Diffraction limit and D2x

Jay,

Aren't you forgetting that the D2X has an anti-alaising filter that
blocks high frequency details above the Nyquist limit of the
sensor. Frequencies above the Nyquist limit of the sensor result
in aliasing, which degrades the image. That is why the low pass
filter is used. For a scientific analysis, refer to this link:

http://www.schneider-kreuznach.com/knowhow/digfoto_e.htm

Low pass filters are not needed with p&s digital cameras, since the
lens itself can not resolve above the Nyquist limit of the sensor.
This may be true for specific lens/sensor combinations, but there's something not quite right about this argument in general - otherwise we wouldn't be seeing the steady improvement in res. chart results as manufacturers have moved to higher resolution sensors in the P&S cameras.

--
Ron Parr
FAQ: http://www.cs.duke.edu/~parr/photography/faq.html
Gallery: http://www.pbase.com/parr/
 
The diffraction limit is reached when wavelength/pixel_size is less than f ratio. Wavelength of yellow light (center of spectrum) is about o.55 micron. So if pixel size is 6 micron, then we diffraction effct sets in at f/11.

--priya
Just thought of one thing... With pixel packed so densely in D2x,
will the diffraction limit sets in earlier? Many lens has
resolution starting to decrease from f/11 or f/16 on 6Mp APS-C
DSLR. Are we going to see the same reduction earlier on D2x?

If so this is a concern for high resolution (> 10Mp) APS-C cameras
(when there are more).

I'm not expert enough to perform calculation to verify, nor do I
own D2x to experiment. But hope someone with either can provide the
answer.

Best,
Photobug
 
Jay,

Aren't you forgetting that the D2X has an anti-alaising filter that
blocks high frequency details above the Nyquist limit of the
sensor. Frequencies above the Nyquist limit of the sensor result
in aliasing, which degrades the image. That is why the low pass
filter is used. For a scientific analysis, refer to this link:

http://www.schneider-kreuznach.com/knowhow/digfoto_e.htm

Low pass filters are not needed with p&s digital cameras, since the
lens itself can not resolve above the Nyquist limit of the sensor.
This may be true for specific lens/sensor combinations, but there's
something not quite right about this argument in general -
otherwise we wouldn't be seeing the steady improvement in res.
chart results as manufacturers have moved to higher resolution
sensors in the P&S cameras.
Isn't that because they use good lenses and limit the aperture to a relatively large value?

See the section on Norman Koren's site regarding diffraction and small format digital cameras. I don't think he would object to my quoting the lines below:

"For very small formats— for compact digital cameras with 11mm diagonal or smaller sensors (1/4 the size of 35mm), the sweet spot is extremely small. Lenses are aberration and diffraction-limited at the same aperture, around f/4 to f/5.6. They are severely diffraction-limited at f/8, where DOF is equivalent to f/32 or more in 35mm. (They rarely go beyond f/8.) But even though lens resolution is less than for 35mm film cameras, tiny digital cameras still produce very sharp images at f/4 and f/5.6 because their tiny pixels— 4 micron spacing or less with no anti-aliasing filters— have far better lp/mm resolution than 35mm film. Image resolution is almost entirely dominated by the lens."

http://www.normankoren.com/Tutorials/MTF6.html
 
Jay,

Aren't you forgetting that the D2X has an anti-alaising filter that
blocks high frequency details above the Nyquist limit of the
sensor. Frequencies above the Nyquist limit of the sensor result
in aliasing, which degrades the image. That is why the low pass
filter is used. For a scientific analysis, refer to this link:

http://www.schneider-kreuznach.com/knowhow/digfoto_e.htm

Low pass filters are not needed with p&s digital cameras, since the
lens itself can not resolve above the Nyquist limit of the sensor.
This may be true for specific lens/sensor combinations, but there's
something not quite right about this argument in general -
otherwise we wouldn't be seeing the steady improvement in res.
chart results as manufacturers have moved to higher resolution
sensors in the P&S cameras.
Isn't that because they use good lenses and limit the aperture to a
relatively large value?

See the section on Norman Koren's site regarding diffraction and
small format digital cameras. I don't think he would object to my
quoting the lines below:

"For very small formats— for compact digital cameras with 11mm
diagonal or smaller sensors (1/4 the size of 35mm), the sweet spot
is extremely small. Lenses are aberration and diffraction-limited
at the same aperture, around f/4 to f/5.6. They are severely
diffraction-limited at f/8, where DOF is equivalent to f/32 or more
in 35mm. (They rarely go beyond f/8.) But even though lens
resolution is less than for 35mm film cameras, tiny digital cameras
still produce very sharp images at f/4 and f/5.6 because their tiny
pixels— 4 micron spacing or less with no anti-aliasing filters—
have far better lp/mm resolution than 35mm film. Image resolution
is almost entirely dominated by the lens."
This doesn't address my point.

--
Ron Parr
FAQ: http://www.cs.duke.edu/~parr/photography/faq.html
Gallery: http://www.pbase.com/parr/
 
to use them for digital. I did the testing 5 years ago, before I'd bought my first digital camera. ;-)

Wayne
I'm surprised that you are still using the USAF charts. As used
with film cameras they measure resolution at about 10% MTF, where
the resolution is much higher than the resolution at MTF 50, which
correlates better with perceived image sharpness.

As you correctly state, digital sensors can not use resolution at
high frequency (the Nyquist limit of the D70 is about 63 lp/mm).
Lens resolution above this limit is not useful and would degrade
the image via aliasing were the anti-alaising filter not in place.
For the D70, it is best to have a lens with high MTF at frequencies
below the Nyquist limit as you stated.

Besides, determining resolution from a test chart with high
contrast lines with digital imaging is quite difficult and
subjective because of alaising, which is not present with film. If
you look at Phil's PIMA/ISO 12233 chart image taken by the D70 at
1:1 resolution in Photoshop, you will note that it is very
difficult to separate false detail from aliasing from true detail
at the higher frequencies.

--
Bill Janes
No I'm not using MTF, I'm using USAF bar charts (or whatever they
are). That's the only reason that there's still room for
improvement in digital optics BTW. It seems that although film does
O.K. with higher resolution and lower contrast digital sensors
really want higher contrast and not so high resolution. That's why
zooms look comparatively better on digital than film when compared
to primes. The digital sensors aren't using the extra resolution of
the primes as well as film can.

Wayne
 
Photobug,

[I've adapted the following text from a post I made in another thread for a different camera. I've altered the values in the example calculations below to suit your query regarding the D2x.]

If you really want to know when the effects of diffraction will become "visible" in the final print, a wee bit of math will give you the precise aperture at which this will occur. The real issue here is whether or not the degradation caused by diffraction will be visible in the final print.

Right away it should be obvious that this depends on how large the spread function is at the sensor (the size of the Airy disks before enlargement), enlargement factor (the bigger the print the more visible will be the Airy disks), viewing distance (a print that looks sharp at three feet can look soft at 10 inches), and the resolving power of the human eye (somewhere between 5 and 8 lp/mm for adults with good vision at a viewing distance of 10 inches).

Here's a simple, but accurate formula, for taking all this into account:

At what aperture will the effects of diffraction become visible in the final print?

Maximum N =
1 / desired print resolution / enlargement factor / 0.00135383

Let's look at using a Nikon D2X. It's sensor has a diagonal of 28.43mm. If you intend to make an 8x10 print that has a diagonal of 348.27 mm, your enlargement factor would end up being 348.27 / 28.43 = 12.25x.

Now what do you want for a desired print resolution? If you want the print to be as sharp as any human being is capable of appreciating at a viewing distance of 10 inches, you'll have to go for print resolution of 8 line pairs / mm. That may be excessive in some people's opinion, but this is entirely subjective. It's your choice. A print that delivers only 4 lp/mm will look just as sharp at a viewing distance of 20 inches as an 8 lp/mm print will look at 10 inches. Yoiu have to decide what viewing distance you want to satisfy and how sharp you want it to look at that viewing distance. For this exercise, let's assume a viewing distance of 10 inches but let's also go with only 4 lp/mm at the print. That's about as "soft" as I personally am willing to go. If the viewer is farther away than 10 inches and/or simply can't focus that closely, it will look sharper. An eagle-eyed human capable of resolving 8 lp/mm at 10 inches will be disappointed, but that's the choice I'm making. Selecting 4 lp/mm, I'm hoping most people won't stand that close to the print.

So here's the formula:

Maximum N =
1 / desired print resolution / enlargement factor / 0.00135383

Maximum N = 1 / 4 / 12.25 / 0.00135383 = 15.0

So, don't stop down below f/15.0 if you want to prevent diffraction's Airy disks from preventing a resolution of 4 lp/mm in the final print.

If the print will be viewed at 20 inches instead of 10 inches, f/30.0 would deliver the same apparent sharpness (in terms of the effects of diffraction). The question goes back to: At what viewing distance do you want your prints to survive scrutiny? Your desired resolution should fall somewhere between 5 and 8 lp/mm for a viewing distance of 10 inches. It can fall between 2.5 and 4 lp/mm for viewing distances no closer than 20 inches - but how are you going to stop people from standing closer than 20 inches?

For more information see: http://home.globalcrossing.net/~zilch0/essays.htm

Mike Davis

--
http://www.accessz.com
 
Mike:

Thanks, that was quite an interesting read.

Question:

Could you put "4 lp/mm" into a dpi for me. Meaning, I normally send an image to the printer at 240dpi pr 300dpi depending on the printer. How does dpi relate to line pairs per mm?

Thanks,
Kathy
 
Aren't you forgetting that the D2X has an anti-alaising filter that
blocks high frequency details above the Nyquist limit of the
sensor. Frequencies above the Nyquist limit of the sensor result
in aliasing, which degrades the image. That is why the low pass
filter is used. For a scientific analysis, refer to this link:
No. I'm not forgetting the anti-alias filter. And I'm at a loss as to why you think I might be. My comments were based on the estimated limit of resolution of about 72 lp/mm for the D2X. That should be the resolution limit with the AA sensor in place.
Low pass filters are not needed with p&s digital cameras, since the
lens itself can not resolve above the Nyquist limit of the sensor.
All the various tests on Dpreview.com that show color moire at the limit of resolution pretty much demonstrate that htis is not consistently the case.

--
Jay Turberville
http://www.jayandwanda.com
 
"For very small formats— for compact digital cameras with 11mm
diagonal or smaller sensors (1/4 the size of 35mm), the sweet spot
is extremely small. Lenses are aberration and diffraction-limited
at the same aperture, around f/4 to f/5.6. They are severely
diffraction-limited at f/8, where DOF is equivalent to f/32 or more
in 35mm. (They rarely go beyond f/8.) But even though lens
resolution is less than for 35mm film cameras, tiny digital cameras
still produce very sharp images at f/4 and f/5.6 because their tiny
pixels— 4 micron spacing or less with no anti-aliasing filters—
have far better lp/mm resolution than 35mm film. Image resolution
is almost entirely dominated by the lens."
While I love Norman Korens site, I think his wording is suspect here. I think the paragraph is more correct if you substitute "diffraction limited" with "noticably affected by diffraction". I think that beyond f/4- f5.6, you don't necessarily lose resolution, though you will be losing MTF response.

It is also worth mentioning that the pixel pitch on these cameras varies considerably - almost by a factor of 2. So different cameras will do better or worse than others at f/8.

And getting back to the original question about when DX type sensors will be limited - we can see that the small sensor world lives with pixel pitches approaching 2microns. So I don't think it is that outrageous to think that DX sensors could live with twice that pixel pitch - which should be around 25Mp.

--
Jay Turberville
http://www.jayandwanda.com
 
it simply isn't needed by anyone that knows what they are doing
(there I said it) or who isn't shooting very very special niche
applications.
I guess I'd say the opposite: Anybody who doesn't want more
resolution probably doesn't know what he's doing. (There - I said
it.) :-)
Ron, you trouble maker you!
Of course, the problem is that more resolution comes at a price in
terms of noise, bigger files and camera speed, as well as the
gotcha that extra resolution is decreasingly useful because of lens
and diffraction limits.
Which is pretty much why I felt the opposite is true given these very real impediments to ever increasing advances in pixel density and resolution.
However, if it were technically possible to capture and efficiently
manipulate more genuine resolution, then anybody in his right mind
would want it. We'd never have to carry big, heavy lenses again.
We could put on our favorite wide angle lens, never take it off,
and compose in photoshop by cropping our 500MP images on ultrafast
computers.
IF it were technically possible sure I am with you on that, but until that breakthrough in getting around the known physical limits of high resolution digital sensors occurs, practical considerations like noise, reduced DR,reduced sensititivity range, and increased cost(in particular production cost for the manufacturer) are going to be like lead walls. The present reality is there comes a point where it simply won't be profitable for the manufacturers to persue the dreams of a tiny minority of consumers, we can disagree over where that point is but my view based on current trends is that point is much closer to 12mp on an APS-C sensor than it is to say 24mp.

Regards,
--

 
The 12mp of the D2x is enough to provide 300dpi prints at 10 x 14,
No, the D2X won't provide 300dpi of detail in a 10x14 print. Just
because the sensor has 4228 sensor sites doesn't mean it can record
that many "dots".
I am referring to image pixels per printed inch not sensor sites, I shouldn't have used dpi as that is usually associated with the final print device. Open a full size image in photoshop and view the image size parameter after setting the ppi to 300. Of course there is the subtelty of the final print device and weather it can render faithfully each pixel...but the D2x provides enough resolution so that if the print device can render each pixel in the image without under sampling it could represent 300 of the image pixels per printed inch at a print size of 9.493 x 14.293". I should have been more careful with my use of dpi.
The actual resolution of the typical DSLR
sensor is about 80% of what is implied by the sensor site count.
Again, I am only referring to the resolution as expressed in the final print as rendered using the pixels in the image. If your printer can resolve each pixel provided by a full size D2x image, at 300 pixels per printed inch you would get a physical print that is 9.493 x 14.293" in area. How the print device uses it's resolution (dpi) to achieve that is indeed a separate matter.
So you get about 11.5 inches at 300dpi on the long dimension of a
print from a D2x. The Foveon X3 is the only color chip that I know
of that will give you a "dot" per sensor site.
Now you are confusing the pixels provided by the image and dots used to render the final print. (whatever a "dot" is for an inkjet, dye sub or color laser..etc.)
But then, the
300dpi criteria is overused. Excellent digital prints can be made
with much less than 300dpi of actual detail.
That depends on weather or not the device can actually render the pixels using whatever it has for a "dot". An inkjet will give you a great print given a source providing 300 ppi of image data over a 8 x 10" print but it will fail to provide as much detail as a dye sub will given the same source, and a color laser will give you a better print still. Each device is more capable of mapping each pixel of image data to a "dot" (whatever that is for the device) so what is "excellent" will vary with the device, print size and media chosen.
Its funny that you say this right after pointing out that Nikon has
a second generation 12Mp chip that improves high ISO values.
I never said they had such a chip, just that it is likely in the works.
High
ISO noise is obviously an important issue as well.
A very important one as it determines if the camera will be resigned to a niche market or a general one...very real cost constraints on the part of the manufacturer and the unstoppable consequences of high density sensors (namely reduced sensitivity range and increased noise) will make it all the more difficult to carve out production expense just to satisfy the niche. I am with you that if it can be done why not, but unfortunately physical limits and cost will increasingly be in the way.
High resolution
and better noise performance are both worth having.
I never said there weren't, the point is they may not be practical for the manufacturer to produce and may be as well impractical for consumers to purchase given the reduced use such bodies will have. [low volume> high price]

Regards,

--

 
Mike,

I read your post with great interest but have one question. You speak of resolution in lp/mm but do not state what MTF is associated with that resolution. Are you using the Rayleigh limit ( 9% MTF), Dawes Limit (0%) or the MTF at 50% contrast, which is better correlated with percieved image sharpness? One should not really speak about resolutiion without reference to the MTF. A low contrast image with high resolution is not that pleasing. Just setting the black and white points for many dull ijages can bring them to life, even though no detail is added.

Naturally, I should be able to answer my question from the constant in yuour equation but it is too late in the day for me to try. Of course the opimum balance between lp/mm and MTF may vary with the image. Images with high spatial frequencies may benefit from high lp/mm and low MTF ilages with lower frequency details would

Bill Janes
Photobug,

[I've adapted the following text from a post I made in another
thread for a different camera. I've altered the values in the
example calculations below to suit your query regarding the D2x.]

If you really want to know when the effects of diffraction will
become "visible" in the final print, a wee bit of math will give
you the precise aperture at which this will occur. The real issue
here is whether or not the degradation caused by diffraction will
be visible in the final print.

Right away it should be obvious that this depends on how large the
spread function is at the sensor (the size of the Airy disks before
enlargement), enlargement factor (the bigger the print the more
visible will be the Airy disks), viewing distance (a print that
looks sharp at three feet can look soft at 10 inches), and the
resolving power of the human eye (somewhere between 5 and 8 lp/mm
for adults with good vision at a viewing distance of 10 inches).

Here's a simple, but accurate formula, for taking all this into
account:

At what aperture will the effects of diffraction become visible in
the final print?

Maximum N =
1 / desired print resolution / enlargement factor / 0.00135383

Let's look at using a Nikon D2X. It's sensor has a diagonal of
28.43mm. If you intend to make an 8x10 print that has a diagonal of
348.27 mm, your enlargement factor would end up being 348.27 /
28.43 = 12.25x.

Now what do you want for a desired print resolution? If you want
the print to be as sharp as any human being is capable of
appreciating at a viewing distance of 10 inches, you'll have to go
for print resolution of 8 line pairs / mm. That may be excessive in
some people's opinion, but this is entirely subjective. It's your
choice. A print that delivers only 4 lp/mm will look just as sharp
at a viewing distance of 20 inches as an 8 lp/mm print will look at
10 inches. Yoiu have to decide what viewing distance you want to
satisfy and how sharp you want it to look at that viewing distance.
For this exercise, let's assume a viewing distance of 10 inches but
let's also go with only 4 lp/mm at the print. That's about as
"soft" as I personally am willing to go. If the viewer is farther
away than 10 inches and/or simply can't focus that closely, it will
look sharper. An eagle-eyed human capable of resolving 8 lp/mm at
10 inches will be disappointed, but that's the choice I'm making.
Selecting 4 lp/mm, I'm hoping most people won't stand that close to
the print.

So here's the formula:

Maximum N =
1 / desired print resolution / enlargement factor / 0.00135383

Maximum N = 1 / 4 / 12.25 / 0.00135383 = 15.0

So, don't stop down below f/15.0 if you want to prevent
diffraction's Airy disks from preventing a resolution of 4 lp/mm in
the final print.

If the print will be viewed at 20 inches instead of 10 inches,
f/30.0 would deliver the same apparent sharpness (in terms of the
effects of diffraction). The question goes back to: At what viewing
distance do you want your prints to survive scrutiny? Your desired
resolution should fall somewhere between 5 and 8 lp/mm for a
viewing distance of 10 inches. It can fall between 2.5 and 4 lp/mm
for viewing distances no closer than 20 inches - but how are you
going to stop people from standing closer than 20 inches?

For more information see:
http://home.globalcrossing.net/~zilch0/essays.htm

Mike Davis

--
http://www.accessz.com
 
Mike,

Thanks for the nice formula and the clear explanation you provided. It sure comes in handy when we shoot with target print size in mind.

However, when the print size is not decided and there is a potential to print at large sizes (like the 4x6 ft poster that we hang over our fire place), I think it'll be a good stradegy to try to maintain the max. resolution offers by the sensor. In that case, the preferred aperture will be larger and depends on sensor resolution.

Well a good photographer should be able to make the right calls depends on the situations.

Photobug
Photobug,

[I've adapted the following text from a post I made in another
thread for a different camera. I've altered the values in the
example calculations below to suit your query regarding the D2x.]

If you really want to know when the effects of diffraction will
become "visible" in the final print, a wee bit of math will give
you the precise aperture at which this will occur. The real issue
here is whether or not the degradation caused by diffraction will
be visible in the final print.

Right away it should be obvious that this depends on how large the
spread function is at the sensor (the size of the Airy disks before
enlargement), enlargement factor (the bigger the print the more
visible will be the Airy disks), viewing distance (a print that
looks sharp at three feet can look soft at 10 inches), and the
resolving power of the human eye (somewhere between 5 and 8 lp/mm
for adults with good vision at a viewing distance of 10 inches).

Here's a simple, but accurate formula, for taking all this into
account:

At what aperture will the effects of diffraction become visible in
the final print?

Maximum N =
1 / desired print resolution / enlargement factor / 0.00135383

Let's look at using a Nikon D2X. It's sensor has a diagonal of
28.43mm. If you intend to make an 8x10 print that has a diagonal of
348.27 mm, your enlargement factor would end up being 348.27 /
28.43 = 12.25x.

Now what do you want for a desired print resolution? If you want
the print to be as sharp as any human being is capable of
appreciating at a viewing distance of 10 inches, you'll have to go
for print resolution of 8 line pairs / mm. That may be excessive in
some people's opinion, but this is entirely subjective. It's your
choice. A print that delivers only 4 lp/mm will look just as sharp
at a viewing distance of 20 inches as an 8 lp/mm print will look at
10 inches. Yoiu have to decide what viewing distance you want to
satisfy and how sharp you want it to look at that viewing distance.
For this exercise, let's assume a viewing distance of 10 inches but
let's also go with only 4 lp/mm at the print. That's about as
"soft" as I personally am willing to go. If the viewer is farther
away than 10 inches and/or simply can't focus that closely, it will
look sharper. An eagle-eyed human capable of resolving 8 lp/mm at
10 inches will be disappointed, but that's the choice I'm making.
Selecting 4 lp/mm, I'm hoping most people won't stand that close to
the print.

So here's the formula:

Maximum N =
1 / desired print resolution / enlargement factor / 0.00135383

Maximum N = 1 / 4 / 12.25 / 0.00135383 = 15.0

So, don't stop down below f/15.0 if you want to prevent
diffraction's Airy disks from preventing a resolution of 4 lp/mm in
the final print.

If the print will be viewed at 20 inches instead of 10 inches,
f/30.0 would deliver the same apparent sharpness (in terms of the
effects of diffraction). The question goes back to: At what viewing
distance do you want your prints to survive scrutiny? Your desired
resolution should fall somewhere between 5 and 8 lp/mm for a
viewing distance of 10 inches. It can fall between 2.5 and 4 lp/mm
for viewing distances no closer than 20 inches - but how are you
going to stop people from standing closer than 20 inches?

For more information see:
http://home.globalcrossing.net/~zilch0/essays.htm

Mike Davis

--
http://www.accessz.com
 
The 12mp of the D2x is enough to provide 300dpi prints at 10 x 14,
No, the D2X won't provide 300dpi of detail in a 10x14 print. Just
because the sensor has 4228 sensor sites doesn't mean it can record
that many "dots".
I am referring to image pixels per printed inch not sensor sites.
Well in the example given, image pixels and sensor sites have the same count. The example strongly implies a 1:1 relationship between dpi and image detail. The discussion of pixels in the absence of a correlation to image detail seems generally irrelevant to me. But maybe that's just me.
So you get about 11.5 inches at 300dpi on the long dimension of a
print from a D2x. The Foveon X3 is the only color chip that I know
of that will give you a "dot" per sensor site.
Now you are confusing the pixels provided by the image and dots
used to render the final print. (whatever a "dot" is for an inkjet,
dye sub or color laser..etc.)
I put the term "dot" in quotes for a reason. I am simply trying to correlate the smallest bit of resolvable data in the image to a print image that can can show 300 of these "smallest bits" in one inch. Most good modern inkjets can deliver a bit over 300 bits of real image detail (using lots more tiny ink dots to accomplish the task).
But then, the
300dpi criteria is overused. Excellent digital prints can be made
with much less than 300dpi of actual detail.
That depends on weather or not the device can actually render the
pixels using whatever it has for a "dot".
Just about any modern inkjet can render 150 lp/inch of actual image detail or 300 "bits" of image detail per inch. Of course excellent prints require more than simply good resolution, but I'd think that most people understand that you can only get excellent prints from printers capable of making excellent prints. The point is and was that the 300dpi criteria that is often quoted is often overkill - even for images intended to be viewed up close.
Its funny that you say this right after pointing out that Nikon has
a second generation 12Mp chip that improves high ISO values.
I never said they had such a chip, just that it is likely in the
works.
You are absolutely right. I misread what you wrote. My mistake. Sorry.
High
ISO noise is obviously an important issue as well.
A very important one as it determines if the camera will be
resigned to a niche market or a general one...very real cost
constraints on the part of the manufacturer and the unstoppable
consequences of high density sensors (namely reduced sensitivity
range and increased noise) will make it all the more difficult to
carve out production expense just to satisfy the niche. I am with
you that if it can be done why not, but unfortunately physical
limits and cost will increasingly be in the way.
Yes they will and eventually diffraction does set a limit. Costs, however seem largely influenced by the size of the silicon real estate. So this seems to argue in favor of a high density DX chip since it would be cheaper to get the extra resolution on that size sensor than on a 36x24 or medium format one. If you consider the very real possibility for future developments like focus depth bracketing, such designs make even more sense.

Right now the more dense 7Mp 1/1.8" sensor is performing quite similarly to the older design and less dense 8Mp 2/3" sensor. When I take clear progress like this and stir it into the pot with other info, I come up with 25Mp as a very reasonable sensor site denisty for DX sensors. In fact, this may even be a bit conservative. Sure, you won't be able to enjoy very much of the extra resolution if you stop down past f/8, and it probably won't be the typical sensor found in the average consumer DSLR. But as digital cameras mature, there will be more and more emphasis placed on satisfying narrower interests.
High resolution
and better noise performance are both worth having.
I never said there weren't, the point is they may not be practical
for the manufacturer to produce and may be as well impractical for
consumers to purchase given the reduced use such bodies will have.
[low volume> high price]
As I said, you shoot your 25Mp DSLR in 6MP or 12Mp mode and the noise will be reduced. Much smaller pixel densities, higher noise and greater aperture limitations are already being dealt with by many millions of people cameras using smaller chips. It doesn't seem impractical at all to me to put 4 micron sensor spacing on a DX sensor when there are current sensors using 2.3 micron spacing. Heck, 2.8 micron spacing gets you almost 50Mp on a DX sensor and the ability to use all of that resolution up to around f/5.6. But hey - Nikon isn't hiring me as a consultant either. Lets check back in around three to five years and we'll see.

Cheers!

P.S. In this "white paper", a Kodak writer seems confident that 12Mp 4/3 sensors are very possible. This equates ot a pixel pitch of about 4.3 microns (The graph of this is plotted incorrectly). That pitch on a DX sensor equates to 20Mp.

http://www.kodak.com/global/plugins/acrobat/en/digital/ccd/papersArticles/3-4TypeImageSensors.pdf

--
Jay Turberville
http://www.jayandwanda.com
 
The 12mp of the D2x is enough to provide 300dpi prints at 10 x 14,
No, the D2X won't provide 300dpi of detail in a 10x14 print. Just
because the sensor has 4228 sensor sites doesn't mean it can record
that many "dots".
I am referring to image pixels per printed inch not sensor sites.
Well in the example given, image pixels and sensor sites have the
same count.
And this fact has nothing to do with how those image pixels are mapped to printed dots which was my original point as clarified in the last post.
The example strongly implies a 1:1 relationship
between
  • snip*
ppi (was my intent not dpi as stated in the last post)
and image detail.
The discussion of pixels in the
absence of a correlation to image detail seems generally irrelevant
to me. But maybe that's just me.
Agreed, and to clarify yet again. ppi is provided by the image and dpi is tied to the print device in the first post (corrected in the second) I used dpi where I should have used ppi. Obviously, weather or not the print device can map the ppi of the image given the desired output dimension, using it's native print dpi (how ever many print "dots" it takes to render each pixel) without undersampling is a different issue tied to the device used.

Regards,

--

 
Mike,

I read your post with great interest but have one question. You
speak of resolution in lp/mm but do not state what MTF is
associated with that resolution. Are you using the Rayleigh limit
( 9% MTF), Dawes Limit (0%) or the MTF at 50% contrast, which is
better correlated with percieved image sharpness? One should not
really speak about resolutiion without reference to the MTF. A low
contrast image with high resolution is not that pleasing. Just
setting the black and white points for many dull ijages can bring
them to life, even though no detail is added.


Naturally, I should be able to answer my question from the constant
in yuour equation but it is too late in the day for me to try. Of
course the opimum balance between lp/mm and MTF may vary with the
image. Images with high spatial frequencies may benefit from high
lp/mm and low MTF ilages with lower frequency details would

Bill Janes
Since I have not heard from Mike, I am answering my own question. In his example, he required a resolution of 49 lp/mm for a resolution of 4 lp/mm at a magnification of 12.25. Resolution at the Rayleigh limit (MTF = 9%) would be 98.8 lp/mm according to his reference. The resolution of 49 lp/mm would be about right for MTF of 50%.

However, this MTF refers only to the lens. For the MTF50 of the printed picture, we need also to take into account the MTF of the sensor and printing device, and this is not done in Mike's analysis. The MTF50 of the total system would be lower than 49 lp/mm and his print might not have the required resolution of 4 lp/mm. To take these factors into account would require some pretty complex math involving Fourier transformation and convolutions as explained by Norman Koren on his web site.

http://www.normankoren.com/Tutorials/MTF.html

It is much easier to determine the optimum aperture experimentally using Norman's program Imitest.

http://www.imatest.com/

I performed an Imitest analysis of the central image using my Nikon D70 and 50mm f/1.8 lens and the results are shown graphically at this link. I performed the analysis in the horizontal axis. Interestingly, the D70 has better resolution horizontally than vertically, both in my tests and Phil's.
http://bjanes.smugmug.com/gallery/438435

The results are in lines/picture height to conform with Phil's tests. In Imitest, picture height refers to the number of pixels on the short axis of the sensor (which gives an advantage to compact digital cameras with an aspect ratio of 4:3 rather than the 3:2 for slr's). To convert to line pairs, divide the results by 2 and divide by the picture height (15.6mm) to get lines/mm. The maximum resolution I observed at MTF50 was 1460 l/ph at f/5.6, which is similar to Phil's result of 1600 (at f/9 with the 50mm f/1.4). He apparently uses visual inspection of the PIMA/ISO 12233 chart rather than MTF50, so some variation is exprected.

http://www.dpreview.com/reviews/nikond70/page26.asp

Using Mike's criterion of 4 lp/mm, this resolution would give a picture height of 182.5 mm (7.2 inches) and a magnification of 11.7x. This is slightly short of a sharp 8 by 10 inch print by Mike's criteria.

At f/16 the resolution at MTF50 was 1078 l/ph. At 4 lp/mm this would give me a picture height of 134 mm (5.3 inches), magnification 8.6.

In summary, I would not advise stopping down to f/16 (or f/15) if maximal resolution is required for 8 by 10 inch prints with this camera/lens combination, but would be a little more consevative. Of course, if you are making 4 by 6 inch prints, you have more lattitude. Nonetheless, I congratulate Mike for an excellent analysis.

The D2X has twice the number of pixels of the D70, but the linear resoltion is only about 1.4 times that of the D70. Both sensors would see the same image projected by the lens, so to get maximal resolution from the D2X, one should stop down slightly less.

Bill Janes
 
Using Mike's criterion of 4 lp/mm, this resolution would give a
picture height of 182.5 mm (7.2 inches) and a magnification of
11.7x. This is slightly short of a sharp 8 by 10 inch print by
Mike's criteria.
At f/16 the resolution at MTF50 was 1078 l/ph. At 4 lp/mm this
would give me a picture height of 134 mm (5.3 inches),
magnification 8.6.

In summary, I would not advise stopping down to f/16 (or f/15) if
maximal resolution is required for 8 by 10 inch prints with this
camera/lens combination, but would be a little more consevative. Of
course, if you are making 4 by 6 inch prints, you have more
lattitude. Nonetheless, I congratulate Mike for an excellent
analysis.
Since sharpening affects the MTF response of an image. I'd be curious if judicious sharpening affects the MTF50 point in your test images. I would guess it would. The sensor will record detail at levels below MTF50, and if some of that detail can be brought up, then more enlargement could be tolerated for the same perceived image quality. This is the prime benefit of sharpening digital images.

--
Jay Turberville
http://www.jayandwanda.com
 
Using Mike's criterion of 4 lp/mm, this resolution would give a
picture height of 182.5 mm (7.2 inches) and a magnification of
11.7x. This is slightly short of a sharp 8 by 10 inch print by
Mike's criteria.
At f/16 the resolution at MTF50 was 1078 l/ph. At 4 lp/mm this
would give me a picture height of 134 mm (5.3 inches),
magnification 8.6.

In summary, I would not advise stopping down to f/16 (or f/15) if
maximal resolution is required for 8 by 10 inch prints with this
camera/lens combination, but would be a little more consevative. Of
course, if you are making 4 by 6 inch prints, you have more
lattitude. Nonetheless, I congratulate Mike for an excellent
analysis.
Since sharpening affects the MTF response of an image. I'd be
curious if judicious sharpening affects the MTF50 point in your
test images. I would guess it would. The sensor will record
detail at levels below MTF50, and if some of that detail can be
brought up, then more enlargement could be tolerated for the same
perceived image quality. This is the prime benefit of sharpening
digital images.

--
Jay Turberville
http://www.jayandwanda.com
Jay,

That's a good point. My tests were done with no sharpening, since my intent was to compare some of my Nikon lenses: 50 f/2.8, Kit Lens, 105 f/2.8 Micro, and 70-200 f/2.8 VR. For this purpose, Norman suggests no sharpening. Unfortunately, I have not completed the project.

Imitest does test for oversharpening and gives a per cent value, which was negative in my tests. The MTF50 U, means unsharpened. Imitest does apply standardized sharpening, which raises the MTF50 from 1459 lp/ph to 1565. Here is a graphical report. You are correct, sharpening does improve the MTF50 and markedly imporves MTFs above 50%.

http://bjanes.smugmug.com/gallery/438435/1/17739347/Large

--
Bill Janes
 
However, this MTF refers only to the lens. For the MTF50 of the
printed picture, we need also to take into account the MTF of the
sensor and printing device, and this is not done in Mike's
analysis. The MTF50 of the total system would be lower than 49
lp/mm and his print might not have the required resolution of 4
lp/mm. To take these factors into account would require some pretty
complex math involving Fourier transformation and convolutions as
explained by Norman Koren on his web site.

http://www.normankoren.com/Tutorials/MTF.html
Hello Bill,

I agree with your doing the experimental approach to getting a good MTF of your system, but let's get your math straight here. If you have the MTFs of each independent component in your system (lens, sensor, printer), then the total system MTF is just the product of each individual MTF. This is the advantage of working in frequency space; now, getting the individual MTFs of each component is another story!

Take care,

Chris
 
Hmmm... doesn't sound too far out. I'll keep my fingers crossed.
I believe Nikon will have a FF iwithin 18 months at $6000. By then
the D2x will be ~$4200-$4200 and they may have released a 16MP APS.
Given the pixel size in this sensor they could have a 28MP FF -
they'll have to. They can't afford not to.

Wayne
 

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