Figure 7. Relative illumination examples. Light collecting efficiency


Light collection efficiency is proportional to 1/ (f/#)2, where f/# = (focal length)/(aperture size). The smaller the f/#, the better the efficiency. There are some trade-offs with a small f/# optical system. As the aperture size increases, there tend to be more vignetting and aberrations, which make the optics more challenging to design. A low f/# system also tends to have shallower depth of field.


Relative illumination (RI) and chief ray angle (CRA) RI is defined as:


The sensor illuminance declines based on the (cos q) law, in a distortion and vignetting free lens system where q is the CRA incident angle on the sensor plane. The result is a relative darkening of the image toward the sensor border. The irradiance fall-off can be reduced by introducing negative distortion in the lens system. The max CRA at the sensor edge should be optimised based on the imager microlens array specification. A smaller CRA helps narrow the bandwidth of the BPF to achieve better ambient light immunity.


The following examples demonstrate how the CRA and the focused light cone sizes (effective f/#) across the field affect the RI. The lens system of Example 1 in Figure 7 has larger CRAs and gradually decreasing imaging cones (that is, increased f/#) as the field


Instrumentation Monthly April 2025


angle increases. The corresponding RI drops significantly with the field angle as shown in the corresponding RI plot. Example 2 in Figure 7 demonstrates that the RI can be well maintained by minimising the CRA as well as keeping uniform f/# across the field.


Stray light


Stray light is any unintended light in a system that could be detected by the sensor. Stray light can come from in or out of field sources that form a ghost image (for example, lens flare) through even numbers of reflections. Stray light can also emanate from opto-mechanical structures and any scattering surfaces. ToF systems are particularly sensitive to stray light because the multipath nature of stray light


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