Copyright 2013 Optical Sensors
Methods for detecting fog and measuring visibility
What is fog?
Fog is large density of small water droplets that are small enough to "float" in the air. The size of fog particles is typically 5 to 50 µm (0.005 to 0.05 mm). The reason why fog particles float in the air is the following:
The smaller a water drop is the lower is the fall velocity. And for small enough size the time it takes for the droplet to fall to the ground is much longer than its lifetime. In a real atmosphere the air is also constantly moving also vertically which compensates for the motion by gravity for some of the droplets.
So under conditions for fog build up - like cooling of moist saturated air - there will be a large number of fog particles present in the air.
How do we define visibility?
The most understandable measure on visibility is the Meteorological Optical Range MOR: The simple definition of MOR is how far we can see objects. But exactly how far away we can see an object during foggy conditions in daylight depends on the optical properties of the object such as colour, structure and (of course) if it is a light source or not, and if so the intensity of the light source. At night time we can of course only talk about visibility distance to a light source. Therefore different standards have been created - in one of them - for daylight conditions - the object is a black and white checkerboard pattern.
Now to a more theoretical definition of MOR:
The attenuation of a light ray that is propagating through a homogenous absorbing or scattering atmosphere can be described using an exponential function as:
Where: Io is the intensity at a certain plane
x is the distance from that plane along the ray
a is a constant (unit m-1) that determines the attenuation.

MOR relates to a as MOR= 3.9/a or MOR =2.5/a or something in between likeMOR =3/a (this last one is probably the most common).
We can interpret a as the inverse of the penetration depth which is the distance the ray has propagated when the intensity has decreased to Io*e(-1) which is about Io*37%. The penetration depth is simply 1/a. Theoretically about 2% to 8% remains at the distance MOR depending on if the value 3.9, 3 or 2.5 is used. MOR varies between 50 km or even more at very clear weather and 10 meters in heavy fog. (During heavy snowfall or snow combined with wind MOR can be even lower.)

The extinction coefficient and fog density
The constant a is often known as the "extinction coefficient" in the literature. At good visibility the extinction coefficient is near to zero and it increases as the visibility decreases. The extinction coefficient can also be named fog density.

Scattering of light in fog.
We start by considering a light beam that hits a small particle in the air. The light source can for instance be a laser or a LED. The wavelength may be inside or a little outside the visible range. The particle is typically a small water drop constituting fog.
A fraction of the laser light propagating from left to right will be scattered in all directions - but with different efficiency - by the particle.
The light that has changed its propagation direction less than 90 degrees is called forward scattered light, and the light that has changed its direction more than 90 degrees is called backscattered light.
All the scattered light is lost for contributing to an image on the retina in the eye. This is the reason why the perception when looking at objects with our eyes (or with a camera) during fog is changed. We also have another phenomena: The light grey haze covering the whole image comes from scattered light from the fog particles.

How can we measure fog using optical techniques?
We will briefly describe the major optical methods used for detecting fog and for measuring visibility.

Transmission method
One classical method to measure visibility is to measure how much light that is transmitted from a light source to a receiver located a distance- for instance 50 meters away.

In foggy weather less light (compared to during clear weather) will reach the receiver because of the scattering along the ray path. The scattered light will of course not be collected by the receiver. The reduction is used as raw data for strait forward calculation of the visibility.
This method is for instance used on airports. The visibility along runways, a very important safety parameter on airports, is often controlled this way.

Forward scatter and back scatter method
The following figures show two other main concepts for building optical sensors for detecting particles in the air by collecting and measuring the light scattered by the particles in an optical receiver. The most common concept is to collect the forward scattered light.
Backscatter method
The backscatter concept is the most compact way of detecting particles in the air since the transmitter and the receiver can be located close to each other in the same box.
The main disadvantage of the backscatter concept is that the optical power reaching the receiver is lower than that in the forward scatter case. This causes lower signal to noise ratio when using the backscatter method but can be compensated for by using high performance electro optic solutions (low noise optical receivers) making range of 10 km possible.

Detection volume and accuracy of sensor readings
The transmission method measures along a narrow path between receiver and transmitter.
Both the backscatter method and the forward scatter method kind of sensors detect particles in a very small volume. That volume is representative for a limited area near the sensor. If we want the readings to represent the weather in a larger region around the sensor we have to do assumptions and accept errors. These errors are normally the dominating error source when measuring visibility using any method.
Let's explain this with an example: Assume that the visibility reading from one sensor is 4000 meters. But 1000 meters away there is a fog bank and we have another sensor there, which gives the reading 500 meters. So it is certainly not possible to see 4000 meters (- in that direction from the location of the first sensor). So what is the visibility? And what do we mean with visibility readings in a case like this?
We can conclude that all optical sensors primarily give a local reading of the density of scattering particles that we can convert to visibility under the assumption that the density is homogenous.
When there is wind (which is very often the case) the local density may still vary, but if the visibility reading is a mean value of samples taken during several minutes the errors are considerably reduced.
If a visibility sensor is used to warn for low visibility the best alternative is to mount it at a location where the fog normally starts and tends to be most dense - for instance near a river or a lake or in a valley.

Measuring visibility during rain- and snowfall
As we all know the visibility is reduced - compared to clear weather - not only during fog but also during rain- and snowfall. A raindrop and a snowflake will of course scatter light and cause reduced visibility. The scattered light is lost for making an image on the retina in the eye in the same way as for a fog particle.
The different optical methods described will however give different results in terms of a or MOR. The reason is that the form of the scattering lobes (also called phase function) is not the same for the different scattering particles involved. The total scattering is the relevant quantity for determining MOR.
The transmission method will give correct results. The reason is as explained above that the relevant quantity - the non scattered light which can be converted to MOR without approximations - is measured.
It has been shown that forward scatter sensors measure within ±15% accuracy if the scattering angle 42 deg is used - which usually is the case today.
The backscatter method will overestimate the visibility during rain and give roughly correct values during snowfall.

Measuring visibility in polluted air
The visibility can also be reduced because of solid particles like desert dust or soot. The sizes of these particles are normally of the order fog particle or smaller. If the particles are very small the visibility will be slightly underestimated by the forward- and back scatter sensors.

We can now compare the different methods to measure visibility in some respects:
The transmission method can measure up to about 50 km visibility.
The forward scatter method is able to measure up to about the same order - or even better - which is in both cases better than backscatter sensors which are able to detect visibilities up to about 10 km.
We use the term correctness for the ability to measure visibility in all conditions that occur. The most interesting cases besides fog are when the visibility is reduced because of rain or snow.
The "winner" in this discipline is the transmission method since it measures the quantity relevant for visibility namely the transmitted light. Forward scatter sensors are ranked as second. The backscatter method overestimates the visibility during rain giving ranking as 3.
The winner is in this case the backscatter method which is easily understood when looking at the figures. The forward scatter sensors are second in this discipline and the transmission method number three.

The backscatter sensors are the cheapest. On second ranking is the forward scatter and the transmission system is ranked as number 3.
The conclusion is that transmission and forward scatter sensors have the best and almost equal performance but back scatter visibility sensors is an interesting alternative in applications where:
- A low price is important.
- Visibility reduction because of fog - and to below 5 to 10 km - is the main concern.

This is generally the case in applications where warning for fog because of safety is the main concern "Fog warning systems"
One important example of such applications is Road weather stations.