Lenses for 3D Time of Flight (ToF) Image Sensors
Lenses for 3D Time-of-Flight (ToF) Image Sensors
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.
Trademarks
All trademarks are the property of their respective owners.
1 Background
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:
- I = Light intensity on the target (W/m2)
- µ = Pixel size (m)
- A = Lens aperture (m)
- η = Lens transmission efficiency
- f = Lens focal length (m)
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.
