Accuracy is not the same as Precision

The words accuracy and precision express slightly different, but related, concepts. They are not just different words for the same thing. For a thorough understanding of parallelism, it is important to distinguish between the two.

Imagine a ruler. Accuracy is whether an inch is really an inch; precision is the number of divisions in the inch.

Or visualize many huge, unconnected pipe sections that are in a perfectly straight line. If you are inside the first section and your eyes are exactly in its center, the other sections and section gaps make a pattern that is uniform on all sides. Sections and gaps between sections are concentric to each other. The overall pattern is symmetrical.

If you move, say, two feet to the left, you no longer see a symmetrical pattern. You see more of the right side than the left. Then, if you return toward the center by one foot, the pattern might appear almost uniform – almost symmetrical. Even though your eyes are not quite in the center, you might say their position is good enough, so your range for acceptable symmetry would be the center "± one foot".

Now we can relate a zig-align alignment module to a pipe:

1. accuracy of the module is equivalent to how close your eyes are to the center of the pipe. Only an extremely accurate module can show you instantly when two planes are exactly parallel.
2. precision shown by the module is equivalent to how much the last few sections of pipe must move or bend before you recognize that the pattern has a different shape when your eyes are at the center of the first pipe section.

Accuracy of parallelism between two planes is related only to how well the alignment module is constructed. Precision is related to the ongoing interaction between module and plain mirror. The alignment pattern is the visible display of this invisible interaction. You might say that accuracy is static and precision is dynamic.

Accuracy of Modules

The object of checking parallelism is to see whether alignment is, at the very least, adequate. The two factors that affect how close to perfect parallelism you get are 1) accuracy of the module so that your eye is at the center if its alignment pattern, and 2) to what extent the alignment pattern is truly symmetrical. The pattern produced by a zig-align module is sensitive enough to show when alignment is perfect.

How do you know whether an alignment device is accurate? The simple answer is, of course, to trust the manufacturer...or learn enough in order to decide for yourself.

accuracy of module components

Manufacturers control the quality of components they use by requiring their suppliers to meet various specs and tolerances. For zig-align, not only must the components that contribute to concentricity between view hole and indicia be made carefully, but also the modules must be assembled carefully.

• LED: Centers of the mirror's view hole and the LED bolt circle are within ±0.0016" of each other.
• ring: Centers of the mirror's view hole and its surrounding ground glass ring are within ±0.0020" of each other.

For an 8x10 print distance of about two feet (the most common distance for enlarger alignment), effective distance of the last (sixth) distinct repeat is 24 feet (288 inches). Compared to that distance, placement of the LED module's view hole varies by less than 5.5 parts per million (0.0016 ÷ 288 5.55 • 10^-6 5.5 ppm); approximately 7 ppm for the ring module, error that makes no practical difference.

accuracy of module assembly

Realizing that a well-made module is sensitive to its own errors of construction, you might wonder: "Will any two modules ever give the same answer?" This is answered in terms of zig-align's practice.

You can compare one LED module to another by using their Total Indicator Readings (TIRs; in this case, the combination of parallelism and flatness between the top and bottom of the module). The alignment pattern displays parallelism only between the bottom of the module (module mirror) and the plain mirror. The pattern does not compensate for either the module's TIR or the lack of parallelism between the top of the module and the plain mirror. Both of these are constraints on using the module to obtain perfect parallelism, since modules are usually hung from the top (see Figure 9).

If mirrors were perfectly flat and modules were made from perfect parts and assembled perfectly, their TIRs would be zero. With such a module, a perfectly symmetrical alignment pattern would mean perfect parallelism. However, the modules are not perfect. The individual TIRs from many module measurements result in the following weighted averages:

• LED module TIR Weighted Average = 0.000235 of an inch (0.0001" to 0.0004" range)
• ring module TIR Weighted Average = 0.000410 of an inch (0.0001" to 0.0010" range)

Parallelism between the top of a module and the plain mirror is incorrect by the TIR amount. If you put a wedge under the left side of the plain mirror in Figure 9, you can make that mirror parallel to the top of the module. Figure 10 shows the required wedge thickness for various print sizes.

 

Print size	Distance	Wedges needed to reach accuracy perfection
in inches	in feet—neg-to-paper	max thickness in inches—for an average module
		Ring LED 0.002 0.001 0.004 0.002 0.008 0.004
8x10	@ 2
16x20	@ 3.5
30x40	@ 5

For a perfectly symmetrical alignment pattern shown by an average LED module at an 8x10 printing distance, one eight-inch side of a horizontal 8x10 plane is within 0.001 inches of perfection when the other eight inch side is perfect. If you use a module whose TIR = 0.0001 instead of the average TIR of 0.000235, one of the eight-inch sides would be within 0.0005 inches of perfection.

Figure 10 also shows that an average LED module errs from perfect parallelism for 30x40s by half the thickness (about 0.004") of a business card. The average ring module has similar error at a 16x20 print distance.

Module error is assumed to be two-dimensional, but usually it is three-dimensional. Analysis of 3D error is complex, but as long as error is this small and the module's precision is equal to or smaller than its accuracy, the error is insignificant.

 

Precision of Alignment Patterns

Precision is the sensitivity of a pattern to changes in parallelism between two planes. The curve in Figure 11 allows you to visualize precision. The more repeats in the pattern for a given distance, the steeper the average slope of the curve, and the more precise the pattern.

From actual measurements of parallel planes separated by 8x10, 16x20, and 30x40 printing distances, zig-align alignment patterns barely change shape when the angle included between the two mirror planes changes as follows:

 

Print size	Distance	Precision angles
in inches	in feet—neg-to-paper	in seconds (3600 sceonds = one degree)
		Ring LED LEDw/ZO1 90 20 10 60 13 6.5 45 10 5
8x10	@ 2
16x20	@ 3.5
30x40	@ 5

Figure 12. Precision angles

Figure 13 is derived from Figure 12.

 

Print size	Distance	Precision wedges
in inches	in feet—neg-to-paper	max thickness in inches—for an average module
		Ring LED LEDw/ZO1 0.004 0.001 0.0005 0.006 0.00125 0.0065 0.009 0.002 0.001
8x10	@ 2
16x20	@ 3.5
30x40	@ 5

Figure 13. Precision wedges

 

Figure 14 combines Figures 10 and 13. Remember that accuracy comes only from the module. Figure 14 shows that precision of an average LED module is equal to or less than its accuracy, meaning its alignment pattern is more sensitive relative to its TIR. It is reasonable then to assume that symmetry of the LED alignment pattern is constrained from showing perfect parallelism mostly by the module's TIR.

According to Figure 14, the LED module is always more sensitive than the ring module for a given print size. This difference in sensitivity is due to the way the eye and mind interact. It is simply easier for us to recognize symmetry if lines are straight than if circles are concentric.

To see a change in the pattern, parallelism must change more for the ring module than for the LED module. Though the two modules share the same theory, the ring module is entry-level for many applications.

Precision is shown by interaction between a module's mirror and a plain mirror. Alignment patterns show this interaction qualitatively; either the pattern is symmetrical or it isn't. Though the top of an LED module (not its mirror on the bottom) usually is registered to the plane of interest, actual error between top and bottom is negligible.

If a symmetrical pattern was always perfect, Figure 12's precision angles would be zero. But without automatic pattern recognition, a small variation in the shape of the pattern is likely. Zig-align's video tap (ZTV) can be used for manual pattern recognition, and it allows you to reduce precision angles to about one-half the LED unassisted eye values (see Figure 15). But even without always-perfect symmetry of the alignment pattern, remaining error in parallelism is insignificant, especially when compared to the usual imperfection of equipment.

Because additional repeats for a given distance increase precision, they also maximize accuracy of parallelism (until reaching the TIR restraint), because more repeats make it easier to recognize changes in symmetry. You might think that the more repeats at any distance, the better. More is often better, but this time more is not necessary.

Now amplification from two mirrors reveals its value. As distance between planes increases, the progressively fewer repeats in the pattern are more than sensitive enough to show when parallelism has changed by the thickness of a thin piece of paper.

System Sensitivity

Figure 15 illustrates the increasing leverage of longer actual distances between planes. For example, comparing eye sensitivity at two feet and ten feet, the fewer repeats at ten feet show about three times the sensitivity available at two feet (35 ÷ 12). (Data is not shown for less than three repeats per LED, the easiest-to-use minimum.)

 

Actual distance	LED module				system sensitivity
	distinct repeats per LED				repeats x actual distance
	ZO1	ZTV	eye		ZO1	ZTV	eye
40'	3	-	-		120	-	-
30'	3	3	-		90	90	-
20'	4	4	-		80	80	-
15'	5	5	3		75	75	45
10'	6	6	3-4		60	60	35
5'	8	8	5		40	40	25
2'	10	8	6		20	16	12

Figure 15. System sensitivity

The effect of head movement on accuracy is mentioned earlier in Virtual Images . If movement when using the LED module is one sixteenth of an inch ( 0.060" or ± 0.030"), the best possible parallelism (symmetrical alignment pattern) is within 100 ppm (0.030 ÷ 288 100 • 10^-6 ) at the actual distance of two feet. At ten feet, ppm for head movement is still less: ([12 ÷ 35] • 100 30 ppm). And ZTV eliminates even that error.

Figure 15 also illustrates how magnification improves precision when mirrors are farther apart. For instance, with ZO1 at two feet, precision is ten seconds of arc (see Figure 12), but at 40 feet it becomes less than two seconds (10 • [20 ÷ 120] 2").

The Bottom "lign"

There is no doubt that alignment patterns, formed from the multi-repeated images made by two mirrors, show extremely small errors in parallelism. By using a two-mirror alignment pattern, you can see errors that you would never find with other inspection techniques. The pattern makes it possible to have precise and highly accurate parallelism so your lens can perform at its best.

The combination of accuracy, precision, simplicity, and speed convert the formerly burdensome task of checking and achieving parallelism into a fast, easy-to-do mini-job. The highest possible standard for image accuracy is just around the corner.

Zig-align your setup and make a print. It will be the best one you have ever made.