What is the Difference Between a Fisheye and Wide Angle Lens?
Yes, there is a real difference between a fisheye lens and a wide-angle lens. According to Warren Smith's Modern Optical Engineering, a fisheye lens is defined as having a field of view of 180° or more. A wide angle lens provides a large field of view but typically less than 180°.
The key insight: a fisheye lens can act as a wide-angle lens when paired with a smaller sensor that crops the image circle. However, a wide-angle lens is not necessarily a fisheye lens. GoPro's marketing team was stuck with "fisheye" terminology because the first product used a cropped fisheye lens—newer GoPros use wide-angle lenses that are not true fisheyes.
Key Understanding
Fisheye lenses with 180°+ field of view do not always provide 180° FOV if used with a smaller sensor. A fisheye with full coverage can provide fields of view as narrow as 160° diagonal when cropped—acting as a "wide angle" lens. This relationship is defined by the fisheye fill factor.
How Does Barrel Distortion Affect Field of View?
Optical distortion is a third-order transverse aberration. The practical explanation: distortion is the change in magnification (angular resolution) versus image height. Distortion is present in all fisheye lenses and most wide-angle lenses, and typically increases with field angle.
Rules of Thumb for Distortion
The distortion profile of a lens dramatically changes the field of view output from a camera system. The charts below demonstrate that a 1.9mm lens can provide anywhere from 106° to 180°+ field of view at a 5.0mm image circle—depending entirely on the projection model used.
The image height chart shows how different projection models map field angle (θ) to radial distance on the sensor. Notice how rectilinear projection approaches infinity at 90°—explaining why it cannot achieve 180° FOV. Fisheye projections (equidistant, equisolid, stereographic) use different mathematical mappings that allow coverage beyond 180°.
The angular resolution chart reveals a critical trade-off: rectilinear projection maintains higher angular resolution (smaller angular extent per pixel) at the center, but resolution falls off rapidly toward the edges. Equidistant projection provides uniform angular resolution across the entire field—ideal for applications like SLAM where consistent feature tracking is required.
What Are the Four Main Fisheye Projection Models?
| Projection | Formula | Key Property | Best Application |
|---|---|---|---|
| Rectilinear | r = f·tan(θ) |
Preserves straight lines | Architecture, measurement |
| Equidistant | r = f·θ |
Linear angle-to-radius | SLAM, visual odometry |
| Equisolid | r = 2f·sin(θ/2) |
Preserves area ratios | Sky coverage, hemispheric |
| Stereographic | r = 2f·tan(θ/2) |
Preserves local shapes | Object recognition |
Rectilinear (Pinhole) Projection
The rectilinear projection follows r = f·tan(θ) and preserves straight lines in the scene
as straight lines in the image. This is the "natural" perspective familiar from human vision and standard
photography. However, the tangent function approaches infinity at 90°, which mathematically prevents
rectilinear lenses from achieving 180° or greater field of view.
Equidistant Projection
The equidistant projection r = f·θ provides a linear relationship between field angle and
image radius. This means angular resolution is uniform across the entire field of view—every pixel
subtends the same angle regardless of its position. This property makes equidistant fisheye lenses
ideal for visual SLAM and odometry where consistent feature tracking from center to edge is critical.
Equisolid-Angle (Equal-Area) Projection
The equisolid projection r = 2f·sin(θ/2) preserves solid angle ratios—equal areas in the
scene occupy equal areas on the sensor. This is valuable for applications like whole-sky imaging,
cloud coverage analysis, and any application where area measurement matters more than shape preservation.
Stereographic Projection
The stereographic projection r = 2f·tan(θ/2) is conformal—it preserves local shapes and
angles. Objects at the extreme edges of the frame maintain their shape better than with other fisheye
projections, making it useful for applications where object recognition must work across the entire
field of view.
Why Does Distortion Matter for Computer Vision?
Distortion changes the scale of objects at different parts of the field of view. The scale changes both radially and tangentially, causing object deformation that affects computer vision algorithms.
⚠️ CNN Training Warning
CNN-based methods should ideally be trained on data that has the distortion profile used by your embedded vision system. Otherwise, activations will occur in incorrect locations, degrading detection and classification accuracy. Alternatively, undistort images before inference—but this adds computational overhead and may crop the field of view.
Impact of Distortion on Detection Algorithms
Research by Pei et al. demonstrates how image degradations including distortion affect CNN-based classification. Distortion changes the scale radially and tangentially, causing line deformation that impacts both object detection and line segment detection algorithms.
Which Applications Benefit from Fisheye vs Wide Angle Lenses?
Mobile Robotics
Wide FOV for obstacle avoidance and navigation
- • Equidistant projection preferred
- • 180°+ diagonal coverage
- • Low F/# for indoor use
Surveillance
Hemispheric coverage for room monitoring
- • Equisolid for coverage mapping
- • IR-corrected optics
- • Day/night operation
Automotive ADAS
Surround view and parking assist
- • IP67 environmental sealing
- • Thermal stability
- • Low distortion variants
How Do I Calibrate a Fisheye Lens for Computer Vision?
OpenCV provides the cv2.fisheye namespace implementing the Kannala-Brandt distortion model,
which is well-suited for fisheye lenses. The calibration process determines both intrinsic camera
parameters and distortion coefficients (k₁, k₂, k₃, k₄).
Kannala-Brandt Distortion Model
The distorted angle θd is related to the undistorted angle θ by:
θd = θ(1 + k₁θ² + k₂θ⁴ + k₃θ⁶ + k₄θ⁸)
This polynomial model captures radial distortion with four coefficients, providing accurate
calibration for wide-angle and fisheye lenses used in machine vision applications.
Calibration Procedure
- Capture calibration images: Take 15-30 images of a checkerboard pattern at various angles and distances, ensuring the pattern appears in different regions of the frame.
- Detect corners: Use
cv2.findChessboardCorners()to locate the checkerboard corners in each image. - Refine corners: Apply
cv2.cornerSubPix()for sub-pixel accuracy. - Calibrate: Call
cv2.fisheye.calibrate()with the object points and image points to obtain camera matrix K and distortion coefficients D. - Undistort: Use
cv2.fisheye.undistortImage()orcv2.fisheye.initUndistortRectifyMap()for real-time correction.
Featured Fisheye & Wide Angle M12 Lenses
Selecting Between Wide Angle and Fisheye for Your Application
| Requirement | Wide Angle (<180°) | Fisheye (≥180°) |
|---|---|---|
| Straight line preservation | ✓ Better (rectilinear) | ✗ Lines curve |
| Hemispheric coverage | ✗ Multiple cameras needed | ✓ Single camera solution |
| Edge resolution | Lower (rectilinear falloff) | Higher (equidistant) |
| CNN compatibility | Better (less distortion) | Requires retraining |
| SLAM performance | Limited FOV reduces features | More features, better loops |
| Measurement accuracy | Higher near center | Uniform with equidistant |
Frequently Asked Questions
What is the difference between a fisheye lens and a wide angle lens?
According to Smith's Modern Optical Engineering, a fisheye lens has a field of view of 180° or more. A wide angle lens provides a large field of view but less than 180°. A fisheye lens can act as a wide angle lens when paired with a smaller sensor that crops the image circle, but a wide angle lens is not necessarily a fisheye.
What is barrel distortion in camera lenses?
Barrel distortion is a third-order transverse optical aberration where magnification decreases with distance from the optical axis, causing straight lines to curve outward like a barrel. It is present in all fisheye lenses and most wide-angle lenses, and increases with field angle.
What are the different fisheye projection models?
The four main fisheye projection models are: Rectilinear (r = f·tan(θ)) which preserves straight lines but cannot exceed 180°; Equidistant (r = f·θ) which provides linear angle-to-radius mapping ideal for measurement; Equisolid/Equal-Area (r = 2f·sin(θ/2)) which preserves area ratios; and Stereographic (r = 2f·tan(θ/2)) which preserves local shapes and angles.
Why does lens distortion matter for computer vision?
Distortion changes the scale of objects at different parts of the field of view both radially and tangentially, causing object deformation. CNN-based methods should ideally be trained on data that matches the distortion profile of your embedded vision system, otherwise activations will occur in incorrect locations.
What is the fisheye fill factor?
Fisheye fill factor describes how the lens image circle relates to the sensor size. Categories include: circular fisheye (image circle smaller than sensor), full-frame fisheye (image circle matches sensor diagonal), and cropped fisheye (sensor crops the image circle). This determines whether you get the full 180°+ FOV or a cropped wide-angle view.
How do I calibrate a fisheye lens for computer vision?
Use OpenCV's cv2.fisheye namespace with the Kannala-Brandt distortion model. Capture 15-30 checkerboard images at various angles, detect corners with cv2.findChessboardCorners(), then call cv2.fisheye.calibrate() to obtain intrinsic parameters and distortion coefficients (k1-k4). This enables accurate undistortion and 3D reconstruction.
What projection model should I choose for SLAM and visual odometry?
Equidistant projection is preferred for SLAM and visual odometry because it provides uniform angular resolution across the field of view, enabling consistent feature tracking from center to edge. Equisolid projection works well when area measurement is important. Stereographic preserves local shapes, useful for object recognition at extreme angles.