I.Concept
The depth of field (DOF) is the distance between the nearest and the farthest objects that are in acceptably sharp focus in an image captured with a camera.According to the extent of the region that appears acceptably sharp, depth of field can be classified as either a shallow depth of field or a large depth of field.

A shallow depth of field has a narrow region of acceptable sharpness, with only objects near the focal plane appearing in focus.A large depth of field has a wide region of acceptable sharpness, with objects over a broad distance range remaining in focus.

Figure 1 shows an example of a shallow depth of field.

Image Source: https://upload.wikimedia.org/wikipedia/commons/thumb/6/63/Tree_bud_in_spring_f1.8.jpg/500px-Tree_bud_in_spring_f1.8.jpg

Figure 2. shows an example of a large depth of field.

Image Source: https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Tree_bud_at_f22.jpg/500px-Tree_bud_at_f22.jpg

II.Factors affecting depth of field
The depth of field can be determined by focal length, distance to subject (object to be imaged), the acceptable circle of confusion size, and aperture.The formula for calculating depth of field is given by: $$\text{DOF} \approx \frac{2 u^2 N c}{f^2}$$ where：

• $\text{DOF}$ : Depth of Field, the range of sharp focus in an image
• $u$: Object distance, distance from the camera lens to the subject
• $N$ : Aperture f-number, the numerical value of lens aperture
• $c$ : Acceptable circle of confusion, the maximum blur spot perceived as sharp
• $f$ : Focal length of the camera lens

(1) Circle of confusion criterion
The circle of confusion criterion is an arbitrarily defined maximum acceptable blur spot size in photographic optics, used to establish the boundary between “sharp” and “blurred” on the imaging plane: when the actual diameter of a circle of confusion is smaller than this threshold, the corresponding object point is considered to lie within the depth of field.

Under the condition that focal length, f-number, and focus distance are all held constant, the circle of confusion criterion is directly proportional to depth of field—the larger the criterion, the deeper the calculated depth of field, and vice versa.

（2) f-number
The f-number is also known as the focal ratio, f-ratio, or f-stop, and it is key in determining the depth of field, diffraction, and exposure of a photograph. It is defined as the focal length divided by the diameter of the entrance pupil, expressed by the formula:

When the focal length $f$, object distance $u$, and acceptable circle of confusion are held constant, the depth of field is directly proportional to the aperture f-number $N$.

Figure 3. Depth of field examples under different f - numbers

Image Source:https://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Dof_blocks_f4_0.jpg/500px-Dof_blocks_f4_0.jpg

（3) Focal length
With aperture (f-number), subject distance, and circle of confusion criterion all held constant, the longer the focal length, the shallower the depth of field; the shorter the focal length, the deeper the depth of field.

（4) Subject distance
With aperture (f-number), focal length, and circle of confusion criterion all held constant, the farther the camera is from the subject, the deeper the depth of field; the closer the camera is to the subject, the shallower the depth of field.

III.Principles of depth of field
In photographic optics, when a lens is focused on a point, only objects lying on the corresponding plane—the plane of focus—are, in theory, rendered in perfect focus. Light rays emanating from an object point on the plane of focus converge to form a sharp point on the image plane (the surface where the image sensor or film is located).

By contrast, light rays from object points situated in front of or behind the plane of focus—on out-of-focus planes—fail to converge to a single point on the image plane. Instead, they spread into a blur spot known as the circle of confusion (CoC). The farther an object point is from the plane of focus, the larger the resulting circle of confusion; the closer, the smaller.

When the diameter of a circle of confusion is sufficiently small—below the resolution limit of the human eye—the eye can no longer distinguish it as a blur spot and instead perceives it as a sharp point. The maximum CoC diameter at which the image still retains acceptable visual sharpness is termed the circle of confusion criterion (also called the permissible circle of confusion). Applying this principle, a range of distance exists before and beyond the subject (the plane of focus) within which the circles of confusion formed by object points on the image plane all fall below the CoC criterion. Within this range, the resulting image appears visually sharp, and the human eye cannot discern any blur. This spatial interval, within which a reasonably sharp image is obtained, is the depth of field (DOF).

The distance from the nearest acceptably sharp point (the near limit) to the plane of focus is called the near depth of field; the distance from the plane of focus to the farthest acceptably sharp point (the far limit) is called the far depth of field.