Does sensor size help IQ in bright light or mostly challenging light?

pcunnin

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I understand the advantage of sensor size when it comes to reducing noise in photos, and in gathering more light and more "information". However does this advantage translate into better photos in bright daylight, or when using a bright "head on" flash to light a scene?
 
I understand the advantage of sensor size when it comes to reducing noise in photos, and in gathering more light and more "information". However does this advantage translate into better photos in bright daylight, or when using a bright "head on" flash to light a scene?
The difference in sensor size has the same effect on measured shot noise regardless of how much light is in the scene. As light levels are reduced, shot noise becomes a lesser part of the total noise in an image. In that sense, sensor size helps more at high light levels.

If you go into the files and calculate the Signal to Noise Ratio (SNR) you'll probably find that difference in sensor size has slightly more effect at low ISO s than at high ISOs. However, most people find it harder to notice a given difference in SNR at high light levels (low ISO settings) than in lower light, so it may look like the difference in signal capture is having less effect.

To the extent that noise is more noticeable in poorly exposed parts of an image, the beneficial effects of a larger sensor may seem more significant in lower light.
 
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I understand the advantage of sensor size when it comes to reducing noise in photos, and in gathering more light and more "information". However does this advantage translate into better photos in bright daylight, or when using a bright "head on" flash to light a scene?
There are two sides to your question. The technical side is that, in general terms, yes a larger sensor is "better". However, if we read between the lines, the answer is no. By that I mean you describe a situation using "bright head on flash to light a scene". There are a number of problems with this illustration. Perhaps the most challenging will be the definitions. What is bright? Is this a reference to contrast (which would be my guess). What is head on? To me that means on the lens axis. But regardless, it is certainly a direction of light issue. Flash? Are we talking pop up flash? Shoe mount flash? A more powerful strobe? What is "a scene"? A portrait? The Rocky Mountains? We could dig deeper into "light a scene". If you are using flash to light a scene, you need to understand that how this all works. As an example, I could take a portrait on a white backdrop using one flash and could make that backdrop black. There is no sensor in the world that will change the physics of that. There is no sensor in the world that alters the light. The camera/sensor is simply the tool used to record the light. Another example from above would be the direction of light. If you have a poor direction to your light, then you have a poor direction to your light. There isn't a sensor that is "better" in such a situation. The problem isn't with the sensor, it's with your light.
 
I believe it helps in both situations if the sensors are of the same generation.

Although if you are using equivalent settings (same shutter speed, DoF, FoV) the images will end up being pretty much the same, equivalent.
 
Does sensor size help IQ in bright light or mostly challenging light? I understand the advantage of sensor size when it comes to reducing noise in photos, and in gathering more light and more "information". However does this advantage translate into better photos in bright daylight, or when using a bright "head on" flash to light a scene?
Larger sensor systems typically have more pixels. Thus, depending on the lens used, will deliver photos with more resolution than smaller sensor systems (sometimes a lot more resolution, depending on the particular scene, lens, and camera), which is often worthwhile for its own sake, but also useful when cropping.

In addition, larger sensor systems record more light for a given exposure, resulting in a less noisy photo. At low ISO settings, the lower noise, per se, is not necessarily noticeable, but may become important when "strong" processing is applied. However, for "minimal" processing and "moderate" display sizes, the resolution / noise advantage of larger formats in good light may go completely unnoticed.

In lower light, it is not the larger sensor, per se, but the larger aperture diameter of the lenses that are available to larger sensor systems, that give larger formats their noise advantage. However, that larger aperture diameter *necessarily* results in a more shallow DOF, which can be a plus, minus, or neither here nor there. Even when considered a minus, however, the lower noise is often more important than a deeper DOF, which is why people often shoot with wider apertures in lower light.

In the end, think of FF vs APS-C, for example, as an f/2.8 lens vs an f/4 lens. The f/2.8 lens offers a more shallow DOF and less noisy photos, and is often at lot sharper at f/4 than the f/4 lens. An f/2.8 lens is a lot bigger and heavier than an f/4 lens of the same focal range, but a lot of people pay a pretty penny for an f/2.8 lens over an f/4 lens. And so it is with larger formats vs smaller formats.
 
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I understand the advantage of sensor size when it comes to reducing noise in photos, and in gathering more light and more "information".
That isn't exactly true.

There are only two ways that a larger sensor can get more total light; One is by using any lens at all and setting the camera to base ISO in Av mode and just letting the exposure time go wherever it needs to, and then the larger sensor collects more total light. The other is when you match a bigger lens (bigger optical aperture) to the larger sensor for the same angle of view, but shallower DOF, when a certain shutter speed is needed that makes base ISO impractical.

If there isn't shallower DOF, there no extra light, when a shutter speed is needed. For any given angle of view, shallow DOF is what parallels more light; not just a larger sensor.

A slow kit lens on a FF camera may get you more noise than a fast zoom on an APS-C camera.
However does this advantage translate into better photos in bright daylight, or when using a bright "head on" flash to light a scene?
The more exposure you have, which is usually associated with lower ISO settings, the less that any noise is going to rise above sublimation and become obvious.

--
John
http://www.pbase.com/image/55384958.jpg
 
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I understand the advantage of sensor size when it comes to reducing noise in photos, and in gathering more light and more "information". However does this advantage translate into better photos in bright daylight, or when using a bright "head on" flash to light a scene?
Equivalence dictates that you only experience better IQ at the edges of the shooting envelope.

As example, if your image with a FF is exposed with 1/125th, f11 and ISO3200. Then you will get the exact same exposure with the same DoF on a smaller sensor like the (m)43 using 1/125th, f5.6 and ISO800. The two stop advantage in noise performance is nullified by equivalence rules - ISO800 vs ISO3200.

However... if your shot on FF is shot with 1/125th, f1.4 and ISO3200... then the smaller sensor is in trouble. You either need to slap a real fast lens on your camera - that lens might not even exist - and/or raise the ISO (or use the same ISO)... but you might not be able to get the exact same shot and you will get better noise performance out of the FF camera with this example.

In bright daylight... it will often be difficult to tell from prints which sensor size was used.

The larger the sensor, the better DR you have as well and if the DR in a shot is large... it might show in the highlights or dark areas. You will also have better results if you need to brighten the darker areas. The result will be cleaner on the larger sensors.
 
The larger the sensor, the better DR you have as well and if the DR in a shot is large... it might show in the highlights or dark areas. You will also have better results if you need to brighten the darker areas. The result will be cleaner on the larger sensors.
The size of a sensor has little to do with DR per se, except that a larger sensor can have more pixels in it, giving more full-image DR than a smaller one with the same size pixels, but less of them, if the pixels have the same pixel DR. If you go by something like "PDR" rather than engineering DR, then the larger sensor has some more weight, because photon noise is factored in moderately in PDR, but for read-noise-based DR, the sensor size itself has little or no value for DR at this point in time.

In reality, FF sensors and APS-C sensors with the same pixel size or density often get less pixel-level DR, for some reason. Think Nikon D500 vs D850, or Canon 7D2 vs 5Ds; in both cases, the APS-C has the same pixel density as the corresponding FF, but has slightly more visible DR at the pixel level. Correlation is mostly with pixel count and readout technology; not sensor size, for base-ISO DR. The FF sensors in these pairs have more image-level DR, but would have even more if they had as much pixel-level DR as their APS-C counterparts.
 
The larger the sensor, the better DR you have as well and if the DR in a shot is large... it might show in the highlights or dark areas. You will also have better results if you need to brighten the darker areas. The result will be cleaner on the larger sensors.
The size of a sensor has little to do with DR per se, except that a larger sensor can have more pixels in it, giving more full-image DR than a smaller one with the same size pixels, but less of them, if the pixels have the same pixel DR. If you go by something like "PDR" rather than engineering DR, then the larger sensor has some more weight, because photon noise is factored in moderately in PDR, but for read-noise-based DR, the sensor size itself has little or no value for DR at this point in time.

In reality, FF sensors and APS-C sensors with the same pixel size or density often get less pixel-level DR, for some reason. Think Nikon D500 vs D850, or Canon 7D2 vs 5Ds; in both cases, the APS-C has the same pixel density as the corresponding FF, but has slightly more visible DR at the pixel level. Correlation is mostly with pixel count and readout technology; not sensor size, for base-ISO DR. The FF sensors in these pairs have more image-level DR, but would have even more if they had as much pixel-level DR as their APS-C counterparts.
Ok... let me phrase it like this... in all test stats I have come across I observer that cameras with smaller sensors have less dynamic range then the cameras with bigger sensors:

sony rx100 < oly omd em1 < sony a7
 
The larger the sensor, the better DR you have as well and if the DR in a shot is large... it might show in the highlights or dark areas. You will also have better results if you need to brighten the darker areas. The result will be cleaner on the larger sensors.
The size of a sensor has little to do with DR per se, except that a larger sensor can have more pixels in it, giving more full-image DR than a smaller one with the same size pixels, but less of them, if the pixels have the same pixel DR. If you go by something like "PDR" rather than engineering DR, then the larger sensor has some more weight, because photon noise is factored in moderately in PDR, but for read-noise-based DR, the sensor size itself has little or no value for DR at this point in time.

In reality, FF sensors and APS-C sensors with the same pixel size or density often get less pixel-level DR, for some reason. Think Nikon D500 vs D850, or Canon 7D2 vs 5Ds; in both cases, the APS-C has the same pixel density as the corresponding FF, but has slightly more visible DR at the pixel level. Correlation is mostly with pixel count and readout technology; not sensor size, for base-ISO DR. The FF sensors in these pairs have more image-level DR, but would have even more if they had as much pixel-level DR as their APS-C counterparts.
Ok... let me phrase it like this... in all test stats I have come across I observer that cameras with smaller sensors have less dynamic range then the cameras with bigger sensors:

sony rx100 < oly omd em1 < sony a7
PDR or engineering DR? What are the pixel counts? What type of readout circuitry?

Either way, you can find examples that would flip the ranking, and what no web site with noise stats shows you is what the noise looks like, and generally speaking, the post-gain read noise in smaller sensors tends to be more random in character.
 
The larger the sensor, the better DR you have as well and if the DR in a shot is large... it might show in the highlights or dark areas. You will also have better results if you need to brighten the darker areas. The result will be cleaner on the larger sensors.
The size of a sensor has little to do with DR per se, except that a larger sensor can have more pixels in it, giving more full-image DR than a smaller one with the same size pixels, but less of them, if the pixels have the same pixel DR. If you go by something like "PDR" rather than engineering DR, then the larger sensor has some more weight, because photon noise is factored in moderately in PDR, but for read-noise-based DR, the sensor size itself has little or no value for DR at this point in time.

In reality, FF sensors and APS-C sensors with the same pixel size or density often get less pixel-level DR, for some reason. Think Nikon D500 vs D850, or Canon 7D2 vs 5Ds; in both cases, the APS-C has the same pixel density as the corresponding FF, but has slightly more visible DR at the pixel level. Correlation is mostly with pixel count and readout technology; not sensor size, for base-ISO DR. The FF sensors in these pairs have more image-level DR, but would have even more if they had as much pixel-level DR as their APS-C counterparts.
Let's consider the following hypothetical situation (which is pretty close to many actual cameras): A FF sensor with pixels that have the same size and technology as an APS-C (1.5x) sensor.

For the same exposure, each pixel will record the same amount of light and each pixel has the same read noise, so the DR/pixel will be the same.

However, let's now compare DR/photo rather than DR/pixel. The same corresponding area of the scene on the FF sensor will have 2.25x as many pixels, and thus receive 2.25x more light. The electronic noise of the 2.25x more pixels will be 1.5x greater. Thus, the DR will be log2 (2.25 / 1.5) = 0.58 stops higher per photo. Furthermore, each level within the DR will be less noisy because it is made with more light.

Of course, this is all *if* the pixels are the same. Since they aren't, real-life differences vary from the above scenario.
 
Sensor size doesn't always carry a direct advantage of reducing noise. It is the single pixel/sensel size that counts. A sensor may have good signal to noise ratio advantage but not a noise reduction.

To put it shortly and almost correctly - sensor size, together with the number of megapixels it has determine the size of each pixel. The bigger the pixel the better/higher the Dynamic Range. The higher the DR the better the signal to noise ratio. Thus it is not always that a bigger sensor has better signal to noise ratio. For example a FF sensor with 5x number of pixels of an APS-C will have smaller pixels.

So taking a step back from noise we see dynamic range. Here is the answer to your question: The bigger pixels result in better image quality in bright light too. The reason is that bigger pixels can gather more photons before clipping.
 
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In lower light, it is not the larger sensor, per se, but the larger aperture diameter of the lenses that are available to larger sensor systems, that give larger formats their noise advantage.
With all the respect but you missed some simple physics.

The larger the sensor format the smaller the possible apertures. Just compare how much slower are MF lenses than FF lenses.

A larger sensor needs larger lenses to cover it. Larger lenses are harder to design and produce in high quality, especially with large apertures.

It is the single pixel size that a larger sensor usually has, that might carry a signal to noise ratio advantage.
 
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Sensor size doesn't always carry a direct advantage of reducing noise. It is the single pixel/sensel size that counts.
You are mistaken. if you were correct, then the D7500 and D850 would have about the same noise performance, while the D850 would be about a stop worse than the D750.. However, the D850 is nearly a stop better than the D7500 and the D750 is only a small fraction better than the D850. These are the results you'd expect if whoel senros sise was the major factor,m and pixel count was a small factor.
A sensor may have good signal to noise ratio advantage but not a noise reduction.
What does that mean?
To put it shortly and almost correctly - sensor size, together with the number of megapixels it has determine the size of each pixel. The bigger the pixel the better/higher the Dynamic Range. of eh pixle.
But the dynamc range of the whole senors depend upon combining the DRs of all the pixles, and with smaller pixels you have more of them to combine.
The higher the DR the better the signal to noise ratio. Thus it is not always that a bigger sensor has better signal to noise ratio. For example a FF sensor with 5x number of pixels of an APS-C will have smaller pixels.
It will have smller pixels bur probably better SNR. Sadly there are no current pairs of FF and APS-C sensors with a 5:1 ratio of pixel counts we could compare to to test you theory. However what we do have available shows performance consistent with total senors size being the major factor, pixel count being a minor factor, and pixl sze (oher than as related to pixel count) not being a factor at all.

Also you are ignoring the fact that smaller individual pixels tend to have less read noise than larger individual pixles.
So taking a step back from noise we see dynamic range. Here is the answer to your question: The bigger pixels result in better image quality in bright light too.
No they do not. The a7S2 has pixels 7/2 time those of the a7R2, but has no significant noise advantage at all.
The reason is that bigger pixels can gather more photons before clipping.
It is irrelevant. A larger sensor captures more light than a smaller sensor. It doesn't mater how many individual pixels that light is divided between, as far as shot noise goes.

The formula for calculating the shot noise Ns of a sensor with Q pixels where the sensor receives a signal of Ss, is

Ns = sqrt(Q(Np)^2), where Np is the shot noise of a single pixel, because the formula for adding noises is to take the square root of the sum of the squares of the individual noises

Np = sqrt(Sp), where Sp is the signal received by a single pixel, because shot noise is the square root of the signal.

Sp = Ss/Q, the signal of a pixel is its share of the signal received by the whole senors.

By substitution we get

Ns = sqrt(Q(sqrt(Sp))^2) = sqrt(Q(sqrt(Ss/Q))^2)

Simplifying we get Ns = sqrt(Q(Ss/Q)) = sqrt(Ss)

The quantify of pixels, and therefore the size of pixels, cancels itself out
 
I believe it helps in both situations if the sensors are of the same generation.

Although if you are using equivalent settings (same shutter speed, DoF, FoV) the images will end up being pretty much the same, equivalent.
Although modern sensors have a better dynamic range than similar sensors 5-10 years ago, size is very important for the dynamic range and the ISO range.

I use everything from 1" cameras, like RX100 and Nikon1 series, to FX cameras, and have older cameras that had an upper limit in useful ISO at under ISO 200, and now I shoot without hesitation ISO 32,000 with my newest DX camera, while my latest Nikon 1, a J5, handles ISO 3,200 fairly well.

The smaller sensors have lower dynamic range, thus are more helped on overcast days, when the light might be bright, but soft, so too in a studio, should you want that. In really harsh light even ISO 160 might be problematic, say on a badly lit sports-stadium, with just a few spotlights on one side, and nothing on the other, and you still want to get decent images on people in the well-lit areas and dark areas.

Let me give you some examples from today:

d19e78ac2fdb4575953536948a88944e.jpg

a915638c4bee4d74bb9b9a49b4cdea15.jpg

Sadly I haven't got my FX camera with me, as I mostly shoot birds, but both images are taken from the same spot, using the same lens, and there was lots of light coming in from the slide doors to the right in both cases, but in the first shot the light was much softer than in the second.

When one shoots a lot one learn a few tricks of the trade, and one is that it is far more easy to shoot at higher ISO in good light, than in low light where you often need as much dynamic range you can find), and that grey filters can be a blessing, as they can allow you to use a little higher ISO in good light without having to use very small apertures (with associated diffraction problems), as every lens has an optimum aperture, and most cameras will not operate over 1/4,000 sec, so you can easily get boxed in.

Small sensors are fairly noisy even at base ISO, while the newest FX cameras need to be provoked to display much noise.

I use a mix of 1" and DX most of the time, and just love to use the same sharp lenses across all the sizes of sensors. In the example above I used a Voigtlander 20/3.5 with both the tiny J5 and the more enthusiast-styled D7500.

And avoid slow lenses, if possible, as they make life so much more difficult as a photographer. I would love to have faster long telephoto lenses, but economics restrict me to buy long lenses that are F/6.3, but I would love to have a few that are f/4.0, or lower!

Crappy lenses are a no-good investment, and cameras age fast (5 years are often said to be the practical limit, after that the service costs start to rise, fast), so invest in as good lenses you can afford, (possibly used, as lenses usually are good for 20 years, or longer) and buy cheap cameras (say a used D700?!), to begin with, upgrading later when your economy allows it, and you are getting a feeling about where you are heading!

Good luck!

****************

Some of my favorite F Mount lenses:

Nikon AF-S 70-200/4.0G (FX - sadly at home just now)

Nikon AF-P 18-55 VR (DX, but I mainly use it on my Nikon1 cameras)

Nikon AF-P 70-300 VR (DX, but I mainly use it on my Nikon1 cameras, if the 70-300 CX is back home, like just now)

Sigma 30 Art (DX)

Voigtlander 20/3.5 (no longer in production - FX)

Sigma 100-400 C (FX)

Nikon 40 macro (DX)

Nikon 85 macro VR (DX)

Three Nikon1 lenses I use:

Nikon1 10 (with a wide adapter, equals a 22)

Nikon1 70-300 CX (equals a 190-810mm on an FX body. Superb, but at home just now)

Nikon1 6.7-13 (behaves like 18-35 on an FX body)

So with the 6.7-13 and the 18-55 on two Nikon1 cameras, cover 18-150 (roughly), and the DX camera covers 150-600 with the Sigma 100-400 C.

******

I have more macros, longer telephoto-zooms, and more Nikon1 lenses, but these are the ones I use most. Normally carry two cameras, one Nikon1 and one DX, one of them with a telephoto lens, the other with a prime, both F Mount. A quick switch and I suddenly either have a long telephoto prime with f/1.8, or my 100-400 C suddenly equals a 300-1000mm lens! With no loss in speed, which would have happened if I added a TC.

--
tordseriksson (at) gmail.....
Owner of a handful of Nikon cameras. And a few lenses.
 
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The larger the sensor, the better DR you have as well and if the DR in a shot is large... it might show in the highlights or dark areas. You will also have better results if you need to brighten the darker areas. The result will be cleaner on the larger sensors.
The size of a sensor has little to do with DR per se, except that a larger sensor can have more pixels in it, giving more full-image DR than a smaller one with the same size pixels, but less of them, if the pixels have the same pixel DR. If you go by something like "PDR" rather than engineering DR, then the larger sensor has some more weight, because photon noise is factored in moderately in PDR, but for read-noise-based DR, the sensor size itself has little or no value for DR at this point in time.

In reality, FF sensors and APS-C sensors with the same pixel size or density often get less pixel-level DR, for some reason. Think Nikon D500 vs D850, or Canon 7D2 vs 5Ds; in both cases, the APS-C has the same pixel density as the corresponding FF, but has slightly more visible DR at the pixel level. Correlation is mostly with pixel count and readout technology; not sensor size, for base-ISO DR. The FF sensors in these pairs have more image-level DR, but would have even more if they had as much pixel-level DR as their APS-C counterparts.
Ok... let me phrase it like this... in all test stats I have come across I observer that cameras with smaller sensors have less dynamic range then the cameras with bigger sensors:

sony rx100 < oly omd em1 < sony a7
PDR or engineering DR? What are the pixel counts? What type of readout circuitry?

Either way, you can find examples that would flip the ranking, and what no web site with noise stats shows you is what the noise looks like, and generally speaking, the post-gain read noise in smaller sensors tends to be more random in character.
My normally used cameras are in the 20MP class, no matter if the camera is a J5, a D7500, or a D600, where the latter is handicapped by a heavy AA-filter.

In really good light the differences are small if any but as the light vanes the differences increase, fast!
 
Sensor size doesn't always carry a direct advantage of reducing noise. It is the single pixel/sensel size that counts.
You are mistaken. if you were correct, then the D7500 and D850 would have about the same noise performance, while the D850 would be about a stop worse than the D750.. However, the D850 is nearly a stop better than the D7500 and the D750 is only a small fraction better than the D850. These are the results you'd expect if whoel senros sise was the major factor,m and pixel count was a small factor.
Look at the DxO Labs comparison:

e2421af124f0496a9de519ccff52c3e1.jpg
A sensor may have good signal to noise ratio but not a noise reduction.
What does that mean?
The OP wrote about sensor size affecting noise reduction. Noise reduction is not the correct term in this sense.

Sensor size is affecting the signal-to-noise ratio to be precize and not the noise reduction which is something applied later to reduced noise which is already recorded.
To put it shortly and almost correctly - sensor size, together with the number of megapixels it has determine the size of each pixel. The bigger the pixel the better/higher the Dynamic Range. of eh pixle.
But the dynamc range of the whole senors depend upon combining the DRs of all the pixles, and with smaller pixels you have more of them to combine.
That is if you view the image downscaled. I am talking about original 100% size sensor performance. Sensor performance better should not be judged downscaled if you wish to avoid the scaling effect masking noise.
The higher the DR the better the signal to noise ratio. Thus it is not always that a bigger sensor has better signal to noise ratio. For example a FF sensor with 5x number of pixels of an APS-C will have smaller pixels.
It will have smller pixels bur probably better SNR.
With all the respect I must disagree given a 5:1 pixel size difference.
So taking a step back from noise we see dynamic range. Here is the answer to your question: The bigger pixels result in better image quality in bright light too.
No they do not. The a7S2 has pixels 7/2 time those of the a7R2, but has no significant noise advantage at all.
I must disagree again. Look at the DxO Labs comparison:

f958e15dd7694ff1a272193efa736685.jpg.png
The reason is that bigger pixels can gather more photons before clipping.
It is irrelevant. A larger sensor captures more light than a smaller sensor. It doesn't mater how many individual pixels that light is divided between, as far as shot noise goes.
The larger sensor captures overall more light, but on more space so given equal sized pixels the quantity of the light per well is the same thus the pixel's snr will be very close, as seen in the lab test above.
 
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In really good light the differences are small if any...
Enjoying the technology advancements. :) Could imagine myself some time ago that such an output would ever be possible from something sized 1".

Lately I often end up using an 1" camera in the daytime..., the last time I was using a "pocket" camera was with the Rollei Prego 90 because it was equipped with real Schneider glass cover with HFT by Rollei.
 
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My normally used cameras are in the 20MP class, no matter if the camera is a J5, a D7500, or a D600, where the latter is handicapped by a heavy AA-filter.
In really good light the differences are small if any but as the light vanes the differences increase, fast!
I don't know why you chose to make your post a child of mine in the threading, since you completely changed the subject and did not address anything I wrote, but I would say that other people would disagree with you about the AA filter.

Some people only want sharpness when it is real detail that is sharp; not sharp evidence of the problem of undersampling. Some people do not notice the difference.

With a 20MP FF camera, potential for aliasing is very great with decent optics. Be careful what you wish for; unless you are stopping way down or shooting a lens that is soft wide-open, pixel density that low without an AA filter can get Nyquist mirror "beat frequencies" very easily, which can not be removed in post-processing. The red and blue color sampling will be highly problematic, with lots of false color.

Big pixels, absent AA filters, and sharp optics do not mix well, especially with color filter arrays.
 
Big pixels, absent AA filters, and sharp optics do not mix well, especially with color filter arrays.
Ain't that a shame? A shame because the problem is not in the large pixels nor in the sharp lenses. Combined together they simply display the limitations of mosaiced/bayer sensors. I hope soon some of the alternative full color technologies see good development.
 

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