At 6:28 PM +0000 6/12/03, olympus-digest wrote:
>Date: Thu, 12 Jun 2003 13:44:33 +0200
>From: Jez.Cunningham@xxxxxxxxxx
>Subject: Re: Subject: [OM] Re: 4/3rds, 16Megapixels? (IC yield scaling)
>
>Joe explained:
>
> The scaling law is the Poisson distribution: Flaws are randomly
> distributed. Even one flaw kills the chip. Double the area of the
> chip, double the average number of flaws in the chip. If the average
> number of flaws per chip is low enough, then most chips will by luck be
> flawless. As the average rises, then more and more chips are unlucky.
> What saves us is that many chips have more than one flaw, allowing
> others to have no flaws. I suspect that for image sensors, which are
> quite large, the average yield (fraction of the chips on a wafer that
> are good) is low, perhaps 25 0f memory serves. The cost per wafer is
> more or less fixed, so the cost per chip basically depends on the yield,
> and one of the most closely guarded business secrets is the actual
> yield. In this regime (~25% yield), changes in chip size have large
> effects on
> yield, but the real law isn't so simple as the square or the cube.
>
>Joe - you probably know that memory chips don't follow these yield laws
>because they have built-in redundancy (spare rows or columns in the array
>that can be configured during testing to replace faulty bits). It's the
>same with image sensors but it's done in the software - so called pixel
>mapping. If there is a faulty pixel it can be interpolated as the average
>of the adjacent pixels. This means that those defects no longer cause the
>whole chip to be failed. The software can even fix pixels that fail during
>normal lifetime. See excellent Oly description for E-10:
>http://www.imaging-resource.com/NEWS/998087928.html
>
You are of course right, and only the most expensive sensors are flawless. I
wasn't planning to go this deeply into the subject, but for consumer cameras,
chips with up to 20? bad pixels are deemed acceptable, and pixel mapping isn't
likely done. (I don't know the exact number of bad pixels deemed OK, but
careful reading of spec sheets often reveals this. Not that 20 out of five
million is such a disaster.) This isn't the kind of flaw I had in mind,
though. There are other kinds of flaw that cripple the entire chip, rather
than generating a sprinkling of bad pixels. It's the crippling flaws that
affect the yield and thus the price.
Even with pixel mapping, the Poisson distribution is used to predict the
fraction of chips will have less than two fatal defects. This increases yield
compared to requiring zero defects, and is very common in memory chips.
Although the cited article doesn't say exactly how pixel mapping in the E-10 is
achieved, I would guess that they generate a list of bad pixels, and correct
images by replacing such pixels with the average of their immediate neighbors.
Don't know how much pixel mapping can be used in an image sensor without
messing the image up, but certainly tens to hundreds of bad pixels could be
fixed without any problem, so long as the bad pixels aren't in clumps.
There isn't any reason one could not do one's own pixel mapping on a raw image
after the fact, if one has located the bad pixels as described in the article.
I don't know if pixel mapping is easy to do automatically in Photoshop, but it
would be easy in many scientific image processing programs. It would also be a
simple program to write in C.
Joe Gwinn
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