectance Pattern highlights a major difficulty in assessing the "quality" of designs - one man's food is another man's poison, to paraphrase Lucretius (had to look that quote up...isn't the Web wonderful?). Maybe the gunslinger is safe after all?

Step 3 - Zero in on a Solution

Our exploration of the Merit Function Map indicates that Jim's solution is as good a place as any to start Optimization. Return to the main BOG window and click Optimize. After about a minute, the program should converge on the following:

As expected from the MF Map, this solution has lower crown and pavilion angles than the original. Based on the selected Merit Function and weights, it is about 3% better. Trying to "force" better tilt performance by increasing the appropriate weighting factor will not be very productive. This distorts the Merit Function "landscape", and will push BOG into a solution with considerably worse ISO brightness. Take a minute to try Tilt_Weight=50 to see this effect (or follow the BOG tutorial).

Step 4 - Do a Sanity Check

We seem to have nudged a bit more performance from Jim's Optimizer design, but it's worth taking a look in the PlayPen to be sure. Click Cancel in the Optimization Progress window then start the PlayPen from the main BOG window. Note that the program has thoughtfully inserted your optimized angles.

Select the Evaluate Tilt Performance option and generate a Raytrace for 20 degrees, Tilt Direction 1. Click Make Ref to place the optimized gem in the reference channel. Note that all the relevant data are copied to the lower Blue panels. Enter the original pavilion and crown reference angles then Raytrace again. The tilt performance plot shows that we have managed to improve the brightness of the gem at intermediate angles without harming the face-up performance.

This ends BOG's take on the Ringo Challenge.

Note that the original file is unchanged (and in fact untouched, since BOG worked with a copy). You must manually perform the tangent ratio calculations. Follow this link for a description of this procedure.

The Score Card:

The optimization procedure described here took about ten minutes on a 4-year old Pentium PC. More effort may produce better "objective" results, although it has been my experience that less tangible factors (idiosyncrasies of a particular stone, personal taste in reflectance patterns, etc.) are more important in refining the final exact angles.

The following table summarizes the results. In each box, I have coded the Original-->BOG Optimized values by blue-->red.

As expected from the PlayPen, the most significant change is a 7% increase in ISO brightness at intermediate angles.