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Table of Contents Page

Foreword ....................................................................................................................................................... 3

Intellectual Property ...................................................................................................................................... 3

Introduction.................................................................................................................................................... 3

1 Scope ........................................................................................................................................................ 5

2 Conformance Notation .............................................................................................................................. 5

3 Order in which the Color Processing Steps are Described ....................................................................... 6

4 Flow of Color through the Digital Cinema System .................................................................................... 6

4.1 Digital Source Master ......................................................................................................................... 6

4.2 D-Cinema Image Color Flow Diagram ............................................................................................... 6

4.3 Reference Projector Input Color Data Flow ....................................................................................... 7

4.4 Exhibition Projector Input Color Data Flow ........................................................................................ 7

5 D-Cinema Colorimetry Encoding .............................................................................................................. 8

5.1 Equations for DCDM Color Encoding ................................................................................................ 9

5.2 Equations for DCDM Color Decoding ................................................................................................ 10

5.3 Comments on the DCDM Encoding and Decoding Equations .......................................................... 10

6 Measurings of Projected Images .............................................................................................................. 11

6.1 Measuring Equipment ........................................................................................................................ 12

6.2 Measuring Locations within the Review Room or Exhibition Theater ................................................ 13

6.3 Projector and Theater Environment ................................................................................................... 13

6.4 Measurement and Ambient Light ....................................................................................................... 13

6.5 Measurement of the Luminance of White .......................................................................................... 13

6.6 Measurement of the Luminance of Theater Black ............................................................................. 15

6.7 Measurement of the Sequential Contrast .......................................................................................... 15

6.8 Measurement of Intra-Frame (Checkerboard) Contrast .................................................................... 16

6.9 Visual Verification of Gray Scale Tracking ......................................................................................... 16

6.10 Visual Assessment of Contouring .................................................................................................... 18

6.11 Measurement of the Transfer Function Exponent ........................................................................... 18

6.12 Measurement of the Color Gamut (Color Primaries) ....................................................................... 18

6.13 Specification of the Color Accuracy of any Displayed Colors .......................................................... 19

7 Conversion of Reference Projector R'G'B' Code Values to DCDM Code Values and then to

Linear Projector Code Values ............................................................................................................... 20

7.1 Background and Theory ................................

..................................................................................... 20

7.2 Derivation of the RGB-to-XYZ and XYZ-to-RGB Matrices, General Equations ................................ 21

Page 1 of 81 pages

SMPTE EG 432-1:2010

Revision of

EG 432-1-2007

SMPTE ENGINEERING GUIDELINE

Digital Source Processing —

Color Processing for D-Cinema

MOTION PICTURE AND TELEVISION ENGINEERS

3 Barker Avenue, White Plains, NY 10601

(914) 761-1100

Approved November 10, 2010

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SMPTE EG 432-1:2010

Page 2 of 81 pages

7.3 Derivation of the RGB-to-XYZ and XYZ-to-RGB Matrices, Reference Projector ............................. 22

7.4 Explanation of Annex C in SMPTE RP 431-2, Reference Projector (conversion example for

R'G'B' to XYZ to

X'Y'Z'

) ................................................................................................................. 24

8 Gamut Mapping and the Value of the Mastering Projector Metadata ...................................................... 28

9 An Example of Color Processing through the Entire System ................................................................... 32

9.1 Specification of Color in the DSM ...................................................................................................... 32

9.2 Conversion froom the DSM Film Printing Density Color Encoding to

X'Y'Z'

..................................... 39

Annex A Bibliography (Informative) ............................................................................................................ 41

Annex B Encoding Schemes Considered (Informative) ............................................................................ 43

Annex C Location of the Encoding Primaries (Informative)........................................................................ 45

Annex D Reason for the Constant 2.6 (Informative) .................................................................................. 47

Annex E Reason for the Constant 4095 (Informative)................................................................................ 50

Annex F Minimum Linear RGB Bit Depth Needed in the Reference Projector (Informative) ..................... 53

Annex G Reason for the Constant 52.37 (Informative) .............................................................................. 55

Annex H Encoding White Points Considered (Informative) ........................................................................ 60

Annex I Encoding of Colorimetry above Theater Black (Informative) ....................................................... 61

Annex J Conversions among xyY, XYZ and

X'Y'Z'

(Informative) ............................................................... 64

Annex K Calculation of the NPM using the Method in RP 177 (Informative) ............................................. 66

Annex L Description of CIELab Space and Delta E*ab (Informative) ........................................................ 71

Annex M Explanation of Annex B in SMPTE 428-1 (Informative) ............................................................... 76

Annex N Glossary and Acronyms (Informative) ......................................................................................... 77

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SMPTE EG 432-1:2010

Page 3 of 81 pages

Foreword

SMPTE (the Society of Motion Picture and Television Engineers) is an internationally-recognized standards

developing organization. Headquartered and incorporated in the United States of America, SMPTE has

members in over 80 countries on six continents. SMPTE’s Engineering Documents, including Standards,

Recommended Practices and Engineering Guidelines, are prepared by SMPTE’s Technology Committees.

Participation in these Committees is open to all with a bona fide interest in their work. SMPTE cooperates

closely with other standards-developing organizations, including ISO, IEC and ITU.

SMPTE Engineering Documents are drafted in accordance with the rules given in Part XIII of its

Administrative Practices.

SMPTE EG 432-1 was prepared by SMPTE Technology Committee 21DC.

Intellectual Property

At the time of publication no notice had been received by SMPTE claiming patent rights essential to the

implementation of this Standard. However, attention is drawn to the possibility that some of the elements of

this document may be the subject of patent rights. SMPTE shall not be held responsible for identifying any or

all such patent rights.

Introduction

The work that led to the writing of the SMPTE standards on the color encoding for Digital Cinema has been

guided by a few underlying principles. They are:

1. The most important desire was to define a color encoding that allows for excellent image quality in all

exhibition theatres. The color quality of the image ought not be limited by the encoding. The image

produced in one theatre should, within tight tolerances, match the image produced in any other

theatre. This led to some decisions that create technical challenges for the production workflows

today and that may lead to (slightly) increased cost of a complete system, but it was felt that the

ability to produce excellent quality in a theatre is sufficiently important that these challenges were

accepted.

2. It was desired that the encoding be designed so that it would encompass a color gamut at least as

large as existing digital projectors and preferably include all possible film colors. In addition, there was

a desire to write a standard that would allow future improvements in display technology to be carried

in the digital cinema encoding that is now being defined.

3. It was desired that the encoding should not be tied to any particular device or technology. This has

become known as device-independent encoding. Device-independent encoding does not, in itself,

lead to a robust encoding, but when coupled with other parameters, it can lead to a robust encoding.

4. It was desired that the digital cinema color encoding be designed to be relatively simple to implement

so that images can be processed and projected in real time.

5. The color encoding standardized by SMPTE is only for the Digital Cinema Distribution Master. There

has been considerable discussion of the encoding for the Digital Source Master, the digital master

that precedes the Distribution Master. However, that master is produced in a post-house and it was

felt that the post-house could create that Source Master in any file format and color space it wanted.

Likewise, the production of the Distribution Master from the Source Master is dependent on the form

of the Source Master, so that transform cannot be standardized. However, because it is an important

topic for many people, comments on the transform from the Source Master to the Distribution Master

will be given in this guideline.

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SMPTE EG 432-1:2010

Page 4 of 81 pages

This Engineering Guideline only deals with the color processing of digital images that a digital projector will

display in a theatre. Therefore, the container for the digital images, the file format of the code values, and the

transport of that container are not a part of this guideline.

Digital Cinema, or D-Cinema as it is also known, is based on the technology of defining an image by a set of

code values (numbers). The definition of any single color requires three, and only three, code values. In

addition, a set of three code values defines one, and only one, color. There has to be a color system defined

in which the code values are directly related to the colors. The SMPTE documents ST 428-1, ST 431-1, ST

431-2, and ST 431-3, listed in the Annex A (Bibliography), define this color system. This guideline explains

how to use those documents to implement that color system.

The overarching objective is to define a system in which an image will be displayed in any theatre by any

projector and the result will be the same within a reasonable set of tolerances. In order to achieve this

objective, there are three elements of the system that have to be defined: (1) The relationship between the

code values and the encoded color. (2) The measurement of the light reflected off the screen. (3) The aims

and tolerances around each measurement. The cited SMPTE documents and this guideline explain each of

these elements of the system and how to put all the elements together to make a working system.

The color encoding for the D-Cinema system is based on the definition of the image that is to be displayed on

the screen. Therefore, the SMPTE documents standardize how to define the relationship between the code

values and the desired colors, but do not deal with how one is to define the desired colors. It is realized that in the

normal production of moving images, the image has to somehow be created before the colors in the D-Cinema

image can be defined. The term, Digital Source Master, has been used to define this original image because

it may be the source of many different digital images, the D-Cinema images, the HDTV images, the DVD

images, etc. There are three reasons why the Digital Source Master has not yet been defined by any of the

SMPTE documents: (1) The Digital Source Master comes before the D-Cinema images. (2) The method by

which the images in the Digital Source Master are created is up to the creator. (3) The Digital Source Master

can be defined in a large number of different, useful ways.

To a large extent the encoding and decoding of the D-Cinema images revolves around the Reference

Projector. The Reference Projector is a working, practical projector that is defined by its capabilities, not by its

technology. It is recognized that there may be many technical solutions to the problem of constructing a

projector that has the capabilities that the Reference Projector must have. The Reference Projector

capabilities are the minimum capabilities any physical projector must have, but these capabilities are not

meant to be limiting capabilities. A physical projector may have capabilities beyond the capabilities of the

Reference Projector. Therefore, the technologies used to build a physical projector are not discussed in any

of the SMPTE documents; only the capabilities are described. There have to be uniform methods by which

the light reflected by a screen can be measured in order to know if the capabilities of any physical projector

meet the capabilities of the Reference Projector. In addition, it is recognized that because physical devices

will always have variation in performance across different devices and across time for any single device, there

have to be reasonable tolerances within which all devices can work and which will ensure that the images are

visually the same in all theatres.

The RGB or XYZ or similar triplets of numbers in this Engineering Guideline are always in the order in which

they are listed. For example, if a variable is called RGB and the numbers [100 200 300] are an example of the

RGB values, the 100 represents the R value, the 200 represents the G value and 300 represents the B value.

The matrices that operate on the RGB or XYZ values are defined for the same order of individual variables.

The reason for stating what seems so obvious is that some devices do not follow the order RGB. Where this

can cause problems is in the definition of the matrices that go from RGB to XYZ and XYZ to RGB. Therefore,

when a matrix is put into a projector (or other device), the user must be certain the matrix and the device are

using the individual variables in the same order.

The CIE XYZ tristimulus values, described in the CIE references in the Bibliography, are linearly related to

light. But because the human visual system does not respond to light in a linear fashion, the encoding of the

CIE XYZ values is more efficient if a function of the XYZ values is encoded instead of the XYZ values

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SMPTE EG 432-1:2010

Page 5 of 81 pages

themselves. These encoded XYZ values are given the symbols X’Y’Z’ in the SMPTE documents relating to

Digital Cinema. This encoding is the main subject of this Engineering Guideline.

This EG is entirely Informative. Stated values are not to be used for equipment design. The user should refer

to the appropriate Standard or RP for target values and tolerances.

1 Scope

This document provides guidelines on the encoding of the color information for the Digital Cinema Distribution

Master (DCDM) and for the decoding of the color signal in the projector. A series of standards and

recommended practices define exactly what to do to encode and decode the color for digital cinema. This

document leads the user through all of those documents so that an image, once created, will both match the

creator’s intent and will be displayed as the same image in every theatre within the recommendations of these

documents. In addition to the guidelines on how to do the color encoding and color processing, this document

will give some historical background on the development of the color encoding. In order to make this

document more readable, the historical information will be put in a series of annexes after the guidelines.

Therefore, this document describes the color transformations required for encoding an image into the DCDM

X’Y’Z’ code values in mastering and the reciprocal process of decoding these code values in the exhibition

projector. Because the appearance of any color patch is dependent on the viewing conditions under which the

color patch is seen, this document will also describe how the contents of the standards and recommended

practices relating to the display of images using digital projection relate to the color encoding and decoding.

The purpose of this guideline is to show how to use all of the Digital Cinema color-related documents in order

to achieve the objectives of interoperability and color consistency.

2 Conformance Notation

Normative text is text that describes elements of the design that are indispensable or contains the

conformance language keywords: "shall", "should", or "may". Informative text is text that is potentially helpful

to the user, but not indispensable, and can be removed, changed, or added editorially without affecting

interoperability. Informative text does not contain any conformance keywords.

All text in this document is, by default, normative, except: the Introduction, any section explicitly labeled as

"Informative" or individual paragraphs that start with "Note:”

The keywords "shall" and "shall not" indicate requirements strictly to be followed in order to conform to the

document and from which no deviation is permitted.

The keywords, "should" and "should not" indicate that, among several possibilities, one is recommended as

particularly suitable, without mentioning or excluding others; or that a certain course of action is preferred but

not necessarily required; or that (in the negative form) a certain possibility or course of action is deprecated

but not prohibited.

The keywords "may" and "need not" indicate courses of action permissible within the limits of the document.

The keyword “reserved” indicates a provision that is not defined at this time, shall not be used, and may be

defined in the future. The keyword “forbidden” indicates “reserved” and in addition indicates that the provision

will never be defined in the future.

Unless otherwise specified, the order of precedence of the types of normative information in this document

shall be as follows: Normative prose shall be the authoritative definition; Tables shall be next; followed by

formal languages; then figures; and then any other language forms.

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