This is a brief conversation between and me and one of our customer. We have been tasked with developing a superior passive (pyroelectric) PIR-sensor-based motion detector for commercial and residential spaces to add to the customer's line of existing successful models. 

The customer having little in-house optical expertise, they have an immediate need for technical assistance in that area (infra-red optics). Would DiYPRO(old name of Fresnel Factory) be able to provide information that would inform my industrial design (housing, light-guide, sensor position) and signals processing.

Among the things I wish to treat mathematically are (assuming a single PIR motion detector mounted in a 90-degree corner, 80 inches above the floor of a 30 x 40 foot room):

- the effects of the 'sharpness' of the focal point where IR impinges on each pyroelectric element in the sensor - on sensitivity.
The element of PIR sensor is covered window. Typically, people say sensor the window, but the actual detection point is the element.

- the effects of progressively diminishing fresnel segment size, from the top row to the bottom row, on "pet immunity".
This is very hard to tell, since it requires optical simulation with deep insight of PIR and optics.

- the performance tradeoffs when comparing injection-molded lenses to other manufacturing methods (pressed).
Pressed has small better in terms of optical quality. However, injection has also huge advantages in terms of cost and align with sensor.

- the tradeoffs among commonly-available IR fresnel lens materials (transmissivity vs sharp focus)
We have DPP and DPE material series for Far Infra Red, and tunned PC for Near infra red. DPP has better hardness and working temp., but DPE has better transmissivity.

- any suggested enhancements to the optics to assist with "white light" immunity

- for a vertically mounted PIR motion detector (common / typical) is there any benefit to using a quad-element sensor on the theory that a "straight-at-you" intruder is more likely to generate a signal as the different fresnel 'rows' come into play, rather than the 'columns' of segments for Left to Right motion? (quad elements, being smaller, generate less signal for a given stimulus).
One of solution for Straight-at-you is cross-detection pattern.