Digital Projector Standards Setup

What is the Setup for a Digital Cinema X'Y'Z' Digital Projector?

In practice there are two normal setups for a P3 compliant digital projector. The setup for a Digital Cinema projector in XYZ color space is:

White Point
 Y = 14.0 ft. L. [ 48.0 cd/m^2] x = 0.314 y = 0.351

2.6 gamma XYZ [gamma XYZ is referred to as X'Y'Z']

for a 12 bit "white frame" with 2.6 gamma XYZ [gamma XYZ is referred to as X'Y'Z'] code values of

 X' = 3794 Y' = 3960 Z' = 3890

What is the P3 Setup for a DI Digital Projector?

The setup for a P3 Digital Intermediate projector in P3 RGB gamma 2.6 color space is:

White Point
 Y = 15.276 ft. L. [ 52.37 cd/m^2] x = 0.314 y = 0.351

for a 12 bit "white frame" with 2.6 gamma P3 code values of

 R = 4095 G = 4095 B = 4095

for a 10 bit "white frame" with 2.6 gamma P3 code values of

 R = 1023 G = 1023 B = 1023

Alternatively, the White Point may be setup at 14 ft. L but with a different "white frame" code value:

White Point
 Y = 14.0 ft. L. [ 48.0 cd/m^2] x = 0.314 y = 0.351

for a 12 bit "white frame" with 2.6 gamma P3 code values of

 R = 3960 G = 3960 B = 3960

for a 10 bit "white frame" with 2.6 gamma P3 code values of

 R = 989 G = 989 B = 989

Derivation of the Code values and P3 RGB Luminance

The Digital Cinema X'Y'Z' code values for white were set such that a wide range of "artistic" white points for the project can ALL achieve 14 ft. L. on the digital projector. This means that for the "P3 White Point Chromaticity" in the Digital Cinema specifications the maximum achievable luminance must be lowered to allow other color white points to achieve 14 ft. L. without clipping one or more of the channels.

For example, the X'Y'Z' code values [CV] for the white frame are:

 DCI X'Y'Z' White Frame CV X' = 3794 Y' = 3960 Z' = 3890 0-1.0 [gamma 1.0] XYZ 0.8200 0.9165 0.8750 XYZ to P3 [gamma 1.0] 0.9165 0.9165 0.9165 P3 [gamma 1.0/2.6] 0.9670 0.9670 0.9670 P3 10 bit [gamma 1.0/2.6] 989 989 989 P3 12 Bit [gamma 1.0/2.6] 3960 3960 3960

The transform of X'Y'Z' to XYZ is done by dividing by the maximum CV [4095 in 12 bit] and raising the result to a 2.6 power. The result is XYZ [0-1.0].

The XYZ values are converted to P3 by the XYZ to P3 matrix:

 XYZ to P3 2.7254 -1.0180 -0.4402 -0.7952 1.6897 0.0226 0.0412 -0.0876 1.1009

The result of the matrix transform to P3 [gamma 1.0] are equal values and therefore are a specific luminance of a P3 chromaticity white position.

In RGB P3 color space this means that to setup a P3 digital projector, the full on [1023,1023,1023 or 4095,4095,4095 CV] should be (14 ft. L. / 0.9165) = 15.276 ft. L.

Conversion of the gamma 1.0 P3 to gamma 1.0/2.6 and then to integer 10 bit or 12 bit gives the target CV for a white frame in P3 space that has the same attainable luminace as that of a X'Y'Z' setup projector. In this case, white point luminance of 15.276 ft. L.

 DCI X'Y'Z' White Frame CV X' = 3794 Y' = 3960 Z' = 3890 X'Y'Z' * (4095/3960) X' = 3923 Y' = 4095 Z' = 4023 0-1.0 [gamma 1.0] XYZ 0.8946 1.000 0.9547 XYZ to P3 [gamma 1.0] 1.000 1.000 1.000 P3 10 bit [gamma 1.0/2.6] 1023 1023 1023 P3 12 bit [gamma 1.0/2.6] 4095 4095 4095