The following calculations have been put together to assist with choice of lenses, by determining the horizontal angle of view that will be generated for a lens with a given focal length, or by showing the focal length you would need to find in order to achieve a given horizontal angle of view.
The results list a number of a different lens types:
- Rectilinear : a lens that displays straight lines as straight lines
- Fisheye lens, using equidistant, stereographic, orthographic or equisolid projection.
A rectilinear lens is what we would generally use in filming and photography, as the projected image appears the same as it looks to the naked eye. Fisheye lenses appear distorted to the eye, however this visual distortion is caused by the lens maintaining an accurate proportional separation between objects; it is therefore more useful for scientific measurement and immersive applications.
The calculations assume that the lens will conform to the projection perfectly. In reality, lenses aren’t perfect, you will therefore see visual deviations (e.g a barrel effect on a wide angle rectilinear lens), this will also translate to variances in focal length and angles of view. The calculations should therefore be used as a guide only.
You will need to know the image circle of the camera/sensor you are using.
This can be calculated using the following form by entering the vertical and horizontal resolution of the active portion of the sensor (generally the resolution that you are filming in), and the pixel pitch of the sensor.
Specific to the IO Industries cameras:
- 4KSDI-Mini and 2KSDI-Mini have a pixel pitch is 3.45 µm
- 4KSDI-MiniRS and 2KSDI-MiniRS have a pixel pitch of 2.4µm
The above calculations use the following equations
- Rectilinear lens : R = f . tan (𝛩)
- Equidistant fisheye lens : R = f . 𝛩
- Equisolid fisheye lens : R = 2f . sin ( 𝛩 / 2 )
- Stereographic lens: R = 2f . tan ( 𝛩 / 2 )
- Orthographic fisheye lens : R = f . sin (𝛩)
- R = Radial position of a point on the image sensor
- f = Focal length of the lens
- 𝛩 = The angle between an object and the optical axis, expressed in radians