If It's 3-D, It's (Maybe) 2K

by Michael Karagosian
©2009 MKPE Consulting LLC All rights reserved worldwide
originally published in the 15 June 2009 issue of Digital Cinema Report

While most people are aware that the DCI Specification calls for a compatible distribution of images having either 2K or 4K resolution, there are several related issues that are worth explaining. One of these is the natural limit in resolution of 3-D images.

A 2K image, as delivered to the cinema, has either a width of 2048 pixels, or a height of 1080 pixels. For 4K, these numbers double, allowing either an image width of 4096 pixels, or an image height of 2160 pixels. Digital cinema picture data is compressed using the JPEG2000 algorithm, the nature of which allows a 4K image to contain a 2K image. This feature allows a single 4K distribution to play in either a 4K or a 2K server and projector.

Compression reduces the amount of data required to store an image. Heavy use of compression produces smaller files, light use of compression produces larger files. Heavy compression can produce visible artifacts, light compression can result in visually lossless images. Heavy compression requires a lower bit rate, or lower bandwidth, in the system electronics, and light compression requires a high bit rate, or higher bandwidth.

In practical systems, one needs limits. When it comes to the degree of image compression, the director and producer determine the lower bandwidth limit, as too low a bandwidth produces visual artifacts. The high bandwidth limit is set by DCI. The DCI specification calls for a maximum bandwidth of 250 Mb/s for image data. If this limit wasn't in place, equipment developers would arbitrarily pick a limit for their products, and without direction, they wouldn't all pick the same limit. Neither would movie directors, who would likely push for high bandwidths for their images, only to learn later that not all digital cinema systems can support their choice. The consequence would be disastrous. There would be no guarantee that a movie plays on one's digital cinema system.

While the bandwidth limitation is necessary, it imposes other constraints. The upper bandwidth limit of 250 Mb/s for image data is for both 2K and 4K images. Since 4K images have 4 times as many pixels as 2K images, the maximum bandwidth allowed per pixel in a 4K image is only 1/4 that of a 2K image. This and other factors that affect the perception of quality, such as contrast and detail in the blacks, are not revealed in the simple comparison of image resolution numbers.

The limit on bandwidth also sets a natural limit for frame rates. DCI wisely included the 48 frame rate in its specification. See Table 1 below, directly taken from Table 1 of the DCI specification:

DCI Image Structure

With a 48 frame rate image, the total number of pixels in any time period are double that of 24 frame rate material. Putting this in the same framework as for the earlier 4K/2K comparison, each pixel of a 48 frame rate image has 1/2 the maximum bandwidth allocation of a 2K image. This sits nicely in-between the maximums allowed for 2K and 4K images.

If you follow the logic, to include a 48 frame image at 4K within the maximum bandwidth allowed by DCI would then reduce the available bandwidth per pixel to 1/8 that of a 2K image. This is deemed to be too low for a quality presentation, so 48 frame rate content is limited to 2K.

Let's apply this to 3-D images. 3-D images are only distributed at the 48 frame rate. From Table 1 above, one can see that 3-D images will only be 2K. DCI does not allow 48 frame rate 3-D at 4K as there isn't enough bandwidth available at that frame rate and resolution to produce a quality image.

Now, how many projectors actually display full 2K images in 3-D is another little secret of the industry. The answer is: not all of them. In fact, only two types of projectors, the "higher brightness" version of the 1.2" DLP array designs, and all of the .98" DLP arrays, can actually produce 3-D in full 2K. All other projectors display less than 2K in 3-D.

If you think this situation would not meet DCI approval, you might be surprised to learn that, at least at this time, DCI does not specify 3-D in its system specification. DCI only specifies the 48 frame rate capability.

Have I thoroughly confused you? Just remember, if it's 3-D, it's 2K, or less, or something like that.