Specifications

Submitted to Studies in Conservation, March 2006
7
computed from S, a [n × 1] vector of the spectral power distribution of the reference light source,
y
, a [n × 1] vector of the reference luminance color matching function, and
xyz
, a [n × 3] matrix
of the reference color matching functions. Matrix
T
!E
00
is a [3 × (i+1)] transformation matrix
from digital counts to tristimulus values fit using nonlinear optimization described below. Matrix
M
!E
00
[n × (i+1)] is a transformation matrix from digital counts to spectral reflectance factor
computed from A,
T
!E
00
, I, an [n × n] identity matrix, and
M
!E
00
. Vector
ˆ
R
!E
00
[n × 1] is the
imaging-based estimated spectral reflectance factors; it is the product of
M
!E
00
and D, a
[(i+1) × 1] vector of camera digital counts with the last element set to unity. In Eq. (3),
T
!E
00
was
optimized using a two stage process. First, nonlinear constrained optimization was used to
minimize the average ∆E
00
compared with the reference tristimulus values using a starting value
for
T
!E
00
of
!
A R
Reference
pinv(D
Reference
)
. These optimized matrix coefficients were used as starting
values for a second nonlinear constrained optimization that minimized
(Mean(ΔE
00
)/Mean(ΔE
00
)
Optimization 1
+ max(ΔE
00
)/max(ΔE
00
)
Optimization 1
). Both optimizations were
subject to the constraint that the coefficients not change more than ±50% from their starting
values. In Eq. (4), the left-most term of the right-hand side of the equation,
A
!
A A
( )
"1
T
#E
00
,
estimated the fundamental stimulus and the right-most term,
I ! A
"
A A
( )
!1
"
A
( )
M
pinv
, estimated
the metameric black. The final linear calibration transformation is shown in Eq. (5). As a linear
operation, it was implemented very efficiently.
Experimental Verification – Targets
The MCSL-Sinar system was tested in the Imaging Department of the National Gallery of Art,
Washington DC (NGA). It was compared with two other systems. The first was our spectral
measurement system consisting of a Quantix monochrome sensor coupled with a Cambridge
Research Institute liquid crystal tunable filter (LCTF), evaluated at NGA previously [2, 15]. The
system used diffuse tungsten illumination. The calibration transformation was based on a
GretagMacbeth ColorChecker DC and a custom target of blue acrylic artist paints, described
below. The second system was a stock Sinarback 54M with a P3 body and a 100mm lens with