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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates generally to the field of optics and more
particularly to an instrument for the measurement of colour.
2. Description of the Prior Art
Standards for the measurement of colour have been set by the Commissioner
International de l'Eclairage (hereinafter referred to as CIE) and are used
universally and reference will be made throughout this disclosure to these
CIE standards.
Colour perception is dependent upon the characteristics of each observer's
eyes and varies from person to person. A luminosity function which
represents the "standard" eye has been formulated by the CIE and is
defined as the y function which peaks in the green part of the spectrum [x
and z are similarly defined functions peaking in the red and blue parts of
the spectrum respectively].
As any particular light source has a specific energy distribution and a
coloured object has a particular absorption characteristic, the perceived
colour of the object is dependent upon both of these factors.
Quantitative specification of colour may be made by three tristimulus
values X, Y, Z which are the integrals of the products of the CIE
functions, x, y, z with the radiant energy distribution functions from the
object.
Two chromaticity values can be derived from the following relations:
##EQU1##
which can be represented on a chromaticity diagram for colour
determination.
The measurement of colour has been well documented in the past and many
devices have been made to perform this function. The modern devices may be
generally divided into two classes:
(a) those using optical transmission filters, and
(b) those using spectrophotometric scanning and subsequent digital
computing.
The first class of devices has high light throughput but suffers from the
inherent disadvantage that an optical transmission filter cannot be made
to accurately conform with the standard distribution functions set by the
CIE and therefore, is not standardized.
The latter class of devices have a relatively slow response, low light
throughput thereby resulting in a poor signal to noise ratio and they
require digitisation of a spectral response curve and subsequent digital
integration to determine tristimulus values and then the chromaticity
coordinate values.
These devices and their theory of operation have been described in "The
Science of Colour" published by the Optical Society of America. Reference
is also made to "New Spectrophotometric and Tristimulus Mask Colourimeter"
by Kok, C.J. and Boshoff, M. C. published in Applied Optics, December
1971, Volume 10, Vol. 12 commencing on page 2617 for a description of an
apparatus which may be used both as a spectrophotometer and as a
tristimulus colour meter.
Other devices related to colour measurement are disclosed in U.S. Pat. No.
3,3134,327 granted to Killpatrick et al on Apr. 18, 1967 and assigned to
Honeywell, Inc. and U.S. Pat. No. 3,522,739 granted to Con et al on Aug.
4, 1970 and assigned to Princeton Applied Research Corporation. The former
patent discloses a device employing spatial filters and three spectra in a
colour meter capable of producing an electrical output indicative of the
colour of a substance. The latter relates to a spectrophotometer apparatus
utilizing a ratio measuring circuit. These devices all provide a method of
specifying a colour of a target or sample in three basic units.
However, the disadvantages of the devices of the prior art have been many.
The optical filters used in the devices of the prior art are complex and
are made to exacting specifications in order to achieve uniformity
resulting in great expense, and whilst having uniformity, they can be made
only to approximate the CIE standard functions.
Instruments having spectral scanning techniques are in general, large and
opto-mechanically complex. They have slow responses due to the need to
scan slowly to achieve an adequate signal to noise ratio for the
absorbtion characteristics of the sample. Subsequent digitisation and
digital computation, involving a digital integration, can result in loss
of accuracy in the case of discontinuous or rapidly varying
characteristics where information is lost between digitised data points.
The devices of the prior art which use spatial filter techniques have not
been developed to the stage that the advantages of fast responses, high
accuracy, wide dynamic range, standardisation and simplicity of
construction and manufacture have been achieved.
SUMMARY OF THE INVENTION
Accordingly, it is an object of the present invention to at least partially
overcome these disadvantages by providing an instrument for the
measurement of colour which comprises a light source which illuminates a
sample, an electro-optical sensing head which receives the light from the
sample and outputs electronic signals, and an electronic signal processing
unit which together with the sensing head form an electro-optical analogue
computer. The sensing head contains a dispersive optical component which
creates a spectrum of the light from the sample and the spectrum is time
and space modulated by a complex moving spatial filter. The light from the
spatial filter is transferred by a photodetector to an electronic signal
which is processed in an analogue electronic unit to give the tristimulus
values X, Y Z and the chromaticity coordinates x, y of the sample with
respect to CIE standards for luminance and chromaticity values. The
spatial filter is so constructed that a simple filament light source is
seen by the instrument as a standard source.
There are many advantages obtained with the automatic computing colour
meter of the present invention. The use of a complex spatial filter which
can be accurately and inexpensively reproduced photographically from a
master, prepared from large scale artworks results in an accurate
representation of the CIE distribution functions. Light throughput is
several orders of magnitude larger than that of the scanning
spectrophotometer thereby resulting in greatly improved signal to noise
ratio. Also, the employment of simple analogue electronic signal
processing in conjunction with the complex spatial filter results in wide
dynamic range, high accuracy, fast response and good signal to noise
ratios, and automatically gives chromaticity values x and y and the
tristimulus values X Y Z. These values are obtained without the necessity
for digital integration techniques, and with reference to a standard
source without the need for an actual standard source. A simple trim mask
is used to balance any deviations from specified data. The construction of
the present device is also relatively simple, resulting in a high
performance to cost ratio instrument which has good application as a
laboratory instrument or for on-line process control.
It is important to note that the response from the present device is
significantly faster than the response produced by the devices of the
prior art. Thus, it is particularly applicable and suitable for use in
"on-line applications" reducing the time required for results from minutes
to seconds.
It is also suitable for discontinuous and large amplitude variations in
absorption spectra. Significantly, the present device will not miss data
between digitising intervals as is found in some of the devices of the
prior art.
To this end, in one of its aspects, the invention provides an apparatus for
the measurement of colour of a sample which comprises:
(a) an illumination means adapted to illuminate a sample;
(b) an electro-optical sensing head adapted to receive the light from said
illuminated sample; and
(c) an electronic processing unit adapted to process said light from said
sample in conjunction with said electro-optical sensing head.
In another of its aspects, the invention provides
(a) a light source adapted to illuminate a sample;
(b) an electro-optical sensing head adapted to receive the light from the
illuminated sample, the head including
(i) means for dispersing the light from the sample to form a spectrum;
(ii) a moving spatial filter adapted to modulate the spectrum in time and
space;
(iii) a masking means adapted to selectivity mask the light from the
modulated spectrum;
(iv) a means for transmitting pulses of light from the light source to a
photodetector via a reference optical path which is independent of the
sample (hereinafter referred to as said reference light pulses);
(v) a photodetector adapted to detect the modulated spectrum and said
reference light pulses and adapted to transform the modulated spectrum and
the reference light pulses into an electronic signal;
(c) an electronic processing unit adapted to process the electronic signal
into the respective chromaticity coordinates and tristimulus values of
said sample, over a wide range of light levels.
In yet another of its aspects, the invention provides an apparatus for the
measurement of colour of a sample which comprises an illumination means
for illumination of the sample with light, the sample reflecting a part of
the light; an electro-optical sensing head to receive the reflected light
from the illuminated sample and to output electronic signals, the head
comprising means for dispersing the reflected light from the sample to
form a spectrum, a moving spatial filter to modulate the spectrum in time
and space, a masking means to selectively mask the light from the
modulated spectrum, means for transmitting pulses of light from the
illumination means to a photodetector via a reference optical path thereby
producing reference light pulses and a photodetector to detect the
modulated spectrum and the reference light pulses to transform the
modulated spectrum and the reference light pulses into an electronic
signal; and an electronic processing unit to process the electronic
signals from the electro-optical sensing head.
In another of its aspects, the invention further provides an apparatus for
the measurement of colour of a sample which comprises:
(a) an illumination means adapted to illuminate a sample, said illumination
means comprising a number of light sources and supports, the supports
supporting the light sources and the sample in an integrating cavity
wherein the light from the light sources illuminates the cavity and is
reflected from the sample through a slit in the cavity;
(b) an electro-optical sensing head adapted to receive the light from the
illuminated sample, the sensing head including
(i) means for dispersing the light from the sample to form a spectrum, said
dispersion means including
(1) a collimating lens adapted to receive said light from said slit in said
integrating cavity,
(2) a diffraction grating adapted to diffract said collimated light from
said collimating lens,
(3) a focusing lens adapted to focus said diffracted light to a spectrum in
a flat focal plane.
(ii) a moving spatial filter adapted to modulate said spectrum in time and
space, said filter including
(1) timing marks on a face of said filter,
(2) detection means adapted to detect the timing marks on the face of said
filter and adapted to convert the movement of said timing marks into an
electronic signal, said detection means being in combination, a pair of
light emitting diodes and a pair of photodetectors adapted to detect the
movement of said timing marks,
(iii) a trim mask adapted to selectively mask said light from said
modulated spectrum,
(iv) a means for transmitting reference light from the illumination means
to the detector, said means consisting of
(a) an assembly of fibre optic light guides adapted to transmit light in a
reference optical path;
(b) an optical chopper adapted to gate the reference light into reference
light pulses including timing marks and a detection means
(v) a photodetector adapted to detect said modulated spectrum and reference
light pulses and adapted to transform said modulated spectrum and
reference light pulses into an electronic signal, said photodetector
including a condenser lens adapted to condense the spectrum to a detection
plane in said photodetector and a detection means in said photodetector
adapted to detect said condensed spectrum;
(c) an electronic signal processing unit adapted to process the electronic
signal into chromaticity coordinates and tristimulus values for the
sample, the unit consisting of:
(i) an automatic zero loop to eliminate errors due to detector dark current
and electronic drifts;
(ii) an automatic gain control loop adapted to allow a large dynamic range
of light levels to be accepted, and to maintain signal voltage levels at
higher values than error voltages specified in the electronic components;
(iii) an automatic means adapted to produce a digital output of tristimulus
values X, Y, Z and chromaticity values x, y to accuracies of the order of
.+-.0.0001 for x, y with half a second response time and 36 watts of
incandescent illumination in an integrating cavity.
BRIEF DESCRIPTION OF THE DRAWINGS
Further objects and advantages of the invention will appear from the
following description taken together with the accompanying drawings in
which:
FIG. 1 is a schematic representation of an instrument having a light
source, a target or sample and three tristimulus transmission filters.
FIG. 2 is a schematic representation of an instrument having a light
source, a target or sample, three tristimulus transmission filters and a
trim filter.
FIG. 3A is a schematic representation of a spatial filter overlayed on a
dispersed spectrum and FIG. 3B is a schematic representation of a slit
overlayed on a dispersed spectrum.
FIGS. 4A and 4B are schematic representations of a moving spatial filter
which is modulating a spectrum in both time and space.
FIG. 5 is a schematic representation of the device of the present
invention.
FIGS. 6A, 6B, 6C and 6D are schematic respresentations of the trim spatial
filter, modulating spatial filter and optical choppers suitable for use
with the present invention.
FIGS. 7, 7A and 7B are block diagrams of the electronic signal processing
unit of the present invention.
FIG. 8 is a diagram showing the timing and signal waveforms in the
electronic signal processing unit of FIGS. 7 and 7A-7B.
FIG. 9 is a drawing showing part of a circular spatial filter and spectral
lines of equal curvature.
FIG. 10 is a cut-away plan view of the device of the present invention.
FIG. 10A is a perspective view of an integrating cavity suitable for use in
the device of FIG. 10.
FIG. 10B is a schematic representation of a micrometer attachment for use
in the present invention.
FIG. 10C is a schematic representation of a disc for slit scanning with the
device of the present invention.
FIG. 10D is a schematic representation of an optical setting and
calibration device of the present invention.
FIG. 11 is a schematic representation of the timing generator of the
present invention.
FIG. 12 is a schematic representation of a second embodiment of a light
source of the present invention.
FIG. 13 is a schematic representation of the use of a liquid sampling cell
for use with the present invention.
FIG. 14 is a schematic representation of the use of a telescope for use
with the present invention.
FIG. 15 is a block diagram of a simple ratio circuit for calibration.
FIG. 16 is a schematic representation of the cavity suitable for use with
another embodiment of the present invention.
FIG. 17 is a schematic view of a spatial filter disc which produces a
multiple source filter.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring first to FIG. 5, there is disclosed a schematic representation of
an embodiment of the device of the present invention.
Light sources 10 (with opaque disc 100 to prevent direct illumination of
the sample) illuminate the inner surface of an integrating cavity 12.
Light incident upon the sample 14 is scattered by the sample 14 and is
received by the field lens 16. (In this case, diffuse reflection is shown
but the instrument may be used for specular reflectance or transmittance
or in a variety of ways well known to one skilled in the art. The present
invention is not to be limited to a device using diffuse reflection).
The light emerging from the field lens 16 passes through entrance slit 18
and is collimated by lens 20 and then dispersed by a diffraction grating
22. Field lens 16 is to optimally couple the light from the sample into
lens 20. Lens 24 and 26 bring a spectrum to focus at plane 28.
It is important that the optical design of lenses 20, 24 and 26 is created
with particular attention to the flatness of the spectrum focal plane and
spectral resolution in order that the spatial filters supported on
substrate 30 and substrate 32 and the spectrum on plane 28 will be as
coplanar as possible.
Substrate 30 carries a trim spatial filter 34 on its surface closest to
plane 28 and substrate 32 carries a spatial filter 36 on its side closest
to the plane 28. The depth of focus allows the close placement of the trim
spatial filter 34 and the spatial filter 36 to the spectrum in plane 28
with negligible loss of resolution or focus.
A transmission filter 38 is placed over the red end of the spectrum to
eliminate the second order diffracted light from the diffraction grating
22. The light which passes through the spatial filters 34 and 36 is then
focused by the condenser lens 40 onto a detector generally indicated at
42. As the image on the detector is that of grating 22, all wavelengths
have been recombined on the detector and therefore, wavelength integration
is performed at the detector 42.
A fibre optic light guide 44 receives light from the light source 10 and
transmits the light through an optical chopper 46 by means of imaging lens
48, 50 to the fibre optic light guide 52. The fibre optic light guide 52
terminates at position 54 at which position the light output from the
light guide can be received by the detector 42. This light is referred to
as "reference light pulses".
FIG. 6A shows a front view of a modulating or complex spatial filter 36
mounted on a glass disc substrate 32. Timing marks 56 and 58 are provided
on the disc which are detected by light emitting diodes and photodetector
pairs 60, 62 which in turn operate a timing generator (not shown). Filter
aperatures 64, 66, 68 and opaque quadrant 70 are shown on the disc. For
convenience, a spectrum 72 has been shown having wavelength variation
along the disc radius. The disc is rotated in the direction shown by the
arrow 74.
FIG. 6B is a side view showing the mounting of the filter 36 on the glass
disc 32, which may be a metal film or clear and opaque parts in a
photographic emulsion.
FIG. 6C shows a front view of a trim spatial filter 34 mounted on a
substrate 30 with the transmission area of the filter indicated as 76.
Both the trim spatial filter and the modulating or complex spatial filter
may be made by photographic means from large scale art works. This allows
for an accurate representation in space of the CIE or any other computed
distribution functions.
FIG. 6D shows a front view of the optical chopper 46 (of FIG. 5). It has a
clear aperture 78 and a timing mark 80 in an opaque disc. A light emitting
diode and phototransistor 82 detect the timing marks 80 and operate the
timing generator as described hereinafter. Light from the fibre optic
light guide 44 is imaged by lens 48 and 50 to the fibre optic light guide
52 through the aperture 78. Moveable vane 270 is provided for control of
the light through aperture 78.
FIG. 10 is a cut-away perspective view of a preferred embodiment of the
present invention illustrating the opto-mechanical stability and
simplicity of construction of the device of the present invention.
Casting 84, has a base plate 86, and supports two end plates 88, 90 and a
cover 92. A gasket 94 is used to effect a light tight seal about the
casting.
The integrating cavity 96 (as shown in FIG. 10A in detail) is constructed
from two hemispheres and has a sample aperature 98 and three lamps 10.
Each lamp has an opaque disc 100 to prevent direct illumination of the
sample which is placed over the aperture 98. The tube 104 connects the
cavity to the end plate 88 by means of a ring 106 which contains the
entrance slit 18. Mirrors 108 and 110 reflect the light to the collimating
lens 20 which contains in its housing 112 a grating 22. The diffracted
light is received by the focusing lens 24 in housing 114 and is directed
to the lens 26 in housing 116.
Lens 24 and 26 produce a spectrum in focus at plane 28 which is coplanar
with the trim mask 34 on support 30 which is held in mount 118. The disc
32 is held on a metal hub 120 on a shaft and bearing assembly 122 which in
turn is driven by a flexible ring 124 from motor 126.
The optical chopper 46 is supported at the rear of the shaft assembly 122.
The fibre optic light guides 44 and 52 and their associated lenses 48, 50
are supported in mounts 128, 130.
The condenser 40 is also held in the mount 118. The condenser 40 condenses
the filtered light onto the photodetector 42 which is held in support 132.
The LED photodetector pairs 60, 62 are supported on the posts 134 and 136
opposite the disc timing marks 56 and 58.
The fibre optic light guide 52 terminates at position 54 in mounting 138
near the detector 42.
This system includes rigidly mounted optics and a single moving part, which
is a dynamically balance flywheel, and thus, the system is free of
vibration and remains in alignment due to the precision bearing assembly.
In instruments which have a grating scan movement, the mechanics of the
sine bar and grating mount are much more complex compared to the device of
the present invention, and require much more stringent environmental
conditions.
A u.v. blocking filter 38 is also used over the red part of the spectrum to
eliminate the second order blue light which is produced by the diffraction
grating. That is, the light of 7800 A (red, first order) is in the same
position as 3900 A blue of the second order. As the specified CIE coverage
is from 3800 A to 7800 A, all light below 3900 A must be blocked at the
red end. The blocking filter is thus inserted over the red end of the
spectrum to block all below 3900 A. The u.v. of less than 3500 A is
absorbed by the optical system.
The optical system of the present invention must be aligned due to the need
for coincidence of the spectrum focal plane 28 with the spatial filter
surfaces 34 and 36, the need for correct dimensional matching of the
spectrum and spatial filters and the need for correct superposition of the
spectrum and spatial filters.
The spatial filters used in the present invention may be reproduced from a
master which in turn, may be produced from photoreduction of large scale
computer generated art works and thus, can be made to exacting standards
relatively inexpensively.
FIG. 10D shows two spatial filters 172 and 174 corresponding to filters 34
and 36 having added to their patterns, sets of lines 176 which correspond
to the spectral line positions of a mercury discharge lamp.
Replacement of the usual light source by a mercury discharge lamp gives a
line spectrum. When the back plate 90, the detector 42 and the condensor
40 are removed, this allows direct viewing of the line spectrum which is
produced in the focal plane 28. A simple microscope or magnifier may be
used to observe the position of the spectral lines wth respect to the
lines 176 on the spatial filters 172, 174 which are held stationary over
the spectrum.
Fine adjustment of the mirror 110, the lens 20, the grating 22, the lens 24
and the trim filter 172 results in both lateral and longitudinal alignment
of the filters and the spectrum. In the final assembly, the trim filter
for any particular instrument is inserted and positioned with reference to
the mercury line spectrum and the lines used for setting are subsequently
masked off.
FIG. 10C shows a third disc 178 which may be used for calibration of the
device to CIE standards. The disc 178 has a spiral slit 180 covering three
quadrants of the disc. The point 182 on the spiral is characterized by the
angle 184 and the radius 186 which uniquely determine the wavelength
transmitted by the slit 180 at any rotational position of the disc.
A standard white sample of known response is used with the usual light
source to calibrate the instrument. This calibration requires that the
overall response function l(.lambda.) I(.lambda.) be measured.
If the disc 36 is replaced by the disc 178, the resulting detector outut
188 is a spectral scan for three quadrants and a reference light pulse 190
for the fourth quadrant. Pulse 190 is used in a simple ratio circuit (see
FIG. 15) to eliminate errors due to detector and electronic gain drifts
and light source amplitude variations (as described hereinafter).
Wavelength calibration is obtained by the use of a shaft encoder 192 which
is a means of precise measurement of angular position of the disc 178.
The detector output 188 and the encoder output can be digitised with high
resolution over many data points and the signal averaged to obtain the
required accuracy. This is a valid procedure as the response
characteristic is smooth. This data is subsequently used in the
calculation of the trim filter function T(.lambda.) and specification of
the function K(.lambda.) (as described hereinafter).
FIG. 10B is a schematic representation of a micrometer attachment which may
also be used to calibrate the device of the present invention. The
micrometer attachment generally indicated as 194 drives a slit 196 over
the spectrum 72. The micrometer setting may be calibrated against the
known mercury spectrum lines thereby giving the wavelength for any
micrometer position. The slit 196 is supported on a substrate which is
optically the same as the trim filter substrate. A disc 198 having three
clear and one opaque quadrant 200 is used in place of the usual disc 36.
The detector output is a signal and reference pulse alternating at the disc
rotational speed. The signal pulse height is proportional to the roduct
l(.lambda.) I(.lambda.) at any given wavelength. The reference pulse is
used in the aforenoted ratio circuit to correct for the same factors of
drift and change.
The mode of operation of the device will now be described. The spectrum
which is produced in plane 28 is space and time modulated by the complex
moving spatial filter 36 and the light from this filter and that, from the
reference light pulses, is transformed by the photodetector 42 to an
electrical signal which is processed in the electronic unit to produce
chromaticity coordinates x, y and the tristimulus values X Y Z of the
sample with respect to the CIE standard.
The following description will now involve a discussion of the theory used
in the present invention.
Referring first to FIG. 1, there is shown a schematic representation of an
instrument having a light source 140, a target or sample 14 and three
tristimulus transmission filters 142, 144 and 146. The distribution
functions of the various aforenoted components as amplitude with respect
to wavelength would therefore become as follows:
(a) for the source 140, a function .rho.(.lambda.)
(b) for the sample 14, a reflectivity function r(.lambda.) and
(c) for the tristimulus filters 142, 144 and 146 functions x(.lambda.),
y(.lambda.) and z(.lambda.).
The tristimulus values, by definition, are as follows:
##EQU2##
expressed in units such that Y is numerically equivalent to the luminous
reflectance value of the sample or target 14. The instrument response with
filter 142 is
##EQU3##
with filter 144 is
##EQU4##
with filter 146 ia
##EQU5##
FIG. 2 shows the addition of a trim filter 148 to the instrument of FIG. 1.
As noted in FIG. 1, the distribution function of the source 140 is
.rho.(.lambda.) and the sample or target 14 has a reflectivity function of
r(.lambda.). The instrument generally indicated as 150, including the
optics, the detector and all the components affecting transmission with
the exception of the trim filter 140 and three tristimulus filters 142,144
and 146, has the overall transmission function I(.lambda.). If it is
assumed that the trim filter 140 has a transmission function T(.lambda.)
and the three tristimulus filters 142,144 and 146 have the function
l(.lambda.), m(.lambda.) and n(.lambda.), then the response for each
filter may be given by the following formulae:
##EQU6##
If the response R.sub.1, R.sub.m and R.sub.n are made equal to a response
which is given by a CIE standard source with function S(.lambda.) and CIE
standard distribution functions x(.lambda.), y(.lambda.), z(.lambda.),
then
##EQU7##
and similarly for m(.lambda.) and n(.lambda.).
The remaining disclosure will deal only with the l(.lambda.) filter
function as m(.lambda.) and n(.lambda.) filter functions will be
analogous.
Following from equation (iv), if
.rho.(.lambda.).multidot.l(.lambda.).multidot.I(.lambda.).multidot.T(.lambd
a.)=S(.lambda.).multidot.x(.lambda.), (v)
then equation (iv) will be satisfied. Further, an arbitrary distribution
function K(.lambda.) may be defined such that:
K(.lambda.)=.rho.(.lambda.).multidot.I(.lambda.).multidot.T(.lambda.) (vi)
where T(.lambda.) is the variable function to satisfy equation (vi).
Referring now to FIGS. 3A and 3B, there is shown a spatial filter 152 which
is overlayed on a dispersed spectrum 72 (FIG. 3A) and a slit 154 (FIG. 3B)
scanning spectrum 72. The slit scan determines the spectral response of
the instrument and source with respect to wavelength, which is defined as
E (.lambda.) where
E(.lambda.)=.rho.(.lambda.).multidot.I(.lambda.). (vii)
Thus, combining equation (vi) and (vii), transposition produces
##EQU8##
Since
K(.lambda.)=.rho.(.lambda.).multidot.I(.lambda.).multidot.T(.lambda.), equ
ation (v) may be rewritten as
##EQU9##
and l(.lambda.) is defined as a tristimulus distribution function related
to the CIE standard S(.lambda.), x(.lambda.) and a defined function
K(.lambda.).
Combining this with the original equation (i), it is found that
##EQU10##
where X.sub.s is a tristimulus value with respect to a CIE standard source
S(.lambda.) and standard CIE distribution function x(.lambda.).
As is well known, the chromaticity coordinates are defined as follows:
##EQU11##
As the denominator is common in the definitions of x, y and z tristimulus
values, the chromaticity coordinates may be written as follows:
##EQU12##
FIGS. 4A and 4B show a schematic representation of a moving spatial filter
which is modulating a spectrum in both time and space. An opaque slide 156
which contains an aperture 158 which is a spatial filter, moves in the
direction shown by the arrow 160. It therefore exposes the spectrum 72
which is dispersed perpendicularly to the direction of motion of the slide
156. Trim filter T(.lambda.) 162 defines an aperture distribution function
T(.lambda.) over spectrum 72 and the spatial filter 158 has an aperture
function l(.lambda.).
As the spatial filter moves over the spectrum, the response is the
convolution of the functions l(.lambda.) and the spectral energy in the
height bounded by T(.lambda.), dependent on the velocity of the aperture
158, which introduces a time variable.
The convolution is written in general, for two functions f(x) and g(x) as
##EQU13##
It is assumed that a(.lambda.), b(.lambda.), c(.lambda.) and d(.lambda.)
are arbitrary functions which control the shape of the spatial filter
edges 164, 166, 168, 170 such that
a(.lambda.)-b(.lambda.)=l(.lambda.) (xviii)
and
c(.lambda.)-d(.lambda.)=T(.lambda.) (xviv).
The energy distribution in the spectral line .lambda..sub.1 at 170 before
the trim spatial filter and with a target having reflectance of
r(.lambda..sub.1)=1 is defined as W(x), where
##EQU14##
and the direction of increasing x is defined by arrow 160.
The trim spatial filter which overlaps the spectrum is a discontinuous
function T(x) at .lambda..sub.1 having value
##EQU15##
Therefore, the trim spatial filter spectrum combination will be a function
W(x).multidot.T(x) where
##EQU16##
determines the value T(x).
The spatial filter 158 has a similar discontinuous function L(x), where
##EQU17##
The convolution therefore may be written for a displacement variable
.alpha. as
##EQU18##
As the spatial filter moves with a velocity v, transposition to time
variables can be made with time increasing in the x direction. Using
.alpha.=vs and x=vt, where s and t are time variables,
##EQU19##
with a change in the function limits
##EQU20##
The convolution
##EQU21##
is limited by
##EQU22##
at any wavelength and the time width of the filter is
##EQU23##
Therefore, an increase in v requires a proportional increase in
l(.lambda..sub.1) to compensate.
Integrating over all wavelength gives the following:
##EQU24##
which is dependent on the velocity v and is a variable with time.
Integration over time with a sample of reflectance r(.lambda.) gives the
following:
##EQU25##
which has a single value for a constant velocity v.
As R.sub.v is a function of l(.lambda.), T(.lambda.),
E(.lambda.)r(.lambda.) and velocity v, it may be written
##EQU26##
where .tau..sub.v is a time constant dependent on velocity.
This data may be extended to many spatial filters in succession, spaced
such that the response from each modulation do not overlap, and alternate
with spatial filter functions l(.lambda.), m(.lambda.), n(.lambda.),
l(.lambda.), m(.lambda.) . . . and this gives periodic responses R.sub.vl,
R.sub.vm, R.sub.vn, R.sub.vm . . . provided that the time integration is
initialized to zero for each filter in turn.
As the time constant is the same for all responses R.sub.v, all filters
having the same velocity, R.sub.v may be used in the calculation of x and
y as follows:
##EQU27##
The device of the present invention embodies the automatic computation of
the complicated triple integral of equation (xxv). This integral is
computed by analogue means and all data is used, thus giving accurate
integrals of all types of functions including those which have rapidly
changing characteristics, discontinuities, and fine structure which are
not suitable for digitising and integration by digital methods.
A response R.sub.vr is also obtained as the integral of the reference light
pulses (which is described in the electronic signal processing) which is
of the form:
##EQU28##
where J(.lambda.) is the spectral response of the reference path and the
detector.
T.sub.v is also the time constant for the optical chopper which is rigidly
coupled to the spatial filter disc 32.
For a source 10 having a constant spectral output, the denominator of
equation (i) is dependent only upon amplitude. The expression for R.sub.vr
following the integration sign is similarly amplitude dependent. By
selection of an appropriate constant factor (which, in practice, may be an
adjustable electronic gain as described hereinafter), the tristimulus
values may be computed from the following equation:
##EQU29##
where k is constant and J(.lambda.) is a fixed function dependent on the
reference optical path and detector characteristics, and R.sub.vr is the
reference response.
X is therefore independent of light source amplitude and similarly
independent of detector sensitivity and electronic gain changes.
By similar calculations, Y and Z may be calculated and
##EQU30##
The foregoing theory and utility upon which the present device is
predicated was derived using rectangular coordinates but is equally
applicable to any other coordinate system with proper transposition. In
this case, the aperture function l(.lambda.) is transposed to an arc
length where the arc length is given by l(.lambda.).multidot.r(.lambda.),
and the radius r(.lambda.) being the corresponding radius on the disc.
This thus compensates for the linearly increasing velocity of the disc
with increasing radius.
A spectrum is shown at 72 in FIG. 6A which has wavelength variation along
the disc radius. Ideally, the line formed by any one wavelength would have
the same radius of curvature as the disc at that point. It is practical to
curve all such spectral lines by the same amount by means of a curved
entrance slit in which case only one wavelength may be transposed exactly
and the remainder will have a small curvature error dependent on the
height of the spectrum. This error is negligibly small for small height
spectra.
Referring now to FIG. 9, there is shown a circular spatial filter and
spectral lines of similar curvature. The curvature of spectral lines 202,
204, 206 are shown similar to that of the filter at radius 208. Other
filter radii are shown at 210, 212. If the filter radius 212 is defined as
R and the radius 204 as R.sub.o, the error E at position 214, to a first
order approximation is given by
##EQU31##
where L is the height 216. For a radius R.sub.o =2, R=2.5 and L=0.25, then
E=0.003 inches. For a 1 inch wide spectrum covering 4000 A bandpass,
##EQU32##
which would be equivalent to a spectral shift at the corner of the
spectrum. As the error is proportional to L.sup.2, it is rapidly reduced
towards the spectrum centre line. It is preferable to have a wedge shaped
spectrum 218 to minimise curvature errors. The trim mask T(.lambda.) is
therefore preferred as a similar overall wedge shape and K(.lambda.) is
defined accordingly, to satisfy any specified wavelength accuracy.
FIG. 7 is a block diagram of the signal process unit of the present
invention. The photodetector 42 has an output which is periodic having a
repeated sequence which corresponds to red, green, blue, dark, reference.
The photodetector output is fed to an amplifier 220 and then to an
inverter stage 222 and then to an integrater 224. The integrater 224 is
discharged or reset after each integration of red, green, blue . . . by
means of a reset pulse 226. The reset pulse and all other signal
processing pulses are shown in FIG. 8 and are generated from the disc
timing marks by the LED/photodetector pairs 60, 62 and 82 input to the
timing generator (as explained hereinafter).
The integrated dark value is sampled and held by circuit 228 which is
controlled by pulse 230. This value is fed to an error integrator
amplifier 232 with a nominal zero reference 234. The output is fed back
into the input of inverter 222 and closes a loop 236 which is an autozero
loop. Adjustment of the reference 234 allows the output of the main
integrator 224 to be zero just prior to the dark reset pulse. By this
means, the photodetector dark current and any offsets in the stages 220,
222 and 224 are eliminated from the system.
Referring to FIG. 8, the sequential maxima of the integrator 238, 240, 242
corresponding to red, green and blue just prior to resetting one
proportional to g.sub.1 R.sub.vl, g.sub.2 R.sub.vn, g.sub.3 R.sub.vn where
g.sub.1, g.sub.2, g.sub.3 are scaling factors due to the disc geometry.
These factors are determined by the differences in the maxima of the
calculated l m n functions rel | | |
