APOD: Apollo 17: A Stereo View from Lunar... (2015 Jan 03)

[Nitpicker]

My calculations based on image 22467 and a scale map of the landing site, locate the CSM at ~0.7 km from the camera, and the peak of the South Massif (immediately behind the CSM) at ~43 km from the camera. So, the peak is about 60 times further away from the camera than the CSM. But that's as far as I'm able to take things. I'm not familiar enough with the way anaglyphs work, to know how much the CSM from image 22466 should have been shifted, to make the CSM appear to be 60 times closer than the peak in the anaglyph. I'm not even sure that's possible to calculate in a universal way for all viewers, given that anaglyphs only create an illusion of 3-D.

[Chris Peterson]

My calculations based on image 22467 and a scale map of the landing site, locate the CSM at ~0.7 km from the camera, and the peak of the South Massif (immediately behind the CSM) at ~43 km from the camera. So, the peak is about 60 times further away from the camera than the CSM. But that's as far as I'm able to take things. I'm not familiar enough with the way anaglyphs work, to know how much the CSM from image 22466 should have been shifted, to make the CSM appear to be 60 times closer than the peak in the anaglyph. I'm not even sure that's possible to calculate in a universal way for all viewers, given that anaglyphs only create an illusion of 3-D.

I wouldn't say that the effect is just an illusion. Stereo pairs create true 3D as perceived by us, or any creature with a pair of eyes. They only differ from reality in the sense that we are presented a single view, and can't change our orientation (although virtual reality displays get around this by presenting different stereo pairs with changing attitude and orientation).

An anaglyph simply presents the stereo pair superimposed, using color filters to separate the left and right eye. Whatever mechanism is used, though, the math is trivial- it's just a simple parallax calculation. So if you know the relative distance between two objects, you also know the relative shift.

Most stereo pair images of astronomical objects create a diorama effect. In this scene, our eyes are far too close together to be able to see any depth on the Moon, or to see that the CSM is between us and the Moon. The two images were made not a few centimeters apart like our eyes, but many meters apart. That creates much more parallax and lets us see true depth... but our brain can only interpret it assuming the short baseline between our eyes, so we tend to interpret the image as if we were looking down on a small model of the Moon, rather than the real thing.

[Nitpicker]

Most stereo pair images of astronomical objects create a diorama effect. In this scene, our eyes are far too close together to be able to see any depth on the Moon, or to see that the CSM is between us and the Moon. The two images were made not a few centimeters apart like our eyes, but many meters apart. That creates much more parallax and lets us see true depth... but our brain can only interpret it assuming the short baseline between our eyes, so we tend to interpret the image as if we were looking down on a small model of the Moon, rather than the real thing.

If we had been in the LM observing this scene, we would have been able to wink alternately, or shift our head a little from side to side, in order to determine that the CSM was much closer than the Moon. But with this anaglyph, the original images were taken a very long way apart compared with human eye spacing. So, our brains perceive a sense of depth that is artificially exaggerated because our brains are unable to interpret it in any other intelligible way. Hence why I'd call it an illusion. The placement of the CSMs in the anaglyph could be altered a little to make it seem closer or further away. I am not sure if that particular trick can be done accurately in a universal way, for all viewers, to represent the actual distance ratios. And I am not sure it has been done accurately in this case, compared with the actual distances measured. But it still looks very, very cool.

[Chris Peterson]

If we had been in the LM observing this scene, we would have been able to wink alternately, or shift our head a little from side to side, in order to determine that the CSM was much closer than the Moon.

In fact, we would not, because there would not be enough parallax to engage our 3D vision.

But with this anaglyph, the original images were taken a very long way apart compared with human eye spacing. So, our brains perceive a sense of depth that is artificially exaggerated because our brains are unable to interpret it in any other intelligible way. Hence why I'd call it an illusion.

I wouldn't call it an illusion. We've simply changed the scale of the 3D parallax by increasing the separation between the two images.

[Nitpicker]

If we had been in the LM observing this scene, we would have been able to wink alternately, or shift our head a little from side to side, in order to determine that the CSM was much closer than the Moon.

In fact, we would not, because there would not be enough parallax to engage our 3D vision.

But with this anaglyph, the original images were taken a very long way apart compared with human eye spacing. So, our brains perceive a sense of depth that is artificially exaggerated because our brains are unable to interpret it in any other intelligible way. Hence why I'd call it an illusion.

I wouldn't call it an illusion. We've simply changed the scale of the 3D parallax by increasing the separation between the two images.

I'll concede that winking alternately, on its own, would not be sufficient in this case. We'd also need to rely on the relative motion of the CSM against the lunar background. Increase the parallax by five times though (by moving ones head side to side by about half a metre, say) and the change in angles increases to an amount detectable, based on the 20/20 human visual acuity of one arcmin.

And based on the most simple definition of an illusion as "a distortion of the senses", I'd call anaglyphs illusions. That the exaggerated depth perception observable in the anaglyph makes this scene look like a small model, is the illusion.

[Chris Peterson]

And based on the most simple definition of an illusion as "a distortion of the senses", I'd call anaglyphs illusions. That the exaggerated depth perception observable in the anaglyph makes this scene look like a small model, is the illusion.

A stereo pair need not distort the senses at all. So while an anaglyph made with a wide separation produces the diorama effect, and could be called an illusion, it could also be made with normal eye separation (as with a conventional stereo camera) and would produce a completely realistic, true 3D image. That certainly would not be an illusion.

[Nitpicker]

And based on the most simple definition of an illusion as "a distortion of the senses", I'd call anaglyphs illusions. That the exaggerated depth perception observable in the anaglyph makes this scene look like a small model, is the illusion.

A stereo pair need not distort the senses at all. So while an anaglyph made with a wide separation produces the diorama effect, and could be called an illusion, it could also be made with normal eye separation (as with a conventional stereo camera) and would produce a completely realistic, true 3D image. That certainly would not be an illusion.

I will agree with you that an anaglyph made with normal eye separation is a special case and does not distort our depth perception compared with the natural scene. Yet all anaglyphs, holograms, etc, may be defined as illusions for other reasons, as 2-D planes in space are perceived by our brains to have depth dimensions, making them 3-D images. This differs from the 3-D image of a statue, for instance, which exists in 3-D space.

[Chris Peterson]

I will agree with you that an anaglyph made with normal eye separation is a special case and does not distort our depth perception compared with the natural scene. Yet all anaglyphs, holograms, etc, may be defined as illusions for other reasons, as 2-D planes in space are perceived by our brains to have depth dimensions, making them 3-D images. This differs from the 3-D image of a statue, for instance, which exists in 3-D space.

By that logic a photograph is an illusion, as well. You may choose to consider it as such, but I would not.

[Nitpicker]

I will agree with you that an anaglyph made with normal eye separation is a special case and does not distort our depth perception compared with the natural scene. Yet all anaglyphs, holograms, etc, may be defined as illusions for other reasons, as 2-D planes in space are perceived by our brains to have depth dimensions, making them 3-D images. This differs from the 3-D image of a statue, for instance, which exists in 3-D space.

By that logic a photograph is an illusion, as well. You may choose to consider it as such, but I would not.

No, I suppose that's where I draw the line (to conjure a mental image). A "2-D image" plane does not give the binocular illusion of depth like a "3-D image" plane. Any illusion of depth provided by a "2-D image" plane is based only on the monocular depth perception available to an immovable, one-eyed person, with the possible addition of a narrower focal depth. A two-eyed person has no advantage in looking at a "2-D image" plane.

[Nitpicker]

This might be of interest.

M-933-72-17-T6.jpg

If I'm reading this correctly, the initial descent orbit insertion (DOI-1) was performed by the CSM while it was still docked with the LM. This placed the pair in a highly eccentric orbit (59 / 14.5 nmi). Then we have separation, followed by a short CSM burn that placed it in a slightly different orbit (61.5 / 11.5 nmi). In this orbit, it was lower than the LM at times. Then, the CSM performed another burn to circularize its orbit (required for redocking). Here, too, the CSM perilune (54 nmi) is below the LM apolune (59 nmi). Finally, the LM performs DOI-2, increasing its apolune and decreasing its perilune (59.6 / 6.2 nmi). Still, we have orbit segments where it is higher than the CSM.

These various orbits were maintained for more than two hours after undocking, so there were ample opportunities to photograph the CSM between the Moon and the LM. I think these images were taken shortly before the PDI burn that braked the LM out of lunar orbit and began the final descent.

I've been looking at this a little more closely ... these low lunar orbits have a period of about two hours, so the source images for the APOD, one orbit before landing, are most likely to have been taken about half an hour after the "CSM SEP" burn and about an hour before the "CSM CIRC" burn. This makes more sense, as I calculate the LM to be only about 18 vertical kilometres above the landing site, which in turn is just less than 5 km higher than the arbitrary zero vertical datum of 1,730 km from the centre of the Moon (which I suspect was used for the Apollo missions). This would put the LM's altitude, relative to the zero datum, at about 23 km, or 12 to 13 nautical miles, which is not too far off the quoted "RESULTING PERILUNE" of the "DOI-1" burn, which occurred about nine orbits earlier. (I would expect the LM to be near its perilune, one orbit before landing.) Also, the quoted "VELOCITY CHANGE" of 1.0 ft/s generated by the little "CSM SEP" burn, would have separated the two craft by 700 metres (my earlier estimation) after 38 minutes and given the CSM a slightly lower perilune, so that is a close match as well.

Note that my estimations were not made with terribly high precision and are predicated on the lens focal length being equal to the nominal 60 mm, which may not be exact in this image. But I'm confident I'm in the right ball park.