Visibility in the daytime is related to the distance at which a large dark object can just be discerned against a light sky. so, if you can barely make out a large tree on the horizon, then the distance between the observer and the tree is the "visibility" or meteorological optical range. Basically, daytime visibility is a measurement of contrasts which is why you need a dark object and a light sky background. A thin lightpole against a light sky is not a good target because the object is not sufficiently large, nor is it a good target against a hillside because in this case, the background is also dark. Being able to see a car tail light may not be the best way to evaluate the visibility. The visibility sensor measures the visibility where it is installed on the side of the road at 8-10 feet. If the road is wet, there is spray and other factors that may cause the visibility at the car level to be even lower. In fog, this may not bee as much of a problem. As you can see, evaluating the visibility in an operational setting such as a fog warning system can be very problematic. If I can provide additional information, please let me know.

Thank you for taking the time to respond. This is helpful.

I suggest you read the paper "Visibility Distance with Headlights: A functional
Approach", SAE Technical Paper Series number 890684, 1989

Visibility ratings for fog devices.

What visibility test was specified in the purchase and test of the system?

A daylight test might specify a seven bar test with threshold distances of
detection, classification and identification. Ambient light provides
illumination of a test card that has four black bars and three white bars of
known width and separation. Trained observers evaluate the visibility and the
observations are averaged, or the shortest distance is used, depending on the
criticality of the application. This is the type test used to establish
Clearview lettering and driver eye tests for visual acuity. Normally 20/40 is
the design limit.

Drivers must have vision correctable to 20/40. What are the vison requirements
of your state?

That acuity number of six inches at 800 feet could be the driver baseline for
detection. What does it say in the performance specification?

The first number represents the distance that person being tested is standing
to differentiate the lines. The second number represents the distance that the
ideal viewer is standing to differentiate the same lines. At twenty feet, the
ideal viewer can distinguish a one arc second width in the lines. That would be
2.8 inches at 800 feet for the person with 20/20 reference vision. and about
5.6 inches for the 20/40 licensed driver. For 800 feet, the acuity target would
be six inches for good contrast (black and white) targets.

The second number represents the distance that the ideal driver can stand and
see with the same acuity as the tested driver. The ideal vision can
differentiate at 40 feet what the test subject differentiates at 20 feet. So a
20/40 driver has to get twice as close to make out the same details as the
ideal driver.

The classification distance is less than detection distance and identification
distance is less than classification distance. Typical test specifications
might be on the order of detecting at 800 feet, classifying at 500 feet and
identifying at 250 feet. Detecting would imply the driver knows something is
there that requires additional viewing. Classifying would imply that the driver
knows that action is required and identification would imply the distance at
which appropriate action must be initiated.

Night vision has the complication of exaggerating the contrast. The eye causes
bright objects to "bloom". This makes the object look larger than it really is.
Blooming also masks dimmer objects which are near the bright object. Blooming
is a function of age and dark adaptation of the eye.

Fog has the further complication of diffusing and attenuating the light coming
from the target and reflecting the light coming from the headlights of the
viewer's car.

Headlight reflection would give the impression of driving inside a milk bottle.
A well lit intersection may be self defeating in the fog in that so much light
is reflected by the fog, that the far side of the intersection is invisible.

Consider two cases of detection. The first would be detection of a light
generated by the object. The brightness of the object would establish one part
of the contrast and the amount of light reflected by the fog would be the other
part. European cars have rear fog lights which are red lamps of higher wattage.
Maybe 30 watt instead of 15 watt. Drivers turn on the rear fog light when
driving in fog as a courtesy to following drivers and as a safety measure for
themselves. If the driver fogets to turn off the rear fog lamp, it is a real
pain to following drivers to be staring at this bright red light which masks
everthing else.

The second consideration is reflected light. Light from the drivers headlights
being reflected from the target. The light will be scattered and attenuated in
both directions.

If the system operates on the principle of evaluating the amount of light from
a test lamp at a known distance, then the threshold might be based on half the
established minimum. What is the distance from the test lamp to the sensor?
Maybe a sixteenth of a mile? If the sensor detects only half the amount of
light as was detected in clear conditions, that might have been the activation
threshold of the system. What was in the spec? If a laser is used as the test
light, then the measure is strictly attenuation. If an incandescent or
fluorescnet or Xenon light was used, then both attenuation and scattering have
to be considered.

How is the driver warning implemented? Is a suggested speed displayed? Or does
the display notify the driver in sufficient time for the driver to slow to a
comfortable speed?

Another factor in fog is the inside windshield of the car. Is there an effort
to get drivers to clean the inside windshield? In foggy conditions, the inside
window will fog, and the reflected light from the fog will make the dust on the
windshield bloom. If the defogger is on in the car, the air conditioner may
also come on, which cools the windshield. The outside of the windsheild will
fog over and require wipers to clear.

Do you operate pathfinder cars in the fog with platoons of cars?

But you already knew all that.