What Is A Diaphragm? What Is The Function of A Diaphragm? How Is The Effective Diaphragm Determined?

1.The definition and function of a diaphragm

The brightness of an image depends on the luminous flux passing through the optical system. The edges of optical elements or specially designed openings (diaphragm) in the system serve to limit the cross-section of the light beam, thus controlling the flow of light energy.

Since any optical system is inherently diffraction-limited, and its resolution is limited by the system's diaphragm, every optical system must have a primary limiting aperture (the diaphragm).

Not every lens edge acts as an effective diaphragm, and additional diaphragms are often added to improve image quality. Therefore, a general method is needed to determine which element in a complex optical system (such as lenses, mirrors, and aperture screens) actually acts as the critical component limiting the incident light beam—that is, the effective diaphragm. Among all the diaphragm, the one that most effectively limits the incident light beam is called the diaphragm or effective diaphragm.

For example, in the diagram below, B is the diaphragm, and B' and B'' are the images of B formed by the optical system before and after the diaphragm, respectively. This is because light rays passing through the edge of B must also pass through the edges of B' and B''.

The definition and function of a diaphragm

2.Entrance pupil and exit pupil

Entrance Pupil: The image of the diaphragm formed by the lens (or lens group) in front of it, as viewed from the object space. It determines the object-space numerical aperture, which is the maximum cone angle of light rays emitted from an object point that can enter the system and contribute to image formation.

Exit Pupil: The image of the aperture stop formed by the lens (or lens group) behind it in the image space. It determines the image-space numerical aperture, which is the maximum cone angle at which the imaging beam converges to the image point.

Conjugate relationship: The exit pupil is the image of the entrance pupil formed by the entire optical system; therefore, the entrance pupil and the exit pupil are conjugate with respect to the entire optical system.

Entrance pupil and exit pupil

3.Method for determining the effective diaphragm

Based on the concepts described above, the effective diaphragm of an optical system can be analyzed and determined. For example, consider the system shown in the diagram below: the diaphragm AB is located inside the object-side focal plane of the lens (at a distance from the lens less than its image-side focal length f'), and its diameter D₁ is smaller than the lens aperture D.  Let's analyze the case where the object point P is located at the object-side focal point F of the lens:

Method for determining the effective diaphragm

Only light beams within the angular range defined by FM and FN can pass through the diaphragm AB. The image of the diaphragm AB formed by the lens in object space is A'B'. The angle u subtended by A'B' with respect to object point P is the apex angle of the beam that can pass through the entire optical system. 

The angle u_L subtended by the lens edge L with respect to the same object point P.

Comparing u and u_L: If u < u_L (i.e., the angle subtended by A'B' at P is smaller than the angle subtended by the lens edge at P), then the diaphragm AB restricts the light beam more strongly than the lens edge; therefore, AB is the effective diaphragm of this optical system for object point P.

General judgment steps:

For every potential diaphragm in the system (including the edges of all lenses and mirrors, and any aperture screens):

①Calculate the image of this diaphragm formed by all the optical elements in front of it (towards the object space).

②Calculate the angles subtended by these images and the edge of the first optical element (usually the first lens) with respect to the specified object point.

③Among all the calculated angles, find the smallest one.

④The original diaphragm (not its image) corresponding to this minimum angular aperture is the effective diaphragm of the optical system for the specified object point.

⑤The entrance pupil and exit pupil can be further determined from the effective diaphragm.

4.Definition of aperture angle

Object-side aperture angle (α): The angle subtended by the two endpoints of the entrance pupil radius at the intersection of the object plane and the optical axis (usually referring to the on-axis object point).

Image-side aperture angle (α'): The angle subtended by the two endpoints of the exit pupil radius at the intersection of the image plane and the optical axis (usually referring to the on-axis image point) (also called the projection angle).

Definition of aperture angle

5.The relationship between the effective diaphragm and the object point position

The image of the diaphragm in object space (i.e., the entrance pupil) is fixed in position, but the angle it subtends to different object points in object space is not equal. Therefore, when comparing the angles subtended by the images of various diaphragms to an object point, the effective diaphragm ultimately determined will vary depending on the position of the object point. Therefore, the effective diaphragm is always relative to a specific object point (reference point).

Exceptional case (thin lens): For an optical system consisting of only a thin lens, the effective diaphragm, entrance pupil, and exit pupil all coincide with the edge of the lens itself, and this conclusion is independent of the object point's position.

Because the position of the diaphragm image is fixed, the angle it subtends to different object points is not equal. Therefore, when comparing the angles subtended by the various diaphragm images to the object point, the effective diaphragm found will vary with the position of the object point. Hence, the effective diaphragm is always defined with respect to a specific reference point.

However, if the optical system consists of only a single thin lens, then the effective diaphragm, entrance pupil, and exit pupil all coincide with the edge of the lens itself and are independent of the object point's position.