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Astronomy TECHNOLOGY TODAY 47

Part 1 of this article appeared last month.In it I introduced the Virtual Observer (VO),a new and unique computer simulator thatprovides definitive and quantitative, answersto the most fundamental questions about tel-escopes and visual observing: “What can Isee?” “How well can I see it?” and “Whatequipment do I need?”

I want to stress the point that this is aunique research tool, based on published re-search, with a totally new capability that hasnever been available until now!

It is a computer simulator of visual tele-scope observations. The VO traces the lightfrom a celestial object, through the atmos-phere, through the telescope and eyepiece, andthen into the eye. But that is the easy part. Atits heart, VO also has a human model com-ponent that evaluates how the mind “inter-prets” the light that falls on the retina in termsof actual image visibility. VO not only actu-ally tells us if we can “see” the object, but alsohow well!

As noted in Part 1, the human model isbased on the report of definitive research workperformed by H. Richard Blackwell, entitled“Contrast Thresholds of the Human Eye,”and published in the Journal of the Optical So-ciety of America, Volume 36, Number 11, No-vember 1946.

At this phase of development, the VOquantifies visibility in terms of a number calledthe “Visibility Index.” The index values range

from 0 to 1 (approximately). Values near 0mean that the mind will not “see” the object.Values near 1 mean that the mental image willappear photo-like.

Last month, in Part 1, I used VO to ana-lyze the effect of magnification and telescopesize on the visibility of M97, the Owl Nebula.I also put out a call for help to any observerswho would like to participate in the finalphase of the VO model research and develop-ment by making a few simple observations.

This month, in Part 2, I will extend theapplication of VO to study the effects of eye-pupil diameter (age), telescope aperture, andlight pollution. I will also make some directcomparisons of the VO model predictions toactual observations. And finally, I’ll providemore information about my call for researchhelp. If time and space permit, future articlesmay address other observational issues andstudy results.

I’ll begin with an actual observational ex-ample of the application of the VO model.This will provide an opportunity to review thekey results from Part 1, and leads into the Part2 objectives. Earlier this year, I made two setsof observations of M97. In both sets, I docu-mented the observational conditions and de-scriptions of what I saw in the eyepiece. Later,I ran VO cases to simulate these conditionsand then compared the VO visibility predic-tions to my actual observations. As you willsee, I would have been better off to have run

VO first, before I made the observations, be-cause it told me something that would havebeen helpful.

The first observation was made under aclear sky with average transparency and amoderate light pollution level of 19.04 magnitudes per square arc-second (msa). Thesecond observation was made under nearlyidentical conditions a few weeks later. The primary change was that I moved to a darkerlocation. My observation notes are shownbelow.

Observation #1 Notes:Target: M97Telescope: 10-inch f/5Eyepieces: 12.5 mm (100x), 25 mm ( 50x)Filters: NoneEye pupil diameter: 3.5 mmSky brightness: 19.04 msaAverted Vision: Barely visible, and only withmotion. Just a vague hazy patch, no bound-aries, no structure.Direct Vision: Not detectable

Observation #2 Notes:Same as #1 except:Sky brightness: 20.25 msaAverted Vision: Easy to spot. I can see thewhole object, but no detail, edge is fuzzy.Direct Vision: almost disappears, but I canbarely see something.

A few months later, I simulated both

By Roger Blake

The VirtualObserver

A New Breakthrough Technology for the Visual Observer - Part 2

observations with the VO computer model.The results are shown, opposite page, in Figure 1 and Figure 2.

These figures are very similar to thoseshown last month, in Part 1 of this article.They show the VO model predictions of thevisibility of M97 for a range of telescope mag-nifications. The red line represents the visibil-ity using “averted” vision and the blue linerepresents “direct” vision. Figure 1 is the pre-diction for the specific conditions of Observa-tion 1, and Figure 2 for Observation 2.

The shape of the lines in both figures isessentially identical. The difference is that theFigure 2 lines are shifted upward, indicatingbetter visibility relative to Figure 1. This is theeffect of the darker sky in Observation 2.

Both blue lines also show a sharp peak,with visibilityfalling off rapidlyat both lower andhigher magnifica-tions. Last monthI referred to thesepeaks as “cusps”

and noted then that the existence of such asharp peak was a surprise to me. There is moreto say about this peak and I’ll get back to it alittle later.

As described in my observation notes, Iobserved M97 at 50x and 100x magnification.The predicted visibility at these magnificationsis shown in the figures with circles. Notice thatusing these two magnifications caused me tomiss the predicted peak visibility at 72x. If I’dknown this before the observation, I wouldhave made an additional observation with an18-mm eyepiece, at about 71x.

Now let’s compare the VO model pre-dictions in Figures 1 and 2, to my actual ob-servations as shown in Table 1. “Obs” is theobservation number, and “Max VO” is themaximum of the two visibility index values at

THE VIRTUAL OBSERVER

48 Astronomy TECHNOLOGY TODAY

Table 1: Actual Observations

Obs Vision Max VO Notes1 Averted +.23 Barely Visible1 Direct -.10 Not Visible2 Averted +.52 Easy to Spot2 Direct +.12 Barely, Only Partially Visible

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50x and 100x, as read from Figure 1 and 2.The agreement is good. As the predicted

visibility index increases from -.10 to .52; theobservation notes describe a real, correspon-ding increase in the actual visibility from “notvisible” to “easy to spot.” This is encouraging(but not conclusive) evidence that the VOmodel represents reality. This is also a good il-lustration of my request for help from readers.Ideally, many different readers would makesimple, but careful observations, documentthe results to me, and then I would run theVO model and make comparisons much likemy example above. This effort would have twoobjectives. First it would provide a basis forjudging the VO capability, and second, itmight enable the calibration of the visibilityindex against actual visual images.

Now let me return to the “cusp” or sharppeak in the “Direct Vision” line that I men-tion above. The presence and location of thispeak is somewhat of a contradiction to theconventional wisdom that I’ve been exposedto during the 30 plus years that I’ve been inthis hobby. So I want to provide a more de-tailed explanation of what the cusp representsand then compare it to conventional wisdom.

The cusp is a common feature in all directvision visibility lines and it always occurs at ex-actly the Minimum Useable Magnification(MUM). The value of the MUM varies foreach observer and telescope combination. Youcan calculate your MUM by dividing the di-ameter of your telescope by your eye pupil di-ameter (both in the same units). A plot oftypical eye pupil diameter versus age is pro-vided in Figure 3.

In my observations, my clear aperture was10 inches, which is 254 mm, and my pupildiameter was 3.5 mm. Therefore, my MUMfor these observations is 254/3.5 = 72.6x, ex-actly where VO calculated the peak.

Now, the VO model doesn’t know any-thing about the MUM per se; it simply calcu-lates visibility based optical physics and thehuman model component, which is based onthe Blackwell research described last month.So what does the term Minimum UseableMagnification (MUM) mean? Well, it de-scribes a characteristic of the telescope andhuman combination that may be unfamiliarto readers. I’ll explain using what I hope will be



a relatively simple and intuitive example.An observer views M97, the Owl Nebula

with a telescope. Three facts should be obvi-ous. (1) The total amount of light that formsthe image of M97 on the retina of the ob-server’s eye was captured by the clear apertureof the telescope. (2) The image of M97 on theretina gets bigger, or smaller, depending on thetelescope magnification used. But the totalamount of light from M97 captured by thetelescope remains constant. (3) It therefore fol-lows that as the image gets bigger, it must alsoget dimmer because the same amount of lightis spread over a larger image.

So, as magnification goes up, the objectappears bigger and dimmer. Conversely, theobject appears smaller and brighter as magni-fication is reduced. So far, this is probably ob-vious to most observers. The maybenot-so-obvious part is that when the magnifi-cation is reduced to the MUM value, the ob-ject brightness no longer increases with furtherreductions in magnification! At magnificationsbelow the MUM, the object continues to de-crease in size, but the brightness on the retinaof the observer remains constant! Why?

The reason is fairly simple. The light shaftthat leaves the eyepiece on its way to the eyehas a diameter called the “exit pupil.” As themagnification is reduced, this diameter getsbigger. At magnifications greater than theMUM, the diameter of the exit pupil is alwayssmaller than the eye pupil, and all light trans-ferred by the telescope gets into the eye. At theMUM, the diameter of the exit pupil is ex-actly equal to the diameter of the eye pupil.Further reduction in magnification causes theexit pupil diameter to exceed that of the eyepupil, causing a partial loss of light. This hap-pens in such a way that the surface brightnessof the image on the retina remains constantfor all magnifications below the MUM.

OK, so what is the conventional wisdom?You usually find it stated something like this,“It is well known that objects are brightest atthe MUM condition, but it is a fallacy com-monly committed by newbie’s that this is thebest magnification for visual observing. Thebest visibility occurs at higher magnifications.”Now, the truth is that this is partiallyright…and partially wrong. Part of the con-fusion is caused by not being specific with re-

gard to averted versus direct vision.The above conventional wisdom is often,

but not always, true for averted vision. Thiswas demonstrated in all the VO plots and con-clusions shown last month. Note also that it isonly barely true in Figure 1 and completelyuntrue for Figure 2. But conventional wisdomis always false for direct vision, for which thebrightest magnification will always be exactlythe MUM, as described above.

Now I’ll move on and apply the VO toinvestigate three important issues that effecthow well visual observers can “see” dim, deepspace objects: (1) What is the effect of the re-duction in eye pupil diameter with age? (2)What is the effect of telescope aperture? (3)What is the effect of light pollution?

As shown in Figure 3, eye pupil diameterdecreases almost linearly with age. As discussedabove, one effect of this is the change in theMUM value which defines the optimummagnification. But what is the net effect on avisual observer’s ability to see deep space ob-jects like M97? This is exactly the type of ques-tion that the VO model is designed to answer!We simply simulate different observers withvarious pupil diameters and see what trendsVO predicts in the values of the visibilityindex. To make it simple, we’ll choose sometypical values for the other key parameterssuch as telescope size, sky brightness and theothers.

The VO results are shown in Figure 4.To make it more meaningful, I’ve convertedfrom pupil diameter to age using Figure 3.The red and blue lines represent the avertedand direct vision results respectively. They rep-resent the VO prediction of the net effect ofthe reduction in pupil diameter on a typicalobserver’s ability to “see” M97.

Now these lines would have been higheror lower if the analysis had been done with adifferent size telescope, or a different light-pol-lution condition, but what is important is thechange in the visibility over time.

At age 25, the visibility as depicted by theblue line is about 0.37. At age 70, this de-creases to about 0.24. This is a decrease ofabout 0.13, or about 13% of the full visibilityscale of 0 to 1.

Now to the red line. This is an amazingresult! It says that the entire range of reduction

in pupil size has absolutely no adverse effecton the averted vision! How can this be true? Ispent a considerable amount of time lookingfor a bug in the VO model, trying to find thecause of this crazy result! But I soon came tothe realization that, again, the VO model hadshown me another truth about visual observ-ing that I never suspected in the 30+ years inthis hobby! So let me explain why, after somethought, it became obvious that VO was cor-rect.

Look back at the red line (averted vision)in Figure 1. Recall the discussion earlier in thisarticle about the Minimum Useable Magnifi-cation, or MUM, as it applied to the peak, orcusp, in the blue line. Note that in Figure 1,there is a similar “corner-like” feature in thered line at the MUM (in this case at 72x). Thecause is the same. Above the MUM, the di-ameter of light-shaft leaving the eyepiece,called the exit pupil, is always smaller than thediameter of the eye pupil and all the light getsinto the eye. Below the MUM there is a par-tial light cutoff.

Now combine this with the conclusionmentioned earlier, that the optimum magnifi-



cation for averted vision is always equal to, andfrequently greater than, the MUM. Combin-ing these two, we see that the optimum viewfor averted vision always occurs at magnifica-tions above the MUM, when the exit pupil issmaller than the eye pupil, and therefore, thediameter of the eye pupil never has any affecton averted vision!

Next, the analysis of telescope aperture(diameter). An observer often ponders thequestion of how big a telescope to buy. It’s aquestion of budget versus performance. Forvisual observing, performance often means theability to see dim, deep space objects. Untilnow, there has been no quantitative way toevaluate this performance question. But

now VO can answer this question definitively.Just choose the telescope, target, and observingconditions and VO will provide a numericalvalue of the visibility. Compare the visibilitiesfor a range of telescopes and targets and thenchoose the results that fit your needs.

A comprehensive analysis of aperturewould include many targets, under a range ofobserving conditions. A much simplifiedanalysis is presented here, using only M97 asthe target, with relatively dark skies of 20.5msa, a middle-aged observer with 5-mmpupils, under typical atmospheric conditions.M97 itself is a good choice because its size andsurface brightness are typical of many of thepopular galaxies and nebulae. The sky

brightness is typical of a good observing site,but is significantly darker than the back yardsof 99 percent of the population. The results ofthe aperture analysis are shown in Figure 5.For both averted and direct vision, the increasein visibility becomes less and less with in-creased aperture. I refer to this as a “saturation”effect.

I’ve noted in the figure the effect of dou-bling the telescope aperture from 8 inches to16 inches. The observer would gain 0.14 indirect vision and 0.23 in averted vision, or14% and 23% respectively of the full visibil-ity scale. Using the same technique, the readercan verify the gains for the other incrementsshown in Table 2.

The results in Table 2 demonstrate thatadding 2 inches of aperture, going from a 4-inch telescope to a 6-inch one, provides a dra-matic change of more that 17%. Increasinganother 2 inches, from 6 to 8 inches, providessignificantly less benefit, only 12% and 9%.Doubling the increment to 4 inches, from 8 to12 inches, gets another 14% and 10%. Thebenefits are even smaller for the larger scopes.The reader should keep in mind that these re-sults are for M97. Brighter objects like M51will have a different set of visibility curves. Inparticular, the direct vision line reaches signif-icant visibility levels.

Now let’s turn to the last analysis, and an-swer the question, “What is the net effect oflight pollution on a visual observer’s ability tosee deep space objects like M97?” Again werun VO computer simulation cases in whichwe vary one parameter, in this case sky bright-ness, while holding everything else constant,and see what trends VO predicts in the valuesof the visibility index. Again, to make it sim-ple, we’ll choose some typical values for the other key parameters and use M97 as thetarget.

The results are shown in Figure 6. Therange of sky brightness shown is from 19.0 to22.0 magnitudes per square arc-second (msa).19.0 msa is a moderately dark location. Mostof the people in the U.S. live under skies thatare brighter than 19.0 msa, and 22.0 msa is asdark as it gets anywhere.

The trend lines are nearly straight, withboth averted and direct vision increasing byabout 60 percent over the entire range. I have



Table 2: Affect of Changing Aperture on Visibility

Change In Aperture Averted Vision Gain % Direct Vision Gain %4 to 6 in. 17.3 17.86 to 8 in. 2.1 9.18 to 12 in 14.1 10.012 to 16 in. 9.3 3.916 to 20 in 6.0 1.220 to 24 in. 5.2 0.7

annotated on the map the effect of movingonly 1 msa, which provides a 20% benefit. Inmost cases, one can find a 1 msa darker loca-tion within 10-20 miles. What is strikingabout Figure 6 is that the benefit gained bymoving to a 1 msa darker location is almost aconstant 20% improvement in visibility, re-gardless how dark the starting point is (up toa max of 22.0).

Everyone can tell the difference between18 msa (urban) skies and 19 msa, but fewercan readily detect the difference from 19 to20, 20 to 21, etc. This creates a dual pitfall.First, an observer may not have been aware,until now, how much benefit could resultfrom a darker site, and second, how to find adarker site, since they are not visually very ob-vious.

The answer is to use light pollution maps.First, find out how dark your site really is andthen look around for darker locations close by.You can use the web based maps associatedwith the Clear Sky Clock, or you can considerusing my PC-based maps, the Dark Sky Atlas.You can download a free demo version at http://www.taurus-tech.com/dsa_demo.htm.

Finally I return to my call for help fromreaders to make some simple observations andreport the results to me for comparison to theVO model. A full range of observers and telescopes are needed. Please visit www.taurus-tech.com for details. I haveposted a list of targets, with photos, and thedates and time of observation windows toavoid the moon, and twilight conditions. I’ve also included sample data sheets listing thekey information to be recorded and samplesof visibility descriptions. VO Project pamphlets will also be distributed and projectactivities organized by a number of star parties scheduled for fall and winter of 2008,so please ask your star party organizers for a copy.

All contributors will be acknowledged inthe final, publicly released, research report.This report will document the results of thecomparisons of the observations to the VOmodel predictions and contributors will re-ceive a free copy. In the end, I sincerely hopethat the VO project will result in a tool thatwill be of significant aid in optimizing your vi-sual observing experiences.



SUMMARY OF VISIBILITY RESULTS FOR M97

1. Vision - deep space observers use two types of vision: direct vision and averted vision (referto discussion in the earlier VO article Part I). Averted vision is 20-40% more sensitive than di-rect vision (compare red and blue curves in figures) , but is much less satisfying because youcan’t really see as much detail with peripheral vision.

2. Magnification - For Direct Vision, there is only one “best” magnification, The MUM (Mini-mum Useable Magnification). MUM = Scope Diameter /Eye Pupil Diameter. Visibility falls offrapidly above and below this magnification. For Averted Vision, visibility falls off rapidly belowthe MUM, and the optimum magnification usually falls between the MUM and 2x MUM

3. Eye Pupil Diameter - Typical eye pupil diameter vs. age is shown in Figure 3. For direct vi-sion, an observer loses about 13% visibility over 45 years. For averted vision, the reductionin eye pupil diameter has no effect.

4. Telescope Aperture - As expected, visibility increases with increases in the telescope clearaperture. The gain is not linear. In my observations of M97, the greatest gain occurs for smalltelescopes, and reduces drastically with larger telescopes. Doubling the aperture from 8 in.to 16 in. provides a 23% gain in averted vision, but only a 14% gain in direct vision. Refer toFigure 5 and Table 2.

5. Light Pollution - Light pollution is the biggest cause of telescope blindness, Moving 10-20miles to a darker observing site can have the same benefit as doubling your telescope aper-ture.

6. Test Results - Limited comparison of actual observations to VO visibility predictions hasshown good agreement. More comparisons are needed.

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