Is the focus point a variable or absolute size?

Question

In illustrations of the focus point of a sense, it looks to me to be infinitely small and as a result the resulting convergence of light would not yield an image. If the focus point is NOT infinitely small at what size is it determined to be optimal from a perspective of focus?

Answer 1

The focus point is not infinitely small. If I understand your question, the smallest point of focus is the Airy disk. This is because light travels as a wave and the disk is the result of the wave nature of light.

See: Airy disk

The smallest size of the Airy disk is based on the wavelength of light and the size of the aperture.

See: Diffraction Limited system

Answer 2

As you know, the lens handles every point it sees on objects and renders them as tiny points (if properly focused) on film or digital sensor. These tiny points are the projected images of object points. We can make a ray trace of each, the trace resembles a cone of light. Sharp focus is obtained when the apex of this cone just kisses the surface of film or digital sensor. These rays traces are made from a cardinal point associated with the lens called the rear nodal. We adjust focus by altering the distance, rear nodal to film or digital sensor. Sharp focus is achieved when the distance yields a super tiny projected circle. This circle called the circle of confusion because it overlaps adjacent circles and each has a scalloped border. This circle is the smallest fraction of an image that caries intelligence.

To appear sharp, these circles must be below the ability of the human eye to resolve them. In other words, we must see them as points of light and not disks. At normal reading distance they must be 0.5mm in diameter or smaller. There is usually leeway as to the needed back focus distance. In other words this distance is a variable provided the circle remains smaller than 0.5mm. This span is called “depth-of-focus”.

Now todays cameras are quite small thus the image made is too small to be useful. We must enlarge the camera image for display. Likely the magnification applied to make an 8x10 inch displayed image will about 10 to 14 diameters (10x thru 14x) more if the camera is a sub-miniature. To withstand 10x magnification, the tolerance at the image plane dictates a circle size of 0.05mm or smaller on the final display. This is the stuff of depth-of-field tables.

As a rule of thumb, the circle size use to calculate depth-of-field is 1/1000 of the focal length. This method attempts to take into consideration the degree of magnification that will be applied to make the final display. For critical work 1/1500 or even 1/1750 is used. Note: depth-of-field calculations are only approximations, there are many variables. These are the acuity of the eyesight of the observer, the size of the displayed image, the contrast of this image, the distance observer to image, amount of illumination associated with the image, etc.

Nobody said this stuff is easy!

Answer 3

What follows is not an answer to the question but rather a request for clarification.

First of all, the question contains an erroneous assertion. If it were possible to have a perfect convergence then it would nevertheless result in an image. However, considering, on the one hand, that lenses are never perfect and, on the other hand, due to the phenomenon of diffraction, convergence is never perfect. Lens defects affect photographs taken at a large aperture and increase with the aperture. Diffraction, due to the nature of light, affects images taken at a small aperture and increases with decreasing aperture. As a result, the images obtained are, from the point of view of sharpness, of better quality at intermediate apertures, this is called the "sweet-spot".

However, the story doesn't stop there. To obtain a photographic image there are still several stages:

• the capture of the image, whether on film or by an electronic sensor
• the image conservation and processing
• the restitution of the image on photographic paper or a screen
• viewing of the image by a person

Each of these points would require specific development.

It would therefore be necessary to clarify the question in order to provide a relevant answer.

Answer 4

Source points of light, which are infinitesimally small w/in the scene, should optimally be focused to be infinitesimally small on the sensor (this is limited by the aperture/diffraction). And this is what most diagrams depict...

But a detail w/in the scene, which consists of many points of light, is typically optimally focused at 2x the size of a pixel on the sensor. That is 4x the area; 4 pixels are used to define/record the detail with full color information (RGGB).