OK here's how the arithmetic goes.
In both cases current brightness of the original 16:9 screen = 100%.Zooming
Zoom by 1.33 vertically and horizontally.
1. New area of the image will be 4/3 * 4/3 = 16/9 times the size of the old area (includes black bars).
2. New brightness is the inverse
of the increase in area = 9/16 or 56.25% of the old brightness.
Optics Note: the "Aperture Effect"
Zooming the projector lens (effectively reducing the focal length) has the effect of increasing the effective aperture, that is, decreasing the effective f-stop value of the lens. For example an f3.1 zoom lens at a 40mm focal length may become an f2.9 lens at a wider (zoomed out) focal length of 30mm. Of course, the widening of the aperture means definition will be lost as well, as more light rays from the imaging chip are passing through the glass of the lens then when it was zoomed narrower.
3. So, because we have zoomed the lens wider to fill the 'scope screen we can add back some extra brightness
due to the "Aperture Effect". This is usually about 10%, making the final brightness 56.25% * 1.1 = 61.9% of the original unzoomed picture brightness
There is no zooming of the projector lens involved with an anamorphic lens. The factors to consider are:
* Transmission loss (internal reflections, density of glass).
* Widening of the image.
1. Transmission loss is usually set around 3.5% or less (depending on how much glass there is in the lens) and how well it is anti-reflection (AR) coated. An uncoated lens will lose around 7-15% per surface, while a coated lens will lost around 0.4% per surface. But let's be pessimistic and leave this figure at the full 3.5%. Our "100%" figure (the original brightness of the image without a lens in front of the projector) is reduced to 96.5%.
2. We are now dealing with only 96.5% of the original light and must still widen the beam by 1.33x. Note, however, that there is no increase in the height, as we're only expanding the image, not zooming it bigger. So the total increase in area is 4/3, due to horizontal expansion only. Applying our inverse rule to figure out the brightness we arrive at the anamorphically expanded image being 75% * 96.5% = 72.4% as bright as the original image
.Comparing the two
The anamorphic image is 72.4% as bright as the original 16:9 image.
The zoomed image is 61.9% as bright as the original 16:9 image.Dividing 72.4% by 61.9 gives us the result that the anamorphic image is 72.4/61.9 = 1.169, or about 17% brighter than the zoomed image
Because you are zooming only about 3/4 of the pixels of the original image with the "Zoom" method, you are losing one-quarter of them off the top and bottom of the screen. 1,920 * 1,080 pixels = 2,073,600 pixels. One quarter of these is 518,400 pixels lost during the process of the zoom method. That's more than a whole DVD screen's worth (345,000 pixels at 480p) of detail sacrificed.
Anamorphic lenses, using ALL pixels, lose ZERO.
To make this starker, consider a 4K projector. Zooming a 4K projector still loses 1/4 of the pixelscompared to using an anamorphic lens. There are 3,840 * 2160 = 8,294,400 pixels in a 4K image. One quarter of this is 2,073,600 pixels lost.Yes, that's right: when you zoom a 4K projector you throw away the equivalent of 1 whole Blu-Ray image's worth of pixels.
Imagine your present 1920 x 1080 screen full of fine detail. Now throw it away. I dare you! THAT's how much detail - or perhaps I should say, "fineness of detail", or "smoothness" - you lose when you don't use an anamorphic lens with 4K.There are many other advantages to using anamorphics, but these two - the extra brightness and the extra smoothness - are two of the most significant.