Dive into Optical Lens Parameters

In an ideal Optical System, the magnification should remain constant in a pair of conjugate object planes. However, in real optical systems, this property is only present when the field of view is small. When the field of view is large or even very large, the magnification of the image will change with the change in the field of view, this phenomenon will lead to the image of the object relative to the loss of the original similarity, resulting in the image of the deformation, which is known as aberration.

In architectural photography, if a wide-angle lens is used to photograph a high-rise building, due to the large field of view of the wide-angle lens, it is easy to produce barrel-shaped distortion, making the edges of the building appear to be curved outward. In order to obtain a more realistic and accurate image of the building's appearance, the photographer may use specialized image-processing software to correct for the distortion, or try to choose the right shooting angle and distance when taking the picture to minimize the effect of the distortion.

Aberration is mathematically defined as the difference between the actual image height y' and the ideal image height y0' (y' - y0'), and in practice it is more commonly expressed as a percentage of the ratio of this to the ideal image height y0', i.e., relative aberration:

When an optical system with aberrations images a concentric object surface with equal spacing, the image will no longer be a concentric circle with equal spacing. If the system has a positive aberration, the actual image height y' will increase with the increase of the field of view and faster than the ideal image height y0', which means that the magnification increases with the increase of the field of view, then the spacing of the concentric circles will be gradually increased from the inside to the outside; on the contrary, if the system has a negative aberration, the spacing of the circles will be gradually reduced from the inside to the outside. Take the square grid object surface as an example, if imaged by the optical system with positive aberrations, the resulting image will appear pillow-shaped; if imaged by the optical system with negative aberrations, the resulting image will appear barrel-shaped, the dotted line in the figure shows the shape of the ideal image.

It is worth noting that aberrations only cause distortion of the image and do not affect the sharpness of the image. Thus, for general optical systems, the imaging defect of aberration does not significantly hinder use as long as the distortion of the image is within acceptable limits. However, in some application scenarios where the image needs to be utilized to accurately determine the size of an object, the effect of aberrations is critical because it directly affects the accuracy of the measurement, so in these cases the aberrations must be strictly corrected.

Depth of field: Depth resolution for a clear image range

When the objective lens is focused on a particular photographic object, there exists a certain range in front of and behind the object within which the object is able to present a clear image on the image plane, this range is defined as the depth of field (Δ1 + Δ2).

In the structure of optical imaging, the image plane A' is the plane on which the target surface of the sensor is located, and its conjugate plane A is the alignment plane. The farthest plane that can form a clear image on the target, i.e., the plane where the object point B1 is located, is called the farscape; the closest plane that can form a clear image on the target, i.e., the plane where the object point B2 is located, is called the near-field. Object point B1, B2 were imaged in front of the target after the projection to the target surface to form a diffuse spot, when the diffuse spot is small to a certain extent, it can be considered to be presented in the image of the surface is a clear image.

The formula for calculating the depth of field is:

Where Δ1 and Δ2 represent the depth of field and depth of field, respectively, p, p1 and p2 represent the distance from the focusing plane, the plane of the far field and the plane of the near field to the objective lens, f' is the focal length of the objective lens, F is the number of apertures of the objective lens, and δ is the diameter of the dispersion circle that can be permitted on the image plane, and the minimum value of which is usually the size of the image element in the case of CCD or CMOS sensors.

It follows that depth of field is closely related to the focal length of the objective lens, the size of the aperture, and the photographic distance. Specifically, the smaller the aperture (the larger the F-number), or the larger the shooting distance, the greater the depth of field, and in general, the depth of field is greater in the far field than in the near field. Lenses with shorter focal lengths have a greater depth of field when shooting at the same distance with the same aperture value; conversely, lenses with longer focal lengths have a relatively smaller depth of field.

Working Distance: A Key Reference to the System's Spatial Dimensions

In the lens selection process, in order to accurately determine the spatial dimensions of the optical system, it is often necessary to understand the lens in the work of the object distance, image distance, as well as the distance between the two main surfaces of the lens and other important parameters. However, as the object distance and image distance are relative to the position of the main surface of the lens optical system, and the main surface of the lens is difficult to determine directly in practice, which leads to the object distance, image distance and other parameters are also difficult to measure directly.

For example, in the application of microscope objective lens, the working distance is a key parameter. When observing cell sections in a biological microscope, it is necessary to select an objective with an appropriate working distance based on the thickness of the sample and the magnification of the objective. If the working distance is too short, the sample may be damaged during the focusing process; and if the working distance is too long, it may not be possible to obtain sufficient magnification and clear images.

Lens manufacturers have introduced the parameter of working distance, and at the same time provide the magnification of the lens at that working distance, as a convenience for the user to confirm the spatial dimensions of the system more easily.

At present, the definition of the working distance has not formed a unified standard, there are mainly two different definitions. One definition is the distance from the subject to the camera negative; the other definition is the distance from the subject to the front surface of the lens. In the current market environment, most camera lens manufacturers generally adopt the first way of definition. Therefore, in the absence of special instructions, the working distance given in the manual usually refers to the distance from the subject to the camera negative.

Through an in-depth understanding and mastery of the parameters of the above optical lens, whether in the optical design, photography and video, or in the field of industrial inspection, etc., are able to more accurately select and use optical lenses, so as to achieve the desired optical imaging effect, and promote the continuous development and progress of related technologies.