#optics-🔭 (Discord ID: 571747131786919944) in The Ice Wall, page 1
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LOGICAL FALLACY: APPEAL TO AUTHORITY: https://imgur.com/P7lh73P
This is how angular resolution works physically in the eye.
Cameras work the same way.
The cones of the retina is a zoom in of the eye. If the angular size of the target is not enough to activate more than a single cones/sensor the object is unresolvable.
There are 3 ways to decrease angular separation.
1. Move the two separate targets further or closer together.
2.Increase the distance.
3. Change the angle of view.
First here is a demonstration of how angle of view changes the angular separation of 2 targets. https://cdn.discordapp.com/attachments/379214321907007488/459806914331541504/unknown.png
For example in this image, as the stop sign's angular size shrinks from distance or angle, the image that prjected onto the retina also shrinks. Eventually it will reach such as small size the eye can not physically detect the light. https://cdn.discordapp.com/attachments/379214321907007488/459808085436006410/refraction_cornea.png
A geometric analogy would be closing a pair of scissors. When the scissor tips are closer together than the spacing between the rods and cones of the eye then you get to see the target. The point where the tips cross from too close to normal vision is the angular resolution.
When the angle of view becomes to much it pretty much goes parallel, but you lose sight of the ground before that. It's the same on the globe too but even worse because the angle of view is increasing quicker because of the curving away of the ball surface.
These next images show someone how the angle stays the same but the area that you are actually observing increases. You can see the 5th image how the bottom of a building would disappear.
They are using this stuff for self-driving cars. To automate the driving they have to turn the perspective view into an orthographic top down view.
The soure of that image.. http://www.bbc.co.uk/science/0/20937803
Even though the title is BS. No one sees further. You ONLY capture more light.
This is how they build telescopes, to capture light.
Large telescope are reflectors. The larger convex lens gets the more distortion. So they made this. It all works the same generally speaking. A telescope will only help so much. It depends on the light collecting ability that is determined by the diameter of the lens. Some of these aren't built yet...
They are making the lens bigger not building 15 mile long telescopes.
Here is a demonstration of angular resultion effects with an eye charts 1D is distance from chart 2D is 2 time the distance etc...
Optical and Geographical Slant.
Links to PDFs and resources.
Source video to shorter version:
A short video explanation: https://www.youtube.com/watch?v=QNg5wqYKkJE
Accompanying information and imagery to go with the above PDFs and resources.
"As he looks downward toward his feet the slant approaches zero, as he looks upward the slant increases, as the center of ckesr vision approaches the horizon the slant becomes maximal, and at the horizon itself the land ceases to be a surface and becomes an edge."
Next we have what is called Spatial Disorientation & Visual Illusions which includes our visible horizon. Sometimes called the offing, this apparent line is where the sky meets the ground and is being perceived as an edge because of perspective due geographical slant and other optical phenomena.
Visible Horizon 1
Visible Horizon 2
"In the offing"
False visual reference illusion
Spatial orientation & Visual Illusions
Angular Resolution https://cdn.discordapp.com/attachments/458196098767388674/459052120495095818/Angular_Resolution_01_v001.webp
Imagine this cone is one of your eye cells at the back of your retina
That's the "angular resolution"
At 5.4km, an object must be AT LEAST 4.8m in diameter to register as a single pixel
Even looking straight and level that pixel will merge with the horizon
An object would disappear bottom first https://cdn.discordapp.com/attachments/458196098767388674/466295250198200320/DeepinScreenshot_select-area_20180710085940.png at 2000 meters https://cdn.discordapp.com/attachments/458196098767388674/466295250701385728/DeepinScreenshot_select-area_20180710091613.png at 5432m the bottom half of your angular resolution is gone https://cdn.discordapp.com/attachments/379214321907007488/466288992611205154/DeepinScreenshot_select-area_20180710085513.png
https://cdn.discordapp.com/attachments/379214321907007488/468546464780386306/Airy_disk_spacing_near_Rayleigh_criterion.png basically asking show him visually what is inbetween the two lights after they have merged
Duh that can't be shown visually. that is the point https://cdn.discordapp.com/attachments/379214321907007488/468552326093996033/ConeMosaics.jpg The other end of the cone is size of the space in between the cells of the retina. Striking a single rod or cone can't form and image. https://cdn.discordapp.com/attachments/379214321907007488/468552750024622112/rayc.gif Think of the 2 peaks as activating a cell each. Two basically right next to each other. As the angle shrinks, like in the middle image, the cells will be weakly activated creating a partially merged image. In the last image the angle is so small only one cell can activate.
It looks like a point.
Even though what the person could be looking at is 100 ft tall but 300 miles away. https://cdn.discordapp.com/attachments/379214321907007488/468554746073186306/unknown.png
Imagine the point on this grid are the cells of the eye. The circle is what is projected by the lens on to the retina
It covers enough cells to form an image. https://cdn.discordapp.com/attachments/379214321907007488/468555465245327380/unknown.png this projected circle is slightly smaller an can only cover one cell and will never form a discernible image
Let's work from the center of vision out to the edges , Up (sky) Down (ground) So this image https://cdn.discordapp.com/attachments/379214321907007488/468559885718519848/unknown.png Below the blue you can only see ground
Now how do we bring the max viewing distance into focus?
max viewing distance of the ground
that is... We can only use the bottom half of our vision.
The central part is unresolvable.
The upper part is looking for the sky. The angle between B and C is fixed. We will say the same as the eye .02 degrees. So we are seeing above and below the blue cone but not the cone itself. Like seeing the horizon...the horizon is unresolvable...but the ground leading to it and the sky above it we can see. Question: So what happens when line A to C gets parallel to the ground? Answer: Whatever is in the cone is gone, the cone turns to a line. Exactly and what's in that cone. Anything in a line extending from A to C to infinity will never intersect the ground . But the cone is the area between B and C. So the ground stops at B , anything above point C can only see sky. So the cone in the drawing is the unresolvable part of the camera lens or our vision.
The cone does reverse inside the eye.
Light is projected on to the retina. We don't see things directly.
It goes through the lens is projected and inverted. https://cdn.discordapp.com/attachments/379214321907007488/466469361562026015/kan_ch26_f001.png https://cdn.discordapp.com/attachments/379214321907007488/466469513500688384/retinaimage.png Those images are right for a single point of light. This is part of another misconception. https://cdn.discordapp.com/attachments/379214321907007488/468563187713835020/unknown.png This illustrate how we would see a SINGLE point of light. Say a single photon reflecting off the molecule of a wall
Take notice how it emanates in a sphere. Now what we see is the light reflecting from EVERY molecule spherical , and traveling out. The important thing is this. The airy disks I started with.
That is what EACH point is.
Trillions (probably more) of points of light. We don't see each point. We can only differentiate points to the angular resolution limit.
So a trillion points in a 4 ft space at 3 miles looks like a point. Think of the horizon as a bunch of points of light, and not as a building , a boat or mountain.
Then equate an entire object to a point of light. As far as the angle goes. The angular size on an object has the same angular size when projected onto the retina.
https://cdn.discordapp.com/attachments/379214321907007488/468565104326082575/unknown.png All those angles between features of objects in the room are identical to the angles of the corresponding projected image of that room. (projected onto the retina)
So something that is 10 ft in real life and has an angular size of 3 degrees. When projected to the retina it's angle is still 3 degrees but it's actual size is .5 mm
projected to the retina.
So knowing that angular size decrease with distance. When I get far enough away from that something and it's angular size shrinks outside AND inside my eye. Eventually the angle being projected on to the retina is too small for the cells and photoreceptors to form an image from. You have to think of it like this. Whatever we see or photograph whatever is being captured by the lens is being projected to the retina. Only it is a physically tiny version of what you are seeing. So if a building is "trillions" of points of light...each point of light on that building will come to the eye at a different angle. The bottom angles will be unresolvable before the top angles because they close sooner in the back of the eye or camera. The angle is tilted away more. Think of rotating a piece of paper. You hold the paper in front.
Rotate the top away until the sheet is parallel.
and you are looking down the edge.
Now imagine you put a circle on top and bottom of the sheet and did it all over again.
Before the tilting of the angle the spots would appear a good distance away from each other. But as you rotate the paper those 2 circles will appear to be close.
The top of a building is not rotated as much from the plane of the retina compared the the bottom at equal distances.
Look , these are the same distances. Obviously the angles are not the same. https://cdn.discordapp.com/attachments/379214321907007488/468569265574903818/unknown.png I can make it even more extreme... https://cdn.discordapp.com/attachments/379214321907007488/468569771735253012/unknown.png But guess what....the top of the building will get cut off. When the entire situation is reverse.
Image looking up with your chest up to the world trade center. You wouldn't see the top because the angle would be too shallow. https://cdn.discordapp.com/attachments/379214321907007488/468570710344728576/unknown.png Look what happens when you are closer to the vertical than the horizontal, the reverse. https://cdn.discordapp.com/attachments/379214321907007488/468570964817608715/unknown.png Here are some questions you can ask yourself. Where is the plane of the eye? What is the relative angle between the surface of target and the plane of the eye? Give that angle , what is the angular separation of the points of light on that target? https://cdn.discordapp.com/attachments/379214321907007488/468574743637786645/unknown.png The relative angle to the plane of the eye and the optical tilt of the target determine the angular separation
If I rotate the green block until it is vertical all the angle will grow. If I rotate it counter clockwise all the angles will shrink. If It was more to scale the angle difference would be more dramatic. https://cdn.discordapp.com/attachments/379214321907007488/468578052302176266/IMG_3195_one_world_trade_center_nyc2015_aagdolla-1038x576.jpg https://cdn.discordapp.com/attachments/379214321907007488/468578348789006336/502382332.jpg Now imagine the building is 3 miles tall and not 1776ft.
https://cdn.discordapp.com/attachments/379214321907007488/468578739572441119/look-down-the-hallway.jpg So here is what happens being closer to one wall than the other. That shows the slant/tilt. Left wall angle is steeper than right wall, relative to the observer. This photo looking upward is a good example also. https://cdn.discordapp.com/attachments/379214321907007488/468579766983720980/OrganicMechanics101.JPG
https://cdn.discordapp.com/attachments/379214321907007488/468599107145957397/unknown.png The first light ray sim is showing that the angular separation on each side of the lens is equal.
The second 2 are to show how the points of light will merge into onehttps://cdn.discordapp.com/attachments/379214321907007488/468601108441595906/unknown.png These are two points of light that are close. https://cdn.discordapp.com/attachments/379214321907007488/468601846089646090/unknown.png
Post 1 of 2
How angular resolution works:
The further an object (i.e. boat, building mountain) gets away from the lens, the angular separation will continue to close until the light blurs together and eventually becomes a line or point or edge"
"As he looks downward toward his feet the slant approaches zero, as he looks upward the slant increases, as the center of clear vision approaches the horizon the slant becomes maximal, and at the horizon itself the land ceases to be a surface and becomes an edge"
As you look down the right side of the hallway, you'll see the angular separation of light begins to close the further you look. Then looking at the left side of the hallway you'll notice the angular separation of light does not close or blur as quickly as the right side.
Post 2 of 2
Here are some questions you can ask yourself. Where is the plane of the eye? What is the relative angle between the surface of target and the plane of the eye? Given that angle , what is the angular separation of the points of light on that target?
Notice the blue cones angle compared to the orange cone. The blue cones angle will lose the light first on the bottom and the ground will start to blur with the object but if you raise in height the resolution will increase shown with the orange cone because the angle of light hitting the retina or camera is made larger. Once the angle becomes too shallow the light turns into a line or Edge. Think of buildings or boats or mountains not as objects but as quadrillions of points of light or photons coming to your retina at different angles and some will become non-resolvable before others. The ones closest to you disappear first as you back away. You will see the ground running up to the horizon then see the horizon as a line and will see things like the sky still or if there's a mountain or building you will still see the top parts but eventually those will also become unresolvable as they get further away and the angle changes.
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