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Andrew Davie wrote:For further on this, see http://www.taswegian.com/NBTV/forum/viewtopic.php?t=135
It is my view that you should not be concerned with the *shape* of the overlap, but the *area* of the overlap. The earlier thread asked for the overlap such that the total light passing through each overlap area would be equal to the total light passing through the non-overlapped area.
Klaas Robers wrote:Andrew, in your picture processing you did something wrong. You started with square holes. When you overlap square holes then in an equally lit area, the cheeks and the grey blocks at the bottom, In the overlap area twice as much light should be visible as in the "central" part of the line. So a strong line structure should be visible, whis is not in your pictures.
In the area of overlap you should ADD the luminance of both lines, not MIDDLE them.
Klaas Robers wrote:Pete, can you continue with your overlapping process? I think the optimum is where the peak to peak "ripple" in the curve is minimal. Then it might be that the lobe in between the lines get somewhat higher than the centre of the line itself.
Then, for the visibility you might plot the square root of the brightness and minimize the ripple in the amplitude, or even better convert it to decibels and then minimize the ripple amplitude.
Don't bother about the horizontal resolution. The resolution can never be better than one line thickness. The remaining resolution is false resolution, as you can see from the images that Andrew made. The blocks in the picture are not contributing to the resolution of the original picture, they are even introducing some form of noise.
With larger holes the vertical resolution is getting worse. So the idea of Graham L is not so bad to use oval shaped holes or still even better horizontal cat's eyes.
ac7zl wrote:Klaas,
I presume that the square root has to do with the fact we're dealing with optical power? Do I understand you correctly?
Below are graphs of the square-root of intensity of overlapping circles. This changes things, of course.
A cursory glance at the new graphs suggests that minimum ripple occurs with a hole-to-hole spacing on the order of 0.96-0.97 diameters.
Pete
AC7ZLKlaas Robers wrote:Pete, can you continue with your overlapping process? I think the optimum is where the peak to peak "ripple" in the curve is minimal. Then it might be that the lobe in between the lines get somewhat higher than the centre of the line itself.
Then, for the visibility you might plot the square root of the brightness and minimize the ripple in the amplitude, or even better convert it to decibels and then minimize the ripple amplitude.
Don't bother about the horizontal resolution. The resolution can never be better than one line thickness. The remaining resolution is false resolution, as you can see from the images that Andrew made. The blocks in the picture are not contributing to the resolution of the original picture, they are even introducing some form of noise.
With larger holes the vertical resolution is getting worse. So the idea of Graham L is not so bad to use oval shaped holes or still even better horizontal cat's eyes.
Andrew Davie wrote:I've done a bit of image manipulation to see if I can see what images might look like using the overlapping resolution. To make things easy, I assumed that the holes are 25% overlapped with their neighbours on each side. So, 50% of the hole is not overlapped, and 50% is.
This allowed me to use the following process...
1) Pixel-resize the original image to 4x the width (so our sample 32 x 48 image is now 128 x 48).
2) Grab alternate 4-pixel-wide columns to a new image. This gives us two images (with 4-pixel wide 'holes'), one containing scanline 1,3,5... and the other containing scanline 2,4,6...
3) From each of these, grab the non-overlapping parts and combine to a new image with the spacing changed, such that there is now just one pixel spacing between each scanline. So we in effect get the middle two pixels from each hole -- those pixels that do not need to be 'merged' and a single pixel space between them -- those pixels that do need to be merged.
4) Now we create a 'merged' pixel set. First, grab the remaining pixels from each of the two images created earlier, and arrange the columns in a new image side by side, such that adjacent columns represent those parts of adjacent holes that will overlap.
5) For each column pair (two pixels wide), resize using smart-sizing (eg: bilinear filter) such that the column is 1 pixel wide, 32 high. Paste this into our new image in the appropriate 'blank' column waiting for the merged bit.
6) The end.
I started with the baird test pattern. I include a super-size image here so you can see the result post-merging. I also include a final result. As you can see -- there's no loss of resolution at all. I just noticed that I goofed in the last few columns -- but the general idea is apparent.
Klaas Robers wrote:Pete, I think you did it in the wrong order.
First add the power of the overlapping and non overlapping areas of the circles in a linear way,
and then plot the square root out of the result or plot the logarithm out of the result. (this is impossible for 0% overlap, because the logarithm of zero is - infinity. So skip 0% overlap.
Both should give aproximately the same ripple. This is done because our eye evaluates the brightness of light in a logarithmical way or an almost square root way. Twice the amount of light shows the same "contrast" as half the amount of light.....
I guess that you first did the square root and then added the light output.
I guess that 25% of overlap is more or less the optimum.
Klaas Robers wrote:Yes, thanks. It looks indeed to be 0,86 or 0,84. This is indeed a clever calculation. Does this say that the diameter should be 1,16 to 1,17 x the pitch of the spiralled holes? Or should I interprete the 0,85 in a different way?
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