Thanks for this most thorough critique of Groves' analysis Thabiguy. There are a few aspects of your reponse where I feel you've been a little disingenuous to Groves, but largely because you now have the benefit of having his analysis in front of you. For the benefit of those readers who don't I hope you won't mind me clarifying certain aspects. Also, some aspects of your response raise questions in my mind, and I hope you won't mind me playing devil's advocate in order to try to understand matters a little better. Many if not all of the answers to these questions may well lie in my fairly basic understanding of photography. I hope that nobody construes my following comments as an indication of a renewed degree of uncertainty. I am, in fact, very close to doing a 'Hatton'. My comments are targeted more at challenging the accuracy and objectivity of Thabiguy's critique, which I doubt anybody would object to, at least in principle:
1.1. Field of view
Groves begins by trying to determine the field of view of Apollo 11 surface photographs taken with the Hasselblad 500 EL/70 cameras with 60 mm Zeiss Biogon lens. The method that he chooses to do this is curious: he takes a different camera (120 Bronica) with different focal length (75 mm), claims to measure the field of view with that one (or pulls the result out of thin air; he offers no reference for the given value other than his purported home experimentation, so it cannot be checked) and does a calculation to determine what the value would have been with the focal length of 60 mm.
For the benefit of those without access to the Groves analysis, he photographed a ruler positioned horizontally, i.e. parallel to the top and bottom of the image, to pass through the centre of the image. Contrary to Thabiguy's comment above, Groves did not 'pull the result out of thin air' nor 'offers no reference for the given value', he provides, within the analysis, a diagram of the arrangement for establishing the FOV showing all relevant dimensions and measurements taken. We do not have to take Groves' word for the results, however, if we are suspicious; we are free to conduct the same or a similar experiment to test it. It is interesting to note why Groves' chose to measure the FOV:
As camera/lens data sheets tend not to have scientific accuracy and the 'angle of view' of the lens can be quoted ambiguously, (either across the image or along a diagonal of the image) the angle of view was determined practically.
I suspect that Groves did not have access to a Hasselblad 500 EL/70 and chose to use the 120 Bronica instead. Whilst it does indeed seem odd that he chose to use a 75mm focal length lens to calculate the field of view (FOV) instead of a 60mm as used on the Hasselblad, his methodology indicates that he is strongly of the view that it matters not because the FOV for a 60mm lens can be accurately calculated from the measurements taken from a 75mm lens. Now, this seems pretty fundamental to me. Either Groves is woefully mistaken in his understanding here, or he isn't. I don't know one way or the other, but is it not a
matter of fact that
for any given camera body the FOV for
any lens with focal length x can be calculated by reference to measurements taken from a calibrated photo taken using a lens with focal length y? If it
is a matter of fact, then Groves methodology must be sound. If not, then his whole analysis collapses right from the get go. Does anybody know the answer to this fundamental question? Picking up on the underlining above, is it not the case that the same lens fitted to two different camera bodies will always derive the same FOV? Groves used a 120 Bronica compared to a Hasselblad 500 EL/70. If so, then, again, Groves' methodology must be sound. If not his analysis collapses. What's the answer to
this fundamental question?
Groves comes to the conclusion that the horizontal/vertical field of view of Apollo 11 surface photographs is 37.987 degrees.
Major flaw: this figure differs significantly from published values.
See Groves' comment above regarding the uncertainty over 'published values', although it seems clear what the FOV figures mean in the NASA Report as they're quoted both across and diagonally (actually, that raises an interesting point that might help answer the questions above: Given that lenses are
circular there is only really one FOV for any one lens. Quoting an FOV 'across' and 'diagonally' must, therefore, be in recognition of the internal 'cropping' effected by the rectangular or square imaging plane within the camera body. Does that not mean, then, that the 'true' FOV is determined by the dimensions of the imaging plane, and
not by the lens itself? If so, then the FOV for every camera type is, presumably, different to varying degrees. It would also mean that Groves' analysis is fundamentally flawed from the out!
The horizontal/vertical field of view is officially reported to be 49.2 degrees (source:
Apollo 15 index of 70 mm photographs, page 4).
Actually, the vertical FOV is not stated in the NASA Report, so I assume you know that the camera had a square imaging plane. Groves also uses the FOV angle obtained from a horizontal measurement and applies it to the analysis of vertical features, so I can only assume he knew that to be the case too.
An interesting observation regarding this report is that the cameras used are not actually specified exactly, other than to identify them simply as 'Hasselblads' with 70mm film width. This seems odd to me, given the formality and nature of the report, unless, of course, the camera body has absolutely no relevance to the images obtained, as queried above. If the camera body
does have some relevance, then it could be argued that the NASA report has little or no relevance to Groves' analysis, given that it relates to the
Apollo 15 mission and the exact camera types/models are
not specified.
This page gives the horizontal field of view as 49.25 degrees.
We don't know Craig Lamson's source of this data, so it cannot be considered to be reliable, and certainly doesn't serve to validate the NASA Report. It could, indeed, be obtained from the NASA Report, although there is a slight inconsistency in the figures provided by each source.
Or we can use
this page and do Groves-style calculation,
new FOV = 2*arctan(tan(old FOV/2)*old focal length/new focal length)
from published value of 37.9 degrees (for 70mm Hasselblad with 80mm lens) to get, again, 49.2 degrees for 60mm focal length.
Again, according to Groves, published values cannot be relied upon, although it does seem to validate the figure provided in the NASA Report. Is it possible that all of the NASA figures are 'theoretical' (and possibly wrong), because none has been obtained 'practically', as Groves' figure is?
This seems to answer the question above that it is indeed a
matter of fact that for any given camera body the FOV of a lens with focal length x can be calculated by reference to the FOV of a lens with focal length y? If it
is a matter of fact, then Groves methodology must be sound. The problem with Groves' methodology for calculating the FOV for the lunar cameras
MUST, therefore, lie in the impact that the
two different camera bodies have on the FOV. Is this logic flawed somewhere?!
For the rest of my comment, I will therefore assume 49.2 degrees to be the approximately correct horizontal/vertical field of view, instead of Groves' unsupported value.
Being completely objective here, I think it's fair to say that Groves' value, given the above, is 'supported' with a far greater degree of certainty than the figure that you have 'assumed' to be 'approximately correct',
subject to my query over the impact that different camera bodies might have.
1.2. Angle of declination
[For the benefit of readers without access to the Groves analysis Groves' claims:
Assuming the lens on the 500 EL/70 camera has insignificant barrel or other non-linear distortions, the 'angle of view' will vary linearly from the centre of the image. For photograph A, if taken with a 60mm lens, the change in angle of view per unit distance (mm) (measured radially from the centre of the image) is ... 0.2034654 [degrees per mm]
]
Wrong. The angle between the optical axis and imaged objects will vary non-linearly, according to this formula:
angle from center = arctan(distance from center*A),
where A = tan(horizontal FOV/2)/(photo width/2) = tan(24.6 deg)/26 mm = 0.01761 mm^-1. (The reported image width/height on original transparencies is about 52 mm. In this comment, I will measure distances between imaged objects in milimeters on original transparencies. This is useful, because published images contain reseau plate crosshairs, which we know to be spaced 10 mm apart on original transparencies, and can therefore use them for reference.)
Groves gives the width of (his) photograph copy as 186.77 mm, and computes that every milimeter on his copy translates (linearly) to 0.2034654 degrees. For comparison, the actual angular equivalents of 1 mm in *his copy of the photograph* would be as follows:
near the center ... 0.2809 degrees per mm
near the edges ... 0.2327 degrees per mm
near the corners ... 0.1984 degrees per mm
The significant non-linearity of the distance-angle conversion can be clearly seen. (Note that the orientation of the measured distance on the image also matters; in the examples above, the hypothetical 1 mm distance is assumed to point towards the center.)
I'm not sure whether you've interpreted this aspect of Groves' analysis correctly. To my mind, the angle of view has to be linear, otherwise the image would need to 'compress' increasingly from the centre towards the edges, which I think is what your saying is the case. That would mean, though, that the image, by definition, is distorted, other than right in the centre, and I don't see how that can be the case. When you write:
The significant non-linearity of the distance-angle conversion can be clearly seen.
what part of the photo, excatly, are you referring to?
Next, Groves measures the distance between the horizon and the center of the image to determine declination of the camera. His result is: 74.41 degrees from the vertical, or 15.59 degrees from the horizontal.
We shall do the correct calculation now. The distance from the image center to the horizon is approximately 22.0 mm on the original transparency (with uncertainty on the order of 0.1 mm), which corresponds (according to the formula above) to camera declination of 68.8 degrees from the vertical, or 21.2 degrees from the horizontal (with uncertainty on the order of 0.1 deg). Groves' result is thus about 26% off.
Only if your interpretation as queried above is correct.
1.3. Distance of Aldrin's visor
Groves then goes on to calculate the distance of Aldrin's visor. He does that by measuring the width of the visor on the image (20.5 mm on his copy), then from his linear conversion factor (0.2034654 deg/mm) and actual width of the visor (280 mm) he determines the distance of 3847 mm. (He actually does it in a slightly more complicated way, but simply 280/(2*sin(20.5*0.2034654/2)) already yields 3847.)
What's the actual distance of Aldrin's visor from the camera? The width on the original transparency is about 5.76 mm.
Just out of interest, how did you undertake this measurement to a 1/100mm accuracy?
As the visor spans the horizontal center of the image, we'll use an approximation similar to Groves' to determine the distance. Using the given width of 280 mm (I can't verify this), the result is 280/(2*sin(arctan(5.76/2*A))) = about 2.7 m (considering the 3D nature of the objects in the scene, it makes hardly any sense to go under 0.1 m). (Note: this may still be off, because I'm using Groves' value of 280 mm for actual visor width, which I was unable to independently confirm.) Groves would therefore appear to be about 42% off here.
Only if your interpretation as queried above is correct. Intuitively, looking at the photo, Aldrin seems to be much farther away than your 2.7m. Looking at Aldrin's shadow refelection in his visor it can be seen that it stretches to just beyond where Armstrong is standing. The shadow is clearly elongated (and could be calculated, at least approximately, if we wished) by the 15-degree low sun angle, as we know from a previous discussion. If the surface was flat (we're assuming it slopes up towards Armstrong!) the shadow length would, I suggest, be in the order of 6m. Again, intuitively, Aldrin does not seem to be standing 6m away from Armstrong, so we can only assume that the ground does indeed slope up towards Armstrong, which not only would account for the apparent partial compensating foreshortening of the elongated shadow, but could be argued to put paid to Groves analysis in an instant!
1.3. continued - Aldrin's eye level
Next, Groves claims to go on to determine the height of the camera above the ground. Because he cannot of course do that, he chooses to do the following: he assumes that there is zero difference in terrain height between the astronauts. In this case, the height of the camera above the ground will simply be exactly equal to the height of the point where the horizon intersects Aldrin's visor above the ground.
I think it is disingenous and misleading not to be clear here that Groves assumes the surface to be flat
only for this part of his analysis. Groves does, as you rightly point out later, purport to take account of the slope.
And how does he determine that? In the following way:
He imagines a line going vertically down from Aldrin's visor. Next, he imagines the point where the optical axis (the line going through the center of the image) intersects this vertical line. In other words - he takes the height difference between Aldrin's visor (as determined by the horizon intersection) and the imaginary point directly under the visor at the level of the central crosshair. He computes that to be about 1073 mm. Luckily for him, his previous errors almost cancel out in this calculation: with our more correct values, the result would be about 1.05 m (the difference is only about an inch).
But that is not the height above the ground. So how does he get that? He simply guesses the remaining distance. He gives the estimated remaining distance as 372.9 - 453.6 mm. These values appear out of thin air and no derivation is shown.
I've checked the PDF copy of the Groves analysis that I emailed to various people and can confirm that the following part of the analysis is clearly present at the bottom of Page 537 and top of 538:
From photograph A[48], the distances D8 and D9 connot be determined directly [For the benefit of readers without access to the Groves analysis these two distances combined are from the centre cross-hair in the photo to the lunar surface, i.e. the balance of the height of the imaging plane of the camera over and above the 1073mm already calculated.]. However, they can be estimated from this data and photocopy B, assuming the astronaut in both images have a similar stance, are of similar height and the ground in the vicinity of astronaut and photographer in photograph A is flat. If these assumptions are valid, the data in Figures 4 and 5 can be used to draw the 'rays' and position of the camera onto the (extended) photocopy B. The scale of the photocopy can be determined as the distance between the top and the bottom of the visor is 260mm
scale 8 = 29.0/260
If the beam in the true horizontal (which intersects with the horizon) is used to 'overlay' the ray trace data, the optical axis intersects with the shins of the astronaut, perhaps a little higher than in photograph A due to departures from the stated assumption. If the optical axis of the camera is drawn on photocopy B so as to intersect with the 'correct' position on the astronaut's shins, a 'range of uncertainty' (e = 80.7mm from photocopy of known scale) in the height of the position of the camera above the surface can be determined.
From photocopy B of scale 'scale 8'
The height D11 of the centre of the imaging plane above the surface is
D11 = D7 + D8 +D9
D11 = 1073.05 + 453.60
D11 = 1526.65
Therefore the range at which the camera is above the surface is between D11 and D11 - e.
That is
THE CENTRE OF THE IMAGING PLANE OF THE CAMERA WAS BETWEEN 1446mm AND 1527mm ABOVE THE SURFACE OF THE MOON WHEN PHOTOGRAPH A WAS RECORDED.
Now, I wouldn't like to say whether I agree with Groves' methodology for this part of his analysis, but to state:
He simply guesses the remaining distance. He gives the estimated remaining distance as 372.9 - 453.6 mm. These values appear out of thin air and no derivation is shown.
... well, ordinarily, I'd be prepared to give you the benefit of the doubt in assuming that, for some very odd reason, you completely and genuinely overlooked this part of the analysis. In fact, though, Groves clearly doesn't 'give the estimated remaining distance as 372.9 - 453.6 mm.' It is obvious, therefore, that you have studied this part of the analysis and paraphrased Groves in such a way as to mislead the reader and try to discredit him where it seems to be unwarranted. I suspect it's because you were intent on showing Groves to be wrong in every single detail, but that you were unable to do so for this part of the analysis because you didn't have access to 'photocopy B', that Groves refers to therein, and which is not presented as part of the analysis.
Through this curious detour, Groves estimates that the height of Aldrin's eye level (where the horizon intersects his visor) above the ground is 1446 - 1527 mm. One wonders why he didn't estimate that directly, and instead did it via estimating the height of a vague point under Aldrin's knees, but never mind.
I don't see what's so 'curious' about this. What seems curious to me is how you mistakenly refer to Groves estimating 'the height of Aldrin's eye level' when the dimensions derived purport to determine the height of the centre of the camera imaging plane, as quoted and highlighted above. I, for one, therefore, am not left wondering, as you seem to be. In any event, even if Groves had estimated the height of Aldrin's shins above the lunar surface, that would still add credence to his analysis far more than estimating Aldrin's entire height, as the margin for error would be significantly reduced.
After all that you do actually concede:
This estimated height range does not seem unreasonable and the real value may be in it, or close to it.
1.3. continued - is the ground flat?
Only at the very end, Groves comes to the main issue: is there really zero difference in terrain height between the astronauts? Or in other words, is the ground flat and horizontal?
This clearly isn't the 'main issue'. It's an issue that could affect the conclusions that might otherwise be drawn, therefore Groves has sought to take account of it.
Fatal flaw: Groves confuses unevenness of terrain between two points and difference in terrain height between two points. Specifically, following his logic, if the shadow is a straight line, then there is no height difference along the shadow. This is clearly false. If the shadow falls on a flat but sloped terrain, its shadow will be perfectly straight, but the height difference will be unknown (but definitely not zero as Groves would have "calculated").
Because of this fatal flaw, the rest of Groves calculation is pointless. He calculates that along the portion of the shadow visible in the photograph, there is a "height difference" of about 99 mm - but even if this calculation is correct, this would be merely difference in distance from an arbitrary straight line on the ground, which is not shown to be horizontal. It would be, at best, maximum irregularity in the (unknown) terrain slope, but not maximum height difference.
I agree with this, which seems to put paid to all of Groves' hard work, whether flawed or not.
On a side note, if Groves' calculation is at least approximately correct, he may have unknowingly confirmed the approximate depth of the crater that Aldrin is standing it (the crater would of course be an irregularity in the terrain, even if the terrain is sloped).
Yes, I agree with this too. Aldrin does seem to be standing lower into the crater than I previously observed.
As shown above, this claim is entirely, absolutely and totally baseless. No calculation whatsoever has been done to determine the height difference, even along the displayed portion of the shadow ...
This isn't correct, and you've shown it not be correct above by referring to the calculation! You might disagree with Groves' methodology, assumptions, apparent ignorance and conclusions, but he certainly did a calculation!
... (Which is, of course, not nearly the entire distance between the two astronauts. Look
here to see the entire shadow and compare it with the part visible in the photograph.) The 'hill' that Groves mentions would appear to be formed by terrain sloped differently inside and outside of Aldrin's crater.
Yes, this could certainly be the case. This image, incidentally, adds weight, I think, to my suggestion that you've miscalculated the distance of only 2.7m between the two astronauts!
This critical examination of Groves' analysis confirms that his YouTube claim that "the variation in height of the surface between the astronauts is typically a few inches" is baseless and unsupported, and furthermore false ...
Unfortunatley, I don't agree that it does. It seems potentially to be as flawed, at least in places, as the analysis that it sets out to discredit. In any event, I do not consider Groves' claim to be 'baseless and unsupported', and don't really think that you honestly do either. His claim is clearly
based on and supported by a thorough and detailed analysis. His claim, however, could well be 'false', and I'm inclined to believe that it is. Even if the aspects that I've raised above were to be shown to be valid, and serve to work in Groves' favour, I personally believe that the margin for error, given the assumptions made by Groves, plus those parts of the analysis that are clearly not as thorough and 'scientific' as other parts, like the all-important question of how much the ground slopes between the two astronauts, are sufficient to conclude that the analysis in no way serves to demonstrate that the photo isn't genuine.
... as it contradicts known facts - specifically, the fact that Armstrong stood about a foot higher than Aldrin, which follows directly from the fact that the horizon intersect Aldrin's image at eye level and the fact that Armstrong's camera was chest-mounted (confirmed by Armstrong's image reflected in Aldrin's visor).
I don't think you can honestly quote any of these as 'fact', remembering that associated with the allegation that the photo could not have been taken with a chest-mounted camera is the allegation that the image appearing in Aldrin's visor is a cut & paste job. All you have as the basis of your 'facts' is that very image. If these were indeed facts I doubt you would have seen the need to critique Groves' analysis, but simply stated the 'facts' instead, which would, by definition, have completely and undisputably countered his analysis.
In closing, I wish to reiterate that the purpose of my responding here is to challenge the seeming lack of objectivity and potentially flawed methodology that has been applied in carrying out this critique. Coupled with the disingenuosity and seeming disregard for parts of Groves' analysis, this serves well to highlight the main purpose of my participating in this thread; the purpose that I pointed out right at the outset, namely to highlight the general disparity between the depth of analysis applied by many of those making the allegations and those defending them. That's not to say that any of the allegations are by any means strengthened by such analyses, particularly when they are inconclusive, as they all are, by definition, but it surprises me when hardly anything, if anything, conclusive has been offered in defence. I'm talking about photo/video anomalies mostly, and not such things as ALSEP.
Suffice to say, and notwithstanding the foregoing, I am now prepared to announce my conviction that man has, indeed, walked on the Moon. I would sincerely like to thank all of you who argued the case so vociferously when you could so easily have not even given me the time of day, so to speak, and I would like to take this opportunity to apologize to anybody I may have offended along the way, either because of my tone and/or words, or equally by the seeming lack of respect that my position must inevitably have implied. Obviously, I am a stubborn, arrogant b******, to name but a couple of negative traits, and I'm not sure that will ever change, so if you encounter me again just bear that in mind, and try not to be offended!
That said, I do not retract everything I wrote, and I believe I was right with some of the semantic arguments, but that doesn't really matter now. What matters is that I've learnt from the experience, as I have done with many other threads in which I've participated, and that's thanks to you guys. Thanks
