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As I understand it, a real optical image is defined as a collection of focus points of light at a plane, existing at the plane whether there is a surface there or not, and independently of any perceiver. E.g. when a converging lens causes rays diverging from a point source to converge and cross over, the focus point is the point of convergence, from which the rays continue on their way unless there is a surface there. The image surface will have to be right smack on the plane of convergence

Apparently a pinhole image is also a real image, but there is no convergence, just rectilinear propagation of a very thin "beam" of light rays that never diverge much, and the image plane is anywhere behind the pinhole and the image surface can be anywhere behind the pinhole.

So what both kinds of optical device are doing is ensuring that the light energy that is passing through each point on the image plane is coming (as much as possible) from a single point in a single direction.

If this is accurate, shouldn't a real image be defined without reference to focus points, and in terms of rays passing through a plane, and specifying light energy?

eg something like "a 2D distribution of light energy passing through a plane in space (located on one side of an optical system), each point of which is light energy coming from a single point in a single direction (on the other side of the optical system"

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So what both kinds of optical device are doing is ensuring that the light energy that is passing through each point on the image plane is coming (as much as possible) from a single point in a single direction.

This is the part that goes wrong. A focusing lens does not produce rays going in the same direction for a given point source:

enter image description here

Note that the blue and green rays represent light coming from the same point source, hitting different parts of the lens, and passing through the focal plane at very different directions.

Image from https://www.bhphotovideo.com/explora/photography/tips-and-solutions/depth-of-field-part-i-the-basics

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  • $\begingroup$ Thanks for the reply Ryan. I'll contemplate your comments. I think I should clarify that by "in a single direction" I meant that "the light energy that is passing through each point on the image plane is coming (as much as possible) from a single point THAT LIES in a single direction", not that rays are going in a single direction. So "in a single direction" is probably redundant and could just be cut out from the sentence. $\endgroup$
    – Tony C
    Commented Jul 15, 2023 at 6:46
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For a "perfect" image to be formed all the rays of light from one point on the object which enter an optical system must arrive at one position and all the rays must have taken the same time to travel from the object to the position where the image is formed (or arrive in phase). Also the light from the points on the object which are nearest neighbours to the point under consideration on the object must arrive at positions which are in the same relative positions to the position under consideration as they were on the object.

So there is a one-to-one correspondence between object and image.

The formation of an image by a lens and a pinhole camera is different.

enter image description here

In the left-hand diagram two red rays are shown to start at position $O$ and after passing through the lens meet at position $I$.
Although the top red ray travels a further distance than the bottom red ray it takes the same time to travel from $O$ to $I$ because it does have as far to travel through the lens (glass) as the bottom ray.
Thus overall the travel times in air and glass are the same and the rays arrive in phase.
The process is repeated for the green rays which have the same travel times form $O'$ to $I'$ and note the relative positions between $O$ and $O'$ are maintained between $I$ and $I'$.

For the pinhole camera a small cone of rays from position $O$ are allowed through the pinhole to around position $I$ and they have roughly the same time of travel.
Thus from a point on the object a small area of illumination is formed.
The same happens for rays from position $O'$ which arrive around position $I'$ which then shows that the relative positions are maintained.
The area of illumination can be made smaller (ie the image is sharper) by making the pinhole smaller but that then reduces the brightness of the image and also diffraction may become significant and increase the area of illumination as illustrated below with different sizes of pinholes being used and explains why it is that a pinhole image can never be "perfect".

enter image description here

As the pinhole size is increased above $0.35\.\rm mm$ the cone of rays illuminates a bigger and bigger area and the area produced by adjacent rays from a neighbouring position of the object overlap more and more and the "image" becomes less and less distinct.

As the pinhole size is decreases below $0.35\.\rm mm$ the cone of rays illuminates a bigger and bigger area because of diffraction.

In this example a pinhole size of about $0.35\.\rm mm$ seems to be the optimum.

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  • $\begingroup$ Thank you Farcher. I'll need to think this over to try to understand. $\endgroup$
    – Tony C
    Commented Jul 15, 2023 at 6:49
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If a real optical focus point or image point is defined as a point where rays originating on an object point converge, and if a real optical image of an object is the total collection of focus points of rays coming from the object, then a pinhole image is not a real optical image, since there is no focussing in the sense of convergence.

But surely a pinhole image is the same kind of thing as an image formed by convergence, as in the case of a converging lens or the optical system of the eye, i.e., a real optical image, the only difference being that a pinhole image can’t be as sharp as the others without becoming very dim.

The issue can’t be “perfection” as such, since there is no such thing as a perfect image point anyway. Due to diffraction, there is always an airy disk.

As Hecht says in his book on optics (which came just yesterday!), a lensless pinhole camera “can form a well-defined, practically undistorted image of objects across an extremely wide angular field (due to great depth of focus) and over a large range of distances (great depth of field),” with “maximum sharpness” attained in the way you describe (to do with the size of the hole), even though as Hecht says there is “no focussing of rays at all.”

I don't mean to tell scientists how to define anything, but I’m saying that if a pinhole image is a real optical image, then I as an interested amateur don’t see how a real optical image point, or a real optical image can be defined in terms of the convergence of rays. It seems that they "should" be defined in terms of something that pinhole images and images formed by lenses have in common, in terms of what both kinds of optical system do.

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