# F-16 Pilot Chris Lehto's Interpretation of the GoFast footage [Focus, Parallax, Inaccurate Range]

The object is tracked 58 degrees left, 35 degrees below. Is that within the radar's field of regard?

Here's a diagram of the 10-mile, 5-mile situation to show how you can calculate the amount of blurring you'd expect if the ocean is out of focus. The diagram assumes the object is in focus. It's based on this Wikipedia section which you can use to check my work.
View attachment 44888

That diagram represents nothing in optics.

And even if you got the lens to be a converging one (it's acting like a diverging one the way you've drawn the lines), there'd still not be enough information on the fixed version of it to calculate anything. Where are the focal length, the aperture, the hyperfocal distance?

That diagram represents nothing in optics.

And even if you got the lens to be a converging one (it's acting like a diverging one the way you've drawn the lines), there'd still not be enough information on the fixed version of it to calculate anything. Where are the focal length, the aperture, the hyperfocal distance?
The focal length is not needed for the calculation. The hyperfocal distance is an approximation based on setting a maximum noticeable size for the circle of confusion (little c in Wikipedia's diagram). That's explained in the section I linked.

Edit: And I mentioned the aperture size being the number that matters. You could draw an aperture in front of the lens but the math is no different from just having a smaller lens, which is why Wikipedia doesn't have that either.

There's always some blur outside the focal plane, even beyond the hyperfocal distance. So I'm calculating an actual upper bound on it by comparing the size of the circle of confusion in the focal plane (big C) to the (known?) size of the object.

The diagram shows that rays that reach the lens from the blue point pass through a disc in the focal plane of half the aperture's diameter. If there were a real disc there in the focal plane, it would form a disc in the final image. But the rays from the blue point follow paths through that virtual disc so they must end up on the same disc in the image (they don't "know" whether they came from a real disc in the focal plane or from somewhere behind it).

You're right that the diagram would look more accurate with the blue rays on the right side crossing over. But that part of the diagram isn't important.

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The focal length is not needed for the calculation.

Consider the fact that I've provided a scenario where an item at distance 10 is insignificantly blurred, and another where it is significantly blurred, when you are focussing on an object at distance 5, and that your diagram makes no distinction between these two cases.

Perhaps you're getting confused by ambiguity of the term "focal plane". That can be use that to mean the plane onto which the light is being focussed - the sensor or the film - which is where the CoC calculations are relevant, but it can also be used to refer to the plane at the distance which is at crispest focus, as per your diagram. Things said about one do not hold true about the other, you can't just map statements between the opposite sides of the lens.

People on Twitter, etc, still keep arguing that you can't have two objects at different distance in focus at the same time.

I was trying to think of a simple general argument against this. Do people here think the following is (a) valid and (b) convincing?

1. In any optical instrument with a lens (camera, telescope, human eye, etc) an object is 'in focus' when the lens refracts rays of light from the same point on the object to the same point on the image.

2. The lens does not know how far the ray of light has come. It just knows the direction of the ray when it meets the lens. If two rays come from the same direction, they will be refracted to the same point of the image, regardless of the distance. [Note: the amount of refraction also depends on the colour, but that is not relevant here.]

3. If the object is relatively close to the lens, rays from the same point of the object will meet the lens from significantly different directions, and the distance of optimum focus will vary according to the distance of the object. [Note: this assumes that the diameter of the lens is not negligible in comparison to the distance of the object.]

4. If on the other hand the object is very distant, all rays from the same point of the object will be meeting the lens from practically the same direction. For example, if the lens is 1 cm in diameter, and the object is at a distance of 5 km, the difference in the angle at which rays from the same point meet the lens will be less than 1/10,000 of a degree. [Note: a 1 cm wide lens will subtend an angle of about 0.00002 degrees at a distance of 5 km.]

5. Experience suggests that such a small difference is too small to make a difference to the focussing of the image, at least with normal cameras. The rays can be treated as effectively parallel when they reach the lens. Increasing the distance will further reduce the divergence of the rays, but beyond a certain distance this makes no practical difference to the focus. For a given camera setting everything beyond that distance will be equally 'in focus', or 'out of focus'.

6. Of course there are many factors apart from focus which may affect the clarity of the image, such as:
a. dust, haze, mist, smoke, etc, in the atmosphere
b. scattering of light (Rayleigh scattering) by the molecules of the air itself
c. diminishing resolution of detail with increasing distance
d. movement of the camera or the object during the 'shot'. The effect of this will vary with the amount and nature of the movement. If the relative movement of the camera is lateral, without rotation, the effect will be greater with closer objects, due to parallax, but if the camera is rotated, the amount of 'motion blur' will increase with distance. [Not sure about the last point, but I'm assuming that with a rotating camera the apparent linear motion of distant objects will be greater, so the object will be 'smeared out' across a greater distance in the image.]

Any thoughts? Most importantly, are there any fallacies? As I've said before, I know next to nothing about cameras, but the argument is more about geometry than anything else.

Consider the fact that I've provided a scenario where an item at distance 10 is insignificantly blurred, and another where it is significantly blurred, when you are focussing on an object at distance 5, and that your diagram makes no distinction between these two cases.
The size of the blur at distance 5 (e.g. in meters) only depends on the aperture size. If you were to have a real disc at distance 5 with half the aperture's diameter, its image would be the same disc as a point behind it at distance 10. If you make the distances 50 and 100 with the same aperture size and focus on 50, the disc size is still A/2 in the object plane but it covers 1/10 the angle because it's 10x farther away (sharper image).

There are only 2 ways to get a blurrier image with the fixed 1:2 distance ratio: increase the ratio of aperture size to the distances involved, or magnify the blur. The focal length would be useful to calculate the magnification, but if you already know the size of something in the object plane then you can convert between meters and pixels in that plane proportionally.

People on Twitter, etc, still keep arguing that you can't have two objects at different distance in focus at the same time.

What do people on twitter think about this image (a split image of the same scene, shallow depth of focus on one side, deep depth of focus on the other):
https://cdn.shopify.com/s/files/1/0...-DOF_200320_020714_1024x1024.png?v=1587845852
From here: https://mastinlabs.com/blogs/photoism/understanding-focal-plane-in-photography
If what they say is correct, then the small aperture photo would be impossible.

Maybe people expand their understanding of "in focus" and "out of focus" from being just a binary predicate. All "in focus" means is "not so out of focus that you can see it's out of focus". For example, if the rays from a point all end up on the same CCD cell, then it didn't matter if they all arrived at exactly the same point or whether they bounced off the sides to get in, if they all ended up in the same bucket, that point is in focus.

Heck, just point them towards any article on "depth of field" in photography. It's been covered myriad ways by myriad sites with myriad example images. If they refuse to believe all of them, they are beyond hope, and I wouldn't waste too much time with them.

One reason I fear that your smaller-range-of-angles analogy won't work with such people is that it could be misinterpreted as implying that more distant things will always somehow be more focussed than near things, which is of course nonsense, and not what you said, but that matters not. Never underestimate the ability of those who don't understand simple concept to misinterpret simple explanations and draw bizarre illogical conclusions, that's probably how they picked up their wrongthink in the first place.

if you already know the size of something in the object plane then you can convert between meters and pixels in that plane proportionally.

{edit: adding} First - when you have a plurality of objects - what do you mean by *the* object plane? There's a good chance we're talking at cross purposes.{end edit}

But you can't do that with the information you claimed to have - you're presuming the distance from the lens to the focal plane. That distance isn't fixed, as the lens moves relative to it as you focus - that's what focussing *is*.

You'll note that the lens moves relatively less in order to change focus between two far distances (say having the objective to focal plane distance at f*1.01 and f*1.02, a movement of f*.01) than it does to change focus between two nearer distances with a similar distance ratio (say f*1.11 and f*1.25, a movement of f*0.14). And that is precisely why the depth of field is wider - as a ratio - for farther objects. than for nearer objects.

Which is why precisely statements of the form "you can't focus on both distances X and 2X" are utterly bogus. There is a distance X_h beyond which everything at distance>X_h can be made in focus, and therefore things at distance X_h*2 are in focus as X_h*2 > X_h.

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One reason I fear that your smaller-range-of-angles analogy won't work with such people is that it could be misinterpreted as implying that more distant things will always somehow be more focussed than near things, which is of course nonsense, and not what you said, but that matters not. Never underestimate the ability of those who don't understand simple concept to misinterpret simple explanations and draw bizarre illogical conclusions, that's probably how they picked up their wrongthink in the first place.
Thanks for the comments and examples. If I ever deploy the argument in a wider forum I will try to guard against the misconception you mention. As you say, 'more distant' does not imply 'more focussed'. My point, which I hope still stands, is that if an object is well focussed at 5 miles, it will still be well focussed at 10 miles. If it isn't well focussed at 5 miles, it won't be at 10 miles either - assuming the same camera set up, obviously. No lens, so far as I know, would be able to distinguish between the two cases, so far as focus is concerned. Of course, other factors such as resolution of detail might come into play.

I'm not too worried about persuading everyone. Unlike some other subjects, like flat earth or chemtrails, UFOs seem to attract some reasonable and intelligent people, who ought to be able to follow arguments and evidence. I hasten to say there is nothing absurd in belief in intelligent aliens as such. I think it is very likely that they exist, so it is quite conceivable that they would visit the earth. I just don't think there is good evidence that they have, and in this case absence of evidence may amount to evidence of absence. If aliens had visited us, wouldn't they have made themselves known more clearly? If they are hostile, they would already have zapped us with their giant death rays. If they are benevolent, they would have given us the cure for cancer and the solution of the Riemann Hypothesis. If even a small proportion of the UFO reports are true, the only logical conclusion is that the aliens have a very twisted sense of humour.

My point, which I hope still stands, is that if an object is well focussed at 5 miles, it will still be well focussed at 10 miles.

If and only if the hyperfocal distance is *less than*, oof, something like 20 miles? (Which it will likely be for any optics you're ever likely to encounter).
Double checking: Focus at 6.67 miles=HFD/3 => focal depth will be HFD/4=5 miles to HFD/2=10 miles.

For comparison of that 20 miles value, the lovely birder lens mentioned earlier had an HFD of 2km at f/8 (so could be stopped higher). Typical cheapie compact cameras will have HFDs of 2-50m.

From the ATFLIR manual as linked by Mick

The radar system provides the functions listed below: a. air target range, range rate

Another focus example. Plane (~5 miles) and Moon (~239,000 miles) both in acceptable focus.

This might be a more fruitful source of examples. If the Moon is high, then there will be far less atmospheric distortion - in fact, it will be similar to the minor distortion in GoFast

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{edit: adding} First - when you have a plurality of objects - what do you mean by *the* object plane? There's a good chance we're talking at cross purposes.{end edit}

But you can't do that with the information you claimed to have - you're presuming the distance from the lens to the focal plane. That distance isn't fixed, as the lens moves relative to it as you focus - that's what focussing *is*.

You'll note that the lens moves relatively less in order to change focus between two far distances (say having the objective to focal plane distance at f*1.01 and f*1.02, a movement of f*.01) than it does to change focus between two nearer distances with a similar distance ratio (say f*1.11 and f*1.25, a movement of f*0.14). And that is precisely why the depth of field is wider - as a ratio - for farther objects. than for nearer objects.
I'm using "object plane" to refer to the plane of the object at 5 miles, which I'm supposing to be in focus. I changed from saying focal plane to avoid ambiguity. I'm not talking about the plane inside the camera, because the focal length doesn't matter.

Here's a simple experiment that would test what I'm saying:
1. Open a camera's aperture fully.
2. Cut a disc shape out of something with the half the diameter of the camera's entrance pupil.
3. Put the disc at any distance and focus the camera on it.
4. Put a tiny light source at twice that distance.
5. In the photo, the bokeh of the light source has the same size as the disc.

Doesn't matter what the distances or focal length are as long as the distances are at a 1:2 ratio and the disc is in focus.

So, Chris Lehto says that the RNG data in the GOFAST video is unreliable. Fine. I wondered what a different approach could tell us, without relying on the RNG data. So I created a model of the scenario in Blender, in order to simulate the camera's sightline, using all other available data.

Findings:
1. The object in the GOFAST video was small. Even if at the surface, it was likely smaller than 6' in diameter. If at 13,000 feet (as the RNG data suggests), the object was likely smaller than 3' in diameter— a party balloon or bird, but almost certainly not a weather balloon.
2. If the object's altitude was 13,000 feet, it was moving at about 36 knots (assuming it was holding altitude).
3. The sightline has a pivot point at 11,750 feet — if the object was near that altitude, it could have been motionless relative to the surface. Based on this pivot point, and the 25,000-foot altitude of the plane traveling at 369 knots, the speed of an object at any altitude, intersecting with the sightline, can easily be calculated.

Here is a video with a couple of clips from the simulation: First, a "police helicopter" view showing how the sightline moves as the jet flies (with an object at 13,000 and the pivot point indicated). Second, a recreation of the onboard ATFLIR's field of view.

Source: https://youtu.be/P-QxQHWT4A4

Methodology:
1. After a couple of poor attempts, I restricted my analysis to 12 seconds of the video when the jet's bank angle was most stable. This interval is synchronized with the simulation in the first part of the video above.
2. By animating the rotation of a white bar against the jet's horizon indicator, I found that the jet’s average bank angle during this interval was 13.6°.
3. Using the calculator here, I found that a jet traveling 369 knots, banked at 13.6°, traces out an arc of a circle with radius 8.25 nautical miles. In my simulation, the jet follows such an arc for 12 seconds (–8.57° heading change).
4. I animated the angles of the sightline and the camera based on the onscreen data for the camera angles. I found the frames of the video in which the numbers change, and then inserted keyframes at those times, and used Blender's bezier interpolation to smooth out the curve. In a few places, I nudged a keyframe by a frame or two to get the curves even smoother.
5. I set the camera to a field of view of 0.7°, which is apparently the field of view in the "NAR" mode with a zoom setting of 1.0.
6. I used Blender's wave texture generator to simulate the ocean surface, with ~50' swells plus smaller waves generated with the detail and distortion parameters.
7. Finally, I manually animated the camera's location a tiny bit just to keep the object near the center of the frame in the ATFLIR simulation. This was purely an aesthetic choice and didn't affect the findings.

In case anyone wants to play around with the simulation or verify my findings, I've attached the Blender file.

#### Attachments

I'm using "object plane" to refer to the plane of the object at 5 miles, which I'm supposing to be in focus. I changed from saying focal plane to avoid ambiguity. I'm not talking about the plane inside the camera, because the focal length doesn't matter.

Here's a simple experiment that would test what I'm saying:
1. Open a camera's aperture fully.
2. Cut a disc shape out of something with the half the diameter of the camera's entrance pupil.
3. Put the disc at any distance and focus the camera on it.
4. Put a tiny light source at twice that distance.
5. In the photo, the bokeh of the light source has the same size as the disc.

Doesn't matter what the distances or focal length are as long as the distances are at a 1:2 ratio and the disc is in focus.

Thanks for the clarification, yes it does appear we were talking at cross purposes, the terminology is a minefield of ambiguities. I was thrown by your initial post, in particular it seems I misinterpreted the "amount of blurring you'd expect if the ocean is out of focus" that you started with to imply that you were supporting the claim that the ocean would suffer from noticeable blurring, and be out of focus, which is the claim I have been countering all along. The 1/dist factor of course makes the blurring seen diminish dramatically. So I had tunnel vision, and thought we were arguing opposite things, when it appears we were not. Apologies.

Another focus example. Plane (~5 miles) and Moon (~239,000 miles) both in acceptable focus.

View attachment 44954

View attachment 44955
This might be a more fruitful source of examples. If the Moon is high, then there will be far less atmospheric distortion - in fact, it will be similar to the minor distortion in GoFast
holy gsus. what camera setup is this? looks insane

holy gsus. what camera setup is this? looks insane

I imagine it's probably one of the big Canon primes 5/6/800mm on an extender like the Canon 2x then cropped in post.

You can get 1000/1200mm at f/8 or 1600mm at f/11 with this setup.

These are £8000-13,000 lenses.

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I imagine it's probably one of the big Canon primes 5/6/800mm on an extender like the Canon 2x then cropped in post.

You can get 1000/1200mm at f/8 or 1600mm at f/11 with this setup.

These are £8000-13,000 lenses.

No need for anything that fancy just for the pixels, it's basically the same resolution as my cheaparse (200e 2nd hand) Canon 55-250mm on D550: http://fatphil.org/images/moon.jpg (no processing only crop, I think that was a 'supermoon', 1 day before full, but the next day was forecast rainy. Oh - no tripod, because hardcore/stupid!)
I do live near a small international airport, I should see what flight paths they follow, and whether that's compatible with any moon flightpaths, snagging a photo like that would really make me chuffed.

No need for anything that fancy just for the pixels, it's basically the same resolution as my cheaparse (200e 2nd hand) Canon 55-250mm on D550: http://fatphil.org/images/moon.jpg (no processing only crop, I think that was a 'supermoon', 1 day before full, but the next day was forecast rainy. Oh - no tripod, because hardcore/stupid!)
I do live near a small international airport, I should see what flight paths they follow, and whether that's compatible with any moon flightpaths, snagging a photo like that would really make me chuffed.

Planes at cruising altitude are not that big/detailed even a A380 on my crop sensor with 400mm, the moon isn't the issue, it's getting the plane that big.

However those planes in the shots may have been on approach/egress from an airport and thus lower.

Planes at cruising altitude are not that big/detailed even a A380 on my crop sensor with 400mm, the moon isn't the issue, it's getting the plane that big.

However those planes in the shots may have been on approach/egress from an airport and thus lower.

I'm ~3-4km from the airport, and were everything to be contrivable together, I think I could get a crater-sized plane. However, for some bizarre reason the moon never transits to the north of me, which is where the last plane headed (presumably to go over the sea rather than over the city). but to be honest, after seeing the last plane go past, the accuracty needed to line things up would be scary, I don't think it's ever going to happen from chez FatPhil.

Planes at cruising altitude are not that big/detailed even a A380 on my crop sensor with 400mm, the moon isn't the issue, it's getting the plane that big.

However those planes in the shots may have been on approach/egress from an airport and thus lower.

One is leaving exhaust contrails, so probably over 30,000 feet.

But yeah, if you can get the moon is that big, then the only challenge is waiting for a plane to fly in front of it. Probably he's by some consistent air routes. Lots of waiting would be involved.

I got one in front of the sun once. Really far away plane though.

Nikon P900, 2000mm (cropped to about 60%) 1/250, F6.5

One is leaving exhaust contrails, so probably over 30,000 feet.

But yeah, if you can get the moon is that big, then the only challenge is waiting for a plane to fly in front of it. Probably he's by some consistent air routes. Lots of waiting would be involved.

I got one in front of the sun once. Really far away plane though.

Nikon P900, 2000mm (cropped to about 60%) 1/250, F6.5

What filter did you use? ND?

Friend of mine captured this one near Greenville/Spartanburg, SC, during the eclipse of 2017. Not perfectly focussed, but pretty close for the various distances involved... and just a neat picture.

Friend of mine captured this one near Greenville/Spartanburg, SC, during the eclipse of 2017. Not perfectly focussed, but pretty close for the various distances involved... and just a neat picture.

View attachment 45028
thats actually not the sun. its a glare. from a bug. reflecting sunlight. /s

thats actually not the sun. its a glare. from a bug. reflecting sunlight. /s
That's not an aura, it's an unsharp mask

The manual states:

"7. The ATFLIR provides two air-to-air modes: pointed, and autotrack. Air-to-Ground and air-to-air laser range finding is also provided."

Apparently it DOES use the laser for A/A range finding.

So why does Chris say (paraphrasing) no one uses the range value in A/A or the laser is only used for ground targets?

The manual states:

"7. The ATFLIR provides two air-to-air modes: pointed, and autotrack. Air-to-Ground and air-to-air laser range finding is also provided."

Apparently it DOES use the laser for A/A range finding.

So why does Chris say (paraphrasing) no one uses the range value in A/A or the laser is only used for ground targets?

I think you can turn on the laser for A/A if you want but it's never used in practice as it's not accurate for A/A if it were firing the LTD/R text would flash.

As in I don't think the range displayed in Go Fast is an inaccurate laser range because the laser is not firing. I think the range comes from a RADAR track correlated to the LOS of the ATFLIR when autotrack is acheived.

So, Chris Lehto says that the RNG data in the GOFAST video is unreliable. Fine. I wondered what a different approach could tell us, without relying on the RNG data. So I created a model of the scenario in Blender, in order to simulate the camera's sightline, using all other available data.

Just watched your youtube video. You mentioned how the ocean speed in the blender sim is different than the actual footage and changed the FOV to compensate, but wouldn't this discrepancy be because of windspeed? the plane only shows speed though the air not speed relative to the ground so wouldn't the better way to compensate for this to be adjust the velocity of the actual jet? Wind would seem to be generally against the jet if your result was slower, as a faster moving jet would counteract the camera turning back more.

When you find the adjustment that works best you would basically determine (roughly) the wind velocity at the jets altitude. (assuming we know for sure the FOV is 0.7 of course)

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A few factors could make the ocean appear to move slower or faster in a sim than in the actual video

Wave size i.e. the size of the ocean surface texture features, wind blown waves, causing an apparent speeding up or slowing down of the sea surface, the FOV of the camera etc.

A few factors could make the ocean appear to move slower or faster in a sim than in the actual video

Wave size i.e. the size of the ocean surface texture features, wind blown waves, causing an apparent speeding up or slowing down of the sea surface, the FOV of the camera etc.
Not sure how wave size would be relevant, what matters is the time it takes for features to cross the screen, not how big they are.

And while I doubt waves from the wind would have much effect given the speed of the panning, even if they did that would mean it would be a mistake to adjust FOV to compensate for what is not an issue.

Of course it could be a combination of FOV/waves/wind, I just think the change to 0.5 FOV is perhaps overkill if there is reasonable certainty that 0.7 is the correct FOV. Not a huge issue but would effect the potential sizes/speeds of the object a bit.

EDIT: Of course turn speed is another potential factor

Not sure how wave size would be relevant, what matters is the time it takes for features to cross the screen, not how big they are.

And while I doubt waves from the wind would have much effect given the speed of the panning, even if they did that would mean it would be a mistake to adjust FOV to compensate for what is not an issue.

Of course it could be a combination of FOV/waves/wind, I just think the change to 0.5 FOV is perhaps overkill if there is reasonable certainty that 0.7 is the correct FOV. Not a huge issue but would effect the potential sizes/speeds of the object a bit.

EDIT: Of course turn speed is another potential factor
If 10 waves go by in a second it matters if they are 1 foot waves or 10 foot waves.

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