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# How to determined necessary minimum widths and pixels of non-sequential detector rectangle

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Dear all,

I am trying to see the far field angular beam size (1/e2 width) in a simple system: source diode + detector rectangle. @Jeff.Wilde already gave a good starting setup here Laser Diode Astigmatism in his responses to my comments. Since I have limited performance laptop at the moment, limiting the analysis rays as well as detector rectangle half widths and pixel numbers are important (well, it will also save a lot of time even for those who have great work stations). I have the following two puzzles:

1. Suppose the detector is located 100mm away from the source diode (sets up only spatial distribution, ideal symmetric Gaussian beam in X- and Y- directions) center-to-center. What will be the necessary minimum of the set of half width/pixel number/analysis rays if I want to achieve 0.1 degree accuracy at 4 degree divergence? I was expecting the pixel resolution of 100*tan(0.1 degree) = 0.175mm but the setup of half widths 15mm/pixel number 89/analysis rays 8E5 didn’t work (I got 4.33 degrees while I set up divergence of 4 degrees). I chose 15mm half widths because in the detector spatial cross-section view the tails sort of decrease to 0 (well, decrease to 0.073% of the peak) at 15mm radius. Then I chose 89 pixels because 15/0.17=88.2. And I chose analysis rays 8E5 because 89*89*100=7.9E5.
2. The detector rectangle half widths and pixel numbers determine the detector mesh, to the best of my knowledge. Will detector 1 and detector 2 shown below with the same mesh cell size yield the same result (far field 1/e2 width) for the same sufficient analysis rays (=100 rays/pixel)?

Regards,

Jiang

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Best answer by Jeff.Wilde 3 January 2023, 20:09

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Dear all,

For the question 1 above, I made a mistake in determining pixel numbers. Since 15mm was half widths so the pixel numbers necessary should be 30/0.17=177 (I divided by 0.17 instead of 0.175 just on a bit safer side). Then the analysis rays should be ~3.1E6. Eventually I got the result in 0.1 degree accuracy.

As for question 2, it seems to my that one should expect the same result (same accuracy). If anyone can confirm the judgement, that would be great.

Regards,

Jiang

Userlevel 6
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Hi Jiang,

I think the answer to your question 2 is yes, the two configurations should yield the same result.  Can’t you just try it and see for yourself (it’s a fairly simple exercise)?

Regards,

Jeff