turbo....no...it's not. someone has misled you and you've continued in many posts to put forth your lighting evangelism. If you want to talk to an expert, let me know and I'll hook you up with a senior engineer at GE Lighting, NELA Park.
Definition: “A lumen is a unit of measurement that describes how much light is contained in a space or the brightness of a light source.”
Lumens are a measure of light output at the source. Brightness of light is measured in two parts...lumens and Kelvin (color). This is a universal definition and a given in engineering and physics. Candlepower is a measure of light rcd at the 'target' and is distance sensitive....a variable given an equal measure of lumens. Your projector design determines the spread of the light, not the voracity at any point in its travel nor it's 'brightness' as it reflects back. There is real science involved in lighting...not guesswork. It's a combination of all three plus color that create the subjective perception of "better". For example, a dual filament bulb, such as an 1157 has two lighting intensities..the running and the stopping. An 1156 with the same 'high' filament intensity, expressed as lumens........will appear brighter in use because the delta between the running light intensity and the the 'high' or stop light will cause the perception of a dimmer output. There are manufactures who have taken this into account and put more watts into the high filament and fewer into the running so the the output appears brighter, but it's a perception issue. Another perception issue arises with comparing LED to incan bulbs. The standard 1157 bulb will output about 400 lumens when both filaments are operating.....the 40+ LED 1157 ouputs considerably less (200 to 380 depending on number of diodes), however, using a red LED of 220 lumens behind a red lens makes the LED appear (perception) equal to and in some cases brighter than an LED replacement 1157 that uses white diodes. This is because of the filtering of non-red light done by the lens and has nothing at all to do with the reflector shape or material behind the bulb.
The generalized purpose of the HID projector style housing is twofold, one to keep from blinding oncoming drivers. Note that the original poster was asking about turn signals, so I was never really sure why the whole HID + projector had any relevance. The second purpose of the projector design is to limit spread of light into a more focused beam patterning that is, in fact, a benefit when facing forward, but of absolutely no importance at the rear of any motorcycle. This pattern given by a properly designed projector housing will be the result of two items, the rear reflector and the magnification lens ahead of the bulb. My engineer buddy tells me that what is achieved in a perfect world is a sharp cut off of light at the edge of the beam....nothing more, nothing less. Again, not relevant to any rear facing lights.