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What is the acceptable CoC (Circle of Confusion) of the human eye to directly observe the object? The human eye has many cells and high pixels. Should the permissible circle of confusion be small?

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    What is the photographic application of this question? I’m pretty sure I see where this is going, with your previous question about depth of field and the thin lens formula. But as worded, this question has nothing to do with photography, which would make it off topic for this site. – scottbb Apr 6 at 0:28
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    Human eyes do NOT have pixels. Perhaps you are inside a circle of confusion. I am, My circle of confusion is directly proportional to the circle of beer bottles at my feet. owlcation.com/stem/Anatomy-of-the-Eye-Human-Eye-Anatomy – Alaska Man Apr 6 at 2:55
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    NO That is not true. They can not be said to have pixels. Those that say it are not understanding the eye and/or pixels. merriam-webster.com/dictionary/pixel The optical nerve sends information to the neural "units" of the brain. – Alaska Man Apr 6 at 3:05
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    I'm voting to close this question as off-topic because it is about the acuity of the human eye, and has no photographic context. – scottbb Apr 6 at 3:25
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    "What is the acceptable CoC... of the human eye...?" – What is the purpose of this question? Suppose you come up with an "acceptable" number. It's not like you can upgrade your eyes. – xiota Apr 6 at 12:11
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There is no single numerical value that corresponds to the size of an "acceptable" circle of confusion for the human eye. – This does not mean that there is no CoC, which is just a spot of light. Rather, there is no set interpretation (by the brain) of CoC of various sizes across the retina.

For photography, an "acceptable" circle of confusion is determined by the film format, final print size, viewing distance, and visual acuity of the viewer. The goal is for a "point" recorded on film to still appear to be a "point" when printed.

When pixel peeping digital photos, the "point" displayed on the monitor is the pixel. There is (more or less) a one-to-one correspondence between sensels and pixels, so the circle of confusion in this case (pixel peeping) should be about the size of a sensel. This doesn't account for demosaicing or light falling across two sensels.

Since there is currently no way to print images "captured" by the human eye, we can treat it similarly to pixel peeping. (Images are "viewed" on a virtual display represented by neural nets in the occipital lobe.) The diameter of cone cells are about 0.5 to 4.0 µm. The diameter of rod cells is about 2 µm. So to activate a single photoreceptor, a point of light should be about 0.5 to 4.0 µm. However, activating individual photoreceptors does not guarantee that a spot of light will be interpreted as a point.

  • Photoreceptors are not evenly distributed. The optic disc contains no photo receptors, while the fovea is most densely packed.
  • Some cells have one-to-one neural connections, while others are connected to neurons in clusters.
  • The eye is constantly moving. Processing by the brain may drop huge amounts of unwanted detail, or multiple "captures" may be "stitched" to improve "resolution".

Depth of Field also has no practical significance with respect to the human eye.

It is possible to calculate a Depth of Field by determining focal length, aperture, CoC, distances, etc. However, this numerical value has little meaning with respect to the human eye because of the uneven density of photoreceptors, binocular vision, and neural processing. There is good sharpness in a fairly small spot in the "center", but horrible "edges". Even if an individual eye could have "infinite" depth of field, the distance mapping (of binocular vision) effectively narrows depth of field ("portrait mode").

You can check depth of field for a single eye with a ruler (close the other eye). In principle, depth of field should increase as distance increases. But, if you can manage to control saccadic movements, you will find that only a small region around the focus point is ever in focus. This is likely caused by the uneven density of photoreceptors across the retina. The brain expands that area by "stitching" multiple images.

With both eyes open, you can see "portrait mode" in action. Make an L shape with your thumb and forefinger. Stretch out your hand with your forefinger pointing away from you. Try to focus on your thumb and forefinger at the same time. Even as you close the gap between thumb and forefinger, if you have normal vision, parallax will prevent both from simultaneously being in focus.

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    CoC are just spots of light. So CoC are formed by light passing through the eye optical system. However, the interpretation of light falling on the retina varies according to density of photoreceptors, neural connections, and optical processing. So the concept as used in photography (to produce acceptably sharp output) does not apply well to the human eye. – xiota Apr 8 at 6:13
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    I have edited my answer to address DOF. You can calculate values, but they don't have any practical significance for various reasons, including the inability to produce prints captured by the human eye. Also, the structure of the retina and image processing makes DOF extremely narrow for images "captured" by the eye and "shown" in the occipital lobe. This is independent of the properties normally used to calculate DOF in photography. – xiota Apr 8 at 6:54
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    The design of corrective lenses is different from that of camera lenses. It's like asking for the DOF of a microscope. You can calculate a nominal value, but it's not useful until you have to produce some output. Photographers stack images to increase depth of field for display, but pathologists don't need to do so to examine microscope slides. (Slides do have depth.) – xiota Apr 8 at 7:07
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    Are you trying to solve a practical problem or just trying to apply photographic concepts to the human eye solely for the sake of doing so? The analogy between camera and eye is imperfect. The lack of persistent capture and output capability renders some photographic concepts useless. It would be like asking plumbing questions about the circulatory system. Some concepts apply, but many won't. – xiota Apr 8 at 7:12
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    @enbinzheng That's what I thought the motivation for this question was. I don't think your explanation of the moon illusion is reasonable, for several reasons. It is based on misapplication and misunderstanding of the principles, and false or inaccurate assumptions. It is motivated reasoning, meaning that you have already arrived at the conclusion, and are trying to fit math and principles that don't really apply in order to justify the conclusion. But more importantly, your explanation of the moon illusion is entirely off-topic at Photo-SE, because it has no photographic context. – scottbb Apr 8 at 12:46
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Defining the circle of confusion as – the largest circle that will appear as a point from a given viewing distance. Under conditions of bright light a person with good vision can resolve lines that sustain an a angle approximately 1/3000 the distance between. However, for pictorial photography, due to image contrast and level of viewing illumination, an angle of 3.4 minutes of arc is more than adequate.

This will be a circle viewed from 1/1000 of the viewing distance. This is the equivalent of 1/100 of an inch viewed from 10 inches. Since the typical viewing distance is 20 inches, we are talking, 2/100 = 1/50 = 0.5mm viewed from 500mm.

When making an 8x10 inch image from a full frame, the degree of enlargement required is about 8x. Thus the circle size at the image plane is 0.5 ÷ 8 = 0.0625mm. For a compact (APS-C) crop factor 1.5 this value becomes 0.0625 ÷ 1.5 = 0.04mm.

Another way: Set the circle size as a fraction of the focal length. As a rule of thumb, this takes into account the degree of magnification that will be applied to make the final display print. Using this method, many depth-of-field charts use 1/1000 of the focal length. For critical work Kodak used 1/1750 and Leica used 1/1500 of the focal length.

Circle size is a variable based image contrast and image illumination intertwined with need.

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  • "an a angle approximately 1/3000 the distance between" What does it mean? – enbin zheng Apr 6 at 1:28
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    This is a small angle -- 3 feet in diameter object viewed from 1.3 miles per "Photographic Lenses" by C.B. Neblette. – Alan Marcus Apr 6 at 2:30
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    @enbinzheng That means tan(α)=1/3000 so α≈1/3000 (radians)≈0.2° – xenoid Apr 6 at 7:47
  • @xenoid Or can you see objects 1 meter high at 3000 meters away? – enbin zheng Apr 6 at 8:36
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Yes, the acceptable circle of confusion (CoC) should be small/smaller... and it should also be larger.

The CoC is not a constant, it is a variable based upon intended use. And the CoC "standard" also varies by intended use; i.e. 35mm cinema uses a different CoC standard than 35mm photography does.

The accepted CoC standard is based upon some assumptions... an image being viewed under "normal conditions" by an individual of "average visual acuity." The assumptions include viewing an image from a distance so that it occupies ~ 45deg horizontal FOV (~ 53deg diagonal) and visual acuity ≈ 20/20.

But if those assumptions do not apply, then the accepted CoC standard also does not apply. E.g. if you are going to be making large format prints for gallery viewing at short distances you would need a smaller CoC. And conversely, if you were going to publish an image as 1/2 of a magazine page you could use a larger CoC.

For the most critical application of an adult with maximal visual acuity, viewing an image at the typical minimum focal distance of 4", the CoC would need to be ~ 1/3 of the accepted standard.

https://wolfcrow.com/notes-by-dr-optoglass-the-resolution-of-the-human-eye/

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  • I mean seeing objects directly with your eyes. There is no circle of confusion on the object. – enbin zheng Apr 8 at 0:55
  • How to calculate the depth of field of eye imaging? – enbin zheng Apr 8 at 1:03

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