The main parameters of optical lenses

In the field of optics, the parameters of optical lenses play a decisive role in their performance and application. The following is a detailed and in-depth analysis of the key parameters of optical lenses, combined with practical application examples to illustrate.

Focal Length: The Controller of Imaging Ratio

Focal length, as one of the key elements of the Optical System, is defined as the distance from the main point to the focal point. It plays a central role in determining the proportional relationship between the image and the actual object. When the object distance is kept constant, long focal length lenses are preferred if a large proportional image is desired.

For example, in wildlife photography, photographers often need to capture sharp details of animals without getting close enough to disturb them. In this case, the use of a long focal length lens (e.g. 600mm or even longer) can bring the distant animal closer, so that it occupies a larger portion of the picture, and the details of the animal's fur, eyes, and other features are clearly shown.

In the architecture of an optical system, there is a difference between the object focal length (front focal length f) and the image focal length (f'). The object focal length is the distance from the principal object point H to the object focal point F. The image focal length is the distance from the principal image point H' to the image focal point F'. Its positive and negative properties depend on the direction of the main point to the focal point and the direction of propagation of light is the same, if the two are the same direction, the focal length of the positive; otherwise, it is negative. It is worth noting that in the case of a system with the same medium on both sides, the image-side focal length and the object-side focal length exhibit the property of being equal in value and opposite in sign, i.e., f' = -f.

Relative Aperture and Aperture Number (F-number): Adjustment Hubs for Image Illumination

The relative aperture is the ratio of the diameter of the pupil to the focal length (D/f), which mainly affects the illuminance of the image plane. The illuminance of the image plane of a photographic lens is proportional to the square of the relative aperture. In scenes with low light, such as night photography, or when very short exposure times are necessary to capture high-speed movement (such as the split-second action of athletes at a sporting event), the need to improve image illuminance is critical, and a large relative aperture is therefore required. Lenses usually use the aperture number F to indicate the size of the aperture, and the aperture number F is the reciprocal of the relative aperture, i.e. F=f'/D.

Field of view and image plane size: defining elements of the shooting field of view

The field of view of a lens determines the extent of the scene being photographed. Given that photographic systems tend to image distant objects, the image plane is generally near the focal plane. Therefore the relationship between the image plane size and the field of view 2W ' can be expressed as the formula: y' = f'tanW', where y' represents the radius of the image plane area.

In the field of industrial cameras, CCD or CMOS sensors as a common image face receiver, divided into face array and line array two types. In the parameters of the lens, the size of the sensor is also often used to indicate the size of the field of view.

Face-array sensors have a rectangular working area, the size of which is usually measured in terms of diagonal length; line-array sensors have pixel units arranged in a single row, and their specifications are expressed in terms of the number and size of pixel units. The specifications of line array sensors are 1K, 2K, 4K, 8K, 12K, etc., and the pixel units are 5 μm, 7 μm, 10 μm, 14 μm, and so on.

For the same sensor, the long focal length lens corresponds to a smaller field of view, can be far away from the scene to shoot a larger image, so in the long-distance photography scene is widely used, known as the telescope head; short focal length lens has a larger field of view, can be near a larger range of scenes into the image surface, so it is called a wide-angle lens, while the field of view is more broadly named as a fisheye lens; between the two In between, the focal length is approximately equal to the diagonal length of the lens is the standard lens.

Operating Wavelength: The spectral range in which a lens operates.

Optical lenses are designed for light waves within a specific wavelength range. Light waves emitted from the object plane can pass through the lens to form a clear image on the image plane only if they are within the wavelength range for which the lens is adapted, and the energy attenuation is relatively small in the process. In the field of astronomical observation, the light emitted by different celestial bodies covers a wide range of wavelengths. For example, the observation of stars requires the use of optical lenses capable of adapting to visible light and some near-infrared wavelengths, because stars radiate strongly in these wavelength ranges. For the observation of some nebulae, because the light they emit may contain specific emission lines, such as some of the spectral lines of hydrogen at specific wavelengths, it is necessary to specialize in these wavelengths designed for the lens to capture their weak light signals, in order to obtain a clear image to help astronomers study the structure and composition of the nebula. Light is essentially an electromagnetic wave, and depending on the wavelength, it can be divided into several spectral bands covering the vacuum ultraviolet, ultraviolet, visible, infrared and other regions, each with unique optical properties.

Resolution: The Judge of Lens Image Quality

Resolution is one of the most important indicators of the quality of a lens, and is defined as the number of pairs of black-and-white stripes that the lens is able to distinguish within a unit millimeter of the image plane.

Resolution is 1/2 d, where d is the line width. The unit of resolution is lp/mm (line pair/mm). In the focal plane of an ideal imaging lens, the corresponding spacing between the two stripes that can be resolved.

Its reciprocal is the resolution of the ideal lens, which is calculated as:

Where λ represents the center wavelength, in millimeters. It can be seen that the resolution of the ideal lens and the relative aperture is closely related to the relative aperture, the larger the relative aperture, the smaller the F/#, the higher the resolution.

In semiconductor lithography, there are extremely high requirements for lens resolution. In order to create smaller circuit structures on the chip, it is necessary to use very high resolution optical lenses. For example, in advanced lithography equipment, the resolution of the lens to be able to distinguish tens of nanometers or even smaller lines and patterns, which requires the lens in the design and manufacturing process to strictly control the aberration and other factors to ensure that the very small scale to achieve high-precision imaging, so as to promote the continuous progress of chip manufacturing technology. However, it should be noted that this formula determines only the resolution of the center of the field of view. At the edge of the field of view, the resolution is reduced because the aperture angle of the imaging beam is smaller than the on-axis point.

In actual photographic lenses, the actual resolution is much lower than that of an ideal lens due to the presence of large residual aberration. Therefore, the actual resolution of a lens is usually characterized by a modulation transfer function (MTF: Modulation Transfer Function), which is defined as the ratio of the contrast of the image plane to the contrast of the object plane at a specific spatial frequency, which is expressed in terms of the number of line pairs per millimeter (lp/mm). For a given lens, the MTF value varies at different spatial frequencies. Generally speaking, as the spatial frequency increases, the MTF value will gradually decrease until it tends to zero, and the spatial frequency when the MTF is zero is called the cutoff frequency of the lens.

In practical industrial applications, because the system uses a surface array or line array sensor as the imaging device, the resolution of the system will also be limited by the image element resolution of the imaging sensor. The pixel resolution is calculated as NF-1/2p, where p is the size of the pixel unit. For example, when the pixel size of a CCD is 5 x 5 microns, the pixel resolution is

The pixel resolution of the sensor fundamentally limits the maximum resolution of the system, even if the lens itself has a high resolution, the system can not distinguish the fine details above the pixel resolution. Therefore, in the actual lens selection process, the lens resolution is usually required to be slightly higher than the pixel resolution to ensure that the system can reach the maximum resolution limited by the sensor.