Fog is a large density of small water droplets who 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 longer than its life time. 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 particles present in the air.

We start by considering a light beam that hits a small particle in the air. The light source can for instance be a LED or a laser. 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 only has changed its propagation direction slightly is called forward scattered light, and the light that has changed its direction around 180 degrees is called backscattered light. The scattered light is lost for making 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 in fog is changed. In this case we also have another phenomena: The light grey haze covering the whole image comes from scattered light from the fog particles.

We will briefly describe the major optical methods used for detecting fog and for measuring visibility.

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 100 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 not be collected by the receiver. The instruments calculate this reduction. And this reduction is used as raw data for further calculations. This method is for instance used on airports. The visibility along runways, a very important safety parameter on airports, is controlled this way.

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.

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 by using high performance electro optic solutions.

The transmission method measures along a 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 use to warn for low visibility the best is to mount it at a location where the fog comes first and tends to be most dense – for instance near a river or a lake or in a valley.

The most understandable measure on visibility is the Meteorological Optical Range MOR: The simple definition of MOR is simply how far we can see objects. But exactly how far 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: I=Io*e-^(x*alfa) Where: Io is the intensity at a certain point x is the distance from that point along the ray alfa is a constant ( unit m_-1) that determines the attenuation.

MOR relates to alfa as MOR= 3.9/alfa or MOR =2.5/alfa or something in between like

MOR =3/alfa ( this is probably the most common).

We can interpret alfa 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/alfa. 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 at very clear weather and 10 meters in heavy fog. ( During heavy snowfall or snow combined with wind MOR can be even lower.)

The constant alfa 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.

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 alfa or MOR. The transmission method will give correct results. The reason is that the relevant quantity – the non scattered light – is measured. The backscatter and forward scatter methods will overestimate the visibility during rain and give reasonably correct values during snowfall. The reason is that conversion factor between the measured scattered light and the alfa value is not the same for fog as for rain and snow.