How sharp is that gobo? Isn't that something like asking how long is a piece of string? The answer to both these questions would appear to be highly subjective. Take a gobo and project it from a luminaire, and we all have our opinions about how sharp the projected image is. What's more, when viewing two fixtures side-by-side, we can usually agree on which one gives the better result. However, until now, we have had no way to either communicate or document that sharpness in numbers or to be able to compare two fixtures viewed at different times. This isn't to say that a sharp image is always desirable — sometimes we want nice soft fuzzy edges, so it would be good to be able to measure and duplicate that fuzziness as well.
There are long standing and well-established methods of measuring and presenting the performance of high quality projection lenses through MTF (Modulation Transfer Function) measurements. However, those techniques and the associated presentation of the data are complex and not appropriate for the quality of lenses commonly used in theatrical luminaires or spotlights. What is needed is something that will:
- provide a simple method for measuring lens quality with particular emphasis on contrast and perceived image quality (sharpness).
- provide simple numerical values representing the lens quality, which can be published on a datasheet in a format that is readily understood and that allows direct comparison of lenses.
Where Do We Start?
If we examine the projection of simple checkerboard test patterns from gobos, we can see the differences in focus quality between different lenses. Figures 1 through 3 show examples of the images of the same gobo projected from three different lenses. It is clear that Lens C is the best, followed by Lens B, and finally, Lens A. However, how much better and how do we enumerate it?
Fortunately, there are two significant and measurable differences between the images shown in these figures. First is the contrast ratio of the image; Lens C has excellent crisp blacks and whites, whereas Lens A has a “bloomed” look with stray light reducing the contrast ratio. Is that all we need to measure? Unfortunately not. Lens C and Lens B have very similar contrast ratios, even though it is obvious to the eye that Lens C is better. The difference this time comes from the steepness, or slope, of the edges. As can be seen from the line profile graphs to the right of each figure, Lens C has very steep sides to its edges, while Lenses A and B have gently sloping edges, indicating a much less defined edge and, thus, softer focus.
Okay, How Do We Measure It?
The contrast ratio is relatively simple to measure; we just measure the light output in the black and white squares of the checkerboard gobo. By keeping the squares large, we ensure that the contrast ratio is measured at a low spatial frequency well within the pass band of the lens. This low frequency grid with 10 squares across the field is illustrated in the top half of Figure 4.
Measuring the edge slope is potentially more difficult. Measurements could be taken off line scans such as those shown in Figures 1 to 3, but such measurements are likely to be subjective and difficult to repeat. It's much easier to measure light levels than edge slopes. Fortunately, there is a solution: create another checkerboard but, this time, one with much smaller squares, one with 100 squares across the field, as shown in the lower half of Figure 4.
The coarse grid measures the low frequency (almost DC) contrast ratio, while the fine grid measures the high frequency response, which is proportional to the edge slope. So now both measurements can be taken by measuring simple luminance levels (this is a simplification of the physics and assumes that the edges are straight lines. However, the assumption is reasonable for this type of lens and yields good comparative figures).
How Practical Is This?
The procedure is very straightforward; using a glass gobo with a pattern like that shown in Figure 4, you measure light level readings at a number of points to calculate average contrast ratios for both the coarse and fine grids. Some simple math detailed in the standard turns these readings into two figures, contrast modulation and sharpness, for that specific lens. These figures are percentages, so a perfect lens would score 100% for both. The standard was approved by ANSI in October 2007*, so you should start to see these figures showing up on luminaire datasheets soon and get an answer to the question, “How sharp is that gobo?” I still have no clue about the piece of string though.
Mike Wood provides research and development, technical, and intellectual property consulting services to the entertainment technology industry. He can be contacted at email@example.com.
*ANSI E1.35-2007, Standard for Lens Quality Measurements for Pattern Projecting Luminaires Intended for Entertainment Use, is available from The ESTA Foundation at www.estafoundation.org/pubs.htm. Visit www.esta.org/tsp for more information about ESTA's Technical Standards Program.