Interlaced is sending 1/2 the vertical resolution on each frame (odd lines) and reconstructing full frames prior to display. It is really that simple. Effectively it means a 1080i 60hz interlaced signal is only effectively showing you the equivalent 1080p / 30 at most. Probably actually 24p, which means you get the full 1080p/24 in a broadcast signal, but the cadence is off and it's up to the TV or set top box to make it progressive again and do the pulldown from 30hz to 24hz. (if at all. cadence can be changed prior to broadcast at the source).
As others have written here, all LCDs and plasmas and so on display progressive scan. Interlaced signals take 2 frames to make 1 final one.
Not in terms of motion. There's a reason they don't shoot live sport at 1080p25 - it would judder too much. They shoot it at 50i or 60i (or progressive 50/60) to give much smoother motion than p24/p25. So it isn't showing effectively equivalent to 1080p30 - unless the source was shot 1080p30 and transmitted in a 1080i signal. In terms of total recorded lines 1080p30 and 1080/60i will be the same, but in smoothness of motion (temporal resolution) 60i provides the most (given appropriate de-interlacing - eg. to 10080p60).
Interlaced signals take 2 frames to make 1 final one
I think you meant two fields to make one frame - but that's not true for content shot in interlaced mode and de-interlaced with a de-interlacer that keeps the motion in the source (eg. keeps 60 different images per second - eg. line doubling would be a simple but low resolution de-interlacing method that would).
You don't mention frame rate. Interlaced shot content has twice the number of samples taken per second. So 1080p24 has 24 pictures per second, 1080p25 has 25 pictures per second, and interlaced 1080i25 (50i) has 50 pictures per second. So when, at the same frame rate, interlaced has twice as many pictures of the scene taken per second, why do you say progressive is smoother? If you're using progressive at 60 fps that will look just as smooth as 60i, and should look better, depending on bitrate. But you need to say more about the content type and frame rate. On Blu-ray, 1080p24 is the only full HD progressive format currently, which will give a lot less smooth motion than 1080i25 (50i) or 1080i30 (60i).
Thanks for your reply sharing your info, I should have mentioned that I film always 60 fps and I was comparing only these frame rates, however it's known that progressive is better for capturing moving objects / speed / sport I understand that interlace might put more pictures per second but it the progressive broadcast itself that is more superior / relaxed filling the screen in the way it works( let's don't get there I bet this has been a long discussion previously) , it's normal for interlace to give in more images per second to compensate...I'll compare it to a diesel and petrol engine both are fast and effective and give us the same result more or less but both has prons and cons, if progressive works for me it might not work for someone else, it depends on what you are filming and the screen you are watching your content on, again I am no pro I am just an end user comparing 2 different filming techniques resulting in full hd represented in a different way .
I always say this in my comments technology is not all about facts and figures more than its self experiment and own believe, your eye is your judge.
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