How many MPx do you want / need?

Emil,

ejmartin wrote:
[snip]
And here's where my interpretation of the facts begins to diverge. I
would say that a 12MP FF camera doesn't have much of a diffraction
issue until around f13-f16.
Wow, that's much more stringent than the example I gave, and worse, it's needlessly stringent for a 12 MP camera.

In terms of diffraction, with a FF sensor, f/13 would support a desired print resolution of 6.96 lp/mm after enlargement to an 8.33 x 11.11-inch print (the maximum enlargement possible with an unresampled image resolution of 360 dpi - necessary to support only 5 lp/mm after Bayer and AA losses). And therein lies a problem - you don't have enough pixels in a 12 MP camera to support a desired print resolution of 6.96 lp/mm, so stopping short at f/13 would be pointless.

Let's look at f/16. That would support a desired print resolution of 5.66 lp/mm - again, this is higher than the 5 lp/mm maximum resolution supported by a 12 MP camera in an 8.33 x 11.11-inch print.

So the the f-Numbers you've chosen for dealing with diffraction in a 12 MP FF camera (f/13 to f/16) are excessively small (your apertures are excessively large) - and thus, they contradict your stated goal of "choosing megapixel count for image resolution." Another way of putting it: Your concern for diffraction is exceeding the realistic limit of resolution that can be achieved with only 12 MP with a CMOS sensor (that suffers Bayer algorithm and AA losses).

[snip]
If you want to maximize the number of diffraction-free stops you can
shoot with, select cameras having enough Megapixels to produce the
print sizes you are seeking at the print resolutions you desire, but
avoid cameras having sensors with high photosite densities (densities
in excess of about 200 pixels/mm).
And as I stated in my previous post, choose the sensor size for image
quality (and I suppose I should add creative DOF control); choose the
MP count for image resolution;
Again, no argument...
ignore photosite density, as it does
not directly measure anything useful.
Wrong. As photosite density increases, the number of f/stops available on a lens that will support a desired print resolution at an anticipated enlargement factor will decrease. In choosing a sensor size for any given number of Megapixels, as you increase the pixel density (shrink the sensor), you'll find yourself having to decrease your enlargement factor to maintain a desired print resolution, or you'll have to decrease your desired print resolution to maintain a given enlargement factor.
  • At around 110 photosites/mm or less, only the smallest one or two apertures (the largest f-Numbers) offered on any lens made to work with any given sensor size will prevent diffraction from inhibiting a desired print resolution of 5 lp/mm at the enlargement factor had when the print is scaled to a corresponding image resolution of 360 dpi (required to compensate Bayer and AA losses).
  • At about 200 photosites/mm, roughly half of all the f-Numbers offered on a lens (and half of all the shutter speeds that would otherwise be available at a given ISO setting) will be incapable of supporting a desired print resolution of 5 lp/mm at the enlargement factor had when the print is scaled to a corresponding image resolution of 360 dpi (required to compensate Bayer and AA losses).
If you're content with resolving subject detail at less than 5 lp/mm, that's your prerogative, certainly - you'll have more diffraction-free stops to work with (and more shutter speeds to choose between.) If you're content with making smaller prints, you're welcome to do that, too.
  • At about 400 photosites/mm, no matter how large the sensor, you'll find yourself forced to shoot wide open, or nearly so, to prevent diffraction from inhibiting a desired print resolution of 5 lp/mm at the enlargement factor had when the print is scaled to a corresponding image resolution of 360 dpi (required to compensate Bayer and AA losses).
  • At 600 photosites/mm and greater, (as with the sensor found in the Pentax Optio A20 and A30, for example, which has a density of 636 photosites/mm), you will find yourself with absolutely NO f-Numbers capable of supporting a desired print resolution of 5 lp/mm at the enlargement factor had when the print is scaled to a corresponding image resolution of 360 dpi (required to compensate Bayer and AA losses). The lens simply won't be fast enough to prevent diffraction from inhibiting that resolution at that enlargement factor.
Again, you are free to reduce your desired print resolution -OR- your enlargement factor, or both. Have at it. I'd much rather use sensors that have a LOW photosite density (less than 200 photosites/mm) - so that I can achieve my desired print resolution in print sizes supported by the pixel count without having to AVOID the use of nearly all, or more than half of the stops offered on a lens.

Photosite density DOES measure "something useful" - it can tell us a lot about the "usefulness" of the f-Numbers offered on any camera's lenses.

Mike Davis
http://www.AccessZ.com
 
You completely failed to include the quantum entanglement effects in your comment.

According the the spooky action at a distance quantum effect (think I'm joking? Check http://arxivblog.com/?p=559 ...), it is perfectly possible to store in the appropriate media an entangled photon image that is capable of reproducing itself at any distance or scale.

Canon will have a working prototype at a next Photokina!

--
My gallery: http://wizofoz2k.deviantart.com/gallery/#_browse
Cheers
Nuno Souto
 
ignore photosite density, as it does
not directly measure anything useful.
Wrong. As photosite density increases, the number of f/stops
available on a lens that will support a desired print resolution at
an anticipated enlargement factor will decrease. In choosing a
sensor size for any given number of Megapixels, as you increase the
pixel density (shrink the sensor), you'll find yourself having to
decrease your enlargement factor to maintain a desired print
resolution, or you'll have to decrease your desired print resolution
to maintain a given enlargement factor.
Mike, I think Emil is talking about a given sensor size and increasing photosite density by increasing the number of photosites not by shrinking the sensor size, in which case the diffraction effect is a constant for a given enlargement size for a given size of sensor up to approximately the apertures and number of MP he stated with some extra breathing room as you point out.

Regards, GordonBGood
 
For what I do, mostly 8x10 or smaller with occasional 16x20 prints and viewed on computer, hdtv, and 12ft. wide projection screens. I do have a 10mp, but prefer the output from my 6 and 2.7mp bodies. I have many great 8x10's made from 2 mp cameras and know a pro that makes a fair part of his living selling framed prints many of which come from a 3.2 mp point and shoot. I also suspect that a large majority of the masses that use digital point and shoots will ever even make an 8x10 print. Most common is most likely 4x6 prints and viewed on computer screen.
 
I'd be happy for years. I can make use of the extra data for printing big.
6mp's is more than enough for most 8x11" users and don't know it.

WayneB.
=========================
 
Hi Gordonbegood,

Whether we're talking about different photosite densities on a sensor of a given size or different photosite densities had by changing the sensor size without changing the number of MP, Emil's contention that photosite density measures nothing useful is incorrect.

It doesn't matter how you get there, how large or small the sensor is, how many or how few MP it has; you can ignore both of these variables and know with certainty that photosite densities at or below 110 photosites/mm will permit you to use nearly every f-Number available on any lens that's purpose-built for a given format (this excludes using large format lenses on a 35mm-sized sensor, for example), without inducing diffraction to inhibit a desired print resolution of 5 lp/mm in a print that's scaled to the dimensions had at an unresampled image resolution of 360 dpi (necessary to support 5 lp/mm in a CMOS sensor that suffers losses due to the Bayer algorithm and AA filter).

And whether you started with a large sensor and reduced its dimensions to increase photosite density without changing the number of MP or you increased photosite density without changing the sensor dimensions, the fact remains that as the photosite density increases, the number of stops that will support a desired print resolution of 5 lp/mm in a print that's scaled to the dimensions had at an unresampled image resolution of 360 dpi will decrease.

Eventually, at about 400 photosites/mm, whether you are using a 5 MP sensor or a 50 MP sensor, a 7mm digonal sensor or a 70mm diagonal sensor, if the combination of pixel count and sensor dimensions yields a photosite density that high (> 400), you'll find yourself limited to shooting wide open or nearly so, with only one or two corresponding shutterspeeds from which to choose, if you are to prevent diffraction from inhibiting a desired print resolution of 5 lp/mm in a print that's scaled to the dimensions had at an unresampled image resolution of 360 dpi (necessary to support 5 lp/mm in a CMOS sensor that suffers losses due to the Bayer algorithm and AA filter).

Even if your personal choice of a desired print resolution is only 1 lp/mm (equivalent to an image resolution of only 72 dpi, taking Bayer and AA losses into account for CMOS sensors) the fact remains that any increase in photosite density (whether we've reduced sensor dimensions or have increased pixel count) will have a corresponding decrease in the number of stops that will support your desired print resolution of 1 lp/mm. With high-density sensors, you are welcome to use all the stops made available on the lens, but you'll have to reduce either your desired print resolution or the enlargement factor.

The f-Number at which diffraction will begin to inhibit a desired print resolution for an anticipated enlargement factor can be calculated as follows:

N = 1 / desired print resolution in lp/mm / enlargement factor / 0.00135383

An increase in the desired print resolution requires a smaller f-Number.
An increase in enlargement factor requires a smaller f-Number.

Conversely...

Use of a larger f-Number (smaller aperture) requires either a decrease in your desired print resolution and/or a decrease in enlargement factor. If you insist on using f-Numbers that are greater than the value calculated with this formula, you'll have to make due with a lower print resolution and/or a smaller print.) Such compromises are frequently necessary with high-density sensors (> 400 photosites/mm), but seldom necessary with low-density sensors (

Mike Davis
http://www.AccessZ.com
 
Hi Gordonbegood,

Whether we're talking about different photosite densities on a sensor
of a given size or different photosite densities had by changing the
sensor size without changing the number of MP, Emil's contention that
photosite density measures nothing useful is incorrect.
Maybe a bit overstated, but essentially correct. By itself, photosite density tells you nothing. In combination with another parameter, such as pixel count or sensor size it begins to give you some information, but by and large, the same information in the old fashioned form of pixel count and sensor size is more useful and easier to understand.
It doesn't matter how you get there, how large or small the sensor
is, how many or how few MP it has; you can ignore both of these
variables and know with certainty that photosite densities at or
below 110 photosites/mm will permit you to use nearly every f-Number
available on any lens that's purpose-built for a given format
This is tripe. Which f-numbers you can use depends entirely on how you wish to use them. For most people, one important consideration is output image resolution, so the size of the sensor is critical, since that determines the magnification, and therefore the rendered size of the CoC.
[snip]
Unfortunately, the vast majority of people working
with high-density sensors are completely unaware of the fact that
they are suffering a compromise in print resolution when they choose
to make prints as large as the pixel count encourages and fail to
select the widest aperture (smallest f-Number) provided by the
manufacturer.
I was going to make a point by point refutation, but there are so many false axioms and misarguments, there's not much point. The main one concerns the idea that somehow one is forced to make prints at a given size for a pixel count. (well, actually, you are more confused than that, for how would you ever be encouraged to print at a given size by a pixel density?). Mainly, I suspect that this notion of yours is based not on a misunderstanding of physics, but by a lack of understanding of basic photographic technique. There are quite a few situations where, pictorially, one would want to use the peak definition of a lens. Not least landscapes. I see everywhere that landscape photography goes with small apertures. Not in my book, it doesn't. Differential focus is one of the main tools in providing 'pop' to a landscape. When you do this, you need to shoot with a good prime, around f/4 or 5.6 (on a FF camera) and I guarantee, you make a good quality large print, and you'll see the difference in detail between the primary subject and the background at infinity. It's enough to make it stand out. But here's the rub. In most landscape situations, with that primary subject a good few metres away, the background is imaged with a CoC still smaller than if you stopped the whole down to f/11. By limiting yourself to f/11 or smaller, or by using a camera incapable of rendering detail above the f/11 level, your reducing the whole lot to the same level of resolution, whichever aperture you select.

As I said in another thread, what's the point of spending cash on high quality glass, if you then put it on a camera only capable of rendering to the level of detail of a disposable camera, f/11 fixed focus lens?

--
Bob
 
I was perfectly happy with the 8mpx on my Oly E-300. Given that 8 - 10 mpx means 1/5 higher pixel density then I'd rather go with slightly cleaner photos at higher ISO than those extra 2 mpx. After all, shooting at high ISO reduces blur while shooting at 10mpx means slightly sharper pics at A3 prints. I know which one of those two I encounter the most often...
 
I was perfectly happy with the 8mpx on my Oly E-300. Given that 8 -
10 mpx means 1/5 higher pixel density then I'd rather go with
slightly cleaner photos at higher ISO than those extra 2 mpx. After
all, shooting at high ISO reduces blur while shooting at 10mpx means
slightly sharper pics at A3 prints. I know which one of those two I
encounter the most often...
If you are serious about higher ISO's then you need a camera with a larger sensor than 4/3. For a given print size, pixel density has little impact on image noise. Sensor size certainly does.
--
Bob
 
I'm saving my pennies for the 6 gigapixel full frame 8x10 view camera with live preview, micro-second response auto focus, 781 zone TTL metering, 64 creative modes, 100x digital zoom, 1080p video capture, 3D histogram with the 6mm-1000mm 1.2-1.8 Super Hyper Ultra Smooth and Noticeably Quiet motor kit lens. But in the mean time I will just keep using my cheesy 10 megapixel DSLR. I guess it will do in a pinch.
--
Organic imagination, digital views...
 
A 4/3 sensor at 7mpx has the same pixel density as a aps-c sensor at 10 mpx. so, 7-8 mpx is probably a good resolution with the current sensor technology for a four-thirds sensor.

I'd just like my iso 800 to be of a little better quality, and then i'd be a happy camper. i've got pretty fast optics and in-body IS, so i rarely need to use iso1600.
 
It doesn't matter how you get there, how large or small the sensor
is, how many or how few MP it has; you can ignore both of these
variables and know with certainty that photosite densities at or
below 110 photosites/mm will permit you to use nearly every f-Number
available on any lens that's purpose-built for a given format
This is tripe. Which f-numbers you can use depends entirely on how
you wish to use them. For most people, one important consideration is
output image resolution, so the size of the sensor is critical, since
that determines the magnification, and therefore the rendered size of
the CoC.
I'm talking about the effects of diffraction here. Of COURSE you can use any f-Number available on the lens if you have no concern for diffraction.
I was going to make a point by point refutation, but there are so
many false axioms and misarguments, there's not much point. The main
one concerns the idea that somehow one is forced to make prints at a
given size for a pixel count.
If have no specific print resolution at which you desire to record subject detail, then fine, make any size print you wish from any number of available pixels.
(well, actually, you are more confused
than that, for how would you ever be encouraged to print at a given
size by a pixel density?).
It isn't the pixel density that determines the print size - I never said that.
Mainly, I suspect that this notion of
yours is based not on a misunderstanding of physics, but by a lack of
understanding of basic photographic technique. There are quite a few
situations where, pictorially, one would want to use the peak
definition of a lens.
You can't possibly find anything I've written here that mandates the use of any specific technique. The scope of my discussion has been limited to the impact of diffraction on print resolution. When someone writes about DoF, do you expect them to list every possible situation where one might want to compromise DoF? The scope of my discussion is limited to the effect of diffraction and its relationship with enlargement factor and desired print resolution.

N = 1 / desired print resolution in lp/mm / enlargement factor / 0.00135383
Not least landscapes. I see everywhere that
landscape photography goes with small apertures. Not in my book, it
doesn't. Differential focus is one of the main tools in providing
'pop' to a landscape.
Wow! You're in the wrong thread...
When you do this, you need to shoot with a good
prime, around f/4 or 5.6 (on a FF camera) and I guarantee, you make a
good quality large print, and you'll see the difference in detail
between the primary subject and the background at infinity. It's
enough to make it stand out. But here's the rub. In most landscape
situations, with that primary subject a good few metres away, the
background is imaged with a CoC still smaller than if you stopped the
whole down to f/11. By limiting yourself to f/11 or smaller, or by
using a camera incapable of rendering detail above the f/11 level,
your reducing the whole lot to the same level of resolution,
whichever aperture you select.
Thank you for sharing that with us. It doesn't contradict a thing I've written.
As I said in another thread,
That's a good idea...

Mike Davis
http://www.AccessZ.com
 
I'm talking about the effects of diffraction here. Of COURSE you can
use any f-Number available on the lens if you have no concern for
diffraction.
Diffraction occurs at every f-stop on your lens, it is simply that at larger apertures, resolution tends to be limited more by aberrations than diffraction. So this point is nonsensical. You are concern with diffraction (or at least need to understand how it works) at every f-number.
If have no specific print resolution at which you desire to record
subject detail, then fine, make any size print you wish from any
number of available pixels.
(well, actually, you are more confused
than that, for how would you ever be encouraged to print at a given
size by a pixel density?).
It isn't the pixel density that determines the print size - I never
said that.
The phrase 'encouraged to print at a given size by the pixel density' was a direct quote from you. You might not have meant it, but you said it. And actually, the whole basis of your argument, and one of the false axioms, is that pixel density of necessity determines the scale at which you print, since you assume printing pixel for pixel at 360dpi. So actually print size in your world is determined by sensor size divided by count. Hey, that's the reciprocal of pixel density.
Mainly, I suspect that this notion of
yours is based not on a misunderstanding of physics, but by a lack of
understanding of basic photographic technique. There are quite a few
situations where, pictorially, one would want to use the peak
definition of a lens.
You can't possibly find anything I've written here that mandates the
use of any specific technique.
Except the technique of always printing pixel for pixel at 360 dpi.
The scope of my discussion has been
limited to the impact of diffraction on print resolution. When
someone writes about DoF, do you expect them to list every possible
situation where one might want to compromise DoF? The scope of my
discussion is limited to the effect of diffraction and its
relationship with enlargement factor and desired print resolution.

N = 1 / desired print resolution in lp/mm / enlargement factor /
0.00135383
Haven't checked your sums, in any case, and I can't remember what N is in any case. However, the simple argument that your case is wrong is that it precludes the possibility of having resolution in reserve so that you can, when the situation demands open up the lens to optimum aperture and print larger. Your definition of 'usable' f-stops is so limited as to be useless.
Not least landscapes. I see everywhere that
landscape photography goes with small apertures. Not in my book, it
doesn't. Differential focus is one of the main tools in providing
'pop' to a landscape.
Wow! You're in the wrong thread...
Why, because I actually take some photographs now and then?
Thank you for sharing that with us. It doesn't contradict a thing
I've written.
Except that, had I followed your advice, and selected a camera where the resolution maxed out at f/11 or so, I wouldn't have had the opportunity to utilise the additional resolution a f/5.6, the sharpness of my major subject would have been levelled down to exactly the same as the background and I'd have lost the 'pop' I was aiming for. DoF effects don't have to be extreme to be useful.

--
Bob
 
Comments as follows:
The f-Number at which diffraction will begin to inhibit a desired
print resolution for an anticipated enlargement factor can be
calculated as follows:

N = 1 / desired print resolution in lp/mm / enlargement factor /
0.00135383

An increase in the desired print resolution requires a smaller f-Number.
An increase in enlargement factor requires a smaller f-Number.

Conversely...

Use of a larger f-Number (smaller aperture) requires either a
decrease in your desired print resolution and/or a decrease in
enlargement factor. If you insist on using f-Numbers that are
greater than the value calculated with this formula, you'll have to
make due with a lower print resolution and/or a smaller print.) Such
compromises are frequently necessary with high-density sensors (> 400
photosites/mm), but seldom necessary with low-density sensors (
photosites/mm). Unfortunately, the vast majority of people working
with high-density sensors are completely unaware of the fact that
they are suffering a compromise in print resolution when they choose
to make prints as large as the pixel count enccourages and fail to
select the widest aperture (smallest f-Number) provided by the
manufacturer.
Mike, given that your equation showing the limits of aperture for a given print size, resolution, and enlargement (I haven't checked the math but it makes sense that such a relationship exists), at no point in your equation is the photosite density actually stated, therefore photosite density is not a variable.

Just because a 24 by 36 mm sensor may have 1 micron photosite spacing for a total number of MP of 864 MP doesn't mean that one has to print at 360 dpi from this sensor (66.67 by 100 inches) and if one prints at the same 8.33 by 12.5 inch print size then the limits on aperture to not be diffraction limited are exactly the same as if that sensor had only 12 MP.

Therefore photosite density is not a factor for a given print size and resolution for a particular sensor size as long as there are enough MP on that sensor to give adequate resolution on that given print size and having many times the required resolution from the sensor for that print size does not limit the range of lens apertures that can be used.

You seem to be assuming that just because one has a very high photosite density sensor one has to print at a constant dpi from that sensor and can not interpolate any given print size form any given sensor resolution as long as the sensor has a high enough resolution to give adequate detail resolution on the desired print size. Why do you reject downsampling of resolution out of hand?

Regards, GordonBGood
 
I'm talking about the effects of diffraction here. Of COURSE you can
use any f-Number available on the lens if you have no concern for
diffraction.
Diffraction occurs at every f-stop on your lens, it is simply that at
larger apertures, resolution tends to be limited more by aberrations
than diffraction. So this point is nonsensical. You are concern with
diffraction (or at least need to understand how it works) at every
f-number
I was responding to your contention that I had implied some apertures can never be used under any circumstances. I pointed out that my discussion is limited to the effects of diffraction on aperture selection and now you're telling me that's "nonsensical"?
It isn't the pixel density that determines the print size - I never
said that.
The phrase 'encouraged to print at a given size by the pixel density'
was a direct quote from you.
Please provide us with the date and time stamp where I wrote that.
You might not have meant it, but you
said it.
That's generous of you, but you're still mistaken.
And actually, the whole basis of your argument, and one of
the false axioms, is that pixel density of necessity determines the
scale at which you print,
I've never said that, either. Maybe you actually are in a different thread and don't know it. You need to support your claims of what I did or didn't say by giving us references.
since you assume printing pixel for pixel
at 360dpi.
I chose 5 lp/mm arbitrarily as an example of how to use the formula I've provided.

Given that one actually wants to record subject detail at the print to a resolution of 5 lp/mm, using a CMOS sensor (not a Foveon sensor), you will have to scale the print no larger than an unresampled image resolution of 360 dpi to support that goal of 5 lp/mm - due to losses imposed by the Bayer Algorithm and the AA filter.
So actually print size in your world is determined by
sensor size divided by count. Hey, that's the reciprocal of pixel
density.
Simply taking the reciprocal of pixel density does not account for losses induced by the Bayer algorithm and anti-aliasing filter common to CMOS sensors.
Mainly, I suspect that this notion of
yours is based not on a misunderstanding of physics, but by a lack of
understanding of basic photographic technique. There are quite a few
situations where, pictorially, one would want to use the peak
definition of a lens.
You can't possibly find anything I've written here that mandates the
use of any specific technique.
Except the technique of always printing pixel for pixel at 360 dpi.
Where did I write that one should always print at 360 dpi? Go find it. Happy hunting...

360 dpi was simply the required image resolution to match a desired print resolution of 5 lp/mm. The formula I provided does not mandate ANY desired print resolution. I used 5 lp/mm and the corresponding 360 dpi as an example, not a mandate.
The scope of my discussion has been
limited to the impact of diffraction on print resolution. When
someone writes about DoF, do you expect them to list every possible
situation where one might want to compromise DoF? The scope of my
discussion is limited to the effect of diffraction and its
relationship with enlargement factor and desired print resolution.

N = 1 / desired print resolution in lp/mm / enlargement factor /
0.00135383
Haven't checked your sums,
That's the easy way out...
in any case, and I can't remember what N
is in any case.
Read my posts in this thread. N, as used in that formula, is the f-Number at which diffraction will begin to inhibit a desired print resolution in lp/mm, at an anticipated enlargement factor. Sound familiar?
However, the simple argument that your case is wrong
is that it precludes the possibility of having resolution in reserve
so that you can, when the situation demands open up the lens to
optimum aperture and print larger.
Nothing in the above statement refutes anything I've said.
Your definition of 'usable'
f-stops is so limited as to be useless.
I'm only talking about diffraction here. You're absolutely welcome to use any stop on your lens if you don't give a hoot about diffraction inhibiting a desired print resolution.
Not least landscapes. I see everywhere that
landscape photography goes with small apertures. Not in my book, it
doesn't. Differential focus is one of the main tools in providing
'pop' to a landscape.
Wow! You're in the wrong thread...
Why, because I actually take some photographs now and then?
No, because the above statement is off-topic. I'm talking about the impact of diffraction. I'm not writing a dissertation on all the factors one should take into account when shooting landscapes or any other subject matter.
Thank you for sharing that with us. It doesn't contradict a thing
I've written.
Except that, had I followed your advice, and selected a camera where
the resolution maxed out at f/11 or so, I wouldn't have had the
opportunity to utilise the additional resolution a f/5.6, the
sharpness of my major subject would have been levelled down to
exactly the same as the background and I'd have lost the 'pop' I was
aiming for. DoF effects don't have to be extreme to be useful.
I never gave the advice you claim I gave. Find it. Quote it. It doesn't exist.

Mike Davis
http://www.AccessZ.com
 
The f-Number at which diffraction will begin to inhibit a desired
print resolution for an anticipated enlargement factor can be
calculated as follows:

N = 1 / desired print resolution in lp/mm / enlargement factor /
0.00135383

An increase in the desired print resolution requires a smaller f-Number.
An increase in enlargement factor requires a smaller f-Number.

Conversely...

Use of a larger f-Number (smaller aperture) requires either a
decrease in your desired print resolution and/or a decrease in
enlargement factor. If you insist on using f-Numbers that are
greater than the value calculated with this formula, you'll have to
make due with a lower print resolution and/or a smaller print.) Such
compromises are frequently necessary with high-density sensors (> 400
photosites/mm), but seldom necessary with low-density sensors (
photosites/mm). Unfortunately, the vast majority of people working
with high-density sensors are completely unaware of the fact that
they are suffering a compromise in print resolution when they choose
to make prints as large as the pixel count enccourages and fail to
select the widest aperture (smallest f-Number) provided by the
manufacturer.
Mike, given that your equation showing the limits of aperture for a
given print size, resolution, and enlargement (I haven't checked the
math but it makes sense that such a relationship exists), at no point
in your equation is the photosite density actually stated, therefore
photosite density is not a variable.
Photosite density is not a variable for determining the f-Number (N) at which diffraction will begin to inhibit a desired print resolution at an anticipated enlargement factor.

There is, however a relationship between photosite density and the number of stops you'll be able to use without inducing diffraction that can inhibit your desired print resolution at the enlargement factor suffered when the print size is scaled to the unresampled image resolution that equates pixel count to your desired print resolution (360 dpi for 5 lp/mm, 288 for 4 lp/mm, 216 for 3 lp/mm, etc.)
Just because a 24 by 36 mm sensor may have 1 micron photosite spacing
for a total number of MP of 864 MP doesn't mean that one has to
print at 360 dpi from this sensor (66.67 by 100 inches)
I never said that we have to print at 360 dpi, except under the one, highly qualified, example scenario where a shooter actually desires to resolve subject detail at a resolution of 5 lp/mm in the print after enlargement.
and if one
prints at the same 8.33 by 12.5 inch print size then the limits on
aperture to not be diffraction limited are exactly the same as if
that sensor had only 12 MP.
That statement doesn't refute anything I've written. If you make like-sized prints from like-sized sensors, the limits of resolution imposed by diffraction will be identical for any given f-Number. But if the guy with more MP decides to make a LARGER print, to take advantage of all or some of those extra pixels, he will be increasing the enlargement factor and thus reducing print resolution if he insists on using the same f-Number and sensor size.
Therefore photosite density is not a factor for a given print size
and resolution for a particular sensor size as long as there are
enough MP on that sensor to give adequate resolution on that given
print size and having many times the required resolution from the
sensor for that print size does not limit the range of lens apertures
that can be used.
I've only made one claim regarding photosite density: As photosite density increases, the number of stops that will support a desired resolution at a given print size will be decrease.
You seem to be assuming that just because one has a very high
photosite density sensor one has to print at a constant dpi from that
sensor
I never said that.
and can not interpolate any given print size form any given
sensor resolution as long as the sensor has a high enough resolution
to give adequate detail resolution on the desired print size.
Ditto
Why do
you reject downsampling of resolution out of hand?
I haven't.

Mike Davis
 

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