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I am aware that the picture you posted is taken at 0.5 cycles and pixels are still resolved to some degree so it seems what we have here is not a "false" 4k projector.
and
Th Sony does not have to have a flat MTF curve to be a 'real' 4K projector. If the MTF goes down with rising frquency (as it goes sooner or later for all projectors) it depends a lot on how early and how much.
I expected you noticed the quotes around the word false

but ok I understand the term I used can be mis-interpreted. Sorry for that.
Most people here know that optical components have MTF. Also imaging devices. Thus pj have MTF that is a part of the equation. Others parts are lum, CR ansi, black floor, global gamma progression and gamma progression in very fisrt IRE, room... Most of us are not new in this world...
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There is much more to a good image than (flat) MTF. The main advantage of upsampled 1080p or 2K via a 4K projector compared to a 2K DLP or LCOS is the lack of visibility of pixels (and for DLP hard pixel edges) together with no or minimal loss of sharpness or even perceptually improved sharpness (due to clever upsampling tricks). The image looks more analogue and free of the sampling grid I always see on 2K projectors with sharp material from where I usually sit (1-1.5 screen widths away). This does not depend on screen size and is true for a large range of sizes.
habbits and preferences concerning digital picture aspect are clearly very different from people to people. It is very subjective. Some prefer the crisp rendering of monoDLP and will never buy a LCoS. Other prefer soft rendering with adequate sharpening and are very happy with LCoS. But sometimes they also complain against a lack of sharpness. Most of the time, HT addict is never happy

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One of the problems associated to digital image is that the distorsion in high frequencies raises rapidly around the Nyquist frequency (sharp edge of pixel rendering) if we compare the rendering at this frequency (staircase function) with a pure sinusoïdal function. The nature of this distorsion depends on the tech used and the optics and can be very different. There is no exact solution to this problem, but some tricks work rather well like for instance :
- attenuate the sharp edge of individual pixel. Hardly decreasing MTF around Nyquist frequency is a way to do it. A pro also said to me that the panels in 3xdlp 2K cinema machine are shifted by 1/6 of their width in factory to obtain this effect.
- make the pixels so small that you can't see them. This is typically the case with 23" 2K LCD flat display seen at 1 meter... For pj, a good way to do it is to go to higher resolution and use upsampling.
- combination of both...
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Maybe it is just me but it seems to be "hip" to bash the Sony VW1000ES just because.
You don't know me but when I wrote " But obviously middle range 4K pj (like the 1000ES) can do at least the same or better than middle value 2K pj. That' a very good point." this is a huge compliment, believe me.

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I have a feeling you have yourself not compared both a 2k and a 4k DLP and the Sony VW1000ES with actual 4k content at suitable viewing distances
I didn't personally but we have the chance on a french forum to have a pro who did. This 30 years-experienced guy has access to virtually all pro cinema 2K and 4K dci-compliant machines (Nec, Christie, Sony. I am not sure for Barco) and also to high-end "consumer" machines (the 1000ES, the SIMs, the JVCs etc.). It also has pro devices and sensors to test them that you couldn't ever buy because of their prices... Discussions are sometimes "hot", especially when resellers are not agree with him, you can easily imagine... Nevertheless the discussions with him are really interesting because he says what he thinks and always test before speaking. He also always fight against vaporwave or over-evaluated pj. I learn a lot thanks to him in 10 years.
Damned, what a long post. I expect my english is not too rough...
Regards,
Emmanuel