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181 replies to this topic

### #126 Gleb1964

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Posted 13 September 2017 - 04:22 PM

Thus... with your reasoning... if you combine two 18" mirrors with a precision greater than 1/4 lambda, they will deliver the resolution of a 25", right?

Peter

That is not so easy. If two identical round apertures would be combined by coherent way as interferometer, the Point Spread Function (PSF) of such sintetic aperture looks like Airy disc of a single aperture dissected by a number of parallel lines. As more separation between apertures (so called base of interferometer), desto more and thinner getting lines (or fringes) splitting Airy disc. For polychromatic light the best contrast would be for zero fringe. As fringe scale depends on wavelength (~wavelength/base), contrast of fringes decrease away from zero fringe. Point Spread Function looks like on a picture below. That is how single stars should look like in such sintetic aperture. Any extended object would look as a convolution of PSF over every point of object resulting quite complicated image. So getting high resolution in interferometry is not so straight forward.

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### #127 GlennLeDrew

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Posted 13 September 2017 - 06:44 PM

Thus... with your reasoning... if you combine two 18" mirrors with a precision greater than 1/4 lambda, they will deliver the resolution of a 25", right?

Peter

By what means is this combination to be effected?

If by long baseline interferometry, the resolution increase along the axis connecting the two apertures scales as the separation between them. The wavefront error suffered by the two optics is a rather minor factor, more so the greater the separation. If the two mirrors are separated by, say, 10m, the one dimensional resolution obtained thereby will be that of a 10m mirror. But perpendicular to this 'super resolution' axis the resolving power will still be that of the individual apertures (18" in this case.) The 3-D plot in the preceding post gives a good idea of the resulting Fresnel pattern of diffraction for a modest objective separation.

### #128 PeterDob

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Posted 14 September 2017 - 04:09 AM

Good. Now... who says that our brain isn't capable of merging the images well enough?

When moving the telescope or changing magnification I have to adjust the telescope regularly to obtain a perfect merger of the images. Yet, even when still far from being perfect my brain already starts compensating the remaining error and perfectly merges the images for me. This is actually a nuisance because it makes adjusting the telescope a bit more difficult and not doing it well enough results in headaches after a while.

Yoohoo! I may have the resolution of a 1,45m telescope!!!

Peter

Edited by PeterDob, 14 September 2017 - 04:26 AM.

### #129 Gleb1964

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Posted 14 September 2017 - 09:12 AM

Now regarding gain in bino resolution power. Until resolution is limited by detector contrast threshold, it would be improved by increasing number of observation, for example taking more shorts or adding observation channels, because averaging pushing threshold down. Probably bino may improve seeing limited resolution in certain condition.

Here is picture demonstrating definition of resolution by detector contrast threshold on MTF graph (MTF - modulation transfer function).

Detector Threshold Contrast increases along spatial frequency scale, contrast transfer of optical system decrease, the intersection point gives maximum resolution. In case of enough light and good contrast object resolution defined by cut-off frequency, where MTF getting zero. MTF is a product of Fourier transform over PSF (point spread function), it defined by diffraction limit in ideal system or by the level of aberrations.

Observing by two eyes pushing down threshold and shifting intersection point into higher frequency. The maximum cut-off frequency of MTF graph is not improved by bino. The size of disc Airy is not changed.

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### #130 PeterDob

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Posted 14 September 2017 - 10:36 AM

That's all very interesting and I already knew that seeing isn't such an issue with binocular viewing since I got my first binoviewer.

However, you haven't answered my question. Who says that our brain doesn't combine both images in the same way as the LBT does?

Seeing was particularly calm when I made my observations and in both cases the airy disks were well defined. So how do you explain that observing with both eyes showed more black between both components or, in the case of STF2696, I only saw one elongated star with one eye and both stars well defined with binocular vision?

I refuse to accept that this is simply due to seeing, just like you can read a text from a further distance with both eyes. Unless I see some relevant scientific evidence, which up till now no-one has presented.

Peter

### #131 GlennLeDrew

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Posted 14 September 2017 - 10:55 AM

Peter,

Our eyes already have a fairly large separation with respect to their aperture, by factor at least 10:1. If the resolution gain was to accrue in the manner of that realized by long baseline interfermetry, naked eye observation should reveal this handily. But remember, such a gain, which attends *only* when wavefront coherence is maintained, is seen only along the axis connecting the two apertures. For a separation 10X larger than the apertures, the horizontal resolution would be 10X better than the vertical; a strange thing indeed, which would have an interesting result if we rotate our viewpoint.

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### #132 GlennLeDrew

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Posted 14 September 2017 - 11:11 AM

Peter,

Assuming non-varying atmospheric seeing, and the same optical quality for both tubes, the seeming increased separation between the Airy disks for a very close double star via bino vision cannot arise purely optically. As laid out previously, each eye is seeing the same thing, just as when you alternately blink your eyes while focused on these letters. And so the gains must result from the improved signal to noise, which permits to discriminate subtler contrast. This should better reveal the brightness dip between two partly overlapped Airy disks.

But actually increase the separation between two already separated Airy disks? I've never come close to experiencing that, nor heard of such before. The best explanation for this might be the illusory increase in image scale which is commonly experienced, especially for smaller or more tightly crowded objects/object groupings.

### #133 PeterDob

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Posted 14 September 2017 - 12:03 PM

So you admit that our eyes do work like the LBT, merging images from both eyes, each with their respective resolution limit (most of the time they're not even identical!) and still extracts a higher resolution from them. So why is it so hard to accept that the same happens when looking through a binoscope? Perhaps our brain is even more capable of merging images than the equipment they use on the LBT! Who knows?

I've browsed the web in search for info about the resolution of binoculars and there it is taken as read that a binocular yields a higher resolution than a single tube...

Peter

### #134 Gleb1964

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Posted 14 September 2017 - 02:53 PM

That's all very interesting and I already knew that seeing isn't such an issue with binocular viewing since I got my first binoviewer.

However, you haven't answered my question. Who says that our brain doesn't combine both images in the same way as the LBT does?

Seeing was particularly calm when I made my observations and in both cases the airy disks were well defined. So how do you explain that observing with both eyes showed more black between both components or, in the case of STF2696, I only saw one elongated star with one eye and both stars well defined with binocular vision?

I refuse to accept that this is simply due to seeing, just like you can read a text from a further distance with both eyes. Unless I see some relevant scientific evidence, which up till now no-one has presented.

Peter

Peter, with detection of electromagnetic wave in visible range the fase information would be lost. There is no such fast enough detectors for visible, IR and even far IR range. If step down in frequency by 3-4 orders to therahertz range, there are detectors which can detect both fase and amplitude, those used in radio interferometry (like VLBI), where it is possible to interfere signals after detection by correlating recorded signals. But in shorter range, including visible, information about fase would be lost, detector fixing only signal's intensity (square of amplitude). So interferometry in visible range required only coherent mixing of light before detection. The same valid for eye, it only provide intensity distribution, no fase to correlate signals in brain, no way. No gain in resolution above limit defined by difraction of every single aperture is possible, no change in size of airy disc.

I thought I have explained exactly that before.

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### #135 Kunama

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Posted 14 September 2017 - 05:15 PM

That's all very interesting and I already knew that seeing isn't such an issue with binocular viewing since I got my first binoviewer.

However, you haven't answered my question. Who says that our brain doesn't combine both images in the same way as the LBT does?

Seeing was particularly calm when I made my observations and in both cases the airy disks were well defined. So how do you explain that observing with both eyes showed more black between both components or, in the case of STF2696, I only saw one elongated star with one eye and both stars well defined with binocular vision?

I refuse to accept that this is simply due to seeing, just like you can read a text from a further distance with both eyes. Unless I see some relevant scientific evidence, which up till now no-one has presented.

Peter

Peter, with detection of electromagnetic wave in visible range the fase information would be lost. There is no such fast enough detectors for visible, IR and even far IR range. If step down in frequency by 3-4 orders to therahertz range, there are detectors which can detect both fase and amplitude, those used in radio interferometry (like VLBI), where it is possible to interfere signals after detection by correlating recorded signals. But in shorter range, including visible, information about fase would be lost, detector fixing only signal's intensity (square of amplitude). So interferometry in visible range required only coherent mixing of light before detection. The same valid for eye, it only provide intensity distribution, no fase to correlate signals in brain, no way. No gain in resolution above limit defined by difraction of every single aperture is possible, no change in size of airy disc.

I thought I have explained exactly that before.

This makes sense!  Especially  "coherent mixing of light before detection"

### #136 Fomalhaut

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Posted 14 September 2017 - 05:39 PM

Now regarding gain in bino resolution power. Until resolution is limited by detector contrast threshold, it would be improved by increasing number of observation, for example taking more shorts or adding observation channels, because averaging pushing threshold down. Probably bino may improve seeing limited resolution in certain condition.

Here is picture demonstrating definition of resolution by detector contrast threshold on MTF graph (MTF - modulation transfer function).

Detector Threshold Contrast increases along spatial frequency scale, contrast transfer of optical system decrease, the intersection point gives maximum resolution. In case of enough light and good contrast object resolution defined by cut-off frequency, where MTF getting zero. MTF is a product of Fourier transform over PSF (point spread function), it defined by diffraction limit in ideal system or by the level of aberrations.

Observing by two eyes pushing down threshold and shifting intersection point into higher frequency. The maximum cut-off frequency of MTF graph is not improved by bino. The size of disc Airy is not changed.

That sentence is the eye-opener to me which reveals what I personally hadn't thought of before.

It's the MTF which demonstrates the most important reason (on the instrument's side, of course) why binocular perception is superior to monocular.  -  In the end it's almost always the MTF...

Thanks for this explanation  !

Chris

Edited by Fomalhaut, 15 September 2017 - 03:43 AM.

### #137 PeterDob

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Posted 15 September 2017 - 02:48 AM

That's all very interesting and I already knew that seeing isn't such an issue with binocular viewing since I got my first binoviewer.

However, you haven't answered my question. Who says that our brain doesn't combine both images in the same way as the LBT does?

Seeing was particularly calm when I made my observations and in both cases the airy disks were well defined. So how do you explain that observing with both eyes showed more black between both components or, in the case of STF2696, I only saw one elongated star with one eye and both stars well defined with binocular vision?

I refuse to accept that this is simply due to seeing, just like you can read a text from a further distance with both eyes. Unless I see some relevant scientific evidence, which up till now no-one has presented.

Peter

Peter, with detection of electromagnetic wave in visible range the fase information would be lost. There is no such fast enough detectors for visible, IR and even far IR range. If step down in frequency by 3-4 orders to therahertz range, there are detectors which can detect both fase and amplitude, those used in radio interferometry (like VLBI), where it is possible to interfere signals after detection by correlating recorded signals. But in shorter range, including visible, information about fase would be lost, detector fixing only signal's intensity (square of amplitude). So interferometry in visible range required only coherent mixing of light before detection. The same valid for eye, it only provide intensity distribution, no fase to correlate signals in brain, no way. No gain in resolution above limit defined by difraction of every single aperture is possible, no change in size of airy disc.

I thought I have explained exactly that before.

So... what you're suggesting is that dual- or multiple-mirror telescopes don't work? Or... that two eyes can't have a higher resolution than one?

Peter

### #138 Kunama

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Posted 15 September 2017 - 04:07 AM

That's all very interesting and I already knew that seeing isn't such an issue with binocular viewing since I got my first binoviewer.

However, you haven't answered my question. Who says that our brain doesn't combine both images in the same way as the LBT does?

Seeing was particularly calm when I made my observations and in both cases the airy disks were well defined. So how do you explain that observing with both eyes showed more black between both components or, in the case of STF2696, I only saw one elongated star with one eye and both stars well defined with binocular vision?

I refuse to accept that this is simply due to seeing, just like you can read a text from a further distance with both eyes. Unless I see some relevant scientific evidence, which up till now no-one has presented.

Peter

Peter, with detection of electromagnetic wave in visible range the fase information would be lost. There is no such fast enough detectors for visible, IR and even far IR range. If step down in frequency by 3-4 orders to therahertz range, there are detectors which can detect both fase and amplitude, those used in radio interferometry (like VLBI), where it is possible to interfere signals after detection by correlating recorded signals. But in shorter range, including visible, information about fase would be lost, detector fixing only signal's intensity (square of amplitude). So interferometry in visible range required only coherent mixing of light before detection. The same valid for eye, it only provide intensity distribution, no fase to correlate signals in brain, no way. No gain in resolution above limit defined by difraction of every single aperture is possible, no change in size of airy disc.

I thought I have explained exactly that before.

So... what you're suggesting is that dual- or multiple-mirror telescopes don't work? Or... that two eyes can't have a higher resolution than one?

Peter

I don't think you're reading that post correctly. Multi mirror telescopes are not used visually. I would think the resolution of an 18" binoscope in binocular visual mode is exactly that of a single 18" mirror.  This looks like a never ending thread....

### #139 GlennLeDrew

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Posted 15 September 2017 - 04:13 AM

Peter,

Multi mirrors do work.

Two eyes result in better resolving power than one.

No one here is suggesting otherwise.

You need to understand that our brain cannot possibly process two images in the manner of long baseline interfometry. Nor are the two optical halves of a bino harnessed by some magical power so as to somehow provide to our wondering eyes an image that has the resolution of an aperture even slightly larger than each individual objective. Binocular summation *only* improves signal to noise, by which we perceive subtler contrasts. This in turn results in the discrimination of smaller details and the detection of fainter targets. But that all occurs in our brain. Our eyes see the same two images together that are seen individually.

### #140 GlennLeDrew

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Posted 15 September 2017 - 04:21 AM

Peter,

I stress again that you should simply carefully study this screen with each eye alternately and both together. The two-eyed gains vs one-eyed views seen in such a test are precisely the same as would be realized with any size optical instrument. After all, your eyes are a complete binocular. Adding lenses in front of them changes nothing as regards binocular summation.

You should do the same under the stars, or look at your backyard at night, in order to test in the realm of faintness and lower contrast.

And of course, if you have a small bino test with it as well.

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### #141 Gleb1964

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Posted 15 September 2017 - 04:39 AM

So... what you're suggesting is that dual- or multiple-mirror telescopes don't work? Or... that two eyes can't have a higher resolution than one?

Peter

They do work. And they can do in different ways.

• Coherent way:  combine multiple sub-apertures in one synthetic aperture by coherent way, like interferometers do. In that case the Point Spread Function (PSF) would correspond to synthetic aperture and resolution would improve by changing Modulation Transfer Function (MTF). MTF would rise on high frequencies and cut-off frequency moves left. Resolution do improve because of MTF, diffraction limit do improve.
• Not coherent way, by contributing into one image: in that case sub-apertures just adding intensities (assuming identical sub-apertures for simplicity), the PSF and MTF are corresponds to a single sub-aperture, cut-off frequency does not changed. Resolution improved until it contrast limited, diffraction limit do not improve.
• By parallel channels, where every sub-aperture imaging to it's own detector. That way noise would be averaged and contrast threshold pushed down. That is the case when observing by bino. Resolution improved until it contrast limited, diffraction limit do not improve.

Two eyes of course have a higher resolution than one. Brains filter out imperfections of each of eye but accumulating best to create one picture. Noise would be averaged. Sampling frequency would be improved. However eye is not diffraction limited system until it not stopped down to somewhat 1mm or less. Otherwise it is aberration limited and brains select best, minimum aberrations, of every eye to combine one image. If you stop eyes down to be diffraction limited, like you do when scope's output pupil less than 1mm, than you reaching diffraction limit, and diffraction limit is the same for both eyes as for every of separated eye.

Edited by Gleb1964, 15 September 2017 - 04:43 AM.

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### #142 PeterDob

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Posted 15 September 2017 - 05:03 AM

Who says our brain cannot combine the two images the "coherent" way?

Peter

### #143 PeterDob

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Posted 15 September 2017 - 05:25 AM

Here's a study about binocular resolution (again for medical purposes). The conclusion is that effective resolution with both eyes, regardless of each eye's individual resolution limit, increases by 16%.

http://www.sciencedi...042698901001912

And here's another one:

https://www.ncbi.nlm...pubmed/16043854

I quote:

Binocular summation for detection and resolution thresholds varies as a function of the width of a parallel-line target. The difference between binocular summation ratios for detection and resolution thresholds increases with decrease in target width and increase in eccentricity from the fovea.

This would suggest that our brain may indeed be capable of stacking the images in a "coherent" way.

Furthermore, I'd like to quote something interesting from the first study I mentioned:

Bearse and Freeman (1994) measured binocular summation for orientation discrimination and found that the extent of summation depended on stimulus contrast and duration. Banton and Levi (1991) measured binocular summation for vernier acuity at different contrasts and found significant summation at low contrast but negligible summation at high contrast. Simmons and Kingdom (1998), examining binocular summation for chromatic contrast, found levels of summation greater than would be expected from probability summation alone. Frisen and Lindblom (1988) reported that the level of summation varied with the complexity of the acuity task, with simple detection tasks displaying greater summation than more complicated tasks such as pattern recognition.

In light of all this, it seems clear that the explicitly low contrast conditions of astronomical observing yield a far greater binocular summation than the average 1.41. Who says that this isn't also the case with resolution?

Peter

### #144 Gleb1964

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Posted 15 September 2017 - 05:40 AM

Who says our brain cannot combine the two images the "coherent" way?

Peter

That is not possible because phase information lost with detection.

You are still insist that you see airy disc reduced in size by observing with two eyes, and airy disc is still round shape? You see what is controversial here - if aperture is not round, but extended in one direction, the diffraction point would be reduced in size along direction of extended aperture, it would be not round any more. How binocular vision can overcome diffraction limit in direction, orthogonal to base line of binocular? That is impossible.

That is suggest that when you are talking about reduces size of airy disc that is some other "impression" effects behind that, but not a physical. Coherent combining of two apertures produced not round PSF, like example on a picture I showed before.

### #145 PeterDob

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Posted 15 September 2017 - 05:57 AM

I didn't say that the airy disk was effectively reduced, and certainly not that it was round. I merely said that there was more black between both components which might suggest a reduced airy disk.

I accept your point and thank you for your elaborate explanation. But still I'm not completely convinced. The airy disks are so small that it would be difficult to detect a slight elongation in one direction.

Peter

### #146 Gleb1964

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Posted 15 September 2017 - 06:36 AM

Sorry, may be I misinterpret what you have actually said about reducing the airy disc.

Regarding too small airy discs - it can be easy overcome by stopping down apertures, until you get airy discs comfortably large. Then you can compare airy disc in details by observing bright star with one and two eyes.

If make a stop screen with two separated round halls within one aperture, you can observe how it looks interferometer like point, with coherent summing.

Edited by Gleb1964, 15 September 2017 - 06:43 AM.

### #147 PeterDob

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Posted 15 September 2017 - 06:46 AM

Good idea! I may give that a try...

Cheers,

Peter

### #148 PeterDob

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Posted 15 September 2017 - 08:11 AM

So... if you are right, also binoculars with a wide objective distance would be meaningless. Yet, they appear to increase resolution considerably.

Of course, they're used for Earth observations and not objects at infinite distance. But still...

Peter

### #149 Gleb1964

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Posted 15 September 2017 - 08:46 AM

Parallax effect creates depth. Capacity to resolve depth is directly proportional to the distance between apertures (or base) and reciprocal to the square of distance to the object. That means wider base improves depth resolution on finite distances. For astronomical objects no depth effect can be resolved.

Edited by Gleb1964, 15 September 2017 - 08:52 AM.

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Posted 15 September 2017 - 09:13 AM

Good idea! I may give that a try...

Cheers,

Peter

Peter, if you try reducing the aperture with your 18" binos, I suggest you use off-axis masks as well as central masks.  Centered masks will have the effect of reducing the size of the Airy disc more than a reduced unobstructed apertures as well as increasing the brightness of the first diffraction ring, since the relative size of the central obstruction would be larger.  On the other hand using a central mask to increase the size of the first ring may make it easier to detect any elongation in the image, assuming a bright enough star.  I look forward to your results.

Dom Q.

Edited by daquad, 15 September 2017 - 09:13 AM.

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