# High Dynamic Range D-Cinema Addendum

Version 1.0
(build f18141e)
Approved for Distribution October 14, 2022
Digital Cinema Initiatives, LLC, Member Representative Committee

## Front Matter🔗

### Notice🔗

Digital Cinema Initiatives, LLC (DCI) is the author and creator of this specification for the purpose of copyright and other laws in all countries throughout the world. The DCI copyright notice must be included in all reproductions, whether in whole or in part, and may not be deleted or attributed to others. DCI hereby grants to its members and their suppliers a limited license to reproduce this specification for their own use, provided it is not sold. Others should obtain permission to reproduce this specification from Digital Cinema Initiatives, LLC.

This document is a specification developed and adopted by Digital Cinema Initiatives, LLC. This document may be revised by DCI. It is intended solely as a guide for companies interested in developing products, which can be compatible with other products, developed using this document. Each DCI member company shall decide independently the extent to which it will utilize, or require adherence to, these specifications. DCI shall not be liable for any exemplary, incidental, proximate or consequential damages or expenses arising from the use of this document. This document defines only one approach to compatibility, and other approaches may be available to the industry.

This document is an authorized and approved publication of DCI. Only DCI has the right and authority to revise or change the material contained in this document, and any revisions by any party other than DCI are unauthorized and prohibited.

Compliance with this document may require use of one or more features covered by proprietary rights (such as features which are the subject of a patent, patent application, copyright, mask work right or trade secret right). By publication of this document, no position is taken by DCI with respect to the validity or infringement of any patent or other proprietary right. DCI hereby expressly disclaims any liability for infringement of intellectual property rights of others by virtue of the use of this document. DCI has not and does not investigate any notices or allegations of infringement prompted by publication of any DCI document, nor does DCI undertake a duty to advise users or potential users of DCI documents of such notices or allegations. DCI hereby expressly advises all users or potential users of this document to investigate and analyze any potential infringement situation, seek the advice of intellectual property counsel, and, if indicated, obtain a license under any applicable intellectual property right or take the necessary steps to avoid infringement of any intellectual property right. DCI expressly disclaims any intent to promote infringement of any intellectual property right by virtue of the evolution, adoption, or publication of this document.

## 1 Introduction🔗

With the publication by Digital Cinema Initiatives, LLC, (DCI) of version 1.0 of the Digital Cinema System Specification in July 2005, DCI recognized that digital cinema had the potential to significantly improve the movie-going experience for the public. In the years since version 1.0, technological developments and innovation have realized that potential in many areas of picture and sound reproduction. Now, further advances in High Dynamic Range (HDR) technology in both reflective projectors and direct view displays offer new opportunities to enhance the theatrical motion picture experience.

DCI believes that these new HDR opportunities require a rational, empirical basis for setting image parameters. To this end, DCI has conducted extensive image testing, employing both lay and expert viewers. The requirements in this addendum are the considered results of these investigations, specified for both reflective and direct view image devices. The DCI member companies believe that their utilization will provide real and achievable benefits to theater audiences, theater owners, filmmakers and distributors.

The proper presentation of a High Dynamic Range Digital Cinema Distribution Master (HDR-DCDM) requires the definition of an HDR Reference Display and controlled environment. This specification defines the HDR Reference Display and specifies the tolerances around the critical image parameters for Review Rooms and Exhibition Theaters so that consistent and repeatable image quality can be achieved.

## 2 Scope🔗

This specification defines the HDR Reference Display and its controlled environment, along with the acceptable tolerances around critical image parameters for Review Room and Exhibition Theater applications. The HDR Reference Display may be an HDR projection system or a direct view display.

The goal is to provide a means for achieving consistent and repeatable color image quality. The HDR Reference Display is a practical device. The nominal parameters are based on industry experience and have been demonstrated by commercially available HDR displays in controlled environments. Two levels of tolerances are specified, a tighter tolerance for Review Rooms where critical color judgments are made, and a wider tolerance for satisfactory reproduction in Exhibition Theaters used for general public viewing. (The use of the term “Review Room” includes the mastering environment where creative color decisions are made on a displayed image.)

This document shall be integrated into DCI’s Digital Cinema System Specification.

## 3 Normative References🔗

The names of standards publications and protocols are placed in [bracketed text]. International and industry standards contain provisions which, through reference in this text, constitute provisions of this specification. The most recent editions of the referenced standards shall be valid unless otherwise exempted in this specification. These referenced standards are subject to revision, and parties to agreements based upon this specification are encouraged to investigate the possibility of applying the most recent edition of the referenced standards.

• ISO 11664-1, Colorimetry -- Part 1: CIE standard colorimetric observers
• ISO 11664-3, Colorimetry -- Part 3: CIE tristimulus values
• ISO/CIE 11664-5, Colorimetry -- Part 5: CIE 1976 L*u*v* colour space and u′, v′ uniform chromaticity scale diagram
• ISO/CIE 11664-6, Colorimetry -- Part 6: CIEDE2000 Colour-difference formula
• SMPTE ST 377:2004, Material Exchange Format (MXF) — File Format Specification
• SMPTE ST 428-1, D-Cinema Distribution Master (DCDM) — Image Characteristics
• SMPTE ST 431-1, Screen Luminance Level, Chromaticity and Uniformity for D-Cinema Quality
• SMPTE RP 431-2, Reference Projector and Environment for D-Cinema Quality
• SMPTE ST 2084, High Dynamic Range Electro-Optical Transfer Function of Mastering Reference Displays
• SMPTE ST 2113, Colorimetry of P3 Color Spaces

## 4 Terms and Definitions🔗

For the purposes of this document, the following terms and definitions apply.

### 4.1 Edit Unit🔗

The smallest unit of d-cinema content that can be successfully edited while maintaining the integrity of the content. The edit unit value shall be an integer multiple of the duration of a single d-cinema frame. In most cases, the edit unit value is the same as the frame duration, but in certain applications, the value can be >1 (for example, stereoscopic d-cinema requires an edit unit value twice that of the frame duration).

### 4.2 Minimum Active Black Level🔗

The Minimum Active Black Level of an HDR Reference Display is the lowest luminance level above code value 0 reproduced within the specified uniformity tolerance.

### 4.3 Double Prime Notation🔗

The double prime notation (e.g., X″) is used to indicate a value encoded using the [SMPTE ST 2084] Electro-Optical Transfer Function (EOTF).

### 4.4 HDR Digital Cinema Distribution Master (HDR-DCDM)🔗

The HDR Digital Cinema Distribution Master (HDR-DCDM) is a [SMPTE ST 428-1] DCDM that contains images and subtitles that are graded to be played on an HDR playback system, adhering to an EOTF complying with [SMPTE ST 2084].

### 4.5 HDR Digital Cinema Package (HDR-DCP)🔗

The HDR Digital Cinema Package (HDR-DCP) is a DCP that is made from the HDR-DCDM. When unpackaged, decrypted and decoded, the image is visually indistinguishable from the original HDR-DCDM image.

## 5 Input Requirements🔗

The HDR Reference Display shall support the HDR-DCDM, with full-range 12 bit image data formatted for [SMPTE ST 2084] EOTF with [ISO/CIE 11664] XYZ colorimetry at 2048x1080 or 4096x2160 image structures and frame rates as described in Table 1.

### 5.1 Signaling HDR in DCP Packaging🔗

HDR content shall be identified by the presence of an HDR flag in both [SMPTE ST 377:2004] MXF and CPL metadata, which indicates that the EOTF is [SMPTE ST 2084].

For MXF picture track files that carry HDR essence, this fact shall be signaled using the "Transfer Characteristic" property of the MXF "Generic Picture Essence Descriptor" to indicate the EOTF is [SMPTE ST 2084]. The UL value to be used shall be 06.0E.2B.34.04.01.01.0D.04.01.01.01.01.0A.00.00.

Composition Playlists containing picture track files that carry HDR essence shall signal this fact using [SMTPE ST 429-16] Metadata as follows:

Scope: http://www.dcimovies.com/schemas/2018/HDR-Metadata Image Encoding Parameters EOTF ST 2084

Below is an example excerpt from such a Composition:

<ExtensionMetadata scope="http://www.dcimovies.com/schemas/2018/HDR-Metadata">
<Name>Image Encoding Parameters</Name>
<PropertyList>
<Property>
<Name>EOTF</Name>
<Value>ST 2084</Value>
</Property>
</PropertyList>


### 5.2 Device Behavior🔗

Devices shall display content in HDR mode when presented with a Composition Playlist and MXF Transfer Characteristic containing the signaling specified in Section 5.1.

### 5.3 Edit Unit🔗

The HDR Reference Display shall support the content frame rates in Table 1, expressed in Edit Units per second:

Table 1: Edit Units Per Second Requirements for HDR Reference Display🔗
Edit Unit/Sec. 2K 2D 2K 3D 4K 2D
24 Required Required Required
48 Required Required Required
60 Required Required Required
96 Required
120 Required

Support for HDR stereoscopic presentations is optional; “Required” in the 2K 3D category of Table 1 applies only to displays in which HDR stereoscopic exhibition is implemented.

Stereoscopic HDR implementations have yet to be sufficiently demonstrated to DCI. Therefore, parameters for stereoscopic HDR are reserved for this specification. Additional requirements for stereographic HDR may be specified by DCI in a future specification.

## 6 Standard Dynamic Range (SDR) Mode🔗

An HDR system in SDR Mode shall display SDR content in a manner that emulates the SDR display on which the content was mastered, including to [SMPTE ST 431-1]. An HDR system in SDR Mode shall not reproduce screen black level values lower than 0.01 cd/m2. In SDR Mode, the grayscale tracking shall conform to [SMPTE RP 431-2], with the exception that screen black level shall only be displayed at luminance levels at or above 0.01 cd/m2.

## 7 Initial Conditions🔗

The display shall be turned on and allowed to thermally stabilize for 20 to 30 minutes prior to all measurements. The room lights shall be turned off, except for the minimal lighting provided for working or safety reasons.

The display shall be calibrated to the target image parameters before final measurements are made.

## 8 Environment🔗

### 8.1 Ambient Luminance🔗

An HDR Reference Display can be either a reflective projector or a direct view display. Stray light reflected from the screen or display should be minimized. Black, non-reflective finishes on all surfaces, along with recessed lighting, should be used.

With the device turned off, measure the luminance of the center of the screen. For both Review Rooms and Exhibition Theaters, the ambient light level measured in the center of the screen should be less than or equal to 0.005 cd/m2. Safety regulations and the placement of exit lights or access lights may result in a higher ambient light level, but it should be noted that this will reduce the contrast of the resulting image.

### 8.2 Reference Viewing Position for Color Grading🔗

The reference viewing position for color grading shall be at a viewing distance of 1.5 to 3.5 screen heights (for constant height presentation), or if constant width is used for both 2.39:1 and 1.85:1 aspect ratios, then this viewing distance refers to the height of the 1.85:1 picture. Lighting on work surfaces or consoles should be masked and filtered to eliminate any spill onto the display.

## 9 HDR Mode Image Parameters🔗

All image parameters shall be measured as light from the screen or display, with the measurements made from the reference viewing position in the Review Room, or from the center of the normal seating area in an Exhibition Theater.

### 9.1 Luminance Uniformity🔗

The variance in the measured luminance from the center to the sides and corners of the screen or display shall not exceed the specified tolerances in Table 2 as measured per [SMPTE RP 431-2].

### 9.2 Calibration White Points and Luminance🔗

When the HDR Reference Display is sent a full frame image with the code values 2060 X″, 2081 Y″, 2116 Z″, the chromaticity coordinates of the displayed image shall be x = 0.3127, y = 0.3291. These code values shall produce a displayed luminance of 100.1 cd/m2 within the specified tolerances in Table 2.

When the HDR Reference Display is sent a full frame image with code values 2524 X″, 2546 Y″, 2583 Z″, the chromaticity coordinates of the displayed image shall be x = 0.3128, y = 0.3290. These code values shall produce a displayed luminance of 299.6 cd/m2 within the specified tolerances in Table 2.

Behavior of code values representing output luminance exceeding 299.6 cd/m2 is undefined.

Other creative white points are possible and can be accommodated, albeit with some marginal differences in peak luminance. Refer to Table 5 for examples of alternative creative white points.

In the event that display or projection technology is developed that is able to meet all provisions of this specification (e.g., peak luminance, screen black level, etc.) but is unable to meet the full-screen luminance requirements stated in this section, DCI leaves open the possibility of developing a new application profile to accommodate such technology.

### 9.3 Minimum Active Black Level🔗

Minimum Active Black Level shall be 0.005 cd/m2 and shall not exceed the specified tolerances in Table 2. Behavior of code values representing output luminance below 0.005 cd/m2 but greater than zero is undefined.

When the HDR Reference Display is sent a full frame images with the code values 60 X″, 62 Y″, 65 Z″, the chromaticity coordinates of the displayed image shall be x = 0.3095, y = 0.3296. These code values shall produce a displayed luminance of 0.005 cd/m2 within the specified tolerances in Table 2.

Minimum active black level shall be measured in a manner that minimizes or eliminates the contribution of ambient light.

### 9.4 White Chromaticity Uniformity🔗

The variance in displayed chromaticity across the display shall not exceed the specified tolerances in Table 2.

### 9.5 Electro-Optical Transfer Function🔗

#### 9.5.1 Encoding Function🔗

The encoding transfer function shall be defined in terms of output-referred [ISO 11664] XYZ tristimulus values produced by the HDR Reference Display unit. The HDR transfer functions are specified using 12bit [SMPTE ST 2084] XYZ Encoding Primaries and [SMPTE ST 2084] EOTF, as shown below:.

where:

${k}_{0}=10,000$, ${k}_{1}=4095$, ${m}_{1}=\frac{2610}{4096}\cdot \frac{1}{4}$, ${m}_{2}=\frac{2523}{4096}\cdot 128$, ${c}_{1}={c}_{3}-{c}_{2}+1$, ${c}_{2}=\frac{2413}{4096}\cdot 32$ and ${c}_{3}=\frac{2392}{4096}\cdot 32$

and the unary function $floor\left(\right)$ yields the largest integer not greater than its argument.

If the data is transported over certain interfaces (like Serial Digital Interface), code values 0-15 and 4080-4095 are reserved (illegal) code values and these code values will be clipped (see [SMPTE ST 372]).

#### 9.5.2 Decoding Function🔗

The following equations can be used to compute X, Y and Z from a set of code values:

#### 9.5.3 Tracking Performance🔗

EOTF tracking performance shall be measured at the code-values described in Table 3 and Table 4 with the tolerances identified in Table 2.

### 9.6 Color Volume🔗

The HDR color volume is a cuboid with vertices determined by the XYZ coordinates of the three color primaries, the white point, and the black point. The color primaries and white point in Table 2 define the minimum color volume for an HDR Reference Display.

### 9.7 Color Accuracy🔗

Within the minimum color volume, all colors shall be accurately reproduced. Table 2 defines tolerances for the color primaries of the minimum color volume. Table 5 provides exact chromaticity and luminance values for a set of test code values that fall within these tolerances.

## Annex A Normative HDR Mode Tables🔗

The HDR Reference Display image parameters and tolerances for the displayed image in Review Rooms and Exhibition Theaters, as measured from the display or screen, and including the room ambient light, are summarized in Table 2. Where the nominal parameters are specified as minimums, it is understood that these parameters shall not be constrained from future improvements as the technology progresses.

Tolerances for Electro-Optical Transfer Function distortion (measured as a percentage error) are calculated as follows:

Percentage error = 100*((measured luminance - target luminance) / target luminance)

where target luminance is derived by decoding the input code value using the decoding equation in Section 9.5.2, using the ranges and tolerances specified in Table 2.

Table 2: Image Parameters & Tolerances for HDR Reference Display🔗
Section Parameter Nominal HDR Reference Projector HDR Direct View Display
Review Room Tolerance Exhibition Theater Tolerance Review Room Tolerance Exhibition Theater Tolerance
9.1, 9.2 Luminance, center, Peak Luminance, White-1 D65 299.6 cd/m2 (87.6 fL) ± 18.0 cd/m2 ± 30.0 cd/m2 ± 9.0 cd/m2 ± 9.0 cd/m2
Luminance, Screen Average, White-1 D65 299.6 cd/m2 (87.6 fL) N/A N/A ± 9.0 cd/m2 ± 9.0 cd/m2
Luminance, sides 299.6 cd/m2 (87.6 fL) 85% to 100% of center 75% to 100% of center ± 9.0 cd/m2 ± 9.0 cd/m2
Luminance, corners 299.6 cd/m2 (87.6 fL) 85% to 100% of center Not Specified ± 9.0 cd/m2 ± 9.0 cd/m2
9.3 Minimum Active Black Level 0.005 cd/m2 (0.0003 fL) ± 0.001 cd/m2 ± 0.001 cd/m2 ± 0.001 cd/m2 ± 0.001 cd/m2
9.4 White chromaticity, center, Peak Luminance, White-1 D65 x = 0.3127
y = 0.3290
± 0.002 x
± 0.002 y
± 0.006 x
± 0.006 y
± 0.002 x
± 0.002 y
± 0.006 x
± 0.006 y
White chromaticity uniformity, corners (tolerance from center) ± 0.000 x
± 0.000 y
± 0.008 x
± 0.008 y
± 0.015 x
± 0.015 y
± 0.008 x
± 0.008 y
± 0.015 x
± 0.015 y
9.5 Electro-Optical Transfer Function Per [SMPTE ST 2084] Y≦0.02 cd/m2 ± 20%; 0.02<Y≦1.0 cd/m2 ± 5%; 1.0<Y≦299.6 cd/m2 ± 3% Y≦0.02 cd/m2 ± 20%; 0.02<Y≦1.0 cd/m2 ± 5%; 1.0<Y≦299.6 cd/m2 ± 3% Y≦0.02 cd/m2 ± 20%; 0.02<Y≦1.0 cd/m2 ± 5%; 1.0<Y≦299.6 cd/m2 ± 3% Y≦0.02 cd/m2 ± 20%; 0.02<Y≦1.0 cd/m2 ± 5%; 1.0<Y≦299.6 cd/m2 ± 3%
9.6 Color Volume Volume in XYZ space defined by the black point & the following points expressed in (Y,x,y), representing a 299.6 nits P3D65 color volume: Red (68.69, 0.6800, 0.3200), Green (207.52, 0.2650, 0.6900), Blue (23.79, 0.1500, 0.0600), Peak White (299.6, 0.3127, 0.3290) N/A N/A N/A N/A
9.7 Color Accuracy The following points are expressed in (x,y): Red (0.6800, 0.3200), Green (0.2650, 0.6900), Blue (0.1500, 0.0600) Red (0.6800 ± .01, 0.3200 ± .01), Green (0.2650 ± .02, 0.6900 ± .02), Blue (0.1500 + 0.01/- 0.03, 0.0600 + 0.02/- 0.04) Red (0.6800 ± .01, 0.3200 ± .01), Green (0.2650 ± .02, 0.6900 ± .02), Blue (0.1500 + 0.01/- 0.03, 0.0600 + 0.02/- 0.04) Red (0.6800 ± .01, 0.3200 ± .01), Green (0.2650 ± .02, 0.6900 ± .02), Blue (0.1500 + 0.01/- 0.03, 0.0600 + 0.02/- 0.04) Red (0.6800 ± .01, 0.3200 ± .01), Green (0.2650 ± .02, 0.6900 ± .02), Blue (0.1500 + 0.01/- 0.03, 0.0600 + 0.02/- 0.04)
Table 3: Black-To-White Gray Step-Scale Test Pattern Code Values, Luminance Values, & Chromaticity Coordinates.🔗
Input Code Values Output Chromaticity Coordinates Output Luminance
Step Number X″ Y″ Z″ x y Y, cd/m2
1 472 481 496 0.3126 0.3292 0.50
2 603 614 632 0.3122 0.3292 1.00
3 758 771 792 0.3121 0.3293 2.00
4 1000 1015 1040 0.3124 0.3291 5.00
5 1211 1227 1255 0.3128 0.3288 10.00
6 1444 1462 1492 0.3128 0.3291 20.00
7 1783 1803 1836 0.3126 0.3292 50.01
8 2060 2081 2116 0.3127 0.3291 100.10
9 2350 2372 2408 0.3127 0.3292 200.21
10 2524 2546 2583 0.3128 0.3290 299.64
All measurements are made in the center of the Screen.
Table 4: Black-To-Dark Gray Step-Scale Test Pattern Code Values, Luminance Values, & Chromaticity Coordinates🔗
Input Code Values Output Chromaticity Coordinates Output Luminance
Step Number X″ Y″ Z″ x y Y, cd/m2
1 60 62 65 0.3095 0.3296 0.0050
2 74 76 79 0.3134 0.3302 0.0075
3 86 88 92 0.3133 0.3281 0.0100
4 105 108 112 0.3124 0.3309 0.0151
5 121 124 129 0.3129 0.3293 0.0202
6 157 161 167 0.3125 0.3300 0.0352
7 185 189 196 0.3138 0.3291 0.0501
8 221 226 234 0.3131 0.3296 0.0752
9 250 255 265 0.3129 0.3279 0.0998
10 332 339 351 0.3121 0.3289 0.1997
All measurements are made in the center of the Screen.
Table 5: Color Accuracy Color Patch Code Values, Luminance Values, & Chromaticity Coordinates🔗
Input Code Values Output Chromaticity Coordinates Output Luminance
Patch X″ Y″ Z″ x y Y, cd/m2
Red-1 2234 1925 68 0.6787 0.3202 68.13
Green-1 1988 2387 1327 0.2651 0.6899 207.35
Blue-1 1871 1525 2565 0.1501 0.0602 23.86
Cyan-1 2218 2434 2583 0.1998 0.3320 231.33
Magenta-1 2383 2049 2565 0.3362 0.1515 92.58
Yellow-1 2423 2510 1327 0.4380 0.5357 275.80
Red-2 2169 1899 1058 0.6401 0.3300 63.83
Green-2 2110 2402 1674 0.3001 0.6001 214.73
Blue-2 1834 1491 2524 0.1501 0.0602 21.70
Cyan-2 2280 2443 2576 0.2245 0.3288 236.21
Magenta-2 2322 2016 2533 0.3213 0.1541 85.39
Yellow-2 2432 2513 1731 0.4190 0.5054 277.72
White-1 D65 2524 2546 2583 0.3128 0.3290 299.64
White-2 D60 2509 2530 2534 0.3217 0.3376 288.81
White-3 D55 2493 2513 2478 0.3319 0.3476 277.72
The accuracy with which these colors shall be displayed is given in Table 2.

## Annex B Subjective Parameters (informative)🔗

The following parameters are also important to picture quality, but because they are difficult to measure with today’s readily available instrumentation, they are generally assessed subjectively.

Instrumentation designers are encouraged to design and manufacture equipment that can be used to translate subjective parameters into objective performance characterization.

## B.1 Grayscale Tracking🔗

Using the black-to-white gray step-scale test pattern, the entire step-scale appears neutral without any visible color non-uniformity. The black-to-white gray step-scale test pattern is centered on the display and occupies a rectangle sized 20% of the screen height by 80% of the screen width. The background is defined by code values [1000 1015 1040], which define a luminance of 5.0 cd/m2 and chromaticity coordinates x = 0.3124 y = 0.3291. Each step is 8% of the screen width and is defined by the code values in Table 3.

Using the black-to-dark gray step-scale test pattern, the entire step-scale appears neutral without any visible color non-uniformity. The black-to-dark gray step-scale test pattern is centered on the display and occupies a rectangle sized 20% of the screen height by 80% of the screen width. The background is defined by code values [122 124 129], which define a luminance of 0.020 cd/m2 and chromaticity coordinates x = 0.3129 y = 0.3293. Each step is 8% of the screen width and is defined by the code values in Table 4.

## B.2 Contouring🔗

Contouring is the appearance of steps or bands where only a continuous or smooth gradient is expected. Because contouring is a function of many variables, it is important to look at a series of test patterns with shallow gradations to simulate naturally occurring gradations in images.

Examples include horizons, particularly at sunset or sunrise, and the natural falloff around high intensity spotlights, particularly if diffused by atmosphere or lens filtration. These test pattern ramps have a step width of no less than 4 pixels with an increment of one code value per step and are placed on a background equal to the minimum value in the ramp, so that the eye is adapted for maximum sensitivity.

Since dynamic fades to black are widely used in real-world content, a dynamic test pattern that fades slowly to black is another useful approach.

Each image is viewed in the proper environment as defined in Section 7, and ought not to exhibit any contouring (step in luminance), or color deviation from the neutral gray.

## Annex C D65 Color Primaries, White Point and Color Conversions (Informative)🔗

The color image encoding parameters for today’s HDR Reference Displays and the corresponding color conversion steps to convert from P3D65 R′G′B′ to X″Y″Z″ and from X″Y″Z″ to P3D65 RGB are shown here as an example for implementation. P3D65 is defined in [SMPTE ST 2113].

### C.1 Color Primaries🔗

Table 6: Chromaticity Coordinates of Primaries.
Encoding Primaries
R (x, y) = (0.6800, 0.3200)
G (x, y) = (0.2650, 0.6900)
B (x, y) = (0.1500, 0.0600)

### C.2 White Reference🔗

Table 7: Chromaticity Coordinates of Primaries. x, y refers to the chromaticity coordinates defined by [ISO 11664].
White Reference
(x, y) = (0.3127,0.3290)

### C.3 Luminance🔗

The Reference White Luminance is 299.6 cd/m2.

### C.4 Color Conversion R′G′B′ to X″Y″Z″🔗

Color conversion from R′G′B′ to X″Y″Z″ typically involves the following five-step process:

1. To the R′G′B′ code values, apply the inverse-quantization process to convert the image’s integer code values to a non-linear R′G′B′ signal in the range [0.0,1.0] from the code value’s integer range, 12bit full-range code values range from [0,4095] and 16 bit full-range code values range from [0,65535].
2. To the non-linear R′G′B′ signal, apply [SMPTE ST 2084] EOTF to convert non-linear R′G′B′ signal to linear RGB signal.
3. To the linear RGB signal, apply the RGB to XYZ primary conversion matrix to convert linear RGB to linear XYZ.
4. To the linear XYZ signal, apply the [SMPTE ST 2084] Inverse-EOTF to convert from linear XYZ to non-linear X″Y″Z″.
5. To the non-linear X″Y″Z″ signal, apply the 12 bit full-range quantization process to convert non-linear X″Y″Z″ to 12 bit X″Y″Z″ code values.

The transfer function of the HDR Reference Display is explicitly specified by [SMPTE ST 2084]. The actual coefficients of the color transform matrices depend on the color primaries of the Mastering HDR Reference Display (encoding side) and the Cinema HDR Display (decoding side), and their respective white points.

[SMPTE ST 2084] is a defined standard, and 12-bit quantization is sufficient, so a normalized PQ is not needed. Using a normalized PQ might impede the cross-utilization of assets in other formats.

The processing steps for converting 12 bit R′G′B′ code values (which range from 0 to 4095) of the color-graded master to device-independent X″Y″Z″ are shown below.

This color space conversion can be implemented within the color corrector or applied in a separate batch process. The equations below combine step #1 (inverse quantization) and step #2 ([SMPTE ST 2084] EOTF):

where:

${k}_{0}=10,000$, ${k}_{1}=4095$, ${m}_{1}=\frac{2610}{4096}\cdot \frac{1}{4}$, ${m}_{2}=\frac{2523}{4096}\cdot 128$, ${c}_{1}={c}_{3}-{c}_{2}+1$, ${c}_{2}=\frac{2413}{4096}\cdot 32$ and ${c}_{3}=\frac{2392}{4096}\cdot 32$

The output (RGB) of this linearization is a floating point number that ranges from 0.0 to 10000.0. The 3x3 linear matrix is then applied to this signal, resulting in a linear XYZ signal with floating point values that range from 0.0 to 10000.0. To minimize quantization errors, this matrix should be implemented as a floating point calculation. The matrix is shown here to 14 significant digits.

Finally, the X″Y″Z″ encoding transfer function is defined by the following expression which performs both step #4 (Inverse-EOTF) and step #5 (12bit Quantization). This equation does not compensate for the screen black level, so it represents an absolute encoding of the light levels independent of the screen black level.

where:

${k}_{0}=10,000$, ${k}_{1}=4095$, ${m}_{1}=\frac{2610}{4096}\cdot \frac{1}{4}$, ${m}_{2}=\frac{2523}{4096}\cdot 128$, ${c}_{1}={c}_{3}-{c}_{2}+1$, ${c}_{2}=\frac{2413}{4096}\cdot 32$ and ${c}_{3}=\frac{2392}{4096}\cdot 32$

The unary function $floor\left(\right)$ yields the largest integer not greater than its argument.

### C.5 Color Conversion X″Y″Z″ to P3D65 RGB🔗

The X″Y″Z″-to-P3D65 RGB processing steps for a Cinema HDR Display with the same color primaries as the HDR Reference Display are shown below and defined by the following steps:

1. Apply Inverse Quantization to the 12 bit X″Y″Z″ code values, converting 12 bit X″Y″Z″ code values to non-linear X″Y″Z″ in the range [0.0,1.0]
2. Apply [SMPTE ST 2084] EOTF to non-linear X″Y″Z″ values, converting non-linear X″Y″Z″ to linear XYZ
3. Apply XYZ to RGB conversion to linear XYZ values

The equations below show step #1 (inverse quantization) and step #2 ([SMPTE ST 2084] EOTF) combined:

where:

${k}_{0}=10,000$, ${k}_{1}=4095$, ${m}_{1}=\frac{2610}{4096}\cdot \frac{1}{4}$, ${m}_{2}=\frac{2523}{4096}\cdot 128$, ${c}_{1}={c}_{3}-{c}_{2}+1$, ${c}_{2}=\frac{2413}{4096}\cdot 32$ and ${c}_{3}=\frac{2392}{4096}\cdot 32$

Apply XYZ to P3D65 color encoding primaries transformation:

The resulting linear RGB light levels may end up being converted to other formats as the image data flows through the image/display processing operations involved in ultimately displaying the image to the viewer via the HDR display.

If other formats within the HDR display that may have a limited precision, it is important to preserve the visual fidelity/accuracy that is achievable with the 12 bit X″Y″Z″ [SMPTE ST 2084] distribution format across the minimum gamut (luminance range and color volume) specified elsewhere in this document to ensure that additional fidelity isn’t loss.

## Bibliography (informative)🔗

• SMPTE ST 372, Dual Link 1.5 Gb/s Digital Interface for 1920 × 1080 and 2048 × 1080 Picture Formats