A General Guide to Fisheye Lenses
What is A Fisheye Lens- An Overview
Nowadays, the use of Fisheye Lenses is commonplace across various applications including photography, weather monitoring, surveillance, and detection due to the unique features of fisheye lenses. What are fisheye lenses indeed? What is the structure of fisheye lenses and what are the advantages and disadvantages of fisheye lenses? In this article, we will discuss the questions about fisheye lenses above and more.
First of all, a Fisheye Lens is an ultra wide-angle lens with an extensive field view and produces wide panoramic or hemispherical images. Fisheye lenses are designed to achieve the maximum photographic angle of the lens, the front lens of this photographic lens is very short in diameter and protrudes towards the front of the lens, which is quite similar to the eye of a fish, hence the name "fisheye lens". Therefore, there is a big difference between the fisheye lens and the real-world scene in people's eyes.
The original design intention of Fisheye lenses is to help meteorologists detect and diagnose the weather. Over time, its applications expand. With its appealing advantages of providing users with massive fields of view and substantial depth of field, fisheye lenses excel in offering expansive visual scopes and find widespread uses in fields like photography, thermal imaging, astronomical observation, etc.
Therefore, building a clear understanding of fisheye lenses might be very worthwhile regardless you’re an optical professional or just an amateur. In this blog from Shalom EO, we delve deep into the topic of fisheye lenses, covering:
- The characteristics of fisheye lenses
- The difference between fisheye lenses and wide angle lenses
- The advantages and disadvantages of fisheye lenses
- Different Types of Fisheye Lenses
- The design inspiration and imaging principle of fisheye lenses
- The Structure of Fisheye Lenses
- The projective model fisheye lenses (fisheye projection)
- The applications of fisheye lenses
The Characteristics of Fisheye Lenses
1. Focal Length: The focal length of a circular fisheye lens is often between 8mm and 10mm; the focal length of a full-frame fisheye lens ranges from 15mm to 16mm.
2. Angle of View: The fisheye lens has a 180° field of view at its widest point.
3. Mapping: The mapping functions used are equidistant, equisolid, orthographic, and stereographic.
4. Image Distortion: The distortion caused by the fisheye lens in the photos formed is barrel distortion. The central part of the photo appears to bulge outward, thus forming a curved image. This is because the magnification of the lens changes as you get further off axis.
5. Depth of Field: Due to the extremely wide-angle characteristics, fisheye lenses also have considerable depth of field.
The Difference Between Fisheye Lenses, Wide Angle Lenses, and Super Wide Angle Lenses
Both wide angle lenses, fisheye lenses, and wide angle lenses have larger FOVs and shorter focal lengths than normal optical lens assemblies.
For regular wide angle lenses, the focal lengths are typically greater than 25mm, and the FOVs are smaller than 90 degrees. While the fisheye lenses and super wide angle lenses have ultra-wide FOVs above 90 degrees and even greater than 180 degrees and very short focal lengths between 16-25mm or less than 16mm.
There’s no definite border line of focal length and field of view to differentiate super wide lenses and fisheye lenses.
In general, there are two major differences between fisheye lenses and super wide angle lenses. The first difference is that the front lens element fisheye lenses protrude outward like the real eye of a fish. The second difference is that fisheye lenses do not aim to provide rectilinear images, but are oriented for capturing a maximized range of areas, producing images with a much stronger curvilinear nature and significant barrel distortions which requires software correction (The image close to the edge is compressed compared to the center of the image, and the straight lines in the image will be more skewed). In comparison, super wide angle lenses tend to offer a more realistic aspect ratio.
The Advantages and Disadvantages of Fisheye Lenses
Advantages:
1. Panoramic fields of view, wide coverage
Fisheye lenses can provide a wide field of view, and one fish-eye lens can cover the areas of multiple regular lenses. With this feature, fisheye lenses provide comprehensive coverage without any corners or areas going unnoticed. This feature is cost-saving because users need not purchase multiple lenses and also reduces the potential danger that some areas are overlooked. For instance, in large open spaces such as parking lots, warehouses, or retail stores with wide aisles, a fisheye camera can monitor the entire area without blind spots.
2. Save costs and more compact, lightweight design
A single fisheye lens module can provide users with an ultra-wide range of sight which needs multiple regular lenses, hence the lower equipment costs, and the bother of maintenance is also reduced. Because only one fisheye lens instead of several normal lenses needs to be installed to monitor or view the entire area, it also means a more compact and lightweight design, which might be a critical factor in some particular circumstances. For example, if the lenses are to be integrated into a camera loaded on drones, a fisheye lens module with lighter weight and smaller volume will be much better than multiple bulky and heavy ordinary lens modules.
Disadvantages:
1. Distortion problems exist
Since fisheye lenses have a very wide viewing angle, fisheye lenses suffer from serious distortion issues. The distortion inherent in fisheye lenses provides enhanced coverage, capturing more details within its wide-angle view. Moreover, the use of correction techniques has made it possible to correct the distortion caused during live viewing or playback.
2. Low pixels and unclear details
Since fisheye surveillance cameras need to cover a wide area, the area of each pixel will be larger at the same resolution. This means less detail can be captured per pixel.
To conclude, fisheye lenses have both pros and cons which constitute their unique nature. Therefore one must take cautious considerations of multiple factors before purchasing fisheye lenses. Fisheye lenses are preferred in particular when users want to achieve the utmost visual scope and is not recommendable when users have high requirements for the similarities between images and the reality.
Different Types of Fisheye Lenses
Depending on how the projected images fulfill the image sensor, fisheye lenses can be classified into three types: Circular Fisheye Lenses, Diagonal Fisheye Lenses (also known as Full-frame fisheye lenses), and Cropped Circle Fisheye Lenses.
The circular fisheye lenses provide 180°field of view over the width of the sensor, projecting the entire hemispherical space onto the image sensor, and the borders of the sensor will appear black.
The diagonal fisheye lenses or full-frame fisheye lenses provide 180°field of view over the diagonal of the camera sensor (this means the vertical and horizontal FOVs will be smaller than 180°). The image circle extends beyond the sensor frame.
The cropped circle fisheye Lenses (also known as the portrait fisheye lenses) are optimized for the width of the format cameras, producing images cropped at the top and bottom. The result is an image in the center and black shades at the corners ( the proportion of black shapes is much less than in the case of the circular fisheye lenses).
The figure below clearly illustrates the differences among the three types of fisheye lenses:
Figure 1. Three Types of Fisheye Lenses
The Design Inspiration and Imaging Principle of a Fisheye Lens
How are images formed in fisheye lenses? why can a fisheye lens have a wider field of view than an ordinary lens module? What is the difference between an ordinary lens module and a fisheye lens?
When fisheye lenses were first invented, the scientist obtained the design inspiration from the vision of real fish. The first concept of a fish eye lens is based on simulating how fish look up underwater.
In 1906, an American physicist named Robert W. Wood coined the term "fish eye." He described the experiment in detail in a paper: He assembled a camera in a bucket filled with water and shot pictures starting from the bottom in the upward direction. The experiment was designed to simulate how fish perceive an ultra-wide hemisphere view from underwater.
Most of the ordinary lenses can be simplified as a pinhole camera model. In this model, the light beam propagates along a straight line, and the image and the object are similar. Or, in other words, a perspective transformation is performed between the image and the object. Under perspective transformation, a straight line is still a straight line after transformation, a curve is still a curve after transformation, and the intersection point of two straight lines is still the point where the two straight lines intersect after transformation, etc.
In a sense, the use of the camera lens is to transform the object space into an image space ( i.e. the optical space coordinatizing the visual representation or component of a scene). The imaging plane can be thought of as cutting a slice in the image space and intercepting a plane to form a captured image.
However, the lens based on the pinhole camera model has a drawback - the line propagates in a straight line, making it difficult for the lens to capture objects at the edge. As shown in the figure below, for red line arrows with identical lengths, as the lines get closer to the edge of the lens, the length of the arrow also becomes longer after imaging. However, the size of our camera sensor is limited, so it will not be possible for an ordinary lens module to capture images of objects that are very close to the edges. If a field of view of 180° is to be reached, the imaging plane is required to be infinite, which is not feasible.
Figure 2. Pinhole Imaging Model
The fundamental principle of a fish eye lens is to make the exit angle of the light smaller than the incident angle so that space within a broad range of FOV can be projected onto an imaging plane of limited size. Think of how a fish looks up underwater. When the fish in the water are close to the water and observe the scene above water, the field of view of the fish can reach about 180°.
Imagine when an incident light ray travels from air to water, because the refractive index of water is greater than that of air, the light rays bend toward the normal, and light rays close to the water's surface will also enter the water at an angle equal to the refraction angle. Based on the above, it can be understood that when fish in the water are close to the water surface, the fish can see the scenes in the 180° angle range above the water surface.
Figure 3. Fisheye Lens Imaging Model
The crystalline lens (the word lens here means the biological structure of the fish eye) of the fish eye and the optical medium can be regarded as an optical structure as a whole. The front surface of the lens and the horizontal plane of the water form a plano-concave lens, and water is the medium of light propagation. If the water medium is replaced by an optical material with a high refractive index, and by forming an optical lens, it is possible to achieve a wide range of vision.
To further expand the field of view, the front plane surface of the plano-concave lens is modified and made into a convex plane, at the same time, the curvature of the back surface is also increased to ensure that the change in optical power is not large, which makes the plano-concave lens transform into a meniscus-shaped lens. This is how the first lenses of fisheye lens modules evolved. The first lenses of fisheye lens modules are all negative lenses that are similar to a parabola and protrude outward a lot.
Figure 3. The evolving of a fisheye lens
The Structure of Fisheye Lenses:
A fisheye lens is an inverted telephoto lens because of the large FOV and short focal length. Fisheye lenses often contain several lenses with negative focal lengths in the front, serving as components to gather light from an entire hemisphere into the aperture stop. The rear lens group, therefore, must have positive focal lengths to counterbalance the total power of the lens module.
Figure 5. The structure of fisheye lenses
The Correction of Distortion Fisheye Lenses (Fisheye Projections):
Distortion implies a lack of similarities between reality and the image. Fisheye lenses produce images with extreme distortions that need exclusive software corrections based on different projection models and mapping functions.
Fisheye lenses are composed of several different lenses. During the imaging process, the incident light is refracted with different degrees and projected onto an imaging plane with a limited scale.
Fisheye projection model: Due to the multi-element structure of the fisheye lens assemblies, the analysis of the refraction relationship of the fisheye lenses becomes quite complicated, as shown in the figure below, a spherical projection model is proposed to illustrate the refraction relationship, this model decomposes the imaging process of the fisheye camera into two steps:
Figure 6. Fisheye projection
Step 1. Project three-dimensional space points onto a virtual unit sphere whose center coincides with the origin of the camera coordinate system.
Step 2. Projecting the points of the unit sphere onto the image plane. According to the different projection functions, the projection model can be further divided into the following table. (There is no single fisheye projection, but instead, there are a class of projection transformations all referred to as fisheye by various lens manufacturers, with names like equisolid angle projection, or equidistance fisheye. Less common are traditional spherical projections which map to circular images, such as the orthographic or stereographic projections.
Fisheye Projection Model |
Mapping Functions |
Characteristics |
stereographic projection |
r=2ftanθ |
The angle at which any straight lines intersect remains unchanged after the projection |
equidistance projection |
r=fθ |
The distance between the object's imaging surface and the center of the image is proportional to the incident angle |
equisolid angle projection |
r=2fsinθ |
Before and after the transformation, the solid angle occupied by the object remains unchanged. |
orthographic projection |
r=fsinθ |
The projection distortion is the largest, and the maximum field of view cannot be greater than 180° |
Note: for the mapping functions, f is the focal lengths of the fisheye lenses;θ is the angle between a point in the real world and the optical axis, which goes from the center of the image through the center of the lens; r is the radial position a point on the image on the film or sensor.
Below is a more detailed discussion of different types of fisheye projections:
1. Stereographic Projection
In comparison to other fisheye projections, the stereographic projection has the smallest distortion. The miniature surface elements on the spherical object surface will still be a small circle in the image after stereographic projection. Therefore, stereographic fisheye projection maintains high similarity in imaging small objects. However, it is this high similarity in imaging that makes this projection method unable to provide sufficient barrel distortion, shrinking the imaging field of view.
2. Equidistance Projection
The equidistant type fisheye lenses are the most prevalent type of fisheye lenses manufactured for cameras so far, especially when intended to be mapped into equirectangular images. These are also known as "tru-theta" or "f-theta" or what is regularly meant by a perfect fisheye mapping. The equidistant fisheye lenses are popular due to the appealing attribute that there is the same number of pixels per subtended angle on the periphery of the lens as the center. This fisheye projection model also has the advantage that its calculation is simpler relative to other fisheye projection models.
3. Equisolid Projection
As the name suggests, equisolid maintains an equal area for each pixel. That is, a pixel projected through the lens into the scene has the same solid angle irrespective of where on the lens it is.
4. Orthographic Projection
The magnification rates in the radial and tangential directions are different in orthogonal projection. When the field of view is 90°, the radial magnification rate is 0, that is, the edge image of the hemispherical object surface will form a straight line after being imaged using the orthogonal projection method.
Orthogonal projection can provide a greater amount of barrel distortion, which is more conducive to the expansion of the field of view. At the same time, the uniformity of the illumination distribution of the picture will be improved, but the orthogonal fisheye projection has few applications in practice.
Figure 7. The mapping functions of the fisheye projection models
The Applications of Fisheye Lenses
In recent years, the application of fisheye lenses has been surging in fields like wide-angle imaging, surveillance, panoramic simulation, dome projection, etc. Compared with other lenses, the fisheye lens has the advantage of providing users with extensive angles of view, but it also has the inconvenience of needing to correct image distortions. In general, there are a large number of scenarios where the advantages of fisheye lenses outweigh the disadvantages of fisheye lenses, hence its widespread usage.
Fisheye lenses can be used to build laser detection systems to realize wide-angle laser detection. Traditional laser detection systems in the past integrate Fabry-Perot interferometers or Michelson interferometers. The former requires a scanning mechanism and therefore cannot detect laser pulses; the latter has a small field of view and a complex structure. The wide-angle laser detection system using a fisheye lens does not require a scanning mechanism and can simultaneously detect the laser wavelength and incident direction.
Fisheye lenses are also an excellent option for monitoring cameras. For example, fisheye lenses built for thermal imaging are a solution to implement panoramic surveillance, realizing scouting with extended fields of view even in poor illumination conditions.
Fisheye lenses can also be used to achieve three-dimensional reconstruction and virtual browsing. By using a fisheye lens with an image of over 180 degrees to take a photo before and after a certain scene, a three-dimensional model can be built, and the user can observe the scene from any angle. Using carrier vehicles such as drones equipped with fisheye lenses to obtain video data, and then converting the video into a sequence of panoramic images arranged in the order of time, a virtual geographical environment model can be established. This large-scale geographical environment modeling technique can be applied to monitoring in firefighting, forestry, and other fields.
Using the diffraction transformation effect of fisheye lenses on a Gaussian beam, a flat-top focused fine laser beam can be obtained. The fine laser beam obtained using fisheye lenses can be used in various fields such as high-precision laser processing and medical treatment.
What Does Shalom EO Offer?
Hangzhou Shalom EO offers Stocked and Custom LWIR (Long-Wave Infrared) Fisheye Lenses and Super-wide Angle Lenses for Thermal Imaging Cameras.
Unlike average fisheye lenses and super wide angle lenses that form images by capturing visible lights, which is positioned between 400nm-700nm in the electromagnetic spectrum, LWIR fisheye lenses and super wide angle lenses work by capturing the LWIR heat radiations emitted from the objects. Any object with temperatures above absolute zero (-273°C) emits infrared electromagnetic radiations, and the long-wave infrared wavelength range is defined as the wavelength range between 8-12 micro (Click here to learn more about LWIR Thermal Imaging Lenses ). The LWIR fisheye lenses and super wide angle lenses focus the 8-12 micro infrared radiation from the objects in the scene onto an infrared detector, the images delivered reflect the heat distribution of the objects. In a monochrome thermal imaging camera, the higher the temperature, the more the thermal radiation, and the brighter the image, while cooler areas are represented using dark shades (There are also colored thermal cameras, where hot regions appear in warmer colors and cool regions appear in cool colors).
LWIR fisheye lenses and super wide angle lenses are made of optical materials and coatings that are transparent to the 8-12 micro radiations. The distinctive advantages of LWIR fisheye or super wide angle lenses over visible fisheye or super wide angle lenses are that the LWIR lenses form images based on the heat of objects rather than the real visible illumination contrast, therefore image shooting will not be affected even in poor light conditions (e.g. at night), and LWIR fisheye lenses/super wide angle lenses can capture more detail which is not visible to the human eye. These advantages are very beneficial because fisheye lenses and super wide angle lenses are often utilized for monitoring and surveillance purposes due to the vast scope of sight they can offer, in some contexts, LWIR fisheye/super wide angle lenses excel over the normal versions, enabling observations independent of the light conditions. For example, in firefighting, LWIR technology has been called upon to help fight them because of the technology’s ability to detect heat signatures. This makes it useful for locating and monitoring fires, even in conditions with limited visible conditions due to smoke, darkness, or other factors.
Compared with MWIR fisheye/super wide-angle lenses, the LWIR lenses work well at room temperatures and are the more conventional option with a more affordable price. However, the LWIR lenses suffer from attenuation of signals resulting from atmospheric moisture, carbon dioxide, and other molecules. The detection of heat sources is also not as sensitive as medium-wave infrared (Click here to view a more detailed comparison between MWIR and LWIR Thermal Imaging).
In comparison with SWIR lenses, the cost of the materials for manufacturing SWIR lenses is cheaper. However, the dependence of SWIR lenses on the visible light condition is far greater because SWIR lenses originate from reflected sunlight or thermal radiation from warm objects.
This is an example of the LWIR Fisheye Lens Modules from Hangzhou Shalom EO.
Hangzhou Shalom EO is an industrial-leading supplier of LWIR fisheye lenses and super wide angle lenses. Empowered with an expert engineering background We provide intelligent lens designs that provide optimized performance and high price competitiveness for your thermal cameras. The fisheye lenses and super wide angle lenses, featuring wide angles of view, high resolution close to the diffraction limit, and compact architectures, being compatible with multiple detector sizes, are available in either manual focusing or fixed focal length versions. Pinhole super wide angle and fisheye lens modules with miniature aperture are also available, which, utilizing the secondary imaging technique, are fit for tight, compact, and concealed designs (e.g. temperature monitoring of crystals-growing and metal-smelting furnaces, security). Full-frame (rectangular) fish eye lenses with 180°diagonal FOV are provided.
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