In a camera, the lens ensures that light coming from a given point in a scene reaches a given pixel. When an ideal lens is in perfect focus, light coming from a given point in the image will reach a given pixel only. This is an important optical component which enables cameras, including 3D time-of-flight (ToF) cameras, to work. 3D ToF cameras have certain distinct characteristics which have special requirements to be met with while selecting or designing the lenses. This document explains how to decide the specifications for 3D ToF cameras. It also describes how to choose or design lens holders.
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Detailed information on 3D ToF cameras is given in Time-of-Flight Camera – An Introduction (SLOA190). This document describes the specifics which set the 3D camera optics requirements distinct from conventional cameras.
A 3D ToF camera works on active lighting only. It cannot get any depth signal from the ambient light. So it is important that the light collection ability of the lens is as efficient as possible. The light collection ability of the lens depends on the lens aperture and the transmission efficiency in the wavelengths of interest. The range of wavelengths the user would be interested in is the transmission spectrum of the LED or Laser being used for the camera. The effective light collection ability of the lens is not the same for each and every pixel. It reduces as you move farther and farther from the center of the lens optical axis. This specification is called relative illumination. For applications requiring good performance at the edges and corners of the scene, relative illumination is an important specification.
In order to optimize the camera, the light power incident on each pixel has to be maximized. More light power on the pixel provides a larger signal power. This increases the Signal-to-Noise Ratio (SNR) of the system resulting in an improved depth resolution. Lenses with the largest absolute aperture do not necessarily give this.
The mathematical relations need to be carefully derived. If the constant light intensity on the target is I, then the per pixel light power, P is given as:
where
Among these parameters, I is purely dependent on the illumination and the object distance and µ is dependent on the sensor. In the camera design, the lens design can affect in terms of the F number and the transmission efficiency.
An example lens specification which works well for a 3D ToF system is shown in Table 1.
Specification | Value | ||
---|---|---|---|
Sensor Format | Horizontal | 80 | pixels |
Vertical | 60 | pixels | |
Sensor Pixel size | Horizontal | 30 | um |
Vertical | 30 | um | |
Light Wavelength | 850 nm | ||
Effect Focal Length (EFL) | 1.62 mm | ||
F.No | 1.2 | ||
Transmission efficiency | >85% @ 850 nm | ||
>80% @ 835 nm to 870 nm | |||
>70% @ 800 nm to 900 nm | |||
Lens Total Length | <10.0 mm | ||
View Angle | Horizontal (deg) | 75° | |
Vertical (deg) | 57.4° | ||
Diagonal (deg) | 90° | ||
Resolution (MTF) | On Axis | > 70% contrast at 17 lp/mm | |
Full Field | > 50% contrast at 17 lp/mm | ||
TV distortion (Trad.) | < 10% | ||
Relative Illumination (Ref.) | 70% | ||
Chief Ray Angle | < 10% | ||
Maximum Image Circle (MIC) | 3.6 mm | ||
Back Focal Length | 1.0 mm | ||
Barrel Thread Size | M12 × 0.5 |
Detailed information on each of these topics is freely available on the internet. This document deals only with the specifications important to the topic.
The F number is the ratio of the focal length (f) to the aperture (A). This is a common way of specifying the aperture of the lens.
The pixel light collection power scales as a second power of the F number. It is important to have a very low F number to get the largest aperture possible.
The low F number has other side effects to account for. Low F number lenses have a very narrow depth-of-field owing to the large aperture sizes. Depth-of-field is the range of distances over which the camera appears to be in focus. The lens depth-of-field must be carefully designed considering the application for the camera. The limits of lens depth-of-field should match or exceed the minimum and maximum distance requirements of the final cameras that the lens would be used in. Depth-of-field increases as the pixel size increases. TI's 3D ToF sensors have pixel sizes larger than usual RGB camera sensors. Owing to the larger pixel size, the OPT8241 will have a very wide depth-of-field compared to a typical RGB camera for the same lens.