If a person looks at a bright light source, such as a light bulb or perhaps the sun for a period of time, and then looks away and closes their eyes, they typically see a bright patch in the shape of the light source for a period of time. The amount of time varies, but can last for many seconds. What explanation can be provided for this effect?
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In your eye there are light receptors of two types: rods and cones. Rods are sensitive to the level of brightness, but cannot discern color, while cones are not very light sensitive, but they allow for color perception. Both of these are types of photoreceptors which transduct physical light.
The physical response of rods and cones to light isn't immediate, and therefore there's a certain transient response of each photoreceptor to light. When the light you're looking at is too bright, some of your photoreceptor cells go into a kind of "saturated" state, and it takes a long time, because of that transient behavior, for them to stabilize back to "seeing" darkness again.
The human eye is an interesting device. One of the most amazing things it does is to adjust for the brightness, and it can do so over 10 orders of magnitude.
From a signal processing perspective it can be explained as follows:
There are a few different ways that this is done, but the most basic way is a high pass filter, with a cutoff of about .25-.3 Hz. So, if you look at a bright source of light for a period of time, then you will see the signal as too bright, until the filter can reset back to a zero mean signal. After that, the image will go away.
There are of course many subtleties, but that is the primary effect.
To illustrate this, I've included 2 plots, the first of a signal changing over a long period of time between 2 extreme values, the second of one changing quickly over time. These plots came from a class which I took and learned how to model the neuron of a fly's eye, which behaves very similar to a human eye. The signal at 0.5 corresponds to a gray type signal value, it's an artifact of some of the other processing steps. This is a complex model, but the crux of it is a high pass filter with a time step of 3 seconds. Time prior to 40 is to allow the filter to normalize prior to injecting a signal, it prevents having to know the initial conditions very well of the system.
The second figure shows what happens with a more typical transient time, on the order of 10 Hz. Note that the signal is passed through almost without any delay.
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The persistence that you observe when you look at a bright light for a short period of time is called flash blindness. The phenomenon is related to your retina's response to the burst of light. Quoting from the Wikipedia article: