Jadak Photo Research SpectraScan PR-7 Series, User Manual

Page: 36 / 142

Chapter 3
– Theory of Operation
32
CIE XYZ Tristimulus and Photometric Values
Once the three Tristimulus values (X, Y, Z) have been derived, useful colorimetric values such as CIE 1931 x, y
and CIE
1976 u’, v’ can be calculated by the following formulae:
CIE 1931 x, y
Z Y X
X
x
+ +
=
Z Y X
Y
y
+ +
=
CIE 1976 u’, v’
( )
Z Y X X u 3 15 / 4 '
+ + =
( )
Z Y X Y v 3 15 / 9 '
+ + =
Where X, Y, and Z are the three CIE Tristimulus values. X represents the red component, Y is the green
component, and Z is the blue component.
Y also serves as the photometric value
– when using the standard MS-75 lens, Y gives candelas / meter² - the SI
unit for luminance. To find footlamberts (English unit of luminance), multiply cd/m² by 0.2919.
683 is a constant used to convert lumens to watts. There are 683 lumens per watt at 555 nm for photopic
(daylight) vision.
S(

) = the corrected spectral data,
( ) ( ) ( )
  
Z Y X , ,
are the three CIE Tristimulus functions (curves) and

(

) is the
data increment
– for the PR-730, PR-740, and PR-788 the increment is 1 nm and 2 nm for the PR-735 and PR-
745.
( ) ( ) ( )
  

 =
780
380
683 X S X
( ) ( ) ( )
  

 =
780
380
683 Y S Y
( ) ( ) ( )
  

 =
780
380
683 Z S Z