Telescope Reviews: Binocular Resolution Testing w/USAF Charts

I finally pulled out my USAF Lens Resolution Testing Charts and performed a series of tests on various pieces of equipment. These charts are line pairs and as I mentioned in another thread, the result cannot be used to directly indicate what you could see for resolution in nighttime viewing.

There are several major differences between resolution readings from these charts in daylight (photoptic light) and night time scotoptic) point source resolution. They are (1) these charts are viewed in broad daylight, photoptic viewing, under which human eye resoltion is considerably better than in darkness, as much as 2x to 3x better; (2) They are very high contrast line pairs, black on white, as opposed to point sources, tiny round points of white on black. Resolution of black lines on a white ground can be observed at 3x to 5x normal point source resolution.

I think the most interesting results you will see come out after the complete explanation. But I can say this, based on all the values I've recorded for point source resolution by observing closest double stars, I'm not all all surprised at the results. And these results do not agree with what I see posted on binocular sites all over the internet.

The resolution of a lens is determined by the Rayleigh Limit. While there are several well known criteria for judging various limits of resolution, such as Dawes criterion and Sparrow criterion, these are empirical measures, and neither represent a value for clean resolution of two points. It is Rayleigh Limit that relies on the laws of physics to give fixed values for the resolution of a lens and even that must be measured under specific criteria. The long explanation and derivation of Rayleigh Limit can be found in CN Technical Reports and it need not be explained here. For any lens, the Rayleigh resolution, based on point sources, is 138.4/D, where D= diameter in milimeters.

Based on the above, the point source resolution limit of various lenses is:
100mm = 1.38 arcseconds, 80mm = 1.73 arcsec, 70mm = 1.97 arcsec, 60mm = 2.3 arcsec, 50mm = 2.76 arcsec, 40mm = 3.45 arcsec. These resolution limits can only be achieved with high magnifications, generally in a range that will produce a 1mm to 0.8mm exit pupil, or magnifications in the range of 25x to 30x per inch of aperture.

The USAF Lens resoluion Chart has a stepped series of patterns, each three lines with two spaces. The width of the lines is equal to the separation between the lines and the lines are 5 times as long as the width. The chart must be observed at a known distance to determine the resoluion value. A formula is given to perform the calculation. The resolution is measured from center to center of two lines, seperated by an equal space.

I actually measured several of the lines with a precise dial caliper. The actual measured values and the formula provided agreed within 1% to 2% in every case. For instance, recording an observation at 100 feet of the lines in group -1, element 4, (or g B-2, e 4 on the charts in Choosing, Using and Repairing Binoculars, by Seyfried) results in 9.47 arcseconds resolution by vernier measure and tangent calculation and 9.57 arcseconds by using the provided formula. The book does not provide the necessary table of conversion values or the formula.

These values were recorded for resolution (values are angular arcseconds):

20x80 Garrett Gemini clearly see 4.9", see horz, susp vert 4.37", no see 3.9"
20x80 Burgess LW clearly see 5.4", see horz lines only 4.83", no see 4.3"
18.7x80 Anttler clearly see 6.08", barely see 5.4", no see 4.83"
16x70 Fujinon FMT SX clearly see 6.08", suspect 5.4", no see 4.83"
15x70 Oberwerk Ultra clear 6.82", seen 6.08", see horz, vert susp 5.4", no 4.83"
15x70 Oberwerk clearly see 6.82", horz only 6.08", suspect 5.4"
12x50 Nikon SE clearly see 8.61", see both 7.65", no see 6.82"
12x50 Nikon AE clearly see 8.61", horz only 7.65", no see 6.82"
10x70 Fujinon FMT SX clearly see 9.67", see 8.61", no see 7.65"
10x60 Oberwerk Mariner clearly see 9.67", suspect 8.61", no see 7.65"
10x50 Nikon AE clearly see 9.67", suspect 8.61", no see 7.65"
10x50 Pentax PCF WP clearly see 10.8", suspect/see 9.67", no see 8.61"
8x56 Oberwerk clearly see 13.64", horz only 12.12", no see 10.83"
8x42 Swift Ultralite clearly see 12.12", suspect 10.83", no see 9.67"
8x42 Fujinon BFL clearly see 12.12", diff. see 10.83", susp barely 9.67"
7x50 Captain's Storm King clearly see 13.64", suspect/see 12.12", no see 10.83"
7x50 William Optics 7x50 ED clearly see 13.64", see 12.12", suspect see 10.83"

As expected, finer resolution is seen with higher power. The aperture makes almost no difference at these magnifications. In every case, the aperture is capable of much higher resolution, but at binocular magnifications, the human eye is just not capable of seeing that fine resolution. The acuity of the observer is the limiting factor.

This next table is exactly the same information as the first, with just one twist. I've taken the observed resolution for each instrument and multiplied it by the magnification of that binocular for the "apparent resolution" as seen by the eye. For example, the 16x70 Fujinon could clearly see 6.08 arcseconds. At a magnification of 16x, that gives an apparent resolution of 6.08 x 16 = 97 arcseconds.

For comparison to point source resolution, the closest pair of stars I have ever cleanly separated with the 16x70s was 9.6 arcseconds, for an apparent resolution of 154 arcseconds. With nearly every instrument listed here, I have cleanly separated stars that result in apparent separations between 154 and 172 arcseconds. Rather than reading a table of results that shows incrementally finer resolution for higher powered binoculars, showing the data by apparent resolution allows the comparison of any one binocular to another binocular, regardless of magnification.

These values represent apparent resolution (angular arcseconds x magnification):

20.8x80 Garrett Gemini clearly see 102", see horz, susp vert 91", no see 81"
20x80 Burgess LW clearly see 108", see horz lines only 97", no see 86"
18.7x80 Anttler clearly see 109", barely see 97", no see 87"
16x70 Fujinon FMT SX clearly see 97", suspect 86", no see 77"
15x70 Oberwerk Ultra clear 102", seen 91", see horz, vert susp 81", no 72"
15x70 Oberwerk clearly see 102", horz only 91", suspect 81"
12x50 Nikon SE clearly see 103", see both 92", no see 82"
12x50 Nikon AE clearly see 103", horz only 92", no see 82"
10x70 Fujinon FMT SX clearly see 97", see 86", no see 77"
10x60 Oberwerk Mariner clearly see 97", suspect 86", no see 77"
10x50 Nikon AE clearly see 97", suspect 86", no see 77"
10x50 Pentax PCF WP clearly see 108", suspect/see 97", no see 86"
8x56 Oberwerk clearly see 109", horz only 97", no see 86"
8x42 Swift Ultralite clearly see 97", suspect 87", no see 77"
8x42 Fujinon BFL clearly see 97", diff. see 87", susp barely 77"
7x50 Captain's Storm King clearly see 95", suspect/see 85", no see 76"
7x50 William Optics 7x50 ED clearly see 95", see 85", suspect see 76"

As you can see from this table of results, apparent resolution falls in a range that varies slightly between approximately 90 and 100 arcseconds, regardless of magnification or aperture. A few binoculars suspected seeing finer, down into the range of low 80s arcseconds. In every case I recorded the no see (even if not reported here). The fineness of the target steps give jumps of about 10 arcseconds, so in many instances a precise value is not determined. But it is easy to see from the results that it does not vary by much.

As you can see from the data, there is no one real standout. A few were not exactly up to par with the rest of the pack, but none jump out as a clear leader and none are so bad I would get rid of them. Also, it is clear the resolution values as determined by a line bar chart in daylight do not represent expected resolution for astronomy. However, since I have both this data and data for pont source resolution for nearly all these instruments, there may be potential to develop a factor for conversion. maybe another post.

8-20-05
Several binoculars were pulled out, in particular the 8x56 was found to be slightly out of collimation. it was adjusted. it and the pentax were tested over and both results improved slightly, not surprisingly, fitting their results more in line with the rest of the other binoculars tested.

edz

8-22-05
Another post brought out this information, which is relevant to this post.

The forumla is dependant on also having the Table of Value Constants (LPM) for each line pair image on the chart. Without the constants, the formula is of no use.

Also, it is extremely important that the chart be exactly sized. On occasion we see people that have photocopies of these charts. Almost all photocopy machines reduce the size of the original to maybe 97-98%. A copy of a copy can very quickly be reduced to a non-standard size and then the Table of Constants would no longer be valid for that copy. The other source is printing the charts off the internet as is possible from the links I've provided below. The caution here is the user must know exactly how to size the chart. As a check, the three bars and two spaces in Group-2 Element 1 should measure exactly 10mmx10mm.

I'll dig out the table of Constants and the Formula later and scan them with some sizing information and post it as pictures to our Binocular gallery.

edz

edited 9-4-06 added a few more including Garrett 20x80 and Obie Ultra 15x70

edited 7-13-07 you will read much further down in this thread that some results published by some testers use boosted magnifiaction. That is, they place an auxilary scope behind the binocular to boost magnification up to 25x, 30x, 40x, etc. Although the instrument normally would not likely be used in this manner, this allows the tester to see much finer resolution and really get to the point where it may be possible to compare ultimate resolution of one binocular to another. Some examples:

15x70 Oberwerk Ultra, with a 2.5x magnifier for a modified power of 15x2.5=37.5x, I could see resolution just barely to 2.7 arcseconds.

16x70 Fujinon with 2.5x multiplier (=40x), (to equalize with the 15x70 I moved several feet further away from the target), I could see the same 2.7 arcseconds resolution.

12x50 Nikon AE at 12x I could clearly see 7.65 arcsec for an apparent res of 92 arcsec and 6.82 arcsec was blurred for 82 arcsec apparent.
12x50 Nikon AE with the 2.5x boost for 30x, I could see 4.3 arcsec and 3.8 arcsec, and the apparent res is 129 arcsec and 115 arcsec.
Using the same Nikon AE 12x50, with a 6x monocular for a net 72x, I could see 3.4 arcsec easily, 3.04 arcsec clearly, 2.7 arcsec barely and 2.4 arcsec suspected. Apparent resolution values are 245, 219, 195, and 174.

Boosted magnification does allow you to see very small resolution. I was able to read 3.4 or 3.0 arcseconds with two different 10x50s boosted to 60x. When the 6x booster was placed on two different 12x50s for 72x I was able to read 2.7 arcseconds and even suspected 2.4. Seems 60x on a 50mm binocular may not be enough to reach the limit of resolution. However, I did have two 10x binocular that couldn't see much better than 5 arcsec when boosted to 60x.

With the 6x booster on a 10x70 Fujinon for 60x, I could see no better than 3.0 arcsec.

Magnification required to see all the potential resolution in a binocular, for some instruments may be in the vicinity of 30x per inch.

Line pairs charts vary by 12% for each increment better or worse. If two binoculars are compared with only a 12% difference in resolution, especially at less than maximum resolution, then one has not been definitively determined as better than the other. However, if there were a 20% difference in resolution in two optics of same dia aperture and at same power, obviously you can tell one is better.

Edited by EdZ (09/02/07 03:57 PM)