Increase in Visibility of Light Signals

This work describes a study of perception of light signals used in aeronautics. Devices known as “obstruction light” (L-810 type, according to the Organization of International Civil Aviation OACI and the Federal Aviation Administration FAA) with LED technology were fed with square pulses of voltage, attaining flashes with imperceptible rise times. The lights were presented to observers, simulating the habitual vision conditions for these devices.


Introduction
When the frequency of a periodic luminous stimulus is lower than certain value, the visual system perceives the successive "offs", producing the sensation of flickering light.The limit or transition frequency is known as critical frequency of fusion (FCF).Above this frequency, the luminance variation stops being seen and the result is the sensation of "steady light".
In this last condition, that is, frequencies higher than FCF, the sensation produced by pulsing lights can be estimated by means of the mathematical relation known as Talbot's law (Moon, 1936;Talbot, 1834), which assigns a temporal integrating function to the visual system.Thus, if an intensity light L 1 (t), flickering periodically, is presented to an observer, the visual sensation L is adjusted to the equation: In the Equation (1), L is the average of the train of light pulses and T is de pulse period.
If the flickering frequency is kept above the critical frequency, the light will be undistinguishable from another steady of equal value to that arising from Talbot's law.The critical frequency is around 30~50 Hz and depends on the stimulus intensity and the observer's age, among other factors.
Below the critical frequency, the light pulses will be perceived individually as a kind of flashes.The apparent brightness of the flashes is in agreement with their duration.For pulses lower than 0.2 s, Bloch's law (Moon, 1936) establishes the persistence in the illumination product in the retina by duration of the "flash".Therefore, the sensation produced by a light pulse of short duration is lower than that generated by the stimulus if it was permanent.There are several mathematic models that try to quantify the phenomenon (Ohno, 2002), being the model suggested by Blondel and Rey (1911) and Illuminating Engineering (1964) one of the most accepted ones at the beginning of the last century.In this model, the Effective Intensity I eff of a pulsing light is expressed by the following equation:  In both experiences, the switching of power source was carried out at random, so that the observer could not suspect which power source was being assessed.The signal was presented during the time necessary for the observer to give his opinion (higher, equal or lower than the previous vision), usually between 10 and 15 s.The switching to the following presentation was fast, tenths of seconds, in order to place a noticeable darkness between both images.The experience ended when the observer did not detect differences between successive presentations of the beacon.
During the tests, the light intensity I was measured permanently with a photo detector oriented in line with the observer's vision.

Voltage, Current and Supply Power
Voltages and currents of reference, either in the case of continuous supply or pulsed supply, were regulated in such a way that the consumed power per beacon was the same in both cases in order to be able to carry out a comparative analysis.
For the continuous supply, the power was: Where 1/N is the fraction of the period where the square signal is not null.
Equally, for the effective voltage The power was: For the carried out tests the cycle of pulses was 50%, that is N=2.
As the beacon is basically a set of diodes, the total operation voltage is the sum of polarization voltages of diodes and is kept approximately constant for a range of current values.The ratio between power and current is approximately linear with a slope given by the total operation voltage of the beacon.This indicates that in a certain range, the beacon power is regulated proportionally with the current (green line in Figure 6).Such ratio was used for adjusting the reference sources.

Continuous -Continuous Supply Comparison
Figure 7 shows the results obtained in this experience.There the intensity values regarding the reference versus each observer's appreciation were yielded.
The dots in the lower curve (I min ) determine the limit where each observer began to notice less light intensity from the variable source than from the reference.The dots of the upper curve (I max ) determine the limit where the observers noticed that the variable source was higher than the reference.
The marked zone (between I min and I max curves) corresponds to ratios for which the observers did not distinguish differences as regards the reference and it determines the perception threshold.For the experience which compares continuous supply versus continuous, this perception threshold was roughly ±15% around the reference, verifying that on average, any variation in intensity within that region was not perceived by the observers.

Continuous Supply -Pulsing Supply Comparison
First, a scanning in frequency was carried out in order to locate the critical frequency for each observer.Then, the source was adjusted close to this value with the condition that flashes could not be distinguished.Next, the steps described for the comparison were followed.The obtained results are indicated in Figure 8.Just like in Figure 7, three regions are determined.Above curve I max and below I min , the observers detected differences (higher and lower than the reference, respectively).Between both curves (marked zone) the observers did not distinguish differences with respect to the reference.The lowest and highest average limit values were 1.09 and 1.45 respectively, and the range of difference was 0.362.
The same experience carried out at a higher frequency than the critical one yielded results similar to those in Figure 7, in some way verifying Talbot's law (Figure 9).

Conclusions and Subsequent Analysis
The group of observers that participated in the tests did not distinguish variations of ±15% in the successive presentations of the beacon with continuous light.Taking into account the approximate symmetry around the reference, the range where existed observers' uncertainty was around 30%.The same tendency was verified by comparing continuous supply with pulsed supply, at higher frequencies than FCF.As expected, equivalence between supply power with continuous voltage and supply with pulses was evidenced.
Instead, the comparison carried out against the light pulsed at a frequency very close to FCF, just in the limit of non-flickering vision indicated that the observers noticed the difference when the continuous intensity was higher than 45% of the reference (as higher limit) or when the steady intensity was lower than 1.09 times the reference (as lower limit).In other words, the sensation produced in the observers by the beacon generating light pulses at the indicated frequency was the same as that produced by a continuous light with intensity between 9%-45% higher.
Translated to supply power (Figure 10) we can see a clear gain with respect to the pulsed light: it is needed higher continuous power (marked stripe) in order to obtain the same perceptive effect as with the pulsed supply (dotted line, taken as reference in the experience).Finally, unlike the isolated pulses that have a slighter effect than its real intensity (Ieff, of Blondel -Rey), multiple pulses, in the limit of continuous perception (critical frequency), would produce certain visual gain.This effect, which could be related to Broca -Sultzer, showed in average levels of perception increase of 36% and may well be used to improve the visibility of signals and beaconing devices Figure 5 of the pulsed signal, the power was the product of effective values:

Figure 7 .
Figure 7.Light intensities and observer's appreciation between two continuous stimuli

Figure 9 .
Figure 9.Light intensities and appreciation for a continuous stimulus and another pulsed (f>FCF)