Yoshi Calculation

Jan. 8, 2002

 

• Yoshi's new version (YO5.2) of Flash Calculator - EXCEL (1 MB).
  This version incorporates the modified Allard method (two time constants) in one file and give results of the four methods for any flash pulse at a time. In addition, this version can scan the pulse duration from 0.001 s to 100 s to plot response curves for any given waveform of pulse.
  
• The results of the pulse duration scan for 10 different waveforms - EXCEL (700 KB)
  Please see the results in this file in reference to the email below.

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January 8, 2002

 

Dear ASTM E12.11.WG05 (Flashing Lights) members,

 

I've made an improved, ultimate version of the Flash Calculator program. This version has incorporated the Modified Allard method (two time constants) in one file and give results of the four methods for any flash pulse at a time. In addition, this version can scan the pulse duration from 0.001 s to 100 s to plot response curves for any given waveform. Please download the file from http://cie2.nist.gov/ASTM_E12_WG05/Yoshi%20calculation_Jan_8.html.

 

This new version gives powerful analyses on the differences between the four methods. Please see the results of the pulse-duration scan for 10 different waveforms also posted on the website. Although I am an amateur of human vision, I could deduce several interesting findings from these results, which are listed below for your comments. I refer to "Blondel-Rey-Douglas" to clarify that the procedure for calculating a train of pulses is based on the 1957 Douglas paper (break times between peaks are included in t2-t1).

 

1) For rectangular and trapezoidal pulses, Form Factor, Blondel-Rey, and Modified Allard all give nearly the same results. Allard method (original) deviates significantly ( up to 30 %) from the other three. For this reason, original Allard method is tentatively excluded in my subsequent analyses because the response for rectangular pulses is considered the most fundamental for flashing light measurement, and the Blondel-Rey equation has been proved to be accurate for rectangular pulses.

 

2) For all triangular pulses, the difference between Form Factor and Blondel-Ray-Douglas is fairly large (~30 % higher in the 0.2 to 2 s region). Modified Allard gives values in between depending on what type of triangle. At the moment, we don't know which is the most accurate.

 

3) The three different triangular pulses are measured with no differences by Form Factor or Blondel-Ray-Douglas. Modified Allard gives different results for different triangles. Intuitively, the visual responses for the rising triangle and falling triangle seem to be different. If that is the case, there is a chance that modified Allard gives more accurate results.

 

4) For "Dennis" pulse (Sine squared with a sharp peak), the result clearly shows that Form Factor has a serious problem. Modified Allard and Blondel-Rey-Douglas have no problem with this type of pulse.

 

5) For the modulated sine-squared pulse (simulating a rotating beacon with a discharge lamp), the differences between Form Factor and Blondel-Ray-Douglas are extremely large (more than factor of 2 at longer than 1 s). Modified Allard gives values in between. For curiosity, I calculated it for the center peak only of the original pulse. At 10 s of total duration of original pulse, Blondel-Rey-Douglas gave 28 % higher result for the center peak only. Intuitively, this seems to be wrong because the visual response cannot be higher when some parts of the pulse is cut off.

 

6) For the train of 4 pulses (sine-square), similar trend is observed as for the modulated pulse described in 4). Difference between Form Factor and Blondel-Rey-Douglas is significantly large (35 % to 100 % higher) at duration longer than 0.2 s.

 

7) A train of xenon flashes (as found in some aircraft anticollision lights) also gives significant differences between the four methods. At 3 seconds of the total pulse duration, the intervals between narrow pulses are 1 second, when the visual response is considered the same as for the single pulse. Then, at this duration and longer, the effective intensity should be about the same as that for a single pulse. I compared these two cases for all four methods and showed the ratios at the right hand side of the sheet. While Modified Allard gave a ratio of nearly 1, Form Factor gave a ratio of 3.3 and Blondel-Rey gave a ratio of 0.30. This clearly indicates that both Form Factor and Blondel-Rey-Douglas fail to produce correct results for a train of narrow pulses.

 

These observations have revealed problems with Blondel-Rey-Douglas and Form Factor method for some types of waveforms, while I did not find any obvious problems with Modified Allard for the waveforms studied this time. It has been shown that Modified Allard method

a) gives nearly equivalent results to Blondel-Rey (-Douglas) for single rectangular pulses (within 5 % difference),

b) solves the problem of "Dennis" pulse,

c) gives the reasonable results for train of pulses at any duration while the other two methods fail.

In addition, the (modified) Allard method has great advantages in instrument realization by simple analog circuit as discussed in my previous circular. For these reasons I now come to believe that this Modified Allard as I formulated (but originally proposed by Dennis) is the most recommendable method. However, I think we need to clarify some remaining questions and to prove by visual experiments that this method produces accurate results for any waveforms. We may also need experimental data to tailor the optimization of the two time constants. (This could be done with the past experimental data as Dr. Schimidt-Clausen made. )

 

Well, these are my one-way thoughts. I'd greatly appreciate your responses and comments to my results and views. Finally, I thank Dennis a lot for his great help in my study this time, which may still continue. I am looking forward to seeing many of you soon in Ft. Lauderdale.

 

Thanks,

Yoshi

 

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