More thoughts on hole spacing

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More thoughts on hole spacing

Postby ac7zl » Tue Jun 05, 2007 10:56 am

It seems to me that someone brought up the issue of proper lateral hole spacing some months back. I have been giving this some thought myself. Period construction articles I've read say that holes should overlap "a trifle," not exactly an engineering measurement.

This is my thinking:

Imagine a mask with a vertical slit, behind which we have mounted a light meter.

Imagine, now, a square hole, punched into a Nipkow disk, which is illuminated from behind. If we pan the hole from left to right with our measuring device, we note that the illumination is uniform across the width of the hole.

If we repeat the experiment with a round (as opposed to square) hole, I would expect the results to be different. The luminous intensity is going to be non-uniform. The round hole will pass the most light near its center, and less to either extreme.

Let's now consider illuminated holes that are adjacent. If if we pan across three square holes, again, the illumination should be uniform. If we pan across three adjacent circular holes, I propose that a plot of those measurements would look something like the "1.0 diameter" graph (below). Furthermore, I would expect that an image scanned by round holes positioned in this manner would result in dark, vertical lines in the image.

I have no doubt that this is the reason why overlapping holes are recommended. The question is, how much overlap should there be?

Using a spreadsheet, I computed intensity curves at hole spacings ranging from 1.0 diameters to 0.86 diameters. The results appear in subsequent images.

I've concluded that there is no way to totally eliminate vertical banding between lines scanned with round holes. As hole-to-hole spacing is decreased, the dark areas are partially filled by "lobes" that seems to equal center-of-the-hole brightness when holes are spaced at 0.87 diameters. However, I see another concern.

The more we overlap adjacent holes, the more horizontal resolution we throw away--- a scarce commodity to begin with, considering only 32 lines.

This, of course, takes me right back to the initial question: How much overlap is optimal? How much horizontal resolution should I be willing to give up?

My gut tells me that something on the order of 0.95 diameter spacing is the ticket, but I wonder what others might think.

Pete
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Attachments
1_0_dia.jpg
1.0 diameter hole-to-hole spacing
1_0_dia.jpg (31.25 KiB) Viewed 7624 times
0_96_dia.jpg
0.96 diameter hole-to-hole spacing
0_96_dia.jpg (30.44 KiB) Viewed 7624 times
0_92_dia.jpg
0.92 diameter hole-to-hole spacing
0_92_dia.jpg (30.42 KiB) Viewed 7624 times
0_88_dia.jpg
0.88 diameter hole-to-hole spacing
0_88_dia.jpg (28.5 KiB) Viewed 7624 times
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Postby Andrew Davie » Tue Jun 05, 2007 2:56 pm

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.
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Postby Tex » Tue Jun 05, 2007 4:02 pm

I haven't had time to really think this through, and I have no experience with NBTV, but I'll throw out a thought which occurs to me. I wonder if you have different considerations scanning an object (camera) vs. playing back an image. For the camera, if the object is to allow light from each point on the object to illuminate the sensor for the same length of time, I think you would be concerned about the shape. The exposure time for a given point on the object being scanned is proportional to the length of that point's path through the scanning hole - ideally that path length, whether through the non-overlapped portion or the sum of the path lengths of two overlapped holes would always be the same - no way to get there with round holes, but I think that overlapping diamonds would work. For playback, on the other hand, the intensity at a given time is proportional to the sum of the light from all points which were visible to the sensor in the camera at that instant - on playback, it is not possible to display the exact intensity of each point - perhaps the best that can be done is to provide "equal areas", so that, for example, if you had a perfectly blank image of uniform intensity (some level of gray), the playback image would appear as uniform as possible? It does seem to me that this is not an obvious or simple problem.

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Postby ac7zl » Tue Jun 05, 2007 4:06 pm

Andrew-

I think you are misinterpreting my graphs. The curves I've presented are dictated by the luminous "contributions" of adjacent holes. The "contributions" are a function of the area of overlap.

Uniform brightness is a given with properly aligned square holes. As you can see, there is no way to provide uniform brightness from hole to hole if you are using round holes... at least not without penalty.

Let me rephrase: You can probably arrange the spacing so that the total luminious energy emitted from the area of intersection equals the brightness of the hole's center, but a) the brightness can't be uniform across the area of intersection itself, and b) you are giving up horizontal resolution...possibly lots of it.

It appears that smooth hole-to-hole brightness can be achieved with a hole spacing of 0.87 diameters, but you are in effect throwing away (or at least muddling up) 13% of your horizontal resolution.

The question is, where is the optimum balance?


Pete



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.
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Postby Andrew Davie » Tue Jun 05, 2007 5:22 pm

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.
Attachments
bairdman.png
Enlarged (4x) image showing post-merge -- here we see each scanline is overlapped 25% on each side.
bairdman.png (8.74 KiB) Viewed 7598 times
ress.png
Original next to 25% overlapping version. Can you tell which is which?
ress.png (6.98 KiB) Viewed 7593 times
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Postby Klaas Robers » Tue Jun 05, 2007 7:29 pm

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.
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Postby Klaas Robers » Tue Jun 05, 2007 7:35 pm

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.
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Postby Andrew Davie » Tue Jun 05, 2007 7:41 pm

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.


Agreed, but I was trying to give an impression of what it might look like when done properly, not what square holes look like. Had I been doing it perfectly, I would also not have chosen 25% as the overlap. The idea was just to make the point that the picture might still look OK using this process, and not lose horizontal resolution, as had been stated. The assumption was that the spacing was such that the overlapping area would have exactly half the area of the non-overlapped area and thus the sum of the brightnesses would equal the brightness of the non-overlapped area. So middling them was OK, given what I was trying to show.
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Postby ac7zl » Wed Jun 06, 2007 2:46 am

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
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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.
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1-0-dia.JPG
power curves, hole spacing 1.0 dia
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Postby ac7zl » Wed Jun 06, 2007 2:49 am

Whoops...forgot to attach the rest of the graphs...


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
AC7ZL

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.
Attachments
0-99-dia.JPG
(48.85 KiB) Downloaded 1294 times
0-98-dia.JPG
(47.54 KiB) Downloaded 1287 times
0-97-dia.JPG
(48.55 KiB) Downloaded 1297 times
0-96-dia.JPG
(48.82 KiB) Downloaded 1299 times
0-95-dia.JPG
(48.91 KiB) Downloaded 1302 times
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Postby ac7zl » Wed Jun 06, 2007 3:07 am

Very interesting.... I have to think about this....

Pete


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.
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Postby Klaas Robers » Wed Jun 06, 2007 3:35 am

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.
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Postby ac7zl » Thu Jun 07, 2007 5:28 am

Ok, maybe I've got the curves right this time... simple addition of contributing brightness, then square root of the sum...

If we are willing to say that hole overlap does not degrade horizontal resolution in a significant way then, ironically, I'm led back to my original conclusion...that the closest you can come to uniform illumination between adjacent round holes is to space them about 0.87 diameters apart.

See the attached (revised) graphs. I'll omit 1.00 Dia to save some disk space.

Pete




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.
Attachments
0-96-dia.JPG
(48.26 KiB) Downloaded 1266 times
0-92-dia.JPG
(47.81 KiB) Downloaded 1267 times
0-88-dia.JPG
(47.52 KiB) Downloaded 1269 times
0-86-dia.JPG
(47.34 KiB) Downloaded 1258 times
0-84-dia.JPG
(47.32 KiB) Downloaded 1273 times
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Postby Klaas Robers » Thu Jun 07, 2007 6:15 am

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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Postby ac7zl » Thu Jun 07, 2007 8:55 am

Klaas,

In my calculations, I've expressed hole spacing in terms of (hole) diameters, as measured from the center of one hole to the center of its neighbor. I expressed hole separation in this manner because it "normalizes" hole size, and allows the results of the analysis to be easily scaled to any hole size you wish.

A hole spacing of 1.0 diameters means that the distance from the center of one hole to the next is one hole-diameter (equal to two radii), so the edges of the holes will just touch. This is the nominal, no-overlap situation.

If you like the 0.86 value, this means that the distance from the center of one hole to the center of its neighbor must be 0.86 times the diameter of the holes that you wish to drill.

For lack of better numbers to serve as an example, consider a pair of 0.050" holes. With an overlap value of 0.86 diameters, they would be positioned such that their respective centers would be 0.043" apart.

If you were drilling these holes into a Nipkow disk, as you progressed around the disk, each hole would be located 0.043" closer to the center of the wheel.

Is this what you were looking for, or have I misinterpreted the intent of your question? Would you like a copy of my spreadsheet? It's ugly, but it does allow one to play "what-if..."

By the way, I have another spreadsheet I've worked out that allows one to specify the Nipkow wheel radius, the number of lines in the image, the aspect ratio, the horizontal offset of the image (from the outer edge of the wheel) and the hole overlap (in diameters.) From this, it computes the hole size you'll need to drill and the radial position of the holes on the disk. This latter spreadsheet seems to work ok now, though I'm still refining it.

Side note: I haven't begun building my own televisor yet. While I have been busy accumulating parts, my real goal has been to consider and work out in advance as much detail as I can through math and circuit simulations. Once I start building, I plan to assemble and maintain a journal with information for possible future publishing.

Klaas, you might find these photo galleries interesting. They represent the last set of projects that wrote books about:

http://www.hpfriedrichs.com/bks-votc-gallery.htm
http://www.hpfriedrichs.com/bks-ioa-gallery1.htm
http://www.hpfriedrichs.com/bks-ioa-gallery2.htm

Pete
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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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