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?
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.
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.
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.