Do you have references for the equivalency of CIE inverse instrument geometries?

FAQ: “…. the schema of the principle of measuring shows other way of light (source of light -> sample -> sphere -> detector) than our Vista (source of light -> sphere -> sample ->  detector). Please can you explain me difference between both construction? difference between both results of measuring?”

This describes the concept of equivalency of inverse geometries for color measuring instruments in reflectance where the source of light -> sphere -> sample ->  detector in a CIE diffuse d:8 geometry is equivalent to the source of light -> sample -> sphere -> detector of an 8:d geometry. The same concept applies to CIE directional 45:0 and 0:45 geometries.

An instrument with directional 45:0 geometry on the left matches the viewing condition of the technician at the window, and is equivalent to the 0:45 geometry on the right matching the technician viewing samples in the light box.

When you look at a sample color, the color you perceive is dependent on the geometry of how you look at it – where source of white light is; where you are standing and where the sample is.

To measure a color as you perceive it, the instrument geometry must match the way you view the sample. A CIE instrument geometry is a formal definition of the relative positions of the light source, sample plane and detector to each other.

There are two main categories with 2 equivalent geometries each – diffuse d:8 (most common) and 8:d and directional 45:0 (most common) and 0:45.

Industrial References for the equivalency of inverse CIE directional geometries

CIE Publication 15.2004 Colorimetry (Section 5)

ASTM E179 Guide for Selection of Geometric Conditions for Measurement of Reflection and Transmission Properties of Materials – Section 8.2

“The Helmholtz Reciprocal Relation – This relation states that the loss of flux density suffered by a bundle of rays due to reflection, refraction, absorption, or scattering by a specimen will not be changed if the direction of travel of the bundle is reversed. In other words, results of intercomparisons of specimens by reflectometers, gloss meters, etc., are not changed if the geometries of incident and viewing beams are interchanged. Because the pupil of the eye is small, visual instruments customarily have small receiver aperture angles. In any instrument with a large received window, rays entering different parts of the window should receive equal weight. Several experimenters have presented evidence tending to refute the Helmholtz Reciprocal Relation, but it is strongly suspected that insufficient attention was given to the foregoing requirements for uniformity of weighting of all light fluxes leaving or entering the instrument apertures involved.”

Note: The inverse geometry equivalency or, Helmholtz Reciprocal Relation, is referenced in section 8.2 of ASTM E179, citing as an original document: Clarke, F. J. J. and Parry, D. J., “Helmholtz Reciprocity: Its Validity and Application to Reflectometry,” Lighting Research and Technology, Vol. 17, 1985, pp 1- 11.

ASTM E1164 Standard Practice for Obtaining Data for Object-Color Evaluation – Section 8.1.1

“For the normal:45° condition, the requirements for illumination and viewing are interchanged from those just described.”

AATCC Evaluation Procedure 6 – Instrumental Color Measurement (Section 2.3.7)

“2.3.7 Instruments with 45/0 or (0/45) geometry illuminate the specimen at the first angle and view the specimen at the second. These two geometries can be either circumferential (viewing or illuminating at 45 to the specimen in a complete circle) or directional. For most textile samples, either 45/0 or 0/45 yield equivalent results.”

The Helmholtz Reciprocal Relation basically states that if you swap the positions of the light source and detector, everything else being equal, the measured values will be the same.  That is, for reflectance measurements, a bidirectional 45:0 instrument geometry is equivalent to a 0:45; and a d:8 sphere is equivalent to a 8:d.

As usual in color science, there are caveats to the Helmholtz Reciprocal Relation:

• The condition of “everything else being equal” between two inverse geometry instruments seldom exists.  Usually some element in the optical path (area of view, sphere diameter, light collection angles etc.) is different which can result in a small bias in measurement results.
• Although it works well in most situations, in strict application, the inverse concept only applies to flat, uniform, non-fluorescent, opaque, solid samples. It will not work for fluorescent or translucent samples, or those that experience light trapping such as plastic pellets.