.
`United States Patent
`McCarthy
`
`115
`
`[54] OPTICAL SPECTRAL ANALYSIS
`APPARATUS
`
`[76]
`
`Inventor: Cornelius J. McCarthy, 35
`Stonington Dr., Pittsford, N.Y.
`14534-2923
`
`[21] Appl. No.: 648,798
`[22] Filed:
`Jan. 31, 1991
`
`[51]
`Int. CLS .....
`wretenereetees G01J 3/00
`[52] WLS. Cl. oo.ecceccssscceceeeneennceseeses aoeeSeaoe
`[58] Field of Search............... 356/402, 405, 406, 407,
`356/416, 419, 425; 250/226; 364/526
`References Cited
`U.S. PATENT DOCUMENTS
`3,910,701 10/1975 Hendersonet al.
`.
`3,916,168 10/1975 McCartyetal. .
`4.458.323
`7/1984 Willis et al
`4,499,486 2/1985 Farneauetal. .
`4,505,583
`3/1985 Konomi .
`4,648,051
`3/1987 Wendell et al.
`
`[56]
`
`.
`
`ACOAAAA
`US005137364A
`[11] Patent Number:
`5,137,364
`[45] Date of Patent:
`Aug. 11, 1992
`
`3/1987 O’Brien .
`4,654,794
`5/1989 Yamaba .
`4,834,541
`4,881,811 11/1989 O’Brien .
`4,937,637 6/1990 Magistro .
`4,957,363
`9/1990 Takeda .
`FOREIGN PATENT DOCUMENTS
`63-14224
`1/1988 Japan .
`OTHER PUBLICATIONS
`F. Grun,C. J. Bartleson, Optical Radiation Measure-
`ments, vol. 2, 1980, Academic Press (pp. 33-47, 146).
`Primary Examiner—F. L. Evans
`Attorney, Agent, or Firm—M. Lukacher
`[57]
`ABSTRACT
`Apparatus for low cost measurement oflight energy in
`terms of multiple spectral integrations with differing
`wavelength-dependent weights for consistency of mea-
`surementsin spite of variations in component character-
`istics or temperature.
`
`24 Claims, 5 Drawing Sheets
`
`APPLE 1022
`
` 1
`
`1
`
`APPLE 1022
`
`

`

`U.S. Patent
`
`Aug. 11, 1992
`
`Sheet 1 of 5
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`5,137,364
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`

`

`U.S. Patent
`
`Aug. 11, 1992
`
`Sheet 2 of 5 5,137,364
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`FIBER HEAD
`MAXIMAL
`
` &mm
`
`
`FIG.2
`==
`
`FIG.3
`FIBER HEAD
`MINIMAL —
`
`3
`
`

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`U.S. Patent
`
`|
`
`Aug. 11, 1992
`
`5,137,364
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`
`4
`
`

`

`U.S. Patent
`
`Aug. 11, 1992
`
`Sheet 4 of 5
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`5,137,364
`
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`
`START
`
`SETUP
`
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`DETECTOR
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`Cisdj} *
`(1{d,s}- D{d})
`
`
`
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`
`

`

`U.S. Patent
`
`Aug. 11, 1992
`
`Sheet 5 of 5
`
`5,137,364
`
`
` Cls,d,j]
`
`=
`TIs,d,j,t]
`
`FIG.9B
`
`6
`
`

`

`1
`
`5,137,364
`
`OPTICAL SPECTRAL ANALYSIS APPARATUS
`
`Although the human visual system is highly capable
`of the perception of spectral energy as brightness and
`coloror color difference,it is less capable when used for
`quantification andrecall. A series of instruments, gener-
`ally called densitometers, colorimeters, spectrophotom-
`eters, radiometers, and chroma meters have been devel-
`oped to perform these functions. This invention relates
`to measurement instruments which can provide high
`quality measurements ofthis class at low cost, and par-
`ticularly to optical spectral analysis appratus incorpo-
`rating a plurality of solid state radiation sources, such as
`light emitting diodes, and a plurality solid state radia-
`tion detectors.
`
`BACKGROUND
`
`spectrophotometers,
`colorimeters,
`Densitometers,
`radiometers and chroma meters all perform the same
`type of physical measurement. They each calculate one
`or more weighted integrations of optical energy over
`wavelength. In the case of densitometers, colorimeters,
`some radiometers and chroma meters, a small number of
`weighted integrations are normally performed. The
`weighting function for densitometers and colorimeters
`is usually the product of the spectral intensity of a light
`source, a filter, the sensitivity profile of a detector, and
`thereflection or transmission of a sample.
`For chroma meters and radiometers the sample is a
`radiant source, and the weighting function is the prod-
`uct of the spectral intensity of the source, a filter param-
`eter, and the spectral sensitivity of a detector. In the
`current practice for measurement of reflectance or
`transmission, the light source is a broad band emitter
`such as a tungsten lamp, and the detector has wide
`range of sensitivity. Im general the same light source and
`detector profiles are used for each weighted integration
`and only thefilter profile changes. These instruments
`are usually calibrated in use by using a sample of known
`transmittance or reflectance. Spectrophotometers and
`spectral radiometers are generally capable of reporting
`tens to thousands of weighted integrations For spectro-
`photometers and spectral radiometers,
`the weighting
`functions usually each have a common shape whichis
`ideally a narrow triangle. Multiple weighted integra-
`tions are obtained by choosing multiple positionsfor the
`center of the weighting function along the wavelength
`axis. Spectrophotometers generally use broad band
`light sources and detectors, but because they may span
`a greater wavelength range, they may have multiple
`sources or detectors. The weighting function is pro-
`vided by continuousfilters, by multiple filters, by mono-
`chromators, by spectrographs, or by interference tech-
`niques. Densitometers, colorimeters and chroma meters
`are designed to produce specific weighed integrations.
`For densitometers used in graphic arts, the weighting of
`the integrations is intended to optimize the response to
`the reflectance of standard inks used in printing. For
`colorimeters and chroma meters the weighting of the
`integrations is intended to generate chromaticity coor-
`dinates as defined by CIE or ASTM.Spectrophotome-
`ters and spectral radiometers are intended to allow the
`reflectance, transmittance or intensity spectrum with
`reference to wavelength of the sample to be represented
`as a set of points, or a curve, or a spectrum. Asall of
`these weighted integrations are linear sums over wave-
`length, each integration may be considered to be a vec-
`
`_ 0
`
`bet 5
`
`20
`
`25
`
`30
`
`40
`
`60
`
`65
`
`2
`tor in a common vector space. A particular set of
`weighted integrations will correspond to a collection of
`vectors from this space which form a subspace. Such
`subspacesare said to be spanned bytheset of weighted
`integrations from which their component vectors may
`be calculated. In these terms each type of instrument
`can be said to measure the subset of the space whichis
`spanned by the vectors represented by its weighted
`integrations. In general, the weighted integrations de-
`signed into densitometers, colorimeters, and chroma
`meters span a subset of the space which is spanned by
`the weighting functions designed into spectrophotome-
`ters and spectral radiometers. When colorimeters, den-
`sitometers, and chroma meters are designed to pub-
`lished standards, the specified integrations are stated in
`terms of sums over spectra, and these instruments are
`usually calibrated against the measurements of a high
`grade spectrophotometer or spectral
`radiometer or
`against samples for which the relectance, transmission,
`or spectral intensity as a function of wavelength has
`been independently determined. Given that each set of
`these weighted integrations can be expressed as subsets
`of the same vector space it follows that any set of
`weighted integrations can be transformedinto any other
`set within the subset of the space spanned by bothsets,
`and further it follows that this calculation will be a
`linear transformation which may be performed as a
`matrix multiplication. This is what occurs when chro-
`maticity coordinates or densities are calculated from
`spectral data produced by a spectrophotometeror spec-
`tral radiometer. It also follows that there will be a col-
`lection of other sets of weighted integrations which will
`span the subset of the space spanned by chromaticity
`coordinates and by density specifications. Any such
`subset may be measured and used to calculate chroma-
`ticity coordinates or density functions.
`SUMMARYOF THE INVENTION
`
`Apparatus is provided which is capable of perform-
`ing any type oflinear transformation on a small number
`of inputs. The apparatus is designed to measure any set
`of weighted integrations, from which the desired results
`can be calculated. Moreparticularly, it has been discov-
`ered in accordance with this invention that a set of
`weighted integrations can be selected based on consid-
`eration of cost and apparatus quality rather than on
`conformance to the weighting functions for which the
`apparatus will report measurements. A set of weighted
`integrations may be created which span as large a subset
`of the vector space as practical with the smallest num-
`ber of inexpensive components. For measurement of
`reflectance and transmission in the optical spectral anal-
`ysis apparatus according to this invention, a small num-
`ber of illumination sources, each of which provides
`optical energy over a subset of the wavelength range of
`interest, and a small numberof detectors, each sensitive
`to the entire wavelength range but each with a differ-
`ently weighted sensitivity as a function of wavelength,
`are used. Each illumination source is made to illuminate
`the sample material in turn and light from the sample is
`directed to all detectors and detector output is re-
`corded. Then after sequencing through all illumination
`sources a set of weighted integrations is derived whose
`numberis equal to the product of the numberofillumi-
`nation sources times the number of detectors The
`weighting functions of these integrations will be the
`products of the individualillumination weightings func-
`tions with the individual detector sensitivity functions.
`
`7
`
`

`

`3
`In the preferred implementations of apparatus for the
`measurementofreflection and transmittancethe illumi-
`nation sources are light emitting diodes, and the detec-
`tors are photodiodes which have been processed,
`treated, or
`filtered to produce different sensitivity
`curves as a function of wavelength.
`The followingtable lists a series of configurations.
`
`Tum
`Photo
`Sources
`Diodes
`1
`1
`2
`1
`3
`1
`4
`1
`4
`2
`
`Integrations
`1
`2
`3
`4
`8
`
`6
`6
`
`3
`4
`
`16
`24
`
`In the preferred implementation the light emiting
`diodes (LED's), and the detectors can be in the form of
`unmounted semiconductorchips. Forreflectance appli-
`cations, the selected collection of detectors and LED’s
`are mounted on a commonsubstrate. At a constant
`temperature and when protected from humidity, light
`emitting diodes and photodiodes are stable devices.
`Therefore, a temperature sensor and optionally temper-
`ature control components are mounted onthe substrate.
`The entire assembly is then sealed against humidity to
`achieve then the sensor outputis used to compensate for
`temperature change by adjusting the linear transforma-
`tion between weighted integrations and reported output
`units. In reflectance measurementapplications, a physi-
`cal shield is used to keep direct light from the LEDs
`from reaching the detectors and the entire assembly
`may be pointed at the sample surface with no optical
`components other than a protective seal of epoxy.
`In practice the LED’s for the red end of the visible
`wavelength range are moreefficient than LED’s for the
`blue end. Although electronic compensation would be
`included, it may be desirable to balance the system by
`using more LED chips at
`lower wavelengths to in-
`creasethe light output in that spectral region. Thus,the
`invention may be implemented with six illumination
`sources may have more than six LED chips because of
`the need for duplication for some wavelengths.
`For precise sampling of small areas a fiber assembly
`maybeused. In this case a small numberof short optical
`fibers are used to direct light from the LED’s to the
`sample and return light to the detectors. Since the ob-
`jective is to achieve a small sampling area, fibers with a
`thin clading layer and thus a large core diameterto clad
`diameter are utilized. One end of the fibers would be
`placed in direct contact with the detectors and LED’s.
`Optical epoxy would be applied to ensure optical cou-
`pling, and support epoxy would hold the fiber assembly
`rigid. FIGS. 2 and 3 show the endsoffiber assemblies
`for preferred implementations. FIG. 4 shows a side
`view of an assembly. Special combinations of detector
`andillumination weighting functions can also be used to
`calculate factors which are not simple weighted integra-
`tionsof relflectance or transmission. If one of the detec-
`tors is conditioned so thatit is not sensitive to illumina-
`tion at wavelengths emitted by one of theillumination
`sources, then response from that detector (when only
`that one illumination source is active) may be a measure
`of fluorescence by the sample.
`
`5,137,364
`
`4
`
`Possible Calculations
`One Axis Accept/Reject
`Whiteness, Yellowness
`One Iiuminant Chromaticity
`Four axis density
`Multi Miuminant
`Chromaticity
`Lowresolution spectra
`Medium resolution spectra
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`FIGS. la & 15 are respectively top and sectional
`(along 16—18 in FIG. 1a) viewsof the emitter/detector
`assembly of an optical spectral analysis apparatus for
`reflectance embodying the invention FIG. 1c showsthe
`computer which operates the apparatus. FIGS. 2 & 3
`are end viewsof optical fiber assemblies which may be
`used to optically couple an emitter detector assembly
`similar to FIG. 1 toa reflectance sample. FIG. 4 isa side
`view of an a fiber assembly similar to FIG. 2 or FIG. 3.
`FIG. 5a & Sb are a logic flow diagram of the program,
`respectively for the setup and measurement operations
`of the apparatus which is implemented in the computer
`whichis included in the apparatus.
`DETAILED DESCRIPTION
`
`FIG. 1 shows a top view and a center section side
`view of an assembly of detectors and emitters for direct
`illumination and viewing. Item 1 is a protective outer
`shell 1. This shell serves, 1) to block externallight, 2) to
`reflect
`light diverging outward from the emitters 2
`toward the center, and 3) to contain the optical epoxy 5
`over the emitters. A set of emitters in the form of LED
`dice 2 are distributed around the circumference of the
`assembly. Detectors 3 with optional filtering layers 4
`are centered in the assembly. A cylinder of opaque
`material 6 serves to block direct light from the emitters
`2 from reaching the detectors 3 and to contain optical
`epoxy 5. The optical epoxy 5, is applied over the emit-
`ters and detectors so that it forms a hermitic seal and so
`that its top surface is plane. A substrate 7 carries electri-
`cal connections and provides thermal contact between
`the emitters 2, the detectors 3, and a optional thermal
`sensing element 8.
`FIG. 2 shows the sample end view and assignments
`for a fiber assembly with eight illumination fibers and
`three detector fibers. These are preferably fibers one
`millimeter diameter so that the maximum width of the
`sample end ofthe fiber assembly is four millimeters. The
`detector fibers are centered and labeled D1, D2, and
`D3. Theillumination fibers are around the circumfer-
`ence of the assembly and are labeled with the center
`wavelength in nanometers of a corresponding light
`emitting diode. The lower wavelengths, 470 nanome-
`ters (nm) and 555 nm,are repeated in this pattern.
`FIG. 3 shows the sample end view and assignments
`for a fiber assembly withsix illumination fibers and one
`detector fiber. The one detectorfiber, labeled D is opti-
`cally coupled to two detectors. The illumination fibers
`surround the detector fiber. These are labeled by the
`center wavelength in nanometers of the illuminating
`light emitting diode. The lowest wavelength, 470 nm,is
`repeated three times for a total of four illumination
`profiles.
`,
`FIG. 4 showsa side view ofthe fiber assembly. Opti-
`cal fibers 4 run from the substrate 7, which mounts the
`emitters 2 and the detectors 3 to the sample 9). Optical
`epoxy 5 couples the fibers 4 to the emitters 2 and the
`detectors 3. Support epoxy is used to pot the assembly
`at the emitter detector end 6 and at the sample end 8.
`Outer shells at the emitter detector end 1 and at the
`sample end 7 protect the assembly and provide the
`outer boundary for the support epoxy.
`Calibration using a programmable computer,built in
`or as a separate element, is part of the apparatus of the
`invention. There may be several classes of instrument
`calibration. Calibration is meant to be a part of a mathe-
`
`15
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`30
`
`35
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`45
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`8
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`

`

`5,137,364
`
`5
`matical calculation to be performed using measured
`weighted integrations as input and generating specific
`user coordinates. User coordinates are the weighted
`integrations the instrument will report
`to the user.
`Chromaticity coordinates are an example of user coor-
`dinates. There are several classes of calibration given
`consideration in implementing calibration.
`1) The instrument (.e., the apparatus) may function
`without calibration and without stabilization. For this
`case the transformation from measured integrations to
`user coordinates would be determined as part of the
`design of the instrument and would be the sameforall
`instruments using the same type of parts to report the
`same user coordinates.
`2) The instrument may function without calibration
`but with on board closed loop temperaturestabilization.
`In this case the emitters and detectors would be main-
`tained at a constant temperature by a closed loop ther-
`mal detector and heating and or cooling system sche-
`matically shownat 9 in FIG. 18,
`3) The instrument may function with instrument spe-
`cific calibration, but without stabilization. In this case
`each individual instrument would be used to measure a
`set of reference materials, with the instrument and the
`material held at a constant nominal temperature. The
`measurements would be used to calculate an insrument
`specific transformation from measurement to user coor-
`dinates. This transformation would be coded into each
`specific instrument.
`4) The instrument may function with instrument spe-
`cific calibration and with temperature correction. In
`this case a thermal sensor in contact with the substrate
`mounting the emitters and detectors would report the
`temperature at the substate to the processor used for
`transformation. Transformations would then be deter-
`mined at multiple temperaturesas per class 3 above, and
`temperature compensation would be applied byselect-
`ing the proper transformation to be used.
`5) Finally the instrument may function with instru-
`ment specific calibration and closed loopstabilization.
`This is the same as case three for an instrument with
`closed loop thermal control at the detectors and emit-
`ters. For some detector types, configurations, and cir-
`‘cuits the electrical signal observed may notbestrictly
`proportional the light energy reaching the detector.
`When this is the case a transformation from the ob-
`served signal to a value which is proportionalto light
`- energy is required before transformation to user coordi-
`nates. Generally at least an offset correction is required.
`Thevalue of such offsets may be calculated during the
`measurement process by observing the electrical signal
`generated by each detector when no illumination
`sourcesare activated.If further correction is required it
`would be determined on a detector by detector basis.
`FIGS. 5a and 54 show a flow diagram for the com-
`puter program. The computeris part of the means for
`operating the apparatus. See FIG. Ic FIG. 5a is a mea-
`surement cycle flow diagram. A setup subroutine 1 is
`called first. After the setup routine a loop 2 is executed
`in which each detector is read with all sources off. The
`readings of the detectors with sources off is stored in
`vector D(d). Whenthis loop is complete a double loop
`over sources and detector is performed.
`Inside the
`source loop each sourceis turned on 3a before the inner
`loop over detectors, and turned off 35 after the inner
`loop over detectors. Within the inner loop over detec-
`tors each detector is read into vector I(d,s) 4. When the
`double loop over sources and detectors is complete, a
`
`6
`triple loop over output vector components, 5, sources,
`and detectors is performed. Within this loop the output
`vector O(j) is set to zero 6 and then each term of the .
`linear transformation is added into the output vector 7.
`These terms are calculated as a coefficient, C(s,d,j),
`times the input with sources on, I(s,d), minus the read-
`ing of the detector with sources off, D(d). After the
`triple loop is complete, the output vector O(j) is output
`to the user 8.
`In the setup subroutine FIG.54, all sourcesareset off
`1, and the existance of a thermal sensorit tested. If no
`thermal sensor is present, then the coefficients of the
`linear transform are constants and are not modified by
`the setup routine. If there is a thermal sensor, then the
`temperature is read from the sensor 3 anda triple loop
`copies a set of constants T(s,d,j,t) indexed by the tem-
`perature is read into the array of coefficients C(s,d,j) 4.
`The considerations which determine the programs
`are discussed next. Chroma meters are designed to re-
`port chromaticity coordinates for sources of light en-
`ergy. The sources to be measured are generally in-
`tended for human observation, such as colored lights
`and signs, color television displays, and color computer
`display devices. Because the sample provides the light
`energy, the description relative to achieving lowercost
`by multiplexing multiple sources and multiple detectors
`does not apply. However, the descriptions relative to
`choice of weighting functions, mounting and thermal
`control of detectors, and calibration of measurement
`apparatus may be applied to an apparatus for the mea-
`surement of radiant sources. For the measurement of
`radiant sources, the reference material used is a set of
`devices of which emmitted light energy of known spec-
`tra] intensities or an apparatus for producing multiple
`knownspectra, such as a stable light source and a mono-
`chromator.
`Although a multiplicity of techniques oflinear alge-
`bra and numerical analysis may be used for the imple-
`mentation of this invention, the following relates to the
`preferred implementation. Let OVECT be a vector
`whose components are spectral energy in each of a
`series of wavelength bands. For example these bands
`may be one nanometer widestarting at 380 nanometers
`and ending at 780 nanometers. In this case OVECT
`would have 401 components. This wavelength range
`and resolution would be sufficient for the mathematical
`description of any instrument which performed mea-
`surements which were intended to correspond to
`human visual judgments. Let UVECTbe a vector of
`user coordinates. In particular, let UVECTbe a set of
`three chromaticity coordinates as defined by the CIE.
`In this case UVECT would have three components.
`Then the definition of UVECT by the CIE may be
`expressed as the matrix multiplication of OVECTby a
`matrix of dimension 3 by 401 determined from pub-
`lished tables, which we will call CHROM.MAT.
`
`20
`
`25
`
`30
`
`40
`
`~
`
`45
`
`50
`
`55
`
`UVECT=[CHROM.MAT]*OVECT
`
`Eq.1
`
`Let DVECT be a vector whose components are
`weighted integrations which are produced by a given
`apparatus. Let APP.MAT be the matrix of weights
`which transforms OVECT to DVECT.
`
`65
`
`DVECT=[APP.MAT}*OVECT
`
`Eq. 2
`
`If the vector space spanned by UVECTis a subset of
`the vector space spanned by UVECTthenthere will be
`
`9
`
`

`

`7
`a matrix which will transform DVECT to UVECTby
`way of matrix multiplication. We will call this matrix
`UAPP.MATand write
`
`5,137,364
`
`8
`which said spectrum is different from said spectrum of
`the others of said sources, means in each of said devices
`for providing a response to radiant energy as a function
`of wavelength which differs from the responseto radi-
`ant energy for each of the others of said devices, and
`means for operating said apparatus byfirst providing
`electrical energy to each said source of radiant energy,
`for each of distinct periods of time during which said
`periodsof timeat least one of the other sourcesof radi-
`ant energy is not provided with electrical energy, and
`second allowing or directing radiant energy produced
`by said sources to interact with the sample in such a
`fashion that someradiant energy reflected from and/or
`transmitted by and/or emitted by said sample is re-
`turned to said devices, and third recording the electrical
`signals from each said device for the conversion of
`radiant energy to electrical signal output during each
`such said period of time, and fourth calculating from
`each said recorded electrical signal output a value
`whichis a weighted integration of radiant energy over
`wavelength, thus producing a set of said weighted inte-
`gration values whose numberis equal to the product of
`the numberofsaid distinct time periods with the num-
`ber of said devices for the conversion of radiant energy
`to electrical signal, and fifth calculating from said set of
`weighted integration values said set of multiple mea-
`surements by linear
`transformation of said set of
`weighted integration values utilizing predetermined
`coefficients for transformation.
`2. Apparatus as per claim 1 wherein said sources are
`electrical to radiant energy conversion devices.
`3. Apparatus as per claim 2 in wherein at least two of
`said devices are light emitting diodes.
`4. Apparatus per claim 1 in which said sources of
`radiant energy and said devices for the conversion of
`radiant energy to electrical signal are mounted on a
`commonsubstrate, which substrate provides mechani-
`cal positioning, electrical connections, and a common
`thermal contact.
`,
`5. Apparatusper claim 4 in whichanelectrical device
`sensitive to temperature is also mounted in thermal
`contact with said substrate.
`6. Apparatus per claim 5 in which a device for the
`creation or removal ofheat energyis in thermal contact
`with said substrate.
`7. Apparatus per claim 4 in which said sources of
`radiant energy, and devices, and commonsubstrate are
`sealed with a material which is transparent
`to light
`energy of the wavelengths of interest in the measure-
`ments performed, but impervious to moisture.
`8. Apparatus per claim 1 in which said operations
`means have means for computing said coefficients of
`said linear transformation at the time of manufacture of
`said apparatus by recording a set of observed weighted
`integrations for each of a numberof objects or materials
`with established optical characteristics, and calculating
`the coefficients of the linear transformation using tech-
`niques of multiple regression.
`9. Apparatus per claim 8 in which a plurality ofsets of
`said coefficients are computed each said set being deter-
`mined while said apparatus is maintained at a tempera~-
`ture different from the temperature maintained during
`the determination of each other said set, and said oper-
`ating means having meansforthe selection of a particu-
`lar set of coefficients from said plurality of sets as a
`function of temperature.
`
`UVECT=[UAPP.MAT]*DVECT
`
`Eq. 3
`
`For the purposes of design, we can calculate UAPP-
`-MATas follows:
`1) Multiply Eq.2 by the transpose of APP.MAT
`yielding
`
`TRAPP. MAT\*DVECT= THAPP. MAT} %APP-
`.MAT}*OVECT
`
`Eq4
`
`2) Multiply Eq.4 by the inverse of the product of
`APP.MATwith its transpose yeilding the follow-
`ing equation for OVECT
`
`15
`
`OVECT= InnTAAPP.MAT] {APP.MAT)) *Tr[APP-
`-MAT)* DVECT
`
`Eq.5
`
`20
`
`3) Substitute this expression in Eq.] to obtain an equa-
`tion equivalent to Eq.3.
`
`UVECT=[CHROM.MAT]*In\ THAPP.MAT)-
`“APP.MAT))* TAPP.MATIDVECT
`
`25
`
`Eq.6
`
`Although the equation 6 appears to be complex,in prac-
`tice UAPP.MATreduces to a collection of constants. If
`OVECTand DVECTeach had three components then
`UAPP.MATwould be a 3 by 3 matrix and there would
`be nine constants for its components.
`Current production colorimeters are designed so that
`DVECTis equal to UVECT, and UAPP.MATis a unit
`matrix. This is neither necessary nor optimal. The num-
`ber and shapesof the weighted integrations which com-
`prise the components of DVECT may be chosento
`make best use of the currently available high quality
`low cost physical components. The selection of these
`components may be performed by a mathematical eval-
`uation of the apparatus being designed using the UAPP-
`MAT matrix which would result from each possible
`selection. In preferred implementations of this inven-
`tion, DVECT will generally have more components
`than UVECT.This generally leads to a superior resolu-
`tion and noise performance in the space spanned by
`UVECT. These
`improvements
`can generally be
`achieved at a minimal increase in production cost. Reso-
`lution and noise performance in the UVECTspace are
`predicted from assumptions in the space spanned by
`DVECTusing UAPP.MAT.
`Asa part of the production process the components
`of UAPP.MAT maybe adjusted by calibration, as dis-
`cussed above, to improve the accuracy of the mapping
`rom DVECT to UVECTfor each physical instance of
`the apparatus produced.In effect, this is accomplished
`by the application of multiple regression techniques to a
`set of materials for which OVECT and/or UVECT
`were known.Theeffects of thermal variation and com-
`ponentvariation in user coordinates may be predictedif
`these effects are known OVECT coordinates or in
`DVECTcoordinates.
`T claim:
`1. Optical spectral analysis apparatus for measure-
`mentsof optical properties of a sample which comprises
`a plurality of sources of radiant energy, a plurality of
`devices for the conversion of radiant energyin to elec-
`trical signals, means in eachof said sources for provid-
`ing a spectrum of energy with reference to wavelength
`
`30
`
`45
`
`50
`
`355
`
`60
`
`65
`
`10
`
`10
`
`

`

`9
`10. Apparatus per claim 9 in which said operating
`means includes meansfor the selection of said coeffici-
`ents of linear transformation as a function of tempera-
`ture by interpolation betweensaid sets of coefficients.
`11. Apparatus per claim 1 in which radiation is di-
`rected to said sample from said sources by multiple
`optical fibers, which fibers have a core diameter which
`is at least 90% oftheir clad diameter.
`12. Apparatus per claim 1 in which radiation is di-
`rected from the sample to said devices for the conver-
`sion of radiant energy to electrical signal by optical
`fibers.
`13. Apparatus per claim 11 in which said optical
`fibers are rigidly positioned.
`14, Apparatus per claim 11 in which a plurality of
`semiconductor chips, provide said sources of radiani
`energy and said devices said chips being in physical
`contact with said optical fibers.
`15. Apparatus for the determination of multiple mea-
`surements of radiant energy emitted by a sample com-
`prising multiple devices for the conversion of radiant
`energy to electrical signal, means for optical coupling
`said devices to said sample, means in said multiple de-
`vices for the conversion of radiant energy to electrical
`signals so that each said device for the conversion of
`radiant energy to electrical signal has a response to
`optical energy as a function of wavelength which dif-
`fers from the responseto radiant energy for the other of
`said devices, and means for operating said apparatus
`including first means for observing and recording the
`electrical output of each of said devices for the conver-
`sion of radiant energyto electrical signal, second means
`for calculating from each said recorded electrical out-
`put a value which is a weighted integration of radiant
`energy over wavelength to produce a set of weighted
`integration values, and third meansfor calculating from
`such set of said weighted integration values said set of
`multiple measurements by linear transformation with
`pre-determined coefficients of such set of weighted
`integration values.
`16. Apparatus per claim 15 in which said devices for
`
`the conversion of radiant energy to electrical signal are.
`
`10
`mounted on a common substrate, which substrate pro-
`vides mechanical positioning, electrical connections,
`and a common thermal contact.
`17. Apparatus per claim 16 in which an electrical
`device sensitive to temperature is also mounted in ther-
`mal contact with said substrate.
`18. Apparatus per claim 17 in which a device for the
`creation or removal of heat energy is in thermal contact
`with said substrate.
`19. Apparatus per claim 16 in which said devices and
`common substrate are sealed with a material which is
`transparentto light energy of the wavelengthsof inter-
`est in the measurements performed, but impervious to
`moisture.
`20. Apparatus per claim 15 in which said operating
`meansincludes means for computing the coefficients of
`said linear transformation operation at the time of man-
`ufacture of said apparatus by recording a set of ob-
`served weighted integrations for each of a number
`sources with established optical characteristics and cal-
`culating the coefficients of the linear transformation
`using techniques of multiple regression.
`21. Apparatus per claim 20 wherein said computing
`meansincluding means for computinga plurality of sets
`of said coefficients, each of said sets while said appara-
`tus is maintained at a temperature different from the
`temperature maintained during the computing of each
`other set, and means for incorporating into said third
`meansa particular set of coefficients from said plurality
`of sets as a function of temperature at which said appa-
`ratus is operating.
`.
`22. Apparatus per claim 21 in which said operatin
`meansincludes meansfor the selection of said coeffici-
`ents of linear transformation as a function of tempera-
`ture by