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A new DSO object visibility chart

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#1 GlennLeDrew

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Posted 29 September 2016 - 09:18 PM

Deep Sky Object Visibility

 

 

DSO-contrast2.jpg

 

This chart graphically indicates the conditions of visibility for extended (not point-like) deep sky objects as a function of object and [object + sky] surface brightness (SB). For selected values of sky SB and object SB, the computed vales of SB for [object + sky] are drawn as curves. This permits to see at a glance when [object + sky] vs sky SB is sufficient to provide the required contrast for detection.

 

The human visual system is first and foremost a contrast detector. But in the low brightness regime of DSO observing visual system noise is a significant factor, worsening with decreasing scene brightness. This imposes a limit of roughly 27 magnitudes per square arcsecond (MPSAS), beyond which visual noise dominates any signal. Hence the lower SB limit of 28 MPSAS plotted here.

 

As the image dims, visual resolution decreases, and the required angular size for detection increases. At the poorest contrast from which a signal difference can be detected, an object must subtend an apparent angle of several degrees, with some small gain accruing perhaps up to a couple tens of degrees. This chart plots curves for angular size detection thresholds of 0.5, 1, 2 and 6 degrees. Even for a 20 degree limit, the curve plotted for such might lie but a couple tenths of a magnitude to the left of that for 6 degrees.

 

Data from the RASC Observer's Handbook is incoprorated, some of which in turn comes from Blackwell (1946).

 

 

CHART LAYOUT

 

Object SB is plotted on the X (horizontal) axis, increasing toward the right, and ranging between 28 and 13 MPSAS. For perspective, the brightest nebulae have SB ~14 MPSAS. Galaxy and globular cluster cores can peak at 15-16 MPSAS. Color is seen to about as faint 18-19 MPSAS. A dim nebula such as the North America has SB about 24 MPSAS.

 

[Object + sky] SB is plotted on the Y (vertical) axis, increasing upward, and ranging between 28 and 13 MPSAS. This scale represents also the sky SB, in the absence of any superimposed source. For perspective, a Full Moon or heavily light polluted urban sky is about 17 MPSAS. A surburban sky might be 19.5 to nearly 21 MPSAS. A pristine site's sky gets to as dark as 22 MPSAS.

 

Immediately apparent is the empty triangular region in the lower right. No combination of object or sky brightness can be plotted here. The straight-line limit running diagonally, and connecting equal values for object and [object + sky] SB, results from the simple fact that [object + sky] SB essentially equals object SB when the latter is at least several magnitudes brighter than the sky SB. The region inside which data can be plotted is colored. Fainter than the color detection threshold of 18-19 MPSAS for [object + sky], this region is tinted a cool blue-grey. Brighter than this, where the eye can perceive color, the tint is a warm peach. Where the object SB has its contribution greater than that of the sky, and hence dominating, a green wash of color is applied.

 

For each full magnitude interval in sky SB, from 17 to 27 MPSAS, a mostly horizontal curve is plotted for the combined SB of [object + sky]. That curve for a pristine sky of 22 MPSAS is highlighted in purple (but just to object SB = 19 MPSAS; no brighter, so as to not further crowd the converging curves.) Where object SB is much less than Sky SB, [object + sky] SB essentially equals that of sky SB. This is why the plotted curves are flat well to the left of (much fainter than) the rightmost limit. Once Object SB gets to within about 4 magnitudes of sky SB, the combined light begins to result in an upward deflection. All curves are precisely identical, the next one lower being simply displaced down and to the left by 1 magnitude in each axis.

 

A key value of [object + sky] SB has it 2X brighter than sky SB. When object SB and sky SB are equal, the combined light is twice as bright, which is a difference of 0.75 magnitudes. On every curve for sky SB this datum is plotted as a larger blue dot, and connected by a blue line. For example, on the curve for Sky MPSAS = 20, this point on that curve occurs where object SB is also 20, and the [object + sky] SB = 20 - 0.75 = 19.25 MPSAS.

 

Another key value of [object + sky] SB has the object SB 3 magnitudes fainter than sky SB. These data are plotted as red dots connected by a red line. Here [object + sky] SB is 0.06 magnitude, or about 6% brighter than sky SB. For most observers, their mediocre sky will permit to see objects at about this level of contrast when the exit pupil is moderate to large. (More specifics later...)

 

If the human visual system had almost infinite dynamic range, or at least a *very* much lower limit for scene brightness before visual noise becomes of any consequence, the same limits of contrast and object apparent angle would apply for the whole region bounded by this chart. But that is not so.

As scene brightness decreases, visual system noise worsens and ever more greatly impairs the detection of contrast. This requires that an object subtend a larger apparent angle in order to be detected. Or conversely, at given angular size the object becomes progressively harder to detect. To visualize the trends that result, four black curves are drawn for size detction limits of 1/2, 1, 2 and 6 degrees. These limits have the required minimum size increasing to the left, toward fainter object SB. Note how the limit values would become exponentially more crowded together toward the left if the interval was linear. That these curves plunge more vertically than the aforementioned limits very directly reveals the impact of the worsening visual noise. And the steepening toward fainter [object + sky] SB shows how the *rate* of increase in visual noise increases. The 6 degree limit curve both intercepts the limit for plotted data *and* becomes nearly vertical at 27 MPSAS; a consequence of the limit where visual noise dominates any signal at about 27 MPSAS. (As noted earlier, extending to a size limit for detection of a couple tens of degrees could gain a couple tenths of a magnitude.)

 

-----

 

Useful formulae and data are included in the othewrwise unused region of the chart.

 

The professional community expresses SB as magnitudes per square arcsecond (MPSAS), and I encourage the amateur to do so, too. Magnitudes per square arcminute has the advantage of resulting in a number nearer to the integrated magnitude, which does correspond exactly when the object has an area of 1 arcminute^2, a size corresponding to numerous planetary nebulae and distant galaxies. The conversion factor from MPSAS to MPSAM is included, for convenience. But it is better to become familiar with and use exclusively MPSAS, in my opinion.

 

To assess the telescopic visibility when the exit pupil is smaller than the observer's iris, it's necessary to calculate the amount of dimming compared to the maximal, iris-equaling exit pupil diameter. One's own fully dilated iris is the benchmark for the full-brightness image. It suffices to relate the exit pupil to *your own dark adapted iris*, whether larger or smaller than the average; there is no pressing need to establish an absolute fiducial corresponding to a particular iris diameter. A more extreme example, to show how significant dimming via a small exit pupil can be: Compared to a 7mm iris, an exit pupil of 0.7mm dims the image by a factor of (7 / 0.7)^2 = 100, or LOG(100) * 2.5 = 5 magnitudes. If the sky is 22 MPSAS, the telescopic sky image will be 22 + 5 = 27 MPSAS.

 

Filters are used to enhance object contrast by transmitting as much light from the object as possible while rejecting the maximum of unwanted light. The filters for which the effect is most consistent are those intended for emission nebulae. Typically 90+ per cent of the visible nebular emission is transmitted, and a good fraction of sky glow is blocked. Two well known Lumicon filters are represented; their equivalents by other makers should have fairly similar efficacy. You can safely enough treat your filter as though transmitting all nebula light, or you can reduce the object SB by 0.1 or 0.2 MPSAS if filter transmission is 90% or 80%, respectively. (Unless you wish to be rigorous and calculate the loss more formally.)

 

 

HOW TO USE THE CHART

 

While intended primarily to reveal trends, and thereby aid in developing an appreciation for the dimensions and magnitude of impact for the relevant variables, this chart can serve as something of a predictor of object visibility. The two variables you *must* have are sky SB and Object SB. These will at least indicate the contrast, and hence if the object could ever be seen given sufficient aperture. When you know the object size, you can see if it meets the detection threshold for size at given magnification and exit pupil dimming (for a particular objective aperture.)

 

-----

 

First we will assume a telescope used at lowest magnification, without filters. The exit pupil equals the eye's iris, and the scene surface brightness is maximal, just about equaling the unaided eye brightness. There is no exit pupil dimming to account for.


Case #1

Sky SB = 21 MPSAS
Object SB = 22 MPSAS (1 mag. dimmer than the sky)
Object size = 10 arcminutes (1/6 degree)
Telescope aperture = 200 mm
Exit pupil = 6mm (same as eye's iris)
Magnification = 200 / 6 = 33.3X

 

Given the above, we calculate the object's apparent angular size as 33.3X * 10' = 333 arcminutes, or 333 / 60 = 5.6 degrees.

 

On the graph, locate the curve for Sky MPSAS = 21 (it's the next one above the purple curve for a sky of 22 MPSAS.) Follow it to the point where it intercepts Object MPSAS = 22, on the X-axis. Estimate the [object + sky] SB from the Y-axis scale. You should obtain ~20.6 MPSAS. This is ~0.4 magnitude, or roughly 40% brighter than the surrounding sky, and represents not particularly poor contrast.

 

Compare this point with the curves for the detection limit for size. We see it lies between the curves for 1/2 and 1 degree, nearer to the former, and can say the object should subtend ~35 arcminutes in order to be seen. This is well below the observed extent of 5.6 degrees, and so the object can be expected to be fairly well seen.

 

We might ask, "What would be the minimum aperture required to see this object, if the exit pupil is also 6mm?"

 

We know the minimum size for detection to be ~35'. A 10' object magnified to 35' requires 35 / 10 = 3.5X. At a 6mm exit pupil, the objective apreture must be 3.5 * 6 = 21mm. A 4X20 bino, or a 6X30 finder should serve to detect this object with reasonable surety.

 

-----

 

Now we consider an object observed using a smaller exit pupil, which dims both the object and the sky equally.

 

Case #2

Sky SB = 21 MPSAS
Object SB = 22 MPSAS (1 mag. dimmer than the sky)
Object size = 2 arcminutes (1/30 degree)
Telescope aperture = 200 mm
Exit pupil = 2mm
Eye's iris = 6mm
Magnification = 200 / 2 = 100X

 

We calculate the object's apparent angular size as 100X * 2' = 200 arcminutes, or 200 / 60 = 3.3 degrees.

 

Now the exit pupil dimming must be accounted for. The brightness ratio = (6 / 2)^2, which is a factor of 9; compared to a 6mm exit pupil, a 2mm exit pupil dims *both* the object and sky to 1/9 their undimmed brightness. In magnitudes this LOG(9) * 2.5 = 2.4. And so through that 2mm exit pupil the Sky SB = 21 + 2.4 = 23.4 MPSAS, and the object SB = 22 + 2.4 = 24.4 MPSAS.

 

On the graph, interpolate for the curve for Sky MPSAS = 23.4, and Follow it to the point where it intercepts Object MPSAS = 24.4, on the X-axis. Estimate the [object + sky] SB from the Y-axis scale. You should obtain ~23 MPSAS. Because the object and sky SB differ by the same 1 magnitude as for Case #1 above, the same ~0.4 magnitude, or roughly 40% brighter than the surrounding sky, obtains for the object relative to the surrounding sky. We have the same intrinsic scene contrast, as expected.

 

Compare this point with the curves for the detection limit for size. We see it lies barely to the right of the curve for 2 degrees, and can say the object should subtend probably something like 1.8 degrees in order to be seen. This is safely enough smaller than the observed extent of 3.3 degrees, and so the object can be expected to be seen without too much trouble.

 

The important lesson here is that for the same object and surface brightness, a dimming by 2.4 magnitudes via a smaller exit pupil demands that for its detection an object must increase in minimum apparent angle by a factor of 3!

 

-----

 

Now we introduce a nebula filter, which passes (nominally) all visible nebular light of consequence but darkens the sky. We will use all conditions for Case #2, the only differences being magnification/exit pupil and the addition of a line filter which we will assume to not dim the nebula at all.


Case #3

Sky SB = 21 MPSAS
Object SB = 22 MPSAS (1 mag. dimmer than the sky)
Object size = 2 arcminutes (1/30 degree)
Telescope aperture = 200 mm
Exit pupil = 6mm
Eye's iris = 6mm
Magnification = 200 / 6 = 33.3X
Line filter (e.g., O-III or H-beta), which dims the sky by 2.6 mag.

 

We calculate the object's apparent angular size as 33.3 * 2 = 66.6 arcminutes, or 66.6 / 60 = 1.1 degrees.

 

Now the dimming of the sky by the filter must be accounted for. The sky SB = 21 + 2.6 = 23.6 MPSAS.

 

The object is not dimmed due to the iris-equalling exit pupil of 6mm and the filter's transmission of all visible nebular emission, and so still has SB = 22 MPSAS, which is now 23.6 - 22 = 1.6 magnitudes *brighter* than the surrounding sky. Contrast has been greatly boosted!

 

On the graph, interpolate for the curve for Sky MPSAS = 23.6, and Follow it to the point where it intercepts Object MPSAS = 22, on the X-axis. Estimate the [object + sky] SB from the Y-axis scale. You should obtain ~21.75 MPSAS. And so the combined light of object and sky make the object appear to be brighter than the sky by 23.6 - 21.75 = 1.85 magnitudes. (versus 0.4 magnitudes when not filtered.)

 

Compare this point with the curves for the detection limit for size. We see it lies well to the right of the curve for 1/2 degree, meaning it should be detected when larger than perhaps 20 arcminutes. This is comfortably smaller than the subtended size of 1.1 degrees, and so can be expected to be reasonably well seen.

 

FINAL NOTES

 

The threshold for color detection must surely vary depending on the degree of color purity and difference. For instance, if the surface brightness for object and sky are the same, the blue-green for an emission nebula seen against a reddish sky glow could well have its hue be more pronounced than for a less spectrally pure object seen against a sky glow of not so different color to that of the object. And so the threshold of 18-19 MPSAS, as well as the demarcation separating the regions where object and sky are dominant, are probably somewhat indistinct. One of the glows could be a bit dimmer, yet nonetheless exhibit its color more strongly.

 

The series of curves for various sky SB, as noted, all have the same form as defined by the brightness *ratios.* They superficially resemble hyperbolas, where the extensions away from the region of greatest inflection converge asymptotically to the left and upper right, as set by the limits of sky SB and object SB, respectively. Outside of 4 magnitudes removed from the intercept where object and sky SB are equal, the curves are essentially flat. This is because by the time one or the other of sky and object SB exceed the other by 4 magnitudes, the dimmer of the two adds practically no light of consequence, and the curve thereafter assumes an essentially straight line.

 

Hopefully the examples provided will sufficiently instruct on the chart useage. At the very least study and appreciate the implication of the impact induced by the differing and changing slope of the curves for minimum size for detection. This reveals much behind the deficiencies of the visual system at such low brightness levels.

 

Perhaps the most useful rule of thumb to derive: In the brightest sky under which one might do any kind of DSO observing, the object can be detected when its SB is as much as 4 magnitudes fainter than the sky SB. But near the limit of sensible sky brightness as seen through a small exit pupil, the object must have SB about equal to sky SB.

 

And to remind: Between the brightest sky just about conceivable for DSO work (17 MPSAS) and the dimmest the visual system can work with (27 MPSAS), we have 10 magnitudes, or a brightness range of factor 10,000.


Edited by GlennLeDrew, 30 September 2016 - 05:18 AM.


#2 GlennLeDrew

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Posted 29 September 2016 - 09:21 PM

I'm not sure how well this chart will appear; it seems it might have been downscaled a bit from the 1200 pixel wide array... Let me know if you have trouble reading it.



#3 Asbytec

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Posted 29 September 2016 - 11:44 PM

Glenn, thank you for all the work you do. Now, let me get some coffee and read it...

 

The chart looks fine. When you download it, it expands out nicely to a larger, readable chart. 


Edited by Asbytec, 29 September 2016 - 11:45 PM.


#4 GlennLeDrew

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Posted 30 September 2016 - 05:25 AM

To plonk this epistle here, I copied the text from a Notepad file, but no double returns were carried over. I had to manually add a good many extra returns in order to separate paragraphs and sections, but missed a few. I just fixed them, and also made a handful of minor tweaks in the text to clarify some passages.

 

You might wish to select/copy the new text and paste it into a file to save locally... If this cannot be done (e.g., when using a phone) from *this* page, I should think it would work if you hit the "quote" reply button, and grab the text from the reply form.


Edited by GlennLeDrew, 30 September 2016 - 05:27 AM.


#5 GlennLeDrew

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Posted 30 September 2016 - 05:29 AM

Norme,

Thanks for the reminder about saving the image. It seems CN cooks up a lower resolution version for display, which moreover has fairly coarse compression applied.



#6 YKSE

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Posted 30 September 2016 - 09:23 AM

Great write up and explanations, thanks.



#7 Asbytec

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Posted 30 September 2016 - 02:48 PM

Glenn, 

 

Here's an interesting case of NGC 925

Sky SB = 21 MPSAS
Object SB = 23.8 MPSAS (2.8 mag. dimmer than the sky)
Object size = 10.5 arcminutes
Telescope aperture = 70 mm
Exit pupil = 1.8mm (same as eye's iris)
Magnification = 70/1.8 = 39X

 

Moving along the 21 MPSAS line to the object brightness of 23.8 MPSAS, gives an object + Sky SB ~ 20.9 or about 8% brighter than the sky. I figured since the object was 8% brighter than the sky, he should see it. A bit premature, maybe, since I do not take into account the critical size for detection. 

 

Also using this converter http://www.unihedron...NELM2BCalc.html

 

Now, moving along the 21 MPSAS line to an object brightness of 23.8, we land almost exactly on the 6 degree (360' arc) line for detection and confirming ~ 20.9 apparent object SB. Since the object is 10.5' arc, it requires about 360/10.5 ~ 34x to attain the proper critical size. So, it seems the critical size criteria is met since the observation was made at 39x. 

 

So, with the critical size and 8% contrast are sufficient, I think a 70mm at ~2mm exit pupil could see NGC 925 under these conditions. However, working the math above in case 1, for a 6mm exit pupil, the solution is for a minimum aperture of 206mm to observe it. Does the minimum aperture required change with exit pupil or object's apparent SB? I might think so since the critical size is achieved and the contrast is sufficient. 

 

Also, assuming a 6mm iris and 2mm exit pupil, we get a sky and object dimming of (6mm/2mm)^2 = 9 times fainter or 2.5 * Log(9) = 2.4 magnitudes. So, the sky becomes 21 MPSAS + 2.4 = 23.4 MPSAS and the object apparent (sky + Obj) SB from 20.9 MPSAS + 2.4 = 23.3 MPSAS thus maintaining 8% contrast. I would not think 23.3 MPSAS is too dim to see when the sky is that dark and the critical size is attained. 

 

Is this a valid means to compute minimum aperture required? Some reports say a 4" is minimum, the math says an 8" is minimum, and I think maybe a 70mm could observe it - under the conditions listed above.


Edited by Asbytec, 30 September 2016 - 02:50 PM.


#8 GlennLeDrew

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Posted 30 September 2016 - 06:14 PM

Norme,

You supply an exit pupil of 1.8mm and say this is the same diameter as the dark adapted iris? Wouldn't that be an abnormally small iris?

 

If that is true, a 6mm exit pupil cannot apply, for the 1.8mm iris would stop down the system.

 

Now, if you intended the observer's iris to be, say, 6mm, rerun the scenario with this in mind.



#9 GlennLeDrew

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Posted 30 September 2016 - 06:24 PM

I must address an oversight in my 'user guide.'

 

Any single surface brightness figure based on the full object dimensions *must* be the average SB. If the object exhibits only small brightness variation, and the area calculated is reasonably representative, the mean SB so derived will be well applicable over the full object. And hence this 'predictor' will supply a fairly reliable result.

 

But if the SB varies widely across the object, and/or the area calculated is not well representative, this 'predictor's' result must be treated with circumspection. For example, a face-on spiral galaxy having a compact core of high SB but a vast disk of very low SB, will have a mean SB calculated as quite faint, yet the core could 'punch through' notable sky glow and be seen with a surprisingly smaller aperture than indicated.

 

In such cases, it would be ideal to estimate the relative contribution of the bright and faint components, derive their integrated magnitude, and then run separate examinations for each, as though fully independent objects that happen to be superimposed.


Edited by GlennLeDrew, 30 September 2016 - 06:27 PM.


#10 Asbytec

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Posted 30 September 2016 - 07:40 PM

"You supply an exit pupil of 1.8mm and say this is the same diameter as the dark adapted iris? Wouldn't that be an abnormally small iris?"

 

No, it's not a normally dark adapted iris, but it is the exit pupil at the magnification required for detection regardless of the iris. That's why I dimmed the image (on the retina) for the smaller exit pupil to see how bright it would be.

 

If we used a 6mm exit pupil with a 70mm aperture we'd have a magnification of 12x and not sufficient magnification to reach the 360' arc critical size and thus not seen. The minimum aperture in the case of a 6mm exit pupil would be about 200mm providing the proper 34x magnification. The surface brightness of the image seems bright enough and brighter than the sky at 20.9 MPSAS, but if we account for a 1.8MM exit pupil and sufficient magnification, we arrive at 23.3 MPSAS for the image.

 

I still think ~23 MPSAS is bright enough to be observed under descent skies - as an average SB for an object that varies in real SB across its angular dimension. He'd likely see the brighter parts, at least. I believe that's what happened when I observed NGC 891 in 19.5 MPSAS skies. On average, the object was approaching 4 magnitudes dimmer than my sky resulting in an average of ~2% brighter than the sky. But, I only saw the brighter core region with some difficulty, not the entire dimmer expanse. 

 

I'm still a little confused over why the exit pupil has to be the same diameter of the iris to determine the smallest aperture required to see the object at its average SB. The ratio of surface brightness is constant (ignoring transmission), but one question is how dim can we observe. I am thinking an object with an average 23 MPSAS is well above the noise level to be observable, at least its brighter parts.

 

I understand a 6mm exit pupil and iris provides plenty of irradiance on the retina, and in a 200mm aperture it also provides sufficient image scale. A 6mm exit pupil does not provide sufficient image scale in a 70mm, but a 1.8mm does even dimmed to 23.3 MPSAS with the same 8% contrast with the sky. That's what's confusing me, I think. 

 

Do we have to use the dark adapted iris as a measure when apparent angular dimension also matters? Need to think that through a bit more...thanks. 



#11 GlennLeDrew

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Posted 30 September 2016 - 07:57 PM

Norme,

The part of the process you skipped over is the dimming of both the sky and the object due to the 1.8mm exit pupil.

 

If sky = 21 and object = 23.8, that small-ish exit pupil will knock off nearly 3 magnitudes from each. The use of the actual figures for object and sky SB as measured or calculated applies only when the exit pupil equals the dark adapted iris. Any cause of object or scene dimming *must* be reflected in a new, fainter object and/or sky.

 

Without doing the calculation, and simply assuming an exit pupil dimming of 3 magnitudes, you now use object and sky SB of 26.8 and 24 MPSAS, respectively.

 

Back to the blackboard with you! ;)


Edited by GlennLeDrew, 30 September 2016 - 07:58 PM.


#12 jetstream

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Posted 30 September 2016 - 11:03 PM

Excellent Glenn, thanks. :waytogo:



#13 Asbytec

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Posted 01 October 2016 - 12:00 AM

Back to the blackboard with you!

 

:)

 

I was just popping back to answer my own question. Because the telescope cannot make the object brighter than it is to the dark adapted eye, then an 8" telescope provides that surface brightness with sufficient image scale at the same exit pupil as the dark adapted eye. Got it, and this is how the chart is calibrated, I believe. 

 

Back to the blackboard, though. Yes, the image of NGC 925 is 23.8 MPSAS requiring 6 degrees angular extent to observe it prior to magnification at a reduced exit pupil. Dimming by reducing the exit pupil to 1.8mm takes the object and the sky to 2.4 magnitudes dimmer at 23.4 and  26.2, respectively. I dimmed the image, but dimmed it from it's apparent sky plus object SB of 20.9 MPSAS adding 2.4 magnitudes to 23.3 MPSAS. I did forget the to recalculate for the dimming and run the chart again to find the apparent angular size required at these dimmed magnitudes.

 

Accounting for the smaller exit pupil, and moving along the sky SB line at 23.4 MPSAS to an object brightness of 26.2 MPSAS, the chart gives a combined surface brightness of about 23.3 MPSAS (as before) and still inside the Obj + Sky SB = 3 curve. It's still just slightly brighter than the sky at this exit pupil rather than the 21 MPSAS and 20.9 MPSAS as seen with a dark adapted iris. However, at the dimmed SB for both, the angular extent to observe the object (assuming a uniform surface brightness) is now well beyond 6 degrees required by a normally dark adapted eye and large exit pupil. 

 

I think I got it...I do remember you saying so not long ago. 



#14 GlennLeDrew

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Posted 01 October 2016 - 12:29 AM

Norme,

The panoply of numbers were making my eyes a bit jumpy. ;) I'll work through the problem, assuming an observer iris diameter of 6mm...

 

Obj = 23.8 MPSAS

Sky = 21 MPSAS

Iris = 6mm

Exit pupil = 1.8mm

 

Exit pupil dimming = LOG((6 / 1.8)^2) * 2.5 = 2.6 mag.

 

Observed SB in the eyepiece for obj = 23.8 + 2.6 = 26.4 MPSAS, and

Sky = 21 + 2.6 = 23.6 MPSAS

 

Now you hit the graph, interpolating to the curve for sky SB = 23.6, and locating the point where it intercepts obj SB = 26.4

 

[obj + sky] ~23.5 MPSAS, or barely brighter than sky SB. This point is *well* to the left of the 6 degree detection threshold--or *any* size threshold. (Recall: the ultimate detection threshold of a couple tens of degrees would gain perhaps a couple tenths of a magnitude vs that for 6 degrees.) The object is not expected to be seen.

 

For our purposes, we can take any plotted point that appears to the left of the 6 degree detection threshold curve as representing likely invisibility. (Bearing in mind the caveat regarding objects which have a portion of significantly higher SB than the rest.)



#15 Asbytec

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Posted 01 October 2016 - 06:24 AM

Got ya. Made my eyes jumpy, too. :)

I see where you described it well enough in case 2, I worked out another problem to see if I could actually run the numbers. Got confused I guess. Hope others can benefit from my jumpy eyeballs...

Thank you, Glenn.

#16 Organic Astrochemist

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Posted 01 October 2016 - 12:04 PM

I think this can be really useful. For example, I think it shows why it's so much harder to see M1 (SB 20.5) under 17MPSAS skies than 18MPSAS.

I think it's helpful that Glenn has added bright skies to the graph, but I think these might be even more disadvantageous than indicated. The chart suggests that, for a given size, the faintest object will be detected with the eyepiece with the longest focal length. I'm not sure that's true under bright skies where the bright view at large exit pupil might preclude attaining a fully dark adapted pupil. The resulting pupil constriction (and photobleaching?) would dim the image without magnifying the object. The reduction of exit pupil of a smaller focal length eyepiece might be partially offset by a greater level of dark adaptation; in combination with increased object size, the (slightly) smaller focal length might permit detection of dimmer objects. I think that's my experience. Does that explanation make sense?

#17 GlennLeDrew

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Posted 01 October 2016 - 03:56 PM

I'm reasonably certain that a 17 MPSAS sky is not bright enough to cause the iris to constrict. It might require a field several magnitudes brighter to do so. If I hadn't lent out my SQM a long time ago, I would determine my own threshold for iris constriction.

 

This can be done indoors where the lighting of a wall can be controlled. Iris diameter is determined by holding an occurring bar close to the eye while looking at a compact, not bright light, and finding the bar width which just barely blocks the light source.

 

I would appreciate if someone having an SQM would try this...



#18 jetstream

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Posted 01 October 2016 - 04:02 PM

I'm reasonably certain that a 17 MPSAS sky is not bright enough to cause the iris to constrict. It might require a field several magnitudes brighter to do so. If I hadn't lent out my SQM a long time ago, I would determine my own threshold for iris constriction.

 

This can be done indoors where the lighting of a wall can be controlled. Iris diameter is determined by holding an occurring bar close to the eye while looking at a compact, not bright light, and finding the bar width which just barely blocks the light source.

 

I would appreciate if someone having an SQM would try this...

Would drill bits work Glenn?



#19 GlennLeDrew

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Posted 01 October 2016 - 05:31 PM

Drill bits have commonly enough been used for this very purpose. Allen keys, too. Or one could make up a gradually tapered strip, with width marks at 1mm or 0.5mm intervals. Or one can (still?) purchase from Sky&Tel a pupil measuring gauge.



#20 Organic Astrochemist

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Posted 01 October 2016 - 08:20 PM

Thanks for responding. As an example of what a great website this is look at what a Google search turned up
http://www.cloudynig...ness-magnitude/
Basically, according to Atchison and Smith (and Clark) 18 MPSAS would yield and eye pupil of 6 mm and brighter than this, the pupil would be smaller.
I think that dark adaptation may be more complex than just pupil size, so other factors may be at work to explain why dark adaptation at 17MPSAS will not be the same at, say, 21 MPSAS. This might affect telescopic observations under these different conditions.

#21 Asbytec

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Posted 01 October 2016 - 08:53 PM

The chart suggests that, for a given size, the faintest object will be detected with the eyepiece with the longest focal length.

 

The idea is, to my understanding struggling with the same problem, a telescope cannot make the image any brighter than the dark adapted naked eye view. The image has the same surface brightness through a dark adapted iris as it does through a telescope with the same size exit pupil. The only difference is the view through the telescope is magnified providing sufficient angular size of the image at that exit pupil (which means the aperture is the variable we're looking for.)  

 

It's likely, with direct lighting in the area under brighter skies, we will not be fully dark adapted. But, a telescope operating at a large exit pupil will still form an image with the same surface brightness of, and contrast between, the sky and the object as before. If our iris is smaller than fully dark adapted, our naked eye view will be dimmed and the view through the telescope's larger exit pupil will be vignetted to a smaller effective aperture.

 

The naked eye image is dimmed by our smaller iris, but not the telescope operating at an exit pupil of our dark adapted eye. In order to regain full effective aperture, the exit pupil will have to reduce to the size of our non dark adapted iris (or smaller than our iris.) Using a smaller exit pupil dims the object and the sky by square of ratio of (max light grasp and fast focal ratio) of the dark adapted iris to the actual exit pupil (magnification) by a factor of (Max Iris/EP)^2. 

 

When the smaller exit pupil is the same size as a our iris, we have to recalculate the surface brightness of the image and the sky as seen by both the non dark adapted iris and the more highly magnified image at the same size exit pupil. Both sky and image are dimmed by the surface area of the smaller exit pupil. The sky and image surface brightness (per sq arcsecond) are not as bright as they would be when dark adapted and using the same size exit pupil. The relationships on the graph still apply, though, including the ratio of image to surface brightness.

 

Complicating matters, to my understanding, the angular size for visual detection and the magnification of the exit pupil do not increase at the same rate. And, yes, there is some chemical process going on within the eye, as well. You iris can expand rapidly, but it takes a short while for the chemicals to build up to full dark adaption.



#22 GlennLeDrew

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Posted 01 October 2016 - 09:09 PM

I *should* be aware of the currently accepted transition in scene surface brightness where the iris is commanded to contract. I had thought that for a full Moon sky SB the iris would still be maximal.

 

There is the *possibility* of a misperception in the conversion between Cd/m^2 and MPSAS, potentially leading to an incorrect appreciation.

 

If indeed the iris commences to stop down at about 18 MPSAS, the effect at 17 MPSAS should not result in a notable diminution.

 

But our own exploration with an SQM and 'pupil gauge' should provide a result from which greater confidence might obtain.



#23 Ptarmigan

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Posted 02 October 2016 - 10:48 PM

Interesting and useful.  :cool:  :waytogo:



#24 Starman1

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Posted 03 October 2016 - 12:09 AM

After all the above, you might find this useful:

http://scopecity.com...-calculator.cfm

 

Note to mods: no commercial business takes place on this website any more.


Edited by Starman1, 03 October 2016 - 12:10 AM.


#25 dingye

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Posted 19 January 2017 - 06:23 AM

Great chart!

 

I have a question, how about the binoculars? Will a 100mm bino work as a 140mm scope or not? How to calculate the exit pupil in this case?

 

Then how about binoviewing?




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