Patent Publication Number: US-2016230270-A1

Title: Temperature-dependent fabrication of integrated computational elements

Description:
BACKGROUND 
     The subject matter of this disclosure is generally related to fabrication of an integrated computational element (ICE) used in optical analysis tools for analyzing a substance of interest, for example, crude petroleum, gas, water, or other wellbore fluids. For instance, the disclosed ICE fabrication includes controlling a temperature of the ICEs being fabricated. 
     Information about a substance can be derived through the interaction of light with that substance. The interaction changes characteristics of the light, for instance the frequency (and corresponding wavelength), intensity, polarization, and/or direction (e.g., through scattering, absorption, reflection or refraction). Chemical, thermal, physical, mechanical, optical or various other characteristics of the substance can be determined based on the changes in the characteristics of the light interacting with the substance. As such, in certain applications, one or more characteristics of crude petroleum, gas, water, or other wellbore fluids can be derived in-situ, e.g., downhole at well sites, as a result of the interaction between these substances and light. 
     Integrated computational elements (ICEs) enable the measurement of various chemical or physical characteristics through the use of regression techniques. An ICE selectively weights, when operated as part of optical analysis tools, light modified by a sample in at least a portion of a wavelength range such that the weightings are related to one or more characteristics of the sample. An ICE can be an optical substrate with multiple stacked dielectric layers (e.g., from about 2 to about 50 layers), each having a different complex refractive index from its adjacent layers. The specific number of layers, N, the optical properties (e.g. real and imaginary components of complex indices of refraction) of the layers, the optical properties of the substrate, and the physical thickness of each of the layers that compose the ICE are selected so that the light processed by the ICE is related to one or more characteristics of the sample. Because ICEs extract information from the light modified by a sample passively, they can be incorporated in low cost and rugged optical analysis tools. Hence, ICE-based downhole optical analysis tools can provide a relatively low cost, rugged and accurate system for monitoring quality of wellbore fluids, for instance. 
     Errors in fabrication of some constituent layers of an ICE design can degrade the ICE&#39;s target performance. In most cases, deviations of &lt;0.1%, and even 0.01% or 0.0001%, from point by point design values of the optical characteristics (e.g., complex refractive indices), and/or physical characteristics (e.g., thicknesses) of the formed layers of the ICE can reduce the ICE&#39;s performance, in some cases to such an extent, that the ICE becomes operationally useless. Examples of fabrication errors include differences between values of complex refractive indices of layers of the ICE as conventionally fabricated—e.g., by reactive magnetron sputtering at room temperature—and as used in a down-hole optical analysis tool—at elevated temperature. In such cases, although complex refractive indices and thicknesses of the layers are found to be on target as fabrication of the ICE is completed at room temperature, the ICE materials&#39; complex refractive indices change as a function of temperature, for some materials significantly, when the fabricated ICE is operated at an operational temperature much higher than the room temperature at which the ICE was fabricated. Such changes in the complex refractive indices of the ICE layers due to differences between fabrication and operational temperatures lead to temperature-dependent performance degradation for the conventionally fabricated ICE. Those familiar or currently practicing in the art will readily appreciate that the ultra-high accuracies required by ICE designs challenge the state of the art in thin film fabrication techniques. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIGS. 1A-1C  show multiple configurations of an example of a system for analyzing wellbore fluids that uses a well logging tool including an ICE. 
         FIG. 2  is a flowchart showing an example of a process for designing an ICE. 
         FIGS. 3A-3C  show multiple configurations of an example of a system for fabricating one or more ICEs in which temperature of the ICE(s) being fabricated is controlled. 
         FIGS. 4A-4I  show aspects of ICE fabrication at temperatures lower than an annealing temperature of the ICE(s). 
         FIGS. 5A-5D  show aspects of ICE fabrication at temperatures higher than the annealing temperature of the ICE(s). 
         FIG. 6  is a flowchart showing an example of an ICE fabrication during which temperature of ICEs being fabricated is controlled. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     Technologies are described for controlling temperature of ICEs during ICE fabrication. For example, temperature of substrates of the ICEs is maintained at a target fabrication temperature by heating a substrate support—that supports the ICEs during fabrication—through electrical conductive heating elements that are part of the substrate support, inductive elements that are adjacent the substrate support, radiative elements (e.g., black body, laser, etc.) that are spaced apart from the substrate support, and the like. In some implementations, the target fabrication temperature at which layers of the ICEs are formed is the operational temperature. In these cases, performance of the fabricated ICEs will be above a minimum required performance at least for temperatures in the vicinity of the operational temperature. In some implementations, the target fabrication temperature at which the layers of the ICEs are formed exceeds an annealing temperature of the constituent materials of the ICE layers. The annealing temperature of a material is a temperature at which the material irreversibly transitions from a stressed state below the annealing temperature to an annealed (stress-relieved) state above the annealing temperature. The latter cases are used when it is required that performance of the fabricated ICEs exceeds the minimum required performance over a broad operational temperature range. 
     Prior to describing example implementations of the disclosed technologies for ICE fabrication, the following technologies are described below: in Section (1)—optical analysis tools based on ICE along with examples of their use in oil/gas exploration, and in Section (2)—techniques for designing an ICE. 
     (1) ICE-Based Analysis of Wellbore Fluids 
       FIGS. 1A-1C  show multiple configurations  100 ,  100 ′,  100 ″ of an example of a system for analyzing wellbore fluids  130 , such that analyses are generated from measurements taken with a well logging tool  110  configured as an ICE-based optical analysis tool. The disclosed system also is referred to as a well logging system. 
     Each of the configurations  100 ,  100 ′,  100 ″ of the well logging system illustrated in  FIGS. 1A-1C  includes a rig  14  above the ground surface  102  and a wellbore  38  below the ground surface. The wellbore  38  extends from the ground surface into the earth  101  and generally passes through multiple geologic formations. In general, the wellbore  38  can contain wellbore fluids  130 . The wellbore fluids  130  can be crude petroleum, mud, water or other substances and combinations thereof. Moreover, the wellbore fluids  130  may be at rest, or may flow toward the ground surface  102 , for instance. Additionally, surface applications of the well logging tool  110  may include water monitoring and gas and crude transportation and processing. 
       FIG. 1A  shows a configuration  100  of the well logging system which includes a permanent installation adjacent to the wellbore  38 . In some implementations, the permanent installation is a set of casing collars that reinforce the wellbore  38 . In this case, a casing collar  28  from among the set of casing collars supports the well logging tool  110  and a telemetry transmitter  30 . A temperature of the wellbore fluids  130  increases as a function of distance (e.g., a depth) relative to the ground surface  102  based on a particular temperature gradient. E.g., the temperature at the ground surface  102  is substantially equal to the ambient temperature, T ambient , has a value of approximately 150° C. adjacent the casing collar  28 , and further increases at larger depths in the wellbore  38 . In this manner, the well logging tool  110  operates at a constant operational temperature T op  adjacent the underground location of the casing collar  28  to determine and log properties of the wellbore fluids  130  at the operational temperature T op . 
       FIG. 1B  shows another configuration  100 ′ of the well logging system which includes a drilling tool  24  attached to a drill string  16 ′. The drilling tool  24  includes a drill bit  26 , the ICE-based well logging tool  110  configured as a measurement while drilling (MWD) and/or logging while drilling (LWD) tool, and the telemetry transmitter  30 . Drilling mud is provided through the drill string  16 ′ to be injected into the borehole  38  through ports of the drill bit  26 . The injected drilling mud flows up the borehole  38  to be returned above the ground level  102 , where the returned drilling mud can be resupplied to the drill string  16 ′ (not shown in  FIG. 1B ). In this case, the MWD/LWD-configured well logging tool  110  generates and logs information about the wellbore fluids  130  (e.g., drilling mud in this case) adjacent the working drill bit  26  at an operational temperature T op  that depends on drilling-related factors such as vertical speed and rotation speed of the drill bit  26 , hardness of formation that currently being drilled, heat transfer properties of the formation and of the drilling mud, and the like. Here, the operational temperature T op  also depends on distance (e.g., depth) of the drilling tool  24  relative the ground level  102 . For these reasons, the operational temperature T op  is significantly higher than the ambient temperature T ambient  and may be changing based on the foregoing environmental parameters adjacent the drill bit  26 . 
       FIG. 1C  shows yet another configuration  100 ″ of the well logging system which includes a tool string  20  attached to a cable  16  that can be lowered or raised in the wellbore  38  by draw works  18 . The tool string  20  includes measurement and/or logging tools to generate and log information about the wellbore fluids  130  in the wellbore  38 . In the configuration  100 ″ of the well logging system, this information is generated as a function of a distance (e.g., a depth) with respect to the ground surface  102 . Moreover, the operational temperature T op  of the tool string  20  varies continuously as a function of wellbore depth, and thus the information about the wellbore fluids  130  in the wellbore  38  generated by the tool string  20  is temperature dependent. In the example illustrated in  FIG. 1C , the tool string  20  includes the well logging tool  110 , one or more additional well logging tool(s)  22 , and the telemetry transmitter  30 . Each of the well logging tools  110  and  22  measures one or more properties of the wellbore fluids  130 . In some implementations, the well logging tool  110  determines values of the one or more properties in real time and reports those values instantaneously as they occur in the flowing stream of wellbore fluids  130 , sequentially to or simultaneously with other measurement/logging tools  22  of the tool string  20 . 
     In each of the above configurations  100 ,  100 ′ and  100 ″ of the well logging system, the values of the one or more properties measured by the well logging tool  110  are provided (e.g., as a detector signal  165 ) to the telemetry transmitter  30 . The latter communicates the measured values to a telemetry receiver  40  located above the ground surface  102 . The telemetry transmitter  30  and the telemetry receiver  40  can communicate through a wired or wireless telemetry channel. In some implementations of the system configurations  100 ′,  100 ″ illustrated in  FIGS. 1B and 1C , e.g., in slickline or coiled tubing applications, measurement data generated by the well logging tool  110  can be written locally to memory of the well logging tool  110 . 
     The measured values of the one or more properties of the wellbore fluids  130  received by the telemetry receiver  40  can be logged and analyzed by a computer system  50  associated with the rig  14 . In this manner, the measurement values provided by the well logging tool  110  can be used to generate physical and chemical information about the wellbore fluids  130  in the wellbore  38  as a function of temperature, for instance. 
     Referring again to  FIG. 1A , the well logging tool  110  includes a light source  120 , an ICE  140  and an optical transducer  160 . The well logging tool  110  has a frame  112  such that these components are arranged in an enclosure  114  thereof. A temperature inside the enclosure  114  is the operational temperature T op . A cross-section of the well logging tool  110  in a plane perpendicular to the page can vary, depending on the space available. For example, the well logging tool&#39;s cross-section can be circular or rectangular, for instance. The well logging tool  110  directs light to the sample  130  through an optical interface  116 , e.g., a window in the frame  112 . The well logging tool  110  is configured to probe the sample  130  (e.g., the wellbore fluids stationary or flowing) in the wellbore  38  through the optical interface  116  and to determine an amount (e.g., a value) of a given characteristic (also referred to as a characteristic to be measured) of the probed sample  130  at the operational temperature T op . The characteristic to be measured can be any one of multiple characteristics of the sample  130  including concentration of a given substance in the sample, a gas-oil-ratio (GOR), pH value, density, viscosity, etc. 
     The light source  120  outputs light with a source spectrum over a particular wavelength range, from a minimum wavelength λ min  to a maximum wavelength λ max . In some implementations, the source spectrum can have non-zero intensity over the entire or most of the wavelength range λ max −λ min . In some implementations, the source spectrum extends through UV-vis (0.2-0.8 μm) and near-IR (0.8-2.5 μm) spectral ranges. Alternatively, or additionally, the source spectrum extends through near-IR and mid-IR (2.5-25 μm) spectral ranges. In some implementations, the source spectrum extends through near-IR, mid-IR and far-IR (25-100 μm) spectral ranges. In some implementations, the light source  120  is tunable and is configured in combination with time resolved signal detection and processing. 
     The light source  120  is arranged to direct a probe beam  125  of the source light towards the optical interface  116  where it illuminates the sample  130  at a location  127 . The source light in the probe beam  125  interacts with the sample  130  and reflects off it as light modified by the sample  130 . The light modified by the sample at T op  has a modified spectrum I(λ;T op )  135 ′ over the particular wavelength range. In the reflective configuration of the well logging tool  110  illustrated in  FIG. 1A  (i.e., where the light to be analyzed reflects at the sample/window interface), the modified spectrum I(λ;T op )  135 ′ is a reflection spectrum associated with the sample  130 . In a transmission configuration of the well logging tool  110  (not shown in  FIG. 1A ), the probe beam is transmitted through the sample as sample modified light, such that the modified spectrum I(λ;T op )  135 ′ is a transmission spectrum associated with the sample. 
     In general, the modified spectrum I(λ;T op )  135 ′ encodes information about multiple characteristics associated with the sample  130 , and more specifically the encoded information relates to current values of the multiple characteristics at the operational temperature T op . In the example illustrated in  FIG. 1A , the modified spectrum  135 ′ contains information about one or more characteristics of the wellbore fluids  130 . 
     With continued reference to  FIG. 1A , and the Cartesian coordinate system provided therein for reference, the ICE  140  is arranged to receive a beam  135  of the sample modified light, and is configured to process it and to output a beam  155  of processed light. The beam  135  of sample modified light is incident on a first surface of the ICE  140  along the z-axis, and the beam  155  of processed light is output along the z-axis after transmission through the ICE  140 . Alternatively or additionally, the beam  155  (or an additional reflected beam) of processed light can be output after reflection off the first surface of the ICE  140 . The ICE  140  is configured to process the sample modified light by weighting it in accordance with an optical spectrum w(λ;T op )  150  associated with a characteristic to be measured at the operational temperature T op . 
     The optical spectrum w(λ;T op )  150  is determined offline by applying conventional processes to a set of calibration spectra I(λ;T op ) of the sample which correspond to respective known values at T op  of the characteristic to be measured. As illustrated by optical spectrum w(λ;T op )  150 , optical spectrums generally may include multiple local maxima (peaks) and minima (valleys) between λ min  and λ max . The peaks and valleys may have the same or different amplitudes. For instance, an optical spectrum w(λ;T op ) can be determined through regression analysis of N c  calibration spectra I j (λ;T op ) of a sample, where j=1, . . . , N c , such that each of the calibration spectra I j (λ;T op ) corresponds to an associated known value at T op  of a given characteristic for the sample. A typical number N c  of calibration spectra I j (λ;T op ) used to determine the optical spectrum w(λ;T op )  150  through such regression analysis can be N c =10, 40 or 100, for instance. The regression analysis outputs, using the N c  calibration spectra I j (λ;T op ) as inputs, a spectral pattern that is unique to the given characteristic at T op . The spectral pattern output by the regression analysis corresponds to the optical spectrum w(λ;T op )  150 . In this manner, when a value of the given characteristic for the sample is unknown at T op , a modified spectrum I u (λ;T op ) of the sample is acquired at T op  and then the modified spectrum I u (λ;T op ) is weighted by the ICE  140  to determine a magnitude of the spectral pattern corresponding to the optical spectrum w(λ;T op )  150  within the modified spectrum I u (λ;T op ). The determined magnitude is proportional to the unknown value at T op  of the given characteristic for the sample. 
     For example, the sample can be a mixture (e.g., the wellbore fluid  130  at T op ) containing substances X, Y and Z, and the characteristic to be measured for the mixture is concentration c X  of substance X in the mixture. In this case, N c  calibration spectra I j (λ;T op ) were acquired for N c  samples of the mixture having respectively known concentration values at T op  for each of the substances contained in the N c  samples. By applying regression analysis to the N c  calibration spectra I j (λ;T op ), a first spectral pattern that is unique to the concentration c X  of the X substance at T op  can be detected (recognized), such that the first spectral pattern corresponds to a first optical spectrum w cX (λ;T op ) associated with a first ICE, for example. Similarly, second and third spectral patterns that are respectively unique to concentrations c Y  and c Z  of the Y and Z substances at T op  can also be detected, such that the second and third spectral patterns respectively correspond to second and third optical spectra w cY (λ;T op ) and w c (λ;T op ) respectively associated with second and third ICEs. In this manner, when a new sample of the mixture (e.g., the wellbore fluid  130  at T op ) has an unknown concentration c X  of the X substance, for instance, a modified spectrum I u (λ;T op ) of the new sample can be acquired at T op  by interacting the probe beam with the mixture, then the modified spectrum I u (λ;T op ) is weighted with the first ICE to determine a magnitude of the first spectral pattern within the modified spectrum I u (λ;T op ). The determined magnitude is proportional to the unknown value at T op  of the concentration c X  of the X substance for the new sample. 
     Referring again to  FIG. 1A , the ICE  140  includes N layers of materials stacked on a substrate, such that complex refractive indices of adjacent layers are different from each other. The total number of stacked layers can be between 6 and 50, for instance. The substrate material can be BK7, diamond, Ge, ZnSe (or other transparent dielectric material), and can have a thickness in the range of 0.02-2 mm, for instance, to insure structural integrity of the ICE  140 . 
     Throughout this specification, a complex index of refraction (or complex refractive index) n* of a material has a complex value, Re(n*)+iIm(n*). Re(n*) represents a real component of the complex index of refraction responsible for refractive properties of the material, and Im(n*) represents an imaginary component of the complex index of refraction (also known as extinction coefficient κ) responsible for absorptive properties of the material. In this specification, when it is said that a material has a high complex index of refraction n* H  and another material has a low complex index of refraction n* L , the real component Re(n* H ) of the high complex index of refraction n* H  is larger than the real component Re(n* L ) of the low complex index of refraction n* L , Re(n* H )&gt;Re(n* L ). Materials of adjacent layers of the ICE are selected to have a high complex index of refraction n* H  (e.g., Si), and a low complex index of refraction n* L  (e.g., SiO 2 ). Here, Re(n* Si )≈2.4&gt;Re(n* SiO2 )≈1.5. For other material pairings, however, the difference between the high complex refractive index n* H  and low complex refractive index n* L  may be much smaller, e.g., Re(n* H )≈1.6&gt;Re(n* L )≈1.5. The use of two materials for fabricating the N layers is chosen for illustrative purposes only. For example, a plurality of materials having different complex indices of refraction, respectively, can be used. Here, the materials used to construct the ICE are chosen to achieve a desired optical spectrum w(λ)  150 . 
     A set of design parameters  145 —which includes the total number of stacked layers N, the complex refractive indices n* H (T op ), n* L (T op ) at T op  of adjacent stacked layers, and the thicknesses of the N stacked layers t(1), t(2), . . . , t(N−1), t(N)—of the ICE  140  can be chosen (as described below in connection with  FIG. 2 ) to be spectrally equivalent, at T op , to the optical spectrum w(λ;T op )  150  associated with the characteristic to be measured. As such, an ICE design  145  is the set of thicknesses {t(i), i=1, . . . , N} of the N layers stacked on the substrate and their alternating complex refractive indices n* H (T op ), n* L (T op ) at T op  that corresponds to the optical spectrum w(λ;T op )  150 . 
     In view of the above, the beam  155  of processed light output by the ICE  140  has a processed spectrum P(λ;T op )=w(λ;T op ) I(λ;T op )  155 ′ over the wavelength range λ max −λ min  at T op , such that the processed spectrum  155 ′ represents the modified spectrum I(λ;T op )  135 ′ weighted by the optical spectrum w(λ;T op )  150  associated with the characteristic to be measured. 
     The beam  155  of processed light is directed from the ICE  140  to the optical transducer  160 , which detects the processed light and outputs a detector signal  165 . A value (e.g., a voltage) of the detector signal  165  is a result of an integration of the processed spectrum  155 ′ over the particular wavelength range and is proportional to the unknown value c(T op )  165 ′ at T op  of the characteristic to be measured for the sample  130 . 
     In some implementations, the well logging tool  110  can include a second ICE (not shown in  FIG. 1A ) associated with a second ICE design that includes a second set of thicknesses {t′(i), i=1, . . . , N′} of a second total number of layers N′ layers with alternating complex refractive indices (n*′ H (T op ),n*′ L (T op )) at T op  stacked on a second substrate that correspond to a second optical spectrum w′(λ;T op ). Here, the second optical spectrum w′(λ;T op ) is associated with a second characteristic of the sample  130  at T op , and a second processed spectrum represents the modified spectrum I(λ;T op )  135 ′ weighted by the second optical spectrum w′(λ;T op ), such that a second value of a second detector signal is proportional to a value at T op  of the second characteristic for the sample  130 . 
     In some implementations, the determined value  165 ′ of the characteristic to be measured can be logged along with the operational temperature T op , a measurement time, geo-location, and other metadata, for instance. In some implementations, the detector signal  165 , which is proportional to a characteristic to be measured by the well logging tool  110 , can be used as a feedback signal to adjust the characteristic of the sample, to modify the sample or environmental conditions associated with the sample, as desired. 
     Characteristics of the wellbore fluids  130  that can be related to the modified spectrum  135 ′ through the optical spectra associated with the ICE  140  and other ICEs (not shown in  FIG. 1A ) are concentrations of one of asphaltene, saturates, resins, aromatics; solid particulate content; hydrocarbon composition and content; gas composition C1-C6 and content: CO 2 , H 2 S and correlated PVT properties including GOR, bubble point, density; a petroleum formation factor; viscosity; a gas component of a gas phase of the petroleum; total stream percentage of water, gas, oil, solid articles, solid types; oil finger printing; reservoir continuity; oil type; and water elements including ion composition and content, anions, cations, salinity, organics, pH, mixing ratios, tracer components, contamination, or other hydrocarbon, gas, solids or water characteristic. 
     (2) Aspects of ICE Design 
     Aspects of a process for designing an ICE associated with a characteristic (e.g., one of the characteristics enumerated above) to be measured at an operational temperature T op  are described below. Here, an input of the ICE design process is a theoretical optical spectrum w th (λ;T op ) associated with the characteristic. An output of the ICE design process is an ICE design that includes specification of (1) a substrate and a number N of layers to be formed on the substrate, each layer having a different complex refractive index from its adjacent layers; and (2) complex refractive indices and thicknesses of the substrate and layers that correspond to a target optical spectrum w t (λ;T op ). The target optical spectrum w t (λ;T op ) is different from the theoretical optical spectrum w th (λ;T op ) associated with the characteristic at T op , such that the difference between the target and theoretical optical spectra cause degradation of a target performance relative to a theoretical performance of the ICE within a target error tolerance. In this example, the target performance represents a finite accuracy with which an ICE having the target optical spectrum w t (λ;T op ) is expected to predict known values at T op  of the characteristic corresponding to a set of validation spectra of a sample with a finite (non-zero) error. Here, the predicted values of the characteristic are obtained through integration of the validation spectra of the sample respectively weighted by the ICE with the target optical spectrum w t (λ;T op ). The theoretical performance represents the maximum accuracy with which the ICE—if it had the theoretical optical spectrum w th (λ;T op )—would predict the known values at T op  of the characteristic corresponding to the set of validation spectra of the sample. Here, the theoretically predicted values of the characteristic would be obtained through integration of the validation spectra of the sample respectively weighted by the ICE, should the ICE have the theoretical optical spectrum w th (λ;T op ). 
       FIG. 2  is a flowchart of an example of a process  200  for generating an ICE design. One of the inputs to the process  200  is a theoretical optical spectrum w th (λ;T op )  205 . For instance, to design an ICE for measuring concentration of a substance X in a mixture at T op , a theoretical optical spectrum w th (λ;T op ), associated with the concentration of the substance X in the mixture, is accessed, e.g., in a data repository. As described above in this specification, the accessed theoretical optical spectrum w th (λ;T op ) corresponds to a spectral pattern detected offline, using a number N c  of calibration spectra of the mixture, each of the N c  calibration spectra corresponding to a known concentration at T op  of the substance X in the mixture. An additional input to the process  200  is a specification of materials for the ICE layers. Materials having different complex refractive indices at T op , respectively, are specified such that adjacent ICE layers are formed from materials with different complex refractive indices. For example, a first material (e.g., Si) having a high complex refractive index n* H  and a second material (SiO x ) having a low complex refractive index n* L  are specified to alternately form ICE layers. As another example, a layer can be made from high index material (e.g., Si), followed by a layer made from low index material (e.g., SiO x ), followed by a layer made from a different high index material (e.g., Ge), followed by a layer made from a different low index material (MgF 2 ), etc. The iterative design process  200  is performed in the following manner. 
     At  210  during the j th  iteration of the design process  200 , thicknesses {t S (j), t(1;j), t(2;j), . . . , t(N−1;j), t(N;j)} of the substrate and a number N of layers of the ICE are iterated. 
     At  220 , a j th  optical spectrum w(λ;T op ;j) of the ICE is determined corresponding to complex refractive indices (n* L (T op ),n* H (T op )) at T op  and previously iterated thicknesses {t S (j), t(1;j), t(2;j), . . . , t(N−1;j), t(N;j)} of the substrate and the N layer, each having a different complex refractive index from is adjacent layers. The iterated thicknesses of the substrate and the N layers are used to determine the corresponding j th  optical spectrum w(λ;T op ;j) of the ICE in accordance with conventional techniques for determining spectra of thin film interference filters. 
     At  230 , performance of the ICE, which has the j th  optical spectrum w(λ;T op ;j) determined at  220 , is obtained. To do so, a set of validation spectra taken at T op  of a sample is accessed, e.g., in a data repository. Respective values at T op  of a characteristic of the sample are known for the validation spectra. For instance, each of N v  validation spectra I(λ;T op ;m) corresponds to a value v(m;T op ) at T op  of the characteristic of the sample, where m=1, . . . , N v . In the example illustrated in  FIG. 2 , N v =11 validation spectra, respectively corresponding to 11 known values of the characteristic to be measured for the sample, are being used. 
     Graph  235  shows (in open circles) values c(m;T op ;1) at T op  of the characteristic of the sample predicted by integration of the validation spectra I(λ;T op ;m) processed by the ICE, which has the j th  optical spectrum w(λ;T op ;j), plotted against the known values v(m;T op ) at T op  of the characteristic of the sample corresponding to the validation spectra I(λ;T op ;m). The predicted values c(m;T op ;1) of the characteristic are found by substituting, in formula  165 ′ of  FIG. 1A , (1) the spectrum I(λ;T op )  135 ′ of sample modified light with the respective validation spectra I(λ;T op ;m) and (2) the target spectrum w t (λ;T op )  150  with the j th  optical spectrum w(λ;T op ;1). In this example, performance of the ICE at T op , which has the j th  optical spectrum w(λ;T op ;j), is quantified in terms of a weighted measure of distances from each of the open circles in graph  235  to the dashed-line bisector between the x and y axes. This weighted measure is referred to as the standard calibration error of the ICE at T op , SEC(T op ). For instance, an ICE having the theoretical spectrum w th (λ;T op ) has a theoretical SEC th (T op ) that represents a lower bound for the SEC(T op ;j) of the ICE having the j th  spectrum w(λ;T op ;j) determined at  220  during the j th  iteration of the design process  200 : SEC(T op ;j)&gt;SEC th (T op ). 
     In this specification, the SEC is chosen as a metric for evaluating ICE performance for the sake of simplicity. Note that there are other figures of merit that may be used to evaluate performance of ICE, as is known in the art. For example, sensitivity—which is defined as the slope of characteristic change as a function of signal strength—can also be used to evaluate ICE performance. As another example, standard error of prediction (SEP)—which is defined in a similar manner to the SEC except it uses a different set of validation spectra—can be used to evaluate ICE performance. Any of the figure(s) of merit known in the art is/are evaluated in the same general way by comparing theoretical performance with that actually achieved. Which figure(s) of merit or combinations are used to evaluate ICE performance is determined by the specific ICE design. 
     The iterative design process  200  continues by iterating, at  210 , the thicknesses of the substrate and the N layers. The iterating is performed such that a (j+1) th  optical spectrum w(λ;T op ;j+1)—determined at  220  from the newly iterated thicknesses—causes, at  230 , improvement in performance of the ICE, to obtain SEC(T op ;j+1)&lt;SEC(T op ;j). In some implementations, the iterative design process  200  is stopped when the ICE&#39;s performance at T op  reaches a local maximum, or equivalently, the SEC of the ICE reaches a local minimum. For example, the iterative process  200  can be stopped at the (j+1) th  iteration when the current SEC(T op ;j+1) is larger than the last SEC(T op ;j), SEC(T op ;j+1)&gt;SEC(T op ;j). In some implementations, the iterative design process  200  is stopped when, for a given number of iterations, the ICE&#39;s performance exceeds a specified threshold performance for a given number of iterations. For example, the iterative design process  200  can be stopped at the j th  iteration when three consecutive SEC values decrease monotonously and are less than a specified threshold value: SEC 0 &gt;SEC(T op ;j−2)&gt;SEC(T op ;j−1)&gt;SEC(T op ;j). 
     In either of these cases, an output of the iterative process  200  represents a target ICE design  245  to be used for fabricating an ICE  140 , like the one described in  FIG. 1A , for instance. The ICE design  245  includes specification of (1) a substrate and N layers, each having a different complex refractive index from its adjacent layers, and (2) complex refractive indices n* S (T op ), n* H (T op ), n* L (T op ) at T op  and thicknesses {t S (j), t(1;j), t(2;j), . . . , t(N−1;j), t(N;j)} of the substrate and N layers corresponding to the j th  iteration of the process  200 . Additional components of the ICE design are the optical spectrum w(λ;T op ;j) and the SEC(T op ;j)—both determined during the j th  iteration based on the thicknesses {t S (j), t(1;j), t(2;j), . . . , t(N−1;j), t(N;j)}. As the ICE design  245  is used as input for fabrication processes described herein, the iteration index j—at which the iterative process  200  terminates—is dropped from the notations used for the components of the ICE design. 
     In this manner, the thicknesses of the substrate and the N layers associated with the ICE design  245  are denoted {t S , t(1), t(2), . . . , t(N−1), t(N)} and are referred to as the target thicknesses; the complex refractive indices (n* L (T op ),n* H (T op )) at T op  are referred to as target complex refractive indices. The optical spectrum associated with the ICE design  245  and corresponding to the target thicknesses is referred to as the target optical spectrum w t (λ;T op )  150 . The SEC associated with the ICE design  245 —obtained in accordance with the target optical spectrum w t (λ;T op )  150  corresponding to the target thicknesses—is referred to as the target SEC t (T op ). In the example illustrated in  FIG. 2 , the ICE design  245  has a total of N=9 alternating Si and SiO 2  layers. The layers&#39; thicknesses (in nm) are shown in the table. An ICE fabricated based on the example of ICE design  245  illustrated in  FIG. 2  is used to predict value(s) of concentration of substance X in wellbore fluids  130  at an operational temperature T op =150° C., for instance. 
     (3) Technologies for Controlling Temperature of ICEs During Fabrication 
     As described above in connection with  FIG. 2 , an ICE design for fabricating ICEs to be operated at an operational temperature T op  (e.g., in a down-hole application) specifies a substrate and a number of material layers, each having a different complex refractive index from its adjacent layers. An ICE fabricated in accordance with such an ICE design has, when operated at T op , (i) a target optical spectrum w t (λ;T op ) and (ii) a target performance SEC t (T op ), both of which corresponding to the temperature-dependent complex refractive indices and target thicknesses of the substrate and the layers specified by the ICE design. Performance of the ICEs fabricated in accordance with an ICE design can be very sensitive to actual values of the complex refractive indices and thicknesses obtained during deposition, such that for some layers of the ICE design, a small error, e.g., 0.1% or 0.001%, in the optical or physical characteristics of a deposited layer can result in a reduction in the performance of an ICE associated with the ICE design below an acceptable threshold. For many reasons, the actual values of the complex refractive indices of materials to be deposited and/or the rate(s) of the deposition can drift when materials used for deposition (Si, SiO 2 ) are differently contaminated, or react differently due to different chamber conditions (e.g., pressure or temperature). As such, a temperature T fab  at which the ICEs are fabricated and the temperature(s) at which the ICEs are operated over (e.g., at T op  in a down-hole application) are correlated, and in some instances matched. As a practical matter, the temperature dependence of the complex refractive indices can be hard to predict. Hence, fabrication of ICEs to operate at high operational temperature T op , or over a wide range of operational temperatures, is all the more challenging. 
     Conventionally, ICEs have been fabricated by reactive magnetron sputtering at ambient (e.g., room) temperature. ICEs fabricated using a particular ICE design—chosen based on a particular set of performance criteria (e.g., SEC, standard error in prediction (SEP), sensitivity, SNR, and/or theoretical temperature performance)—are subjected to ex-situ post-fabrication measurements to measure the ICEs&#39; optical spectra w t (λ;T). Results of these ex-situ measurements are used to determine optical properties of the individual layer materials at various temperatures, e.g., n* H (T), dn* H /dT, and n* L (T), dn* L /dT. Such measurements generate information on how the ICEs will ultimately perform at the operational temperature(s) by extrapolation. Additionally, ICEs fabricated conventionally at ambient temperature to be used at elevated temperatures or over a broad temperature range, are annealed ex-situ (e.g., by placing the completed ICEs in a high temperature state for a period of time) to minimize ICE performance drift at elevated operational temperature(s) T op . Such annealing—which may require additional measurements to determine changes in optical spectrum w t (λ;T) caused by the annealing process—further complicates conventional ICE fabrication. 
     The disclosed technologies relate to heating the ICEs&#39; substrate during fabrication to eliminate (or move in-situ) parts of the ex-situ post-fabrication processing and analysis. Heating of the ICEs&#39; substrate can be accomplished in-situ by conduction or radiation. Conduction heating techniques typically include adding conductive heating elements onto a substrate holder, usually a drum, plate or platen. Intensity of current through the conductive heating elements is adjusted to achieve a desired temperature of the ICEs&#39; substrate. Radiative heating techniques include using an infrared (IR) emitter (e.g., a blackbody radiation emitter or an IR laser) that is spaced apart from the substrate holder or an inductive emitter that is adjacent the substrate holder. Both of the latter types of emitters are focused on one or more portions of the substrate holder to achieve a desired temperature of the ICEs&#39; substrate. 
     The disclosed technologies can be used to fabricate ICEs to have a target optical spectrum and a corresponding ICE performance at an operational temperature T op . As the optical properties of the materials used in fabricating ICEs are dependent on temperature, the ICEs&#39; substrate temperature during deposition and the materials&#39; temperature as they are being deposited are controlled to obtain complex refractive indices of the ICE layers with target values n* H (T op ) n* L (T op ) at the operational temperature T op . These results lead to a desired ICE performance at the operational temperature T op . For example, the ICEs&#39; substrate temperature is raised to the expected operational temperature (e.g., downhole T op =150° C.). Here, the ICE materials&#39; optical properties can be monitored and controlled as the materials are deposited at the expected operational conditions. As another example, the ICEs&#39; substrate temperature is used during deposition of the ICE layers as an extremely accurate and fine tunable control to obtain the complex refractive indices having target values n* H (T op ) n* L (T op ) at the operational temperature T op . Here, changing the ICEs&#39; substrate temperature during material deposition results in controlled values n* H (T) or n* L (T) of the complex refractive indices of a layer currently being deposited or of layers remaining to be deposited. 
     In this manner, the disclosed technologies enable ICEs to be designed and fabricated for use over a target operational temperature range more accurately and rapidly than conventional ICE design and fabrication. Details of one or more of the foregoing embodiments are described below. 
     (3.1) System for ICE Fabrication that Allows for In-Situ Controlling Temperature of ICEs 
     Once a target ICE design is established to specify values of complex refractive indices n* H (T op ), n* L (T op ) corresponding to an operational temperature T op  at which ICEs are to be operated, the target ICE design can be provided to an ICE fabrication system in which one or more ICEs are fabricated based on the target ICE design. Technologies for controlling temperature of ICEs during fabrication are disclosed below to ensure accurate performance of the fabricated ICEs at the operational temperature T op . A fabrication system for implementing these technologies is described first. 
       FIGS. 3A-3C  shows different configurations of an example of an ICE fabrication system  300 . The ICE fabrication system  300  includes a deposition chamber  301  to fabricate one or more ICEs  306 , a measurement system  304  to measure characteristics of formed layers of the ICEs while the ICEs are being fabricated, and a computer system  305  to control the fabrication of the one or more ICEs  306  based at least in part on results of the measurements. 
     The deposition chamber  301  includes one or more deposition sources  303  to provide materials with a low complex index of refraction n* L  and a high complex index of refraction n* H  used to form layers of the ICEs  306 . Substrates on which layers of the ICEs  306  will be deposited are placed on a substrate support  302 , such that the ICEs  306  are within the field of view of the deposition source(s)  303 . The substrates have a thickness t S  and a complex refractive index n* S (T op ) specified by the ICE design  307 . Various physical vapor deposition (PVD) techniques can be used to form a stack of layers of each of the ICEs  306  in accordance with a target ICE design  307  (e.g., ICE design  145  or  245 , for instance.) Here, the ICE design  307  includes specification of a complex index of refraction n S (T op ) at an operational temperature T op  and thickness t S  of a substrate; complex indices of refraction n* H (T op ), n* L (T op ) at T op  and target thicknesses {t(i), i=1−N} of N layers; and a corresponding target optical spectrum w t (λ;T op ), where λ is within an operational wavelength range [λ min , λ max ] of the ICEs. 
     In accordance with PVD techniques, the layers of the ICE are formed by condensation of a vaporized form of material(s) of the source(s)  305 , while maintaining vacuum in the deposition chamber  301 . One such example of PVD technique is electron beam (E-beam) deposition, in which a beam of high energy electrons is electromagnetically focused onto material(s) of the deposition source(s)  303 , e.g., either Si, or SiO 2 , to evaporate atomic species. In some cases, E-beam deposition is assisted by ions, provided by ion-sources (not shown in  FIGS. 3A-3C ), to clean or etch the ICE substrate(s); and/or to increase the energies of the evaporated material(s), such that they are deposited onto the substrates more densely, for instance. Other examples of PVD techniques that can be used to form the stack of layers of each of the ICEs  306  are cathodic arc deposition, in which an electric arc discharged at the material(s) of the deposition source(s)  303  blasts away some into ionized vapor to be deposited onto the ICEs  306  being formed; evaporative deposition, in which material(s) included in the deposition source(s)  303  is(are) heated to a high vapor pressure by electrically resistive heating; pulsed laser deposition, in which a laser ablates material(s) from the deposition source(s)  303  into a vapor; or sputter deposition, in which a glow plasma discharge (usually localized around the deposition source(s)  303  by a magnet—not shown in  FIGS. 3A-3C ) bombards the material(s) of the source(s)  303  sputtering some away as a vapor for subsequent deposition. 
     A relative orientation of and separation between the deposition source(s)  303  and the substrate support  302  are configured to provide desired deposition rate(s) and spatial uniformity across the ICEs  306  disposed on the substrate support  302 . As a spatial distribution of a deposition plume provided by the deposition source(s)  303  is non-uniform along at least a first direction, current instances of ICEs  306  are periodically moved by the substrate support  302  relative to the deposition source  303  along the first direction (e.g., rotated along an azimuthal direction “θ” relative to an axis that passes through the deposition source(s)  303 ) to obtain reproducibly uniform layer deposition of the ICEs  306  within a batch. 
     A heating source  310  provides heat to the current instances of the ICEs  306  distributed on the substrate support  302  to maintain their temperature within a target fabrication temperature range ΔT fab  around a target fabrication temperature T fab . A width of the target fabrication temperature range ΔT fab  is a fraction, e.g., 5%, 10%, 20%, or 30% of the target fabrication temperature T fab . For instance, when the target fabrication temperature T fab =150° C., the temperature range ΔT fab  can be [146.25° C., 153.75° C.], [142.5° C., 157.5° C.], [135° C., 165° C.] or [127.5° C., 172.5° C.]. A process parameter  315  that includes the target fabrication temperature T fab  and the target fabrication temperature range ΔT fab  is accessed by the computer system  305  and used to control the temperature of current instances of ICEs  306  during fabrication of ICEs associated with the ICE design  307 . 
     In a configuration  310 -A of the heating source associated with a configuration  300 -A of the ICE fabrication system, the heating source includes electrical heating elements distributed throughout the substrate support  302  to maintain the target fabrication temperature T fab  of the current instances of ICEs  306  uniformly across the substrate support  302 . An intensity of current carried through the electrical conductive heating elements is adjusted to obtain the target fabrication temperature T fab  for the current instances of ICEs  306 . 
     In another configuration  310 -B of the heating source associated with a configuration  300 -B of the ICE fabrication system, the heating source includes an IR or blackbody radiation emitter placed apart from the substrate support  302  and focused on, at least, a portion of the substrate support  302 . Here, the IR emitter can be an IR laser, for instance. A radiation flux (intensity per unit area) provided by the IR or blackbody radiation emitter onto the substrate support  302  is adjusted in conjunction with a period of rotation of the substrate support  302  to maintain the current instances of ICEs  306  across the substrate support  302  at the target fabrication temperature T fab . 
     In yet another configuration  310 -C of the heating source associated with a configuration  300 -C of the ICE fabrication system, the heating source includes an inductive emitter disposed adjacent the substrate support  302  such that electromagnetic radiation provided by the inductive emitter is focused on, at least, a portion of the substrate support  302 . The inductive emitter can be configured as one or more solenoids in a bipolar configuration, quadrupolar configuration, etc. A time-varying electromagnetic flux provided by the inductive emitter onto the substrate support  302  is adjusted in conjunction with the period of rotation of the substrate support  302  to maintain the current instances of ICEs  306  across the substrate support  302  at the target fabrication temperature T fab . 
     The target fabrication temperature T fab  at which the current instances of the ICE  306  are heated during deposition is specified in the process parameter  315  such that complex refractive indices of layers of the fabricated ICE have target values n* H (T op ), n* L (T op )—at the operational temperature T op , or more generally, over an operational temperature range ΔT op , at or over which the fabricated ICEs will be operated—in accordance with the ICE design  307 . The target fabrication temperature T fab  is correlated with the operational temperature T op  based on materials information  308  accessed by the computer system  305 . The materials information  308  includes a predetermined temperature dependence n* H (T) and n* L (T) of the complex refractive indices of layers associated with the ICE design and their respective rate of change as a function of temperature dn* H (T)/dT and dn* L (T)/dT, over a temperature interval [T min , T max ]. Additionally, the materials information  308  includes a predetermined temperature dependence n* S (T) of the complex refractive index of the substrate specified by the ICE design and its respective rate of change as a function of temperature dn* S (T)/dT, over the temperature interval [T min , T max ]. Here, a temperature dependence of a complex refractive index n*(T) includes respective temperature dependencies for a real component of the complex refractive index n(T)=Re(n*(T)) and an imaginary component of the complex refractive index κ(T)=Im(n*(T)). Similarly, a rate of change of a complex refractive index dn*(T)/dT includes respective rates of change for a real component of the complex refractive index do/dT=d(Re(n*(T)))/dT and an imaginary component of the complex refractive index dκ/dT=d(Im(n*(T)))/dT with temperature. In some cases, T min  is the temperature at the ground level  102  of the borehole  38  and T max  is 300° C. In other cases, T min =−40° C. and T max  is 400° C. The temperature ranges [T min , T max ] noted above can correspond to respective operational temperature ranges ΔT op  associated with different applications of respective ICE designs. The foregoing materials information  308  can be used by the computer system  305  to control the heating source  310  for maintaining the temperature of the current instances of the ICEs  306  within a target fabrication temperature range ΔT fab  of a T fab  that is correlated with the T op , as described in detail below. 
     For instance, the target fabrication temperature T fab  and range ΔT fab  depend on whether the ICEs  306  are fabricated to be used in an annealed state or an un-annealed state. As discussed above, an ICE is irreversibly annealed when heated at least through an upper bound of an annealing temperature range associated with the ICE design  307 . For example, a finite (non-zero) annealing temperature range associated with the ICE design  307  is bound by an annealing temperature T AL  of a layer material with low complex refractive index n* L (T) and an annealing temperature T AH  of an adjacent layer material with high complex refractive index n* H (T). Here, a constituent material of the ICE with low/high complex refractive index n* L (T)/n* H (T) irreversibly transitions from a stressed state to an annealed (stress-relieved) state when heated through the annealing temperature T AL /T AH . As another example, the foregoing annealing temperature range collapses to a single annealing temperature T A  associated with the ICE design  307  if the stress is relieved—not in the bulk of the individual materials of the adjacent layers of the ICE, but—at the interface between the adjacent layers having complex refractive indices n* L (T) and n* H (T). Here the ICE irreversibly transitions from an interface-stressed state to an interface-annealed (stress-relieved) state when heated through the annealing temperature T A . 
     Example 1 
     In some implementations, ICEs are fabricated to be used in their un-annealed state at an operational temperature T op  over a narrow operational temperature range ΔT op , e.g., less than 30%, relative to its center value T op . Un-annealed ICEs are exposed, both during and after fabrication, to temperatures that do not exceed the lower bound of the annealing temperature range. 
       FIG. 4A  shows a graph  400  in which a temperature dependence n H (T) of real part of the high complex refractive index of a first material—from which some of the layers of the ICEs are formed—is represented as curve  402  for temperatures much lower than the annealing temperature T AH  of the first material, T max &lt;&lt;T AH . The arrows at both ends of curve  402  signify that a change of n H (T) for the un-annealed first material is reversible over the temperature interval [T min , T max ]. A rate of change of the high complex refractive index with temperature dn H (T)/dT represents a slope of the temperature dependence n H (T) of the high complex refractive index (or, equivalently, a first derivative of curve  402 .) A value of the real part of the high complex refractive index n* H (T op ) for the un-annealed first material at an operational temperature T op  is specified as the coordinate of a point where a normal through T op  intersects curve  402 . 
       FIG. 4B  shows a graph  430  in which a temperature dependence n L (T) of real part of the low complex refractive index of a second material—from which remaining of the layers of the ICEs are formed—is represented as curve  432  for temperatures much lower than the annealing temperature T AL  of the second material, T max &lt;&lt;T AL . The arrows at both ends of curve  432  signify that a change of n L (T) for the un-annealed second material is reversible over the temperature interval [T min , T max ]. A rate of change of the low complex refractive index with temperature dn L (T)/dT represents a slope of the temperature dependence n L (T) of the low complex refractive index (or a first derivative of curve  432 .) A value of the real part of the low complex refractive index n* L (T op ) for the un-annealed second material at an operational temperature T op  is specified as the coordinate of a point where a normal through T op  intersects curve  432 . Although not explicitly shown herein, temperature dependencies of imaginary parts of the high and low complex refractive indices of the first and second materials—from which adjacent layers of the ICEs are formed—can be represented in graphs similar to the graphs  400  and  430  and are available to the computer system  305 . Additionally, a temperature dependence n S (T) of the real component of a complex refractive index of a material of the substrate can be represented in a graph similar to the graphs  400  and  430  and is available to the computer system  305 . 
     A temperature dependence of SEC t (T) representing a measure of performance degradation for an un-annealed ICE—if the un-annealed ICEs were operated over the temperature interval [T min , T max ]—can be predicted based, at least in part, on the temperature dependence n H (T), n L (T) of the complex refractive indices shown in  FIGS. 4A-4B  and the target thicknesses t(1), . . . , t(N) of layers L(1), . . . , L(N) specified in the ICE design.  FIG. 4C  shows a graph  460  in which SEC t (T) is represented as curve  462  over temperatures much lower than the annealing temperature range [T AL , T AH ] of the ICE, T max &lt;&lt;T AL . The arrows at both ends of curve  462  signify that the temperature dependence of the SEC t (T) of un-annealed ICEs is reversible. Here, SEC t (T) is caused by a temperature dependence of deviations of the complex refractive indices n* H (T), n* L (T) of the layers of the un-annealed ICEs from their respective target complex refractive indices n* H (T op ), n* L (T op ) specified by the ICE design. A rate of change of the SEC t (T) of un-annealed ICEs with temperature dSEC t (T)/dT represents a slope of SEC t (T) (or a first derivative of curve  462 .) As expected, a minimum of SEC t (T) (corresponding to maximum performance) for the un-annealed ICEs is obtained for a temperature about equal to the operational temperature T op . In the vicinity of T op , a slope of curve  462  is approximately zero. Additionally, an overall curvature of SECt(T) is mostly negative (or, equivalently, a derivative of dSECt(T)/dT is negative.) The temperature dependence of the SEC t (T) of un-annealed ICEs and specification of maximum allowed SEC max  can be used to establish an operational temperature range ΔT op  of the un-annealed ICEs to be fabricated in the following manner. A lower/upper bound of the operational temperature range ΔT op  is a temperature smaller/larger than the operational temperature T op  where the maximum allowed SEC max  intersects curve  462 . Note that the temperature dependence of the SEC t (T) of un-annealed ICEs shown in  FIG. 4C  results in a narrow operational temperature range ΔT op  for these un-annealed ICEs. 
     In this manner, the target fabrication temperature range ΔT fab  within which the temperature of the un-annealed ICEs will be maintained during fabrication is such that an upper bound of the target fabrication temperature range ΔT fab  is smaller than a lower bound T AL  of the annealing temperature range [T AL , T AH ] of the ICEs. In the examples illustrated in  FIGS. 4A-4B , the target fabrication temperature range ΔT fab  during fabrication of the un-annealed ICEs is centered on the operational temperature T op . For instance, if ICEs with an annealing temperature range [T AL , T AH ]=[245° C., 275° C.] were to be operated in an un-annealed state over an operational temperature interval ΔT op =[60° C., 90° C.] centered on an operational temperature T op =75° C., then the target fabrication temperature range to be maintained during the fabrication of these un-annealed ICEs is set in accordance with one of the following examples. 
       FIG. 4D  shows an example of a narrow fabrication temperature range ΔT fab =[70° C., 80° C.] that is contained within the operational temperature range ΔT op . In some cases, T fab  coincides with T op , such that the narrow fabrication temperature range ΔT fab  is centered on the operational temperature range ΔT op . 
       FIG. 4E  shows an example of a broad fabrication temperature range ΔT fab =[45° C., 105° C.] that encompasses the operational temperature range ΔT op . In some cases, T fab  coincides with T op , such that the operational temperature range ΔT op  is centered on the broad fabrication temperature range ΔT fab . 
       FIG. 4F  shows an example of a fabrication temperature range ΔT fab =[105° C., 115° C.] that does not overlap and is above the operational temperature range ΔT op , such that a lower bound of the fabrication temperature range ΔT fab  is larger than an upper bound of the operational temperature range ΔT op . In these cases, T fab  also is larger than the upper bound of the operational temperature range ΔT op . 
       FIG. 4G  shows an example of a fabrication temperature range ΔT fab =[80° C., 115° C.] that overlaps and extends above the operational temperature range ΔT op . Here, an upper bound of the operational temperature range ΔT op  is contained within the fabrication temperature range ΔT fab . In these cases, T fab  can be smaller or larger than the upper bound of the operational temperature range ΔT op . 
       FIG. 4H  shows an example of a fabrication temperature range ΔT fab =[45° C., 70° C.] that overlaps and extends below the operational temperature range ΔT op . Here, a lower bound of the operational temperature range ΔT op  is contained within the fabrication temperature range ΔT fab . In these cases, T fab  can be smaller or larger than the lower bound of the operational temperature range ΔT op . 
       FIG. 4I  shows an example of a fabrication temperature range ΔT fab =[30° C., 45° C.] that does not overlap and is below the operational temperature range ΔT op , such that an upper bound of the fabrication temperature range ΔT fab  is smaller than a lower bound of the operational temperature range ΔT op . In these cases, T fab  also is smaller than the lower bound of the operational temperature range ΔT op . 
     Example 2 
     In other implementations, ICEs are fabricated to be used in their annealed state, e.g., over a broad operational temperature range ΔT op , e.g., more than 50%, relative to its center value T op , or at an operational temperature T op  comparable with the annealing temperature range. Annealed ICEs are exposed, at least during fabrication, at temperatures that exceed the lower bound of the annealing temperature range. 
       FIG. 5A  shows a graph  500  in which a temperature dependence n H (T) of real part of the high complex refractive index of a first material—from which some of the layers of the ICEs are formed—is represented as curves  501 ,  502  for temperatures that extend from below an annealing temperature T AH  of the first material to above this temperature, T min &lt;T AH &lt;T max . Curve  501  is the temperature dependence n H (T) of the high complex refractive index as the un-annealed first material is heated for the first time from T min  to T max  through the annealing temperature T AH . An arrow at the high-temperature end of curve  501  and no arrow at the low-temperature end of it signify that the increase in n H (T) is irreversible when the temperature of the un-annealed first material is raised from T min  to T max  through T AH . Curve  502  is the temperature dependence n H (T) of the high complex refractive index of the annealed first material over the temperature interval [T min , T max ]. The arrows at both ends of curve  502  signify that a change of n H (T) for the annealed first material is reversible over the temperature interval [T min , T max ]. A rate of change of the high complex refractive index with temperature dn H (T)/dT represents a slope of the temperature dependence n H (T) of the high complex refractive index (or a first derivative of curve  502 .) A value of the real part of the high complex refractive index n* H (T op ) for the annealed first material at an operational temperature T op  is specified as the coordinate of a point where a normal through T op  intersects curve  502 . 
       FIG. 5B  shows a graph  530  in which a temperature dependence n L (T) of real part of the low complex refractive index of a second material—from which remaining of the layers of the ICEs are formed—is represented as curves  531 ,  532  for temperatures that extend from below an annealing temperature T AL  of the second material to above this temperature, T min &lt;T AL &lt;T max . Curve  531  is the temperature dependence n L (T) of the low complex refractive index as the un-annealed second material is heated for the first time from T min  to T max  through the annealing temperature T AL . An arrow at the high-temperature end of curve  531  and no arrow at the low-temperature end of it signify that the increase in n L (T) is irreversible when the temperature of the un-annealed second material is raised from T min  to T max  through T AL . Curve  532  is the temperature dependence n L (T) of the low complex refractive index of the annealed second material over the temperature interval [T min , T max ]. The arrows at both ends of curve  502  signify that a change of n L (T) for the annealed second material is reversible over the temperature interval [T min , T max ]. A rate of change of the low complex refractive index with temperature dn L (T)/dT represents a slope of the temperature dependence n L (T) of the low complex refractive index (or a first derivative of curve  532 .) A value of the real part of the low complex refractive index n* L (T op ) for the annealed second material at an operational temperature T op  is specified as the coordinate of a point where a normal through T op  intersects curve  532 . 
     Note that the first and second materials of Example 2 may, but need not be, the same as the first and second materials described above in Example 1. For instance, if the first and second materials of Examples 1 and 2 are the same, than the temperature interval [T min , T max ] referenced in Example 2 extends to higher temperatures than the temperature interval [T min , T max ] referenced in Example 1. Alternatively, if the first and second materials of Example 2 have an annealing temperature interval [T AL , T AH ] at lower temperatures than the annealing temperature interval [T AL , T AH ] of the first and second materials of Example 1, than the temperature interval [T min , T max ] can be the same in the Examples 1 and 2. 
     A temperature dependence of SEC t (T) representing a measure of performance degradation of an ICE—if the ICEs were operated over the temperature interval [T min , T max ]—can be predicted based, at least in part, on the temperature dependence n H (T), n L (T) of the complex refractive indices shown in  FIGS. 5A-5B  and the target thicknesses t(1), . . . , t(N) of layers L(1), . . . , L(N) specified in the ICE design.  FIG. 5C  shows a graph  560  in which SEC t (T) is represented as curves  561 ,  562  over a temperature interval [T min , T max ] that includes the annealing temperature range [T AL , T AH ] of the ICE. Here, SEC t (T) is caused by a temperature dependence of deviations of the complex refractive indices n* H (T), n* L (T) of the layers of the ICE from their respective target complex refractive indices n* H (T op ), n* L (T op ) specified by the ICE design. Curve  561  is the temperature dependence of SEC t (T) representing the performance degradation of un-annealed ICEs when the un-annealed ICEs are heated for the first time from T min  to T max  through the annealing temperature range [T AL , T AH ]. An arrow at the high-temperature end of curve  561  and no arrow at the low-temperature end of it signify that the decrease in SEC t (T) is irreversible when the temperature of the un-annealed ICEs is raised from T min  to T max  through [T AL , T AH ]. Curve  562  is the temperature dependence of SEC t (T) representing the performance degradation of the annealed ICEs over the temperature interval [T min , T max ]. The arrows at both ends of curve  562  signify that the temperature dependence of the SEC t (T) of annealed ICEs is reversible. A rate of change of the SEC t (T) of annealed ICEs with temperature dSEC t (T)/dT represents a slope of SEC t (T) (or a first derivative of curve  562 .) As expected, a minimum of SEC t (T) (corresponding to maximum performance) is obtained for a temperature about equal to the operational temperature T op . However, in this example, a slope of curve  562  is approximately zero over a broad temperature range and not only in the vicinity of T op . As described above, an operational temperature range ΔT op  for the annealed ICE corresponds to temperatures for which SEC t (T) does not exceed a maximum allowed SEC max  specified in the ICE design. Note that the temperature dependence of the SEC t (T) of annealed ICEs shown in  FIG. 5C  results in a broad operational temperature range ΔT op  for these annealed ICEs. 
     In this manner, the target fabrication temperature range ΔT fab  within which the temperature of the un-annealed ICEs will be maintained during fabrication is such that a lower bound of the target fabrication temperature range ΔT fab  is larger than a higher bound T AH  of the annealing temperature range [T AL , T AH ] of the ICEs. In this manner, the annealing temperature range [T AL , T AH ] of the ICEs is contained within the target fabrication temperature range ΔT fab , to ensure that the constituent materials of the ICE are annealed during fabrication. As such, if ICEs with an annealing temperature range [T AL , T AH ]=[145° C., 175° C.] were to be operated in an annealed state over a temperature range ΔT op =[25° C., 225° C.], then the target fabrication temperature range to be maintained during the fabrication of these annealed ICEs is set to ΔT fab =[185° C., 215° C.], as shown in  FIG. 5D . In these cases, T fab  also is larger than the upper bound of the annealing temperature range [T AL , T AH ]. 
     Referring again to  FIGS. 3A-3C , the measurement system  304  associated with the ICE fabrication system  300  includes one or more instruments. For example, a physical thickness monitor (PM) (e.g., a quartz crystal microbalance) of the measurement system  304  is used to measure one or more deposition rates, R. The measured deposition rate(s) R is/are used to control power provided to the deposition source(s)  303  and its (their) arrangement relative to the current instances of ICEs  306  being fabricated at the target fabrication temperature Tfab to obtain a specified deposition rate R. For instance, if an ICE design specifies that a j th  layer L(j) of the N layers of an ICE is a Si layer with a target thickness t(j), a stack including the previously formed ICE layers L(1), L(2), . . . , L(j−1) is exposed to a Si source—from among the deposition sources  303 —for a duration ΔT(j)=t(j)/R Si , where the R Si  is a deposition rate of the Si source. The measured deposition rate(s) R and the times used to deposit the formed layers L(1), L(2), . . . , L(j−1), L(j) can be used by the computer system  305  to determine actual values of the thicknesses t′(1), t′(2), . . . , t′(j−1), t′(j) of these layers. 
     Actual values n* Si (T fab ), n* SiO2 (T fab ) of complex refractive indices of materials of formed adjacent layers at the target fabrication temperature and thicknesses t′(1), t′(2), . . . , t′(j−1), t′(j) of the formed layers L(1), L(2), . . . , L(j−1), L(j) also are determined by measuring—with the measurement system  304 —characteristics of probe-light that interacted with the formed layers. Note that probe-light represents any type of electromagnetic radiation having one or more probe wavelengths from an appropriate region of the electromagnetic spectrum. Throughout this specification, determining a complex refractive index n* of a layer means that both the real component Re(n*) and the imaginary component Im(n*) of the complex refractive index are being determined. The characteristics of the formed layers are measured with other instruments of the measurement system  304 . 
     In some implementations, the measurement system  304  includes an ellipsometer used to measure, after forming the j th  layer of the ICEs  306 , amplitude and phase components (Ψ(j), Δ(j)) of elliptically polarized probe-light—provided by an optical source (OS)—after reflection from the stack with j layers of ICEs that are being fabricated in the deposition chamber  301 . In this case, the probe-light is provided by the source OS through a probe window of the deposition chamber  301  associated with the ellipsometer, and the reflected probe-light is collected by an optical detector (OD) through a detector window of the deposition chamber  301  associated with the ellipsometer. Here, the measured amplitude and phase components (Ψ(j), Δ(j)) are used by the computer system  305  to determine the (real and imaginary components of) complex refractive indices and thicknesses of each of the layers in the stack formed at the target fabrication temperature T fab : n* Si (T fab ), n* SiO2 (T fab ), t′(1), t′(2), . . . , t′(j−1), t′(j). The computer system  305  makes this determination by solving Maxwell&#39;s equations for propagating the interacted probe-light through the formed layers in the stack. 
     In other implementations, the measurement system  304  is a spectrometer used to measure, after forming the j th  layer of the ICE  306 , a spectrum S(j;λ) of probe-light—provided by an optical source OS over a broad wavelength range [λ min , λ max ]—after reflection from (or transmission through—not illustrated in  FIGS. 3A-3C ) the stack with j layers of the ICEs that are being fabricated in the deposition chamber  301 . In this case, the broad wavelength range source OS provides probe-light through a probe window of the deposition chamber  301  associated with the spectrometer, and an optical detector OD collects the reflected (or transmitted) probe-light through a detector window of the deposition chamber  301  associated with the spectrometer. Here, the measured spectrum S(j;λ) over the wavelength range [λ min , λ max ] is used by the computer system  305  to determine the (real and imaginary components of) complex refractive indices and thicknesses of each of the layers in the stack formed at the target fabrication temperature T fab : n* Si (T fab ), n* SiO2 (T fab ), t′(1), t′(2), . . . , t′(j−1), t′(j). The computer system  305  makes this determination by solving Maxwell&#39;s equations for propagating the interacted probe-light through the formed layers in the stack. 
     In some other implementations, the measurement system  304  is an optical monitor used to measure, after forming the j th  layer of the ICE  306 , change of intensity I(j;λ k ) of probe-light—provided by an optical source (OS)—due to reflection from (or transmission through—not illustrated in  FIGS. 3A-3C ) the stack with j layers of the ICEs that are being fabricated in the deposition chamber  301 . Here, the probe-light has one or more “discrete” wavelengths {λ k , k=1, 2, . . . }. A discrete wavelength λ k  includes a center wavelength λ k  within a narrow bandwidth Δλ k , e.g., ±5 nm or less; two or more wavelengths, λ 1  and λ 2 , contained in the probe-light have respective bandwidths Δλ 1  and Δλ 2  that are not overlapping. The source OS can be a continuous wave (CW) laser, for instance. The optical monitor&#39;s source OS provides probe-light through a probe window of the deposition chamber  301  associated with the optical monitor, and an optical detector OD collects, through a detector window of the deposition chamber  301  associated with the optical monitor, the reflected (or transmitted) light with an intensity I(j;λ k ). Here, the measured change of intensity I(j;λ k ) is used by the computer system  305  to determine the (real and imaginary components of) complex refractive indices and thicknesses of each of the layers in the stack formed at the target fabrication temperature T fab : n* Si (T fab ), n* SiO2 (T fab ), t′(1), t′(2), . . . , t′(j−1), t′(j). The computer system  305  makes this determination by solving Maxwell&#39;s equations for propagating the interacted probe-light through the formed layers in the stack. 
     The computer system  305  includes one or more hardware processors and memory. The memory encodes instructions that, when executed by the one or more hardware processors, cause the fabrication system  300  to perform processes for fabricating the ICEs  306 . Examples of such processes are described below in connection with  FIG. 6 . The computer system  305  also includes or is communicatively coupled with a storage system that stores one or more ICE designs  307 , materials information  308  that includes predetermined temperature dependence of complex refractive indices and their respective rate of change, over a temperature interval [T min , T max ], e.g., given by curves  402 ,  432  or curves  502 ,  532 . As described above in connection with  FIGS. 4A-4C and 5A-5C , the temperature interval [T min , T max ] includes the target fabrication temperature range ΔT fab , and optionally, it can include the operational temperature range ΔT op . For example, T min  is an ambient temperature smaller than both ΔT op  and ΔT fab , and T max  is the maximum temperature of ΔT fab . The foregoing materials information  308  can be used by the computer system  305  to control the heating source  310  for maintaining the temperature of the current instances of the ICEs  306  within a target fabrication temperature range ΔT fab  correlated with an operational temperature T op , as described in Examples 1 and 2 above, or for adjusting deposition of a layer currently being deposited and of other layers remaining to be deposited. 
     The stored ICE designs can be organized in design libraries by a variety of criteria, such as ICE designs used to fabricate ICEs for determining values of a particular characteristic over many substances (e.g. the GOR ratio in crude oil, refined hydrocarbons, mud, etc.), or ICE designs used to fabricate ICEs for determining values of many properties of a given substance (e.g., viscosity, GOR, density, etc., of crude oil.) Additionally, the stored designs can be organized by operational temperature at which the fabricated ICEs will be used. For example, ICEs for determining the GOR ratio of wellbore fluids as part of a fixed-installation (e.g., like the one illustrated in  FIG. 1A ) at a first operational temperature corresponding to the ground surface  102 , at a second operational temperature corresponding to a depth of 100 m under the ground surface, at a third operational temperature corresponding to a depth of 200 m under the ground surface, etc. As another example, ICEs for determining the GOR ratio of wellbore fluids as part of a wireline tool over a broad operational temperature range corresponding to temperature differences between two depth levels, e.g., between the ground surface  102  and a depth of 1000 m. In this manner, upon receipt of an instruction to fabricate an ICE for measuring a given characteristic of a substance at a specified operational temperature T op  or over a specified operational temperature interval ΔT op , the computer system  305  accesses such a design library and retrieves an appropriate ICE design  310  that is associated with the given characteristic of the substance at the specified T op  or over the specified ΔT op . 
     The retrieved ICE design  307  includes specification of a total number N of layers to be formed in the deposition chamber  301 ; specification of complex refractive indices n* H (T op ) and n* L (T op ) of first and second materials (e.g., Si and SiO 2 )—corresponding to the operational temperature T op —to form the N layers with adjacent layers having different complex refractive indices; and specification of target thicknesses {t(k), k=1−N} of the N layers. Implicitly or explicitly, the ICE design  307  also can include specification of a target optical spectrum w t (λ;T op ) associated with the given characteristic at T op ; and specification of a target SEC t (T op ) representing expected performance degradation at T op  of an ICE associated with the retrieved ICE design  307 . The foregoing items of the retrieved ICE design  307  were determined, prior to fabricating the ICEs  306 , in accordance with the ICE design process  200  described above in connection with  FIG. 2 . In some implementations, the ICE design  307  can include indication of maximum allowed degradation SEC max  of the ICE caused by fabrication errors. 
     The complex refractive indices n* H (T op ), n* L (T op ) and target thicknesses {t(k), k=1−N)} of the N layers, as specified by the retrieved ICE design  307 , are used by the computer system  305  to control deposition rate(s) of the deposition source(s)  303  and respective deposition times for forming the ICE layers, and the process parameters  315  are used by the computer system  305  to control temperature of the ICEs during the forming of the ICE layers. The temperature is controlled by the computer system  305  by monitoring whether a current instance of the ICEs&#39; temperature matches a target fabrication temperature, and if not so, adjusting the current instance of the ICEs&#39; temperature to match the target fabrication temperature using a heating source  310  (e.g., conductive heating source  310 -A or radiative heating source  310 -B,  310 -C.) Also while forming the ICE layers, the computer system  305  instructs the measurement system  304  associated with the ICE fabrication system  300  to measure characteristics of probe-light that interacted with formed layers of ICEs being fabricated. The measured characteristics of the probe-light that interacted with the formed layers of the ICEs are used by the computer system  305  to determine complex refractive indices at the target fabrication temperature and thicknesses of the formed layers. If necessary, the computer system  305  also instructs the ICE fabrication system  300  to adjust the forming of layers remaining to be formed based on the determined complex refractive indices and thicknesses of the formed layers of the ICEs. 
     (3.2) ICE Fabrication by In-Situ Controlling Temperature of ICEs 
       FIG. 6  is a flowchart of an example of an ICE fabrication process  600  for fabricating ICEs that allows for controlling temperature of the ICEs being fabricated. The process  600  can be implemented in conjunction with the ICE fabrication system  300  to fabricate ICEs to be used down-hole at elevated temperature, e.g., about 150° C., or over a wide temperature range, e.g., from about ambient temperature at the ground level to about 150° C. down-hole. In some cases, the fabricated ICEs will be operated at temperatures between −40° C. and 400° C. In such a context, the process  600  can be implemented as instructions encoded in the memory of the computer system  305 , such that execution of the instructions, by the one or more hardware processors of the computer system  305 , causes the ICE fabrication system  300  to perform the following operations. 
     At  610 , an ICE design is received. The received ICE design includes specification of a substrate and N layers L(1), L(2), . . . , L(N), each having a different complex refractive index from its adjacent layers, and specification of complex refractive indices at an operational temperature T op  and target thicknesses t S , t(1), t(2), . . . , t(N) of the substrate and the N layers. In this manner, an ICE fabricated in accordance with the received ICE design selectively weights, when operated at T op , light in at least a portion of a wavelength range by differing amounts. The differing amounts weighted over the wavelength range correspond to a target optical spectrum w t (λ;T op ) of the ICE and are related to a characteristic of a sample at T op . For example, a design process for determining the specified (1) substrate and number N of layers of the ICE, each having a different complex refractive index from its adjacent layers, and (2) complex refractive indices and thicknesses of the substrate and the N layers that correspond to the target optical spectrum w t (λ;T op ) of the ICE is described above in connection with  FIG. 2 . When fabricated ICEs are used in down-hole applications, the operational temperature T op  can be specified as a narrow operational temperature range ΔT op  around a desired center value, e.g., ±5° C. around 150° C., or as a broad operational temperature range ΔT op , e.g., from 20° C. to 170° C. In other cases, the broad operational temperature range ΔT op  can extend from −40° C. to 400° C. As described above in connection with  FIGS. 4C and 5C , the operational temperature range ΔT op  is a temperature interval over which degradation from ICE&#39;s performance due to temperature dependence of the complex refractive indices of the ICE is at most equal to a maximum allowed SEC max  of the ICE, where SEC max  represents degradation from a target ICE performance caused by fabrication errors. In this example, the target performance represents an accuracy with which the ICE predicts, when operated at T op , known values of the characteristic corresponding to validation spectra of the sample taken at T op . Here, predicted values of the characteristic are obtained when the validation spectra processed by the ICE are respectively integrated. In some implementations, the received ICE design also can include indication of the maximum allowed degradation SEC max . 
     Loop  615  is used to fabricate one or more ICEs based on the received ICE design. Each iteration “i” of the loop  615  is used to form a layer L(i) of a total number N of layers. Here, the total number N of layers can be either specified in the received ICE design or updated during the ICE fabrication. Updates to the received ICE design are performed when necessary for preventing performance of the fabricated ICE to degrade under a threshold value. 
     At  620 , a temperature of a current instance of the ICEs being fabricated is adjusted, if necessary, to a target fabrication temperature T fab . In the example illustrated in  FIGS. 3A-3C , a heating source  310  (e.g., electrical conductive elements  310 -A included in a substrate support  302  in configuration  300 -A of the ICE fabrication system, an IR laser or a black body emitter  310 -B spaced apart from the substrate support  302  in configuration  300 -B of the ICE fabrication system, or an inductive emitter  310 -C adjacent the substrate support  302  in configuration  300 -C of the ICE fabrication system) is used to maintain a temperature of substrates of the ICEs  306  being fabricated at the target fabrication temperature T fab . The target fabrication temperature T fab  can be specified in terms of a target fabrication temperature range, ΔT fab =[T fab −δT, T fab +δT], such that the temperature of the substrates of the ICEs  306  is maintained, during fabrication, within the target fabrication temperature range ΔT fab . 
     In some implementations, when the ICEs to be fabricated will be operated in an un-annealed state at an operational temperature T op  lower than an annealing temperature range of the ICEs, an upper bound of the target fabrication temperature range ΔT fab  while forming the ICE layers is less than a lower bound of the annealing temperature range of the ICEs. The annealing temperature range of the ICEs is a temperature interval bound by respective annealing temperatures of constitutive materials of the ICEs. For example, the target fabrication temperature range ΔT fab  can be centered on the operational temperature T op . Here, the target fabrication temperature range ΔT fab  can be contained within the operational temperature range ΔT op . Or, the target fabrication temperature range ΔT fab  can contain the operational temperature range ΔT op . As another example, at least an upper bound of the target fabrication temperature range ΔT fab  can be larger than the upper bound of the operational temperature range ΔT op . As yet another example, at least a lower bound of the target fabrication temperature range ΔT fab  can be lower than the lower bound of the operational temperature range ΔT op . 
     In other implementations, when the ICEs to be fabricated will be operated in an annealed state (at an operational temperature T op  lower than, included in or higher than an annealing temperature range of the ICEs), a lower bound of the target fabrication temperature range ΔT fab  exceeds an upper bound of the annealing temperature range of the ICEs. Here, the target fabrication temperature range ΔT fab  may be larger than the annealing temperature range by about 5, 10, or 20% of a value of T fab , for instance. 
     At  630 , the layer L(i) of the ICEs  306  is formed to a target thickness t(i) while a temperature of the current instance of the ICEs  306  is the target fabrication temperature T fab . The target thickness t(i) of the layer L(i) can be specified by the received ICE design or updated based on optimization(s) carried out after forming previous one or more of the layers of the ICE. For some of the layers of the ICE, a deposition source having a deposition rate R is used for a total time duration ΔT(i)=t(i)/R to deposit the layer L(i) to its target thickness as part of a single deposition step. Other layers are deposited to the target thickness t(i) using multiple deposition steps by discretely or continuously forming respective sub-layers of the layer L(i). Here, the deposition rate used for depositing each of the sub-layers can be the same or different from each other. In the case when the deposition rates for forming the sub-layers are different, the last few sub-layers of the layer L(i) can be formed using slower rates than the ones used for forming the first few sub-layers of the layer L(i). 
     At  640 , deposition of the layer L(i) is monitored in-situ. For instance, while the layer L(i) is formed, in-situ optical and/or physical measurements are performed to determine one or more one or more characteristics of the formed layer L(i). In the examples illustrated in  FIGS. 3A-3C , the optical measurements performed using the measurement system  304  include at least one of (1) in-situ ellipsometry to measure amplitude and phase components {Ψ(i),Δ(i)} of probe-light interacted with a current instance of the ICE(s) being fabricated, (2) in-situ optical monitoring to measure change of intensity I(i;λ k ) of probe-light interacted with the current instance of the ICE(s) being fabricated, and (3) in-situ spectroscopy to measure a spectrum S(i;λ) of probe-light interacted with the current instance of the ICE(s) being fabricated. In-situ physical monitoring, e.g., with a crystal microbalance, is used to measure deposition rates, for instance. 
     For some of the layers of the received ICE design, the optical measurements can be skipped altogether. For some other layers, the optical measurements are carried out continuously during the deposition of a layer L(i), in some implementations. In other implementations, the optical measurements are taken a finite number of times during the deposition of the layer L(i). In the latter case, the finite number of times can represent times when at least some of sub-layers of the layer L(i) are completed. 
     At  650 , complex refractive indices n*′ H (T fab ) and n′ L (T fab ) at T fab  and thicknesses t′(1), t′(2), . . . , t′(i−1), t′(i) of the layers L(1), L(2), . . . , L(i−1) formed in previous iterations of the loop  615  and the layer L(i) that is currently being formed are determined based only on the characteristics measured at  640 . Alternatively, predetermined temperature dependencies n* H (T), n* L (T) and dn* H (T)/dT, dn* L (T)/dT of the complex refractive indices and their derivatives (or rates of change with temperature) are used to interpolate values of the complex refractive indices n* H (T fab ) and n* L (T fab ) at T fab . Curves  402 ,  432  and  502 ,  532  are examples of such temperature dependencies described above in connection with  FIGS. 4A-4B and 5A-5B . Here, the thicknesses t′(1), t′(2), . . . , t′(i−1), t′(i) of the layers L(1), L(2), . . . , L(i−1) formed in previous iterations of the loop  615  and the layer L(i) that is currently being formed are determined based on the characteristics measured at  640  and the interpolated values of the complex refractive indices n* H (T fab ) and n* L (T fab ) at T fab . In some implementations, the values of the complex refractive indices n*′ H (T fab ) and n*′ L (T fab ) at T fab  determined from the characteristics measured at  640  and the values n* H (Tfab) and n* L (Tfab) at Tfab interpolated from the predetermined temperature dependencies n* H (T), n* L (T) and dn* H (T)/dT, dn* L (T)/dT are weighted to determine the complex refractive indices n*″ H (T fab ) and n*″ L (T fab ) at T fab  in the following manner: 
         n*″   H ( T   fab )= w   meas   ·n*′   H ( T   fab )+ w   inter   ·n*   H ( T   fab )  (1)
 
         n*″   L ( T   fab )= w   meas   ·n*′   L ( T   fab )+ w   inter   ·n*   L ( T   fab )  (2)
 
     In equations (1) and (2), a weight w meas  is used to weight the values of the complex refractive indices n′ H (T fab ) and n*′ L (T fab ) at T fab  determined from the characteristics measured at  640 , and a weight w inter  is used to weight the values n* H (T fab ) and n* L (T fab ) at T fab  interpolated from the predetermined temperature dependencies n* H (T), n* L (T) and dn* H (T)/dT, dn* L (T)/dT. In some implementations, the weights w meas  and w inter  are about equal to each other, w meas ≈w inter . In other implementations, the weight w meas  is greater than the weight w inter , w meas &gt;w inter , if an accuracy of measured characteristics of the probe-light exceeds a target accuracy, e.g., when multiple characteristics of the probe-light have been measured, e.g., through in-situ spectral ellipsometry, or through a combination of at least two in-situ ellipsometry, spectroscopy and optical monitoring measurements. In some other implementations, the weight w meas  is smaller than the weight w inter , w meas &lt;w inter , if the accuracy with which the characteristics of the probe-light have been measured fails to meet the accuracy target. 
     At  660 , deposition of current and subsequent layers L(i), L(i+1), . . . of the ICE(s) is adjusted, if necessary, based on determined complex refractive indices and thicknesses t′(1), t′(2), . . . , t′(i−1), t′(i) of deposited layers L(1), L(2), . . . , L(i−1) and the layer L(i) currently being deposited. For example, complex refractive indices corresponding to the layer L(i) being currently formed and other layers L(i+1), L(i+2), . . . remaining to be formed can be adjusted based on (1) a comparison between values of the complex refractive indices and thicknesses of the layers of the current instance of the ICEs and their respective target values, and (2) the predetermined temperature dependencies n* H (T), n* L (T) and dn* H (T)/dT, dn* L (T)/dT. Here, if values of the determined complex refractive indices are smaller/greater than the respective target values n* H (T fab ) and n* L (T fab ) at T fab , then the computer system  305  instructs the heating source  310  to increase/decrease the temperature of the instance of the ICEs being fabricated by an incremental temperature ∈ to a new target fabrication temperature T′ fab =T fab +/−∈. The incremental temperature ∈ is determined by interpolating the predetermined temperature dependencies n* H (T), n* L (T) and dn* H (T)/dT, dn* L (T)/dT. Here, the comparison is performed using either the complex refractive indices n*′ H (T fab ) and n*′ L (T fab ) at T fab  determined from the characteristics measured at  640  or the weighted complex refractive indices n*″ H (T fab ) and n*″ L (T fab ) at T fab  determined in accordance with equations (1) and (2). 
     As another example, a deposition rate and/or time used to form the layer L(i) currently being formed and other layers L(i+1), L(i+2), . . . remaining to be formed can be adjusted based on a comparison between values of the complex refractive indices and thicknesses of the layers of the current instance of the ICEs and their respective target values. As yet another example, in order to determine whether target thicknesses of the layer L(i) being current formed and other layers L(i+1), L(i+2), . . . , L(N) remaining to be formed should be updated, the following verification can be performed. 
     An SEC(i;N;T op ) of the ICE is predicted to representing degradation in the ICE&#39;s performance at T op  if the ICE were completed to have the formed layers L(1), L(2), . . . , L(i−1) with the determined thicknesses t′(1), t′(2), . . . , t′(i−1), and the layer L(i) currently being formed and other layers L(i+1), L(i+2), . . . , L(N) remaining to be formed with target thicknesses t(i), t(i), . . . , t(N). Values of the complex refractive indices used for this prediction are either specified in the ICE design received at  610  or determined at  650  or a combination thereof. Here, the predicted SEC(i;N;T op ) is caused by deviations of the determined complex refractive indices and thicknesses of the formed layers from their respective complex refractive indices and target thicknesses specified by the current ICE design. 
     If the predicted SEC(i;N;T op ) at T op  does not exceed the maximum allowed SEC max , SEC(i;N;T op )≦SEC max , then the forming of the current layer L(i) is completed in accordance to its target thickness t(i) and a next iteration of the loop  615  will be triggered to form the next layer L(i+1) to its target thickness t(i+1). If however, the predicted SEC(i;N;T op ) at T op  exceeds the maximum allowed SEC max , SEC(i;N;T op )&gt;SEC max , then target thicknesses of the layer L(i) currently being formed and other layers L(i+1), L(i+2), . . . , L(N) remaining to be formed are modified based on the determined complex refractive indices and thicknesses of the formed layers L(1), L(2), . . . , L(i). This optimization may change the total number of layers of the ICE from the specified total number N of layers to a new total number N′ of layers, but constrains the thicknesses of the layers L(1), L(2), . . . , L(i) (of the current instance of the ICE) to the determined thicknesses t′(1), t′(2), . . . , t′(i). In this manner, the optimization obtains, in analogy with the process  200  described above in connection with  FIG. 2 , new target thicknesses t″(i), t″(i+1), . . . , t″(N′) of the layer L(i) currently being formed and other layers L(i+1), . . . , L(N′) remaining to be formed, such that a new target SEC′ t (i;N′;T op ) of the ICE at T op —for the ICE having the first layers L(1), L(2), . . . , L(i−1) formed with the determined thicknesses t′(1), t′(2), . . . , t′(i−1), and the layer L(i) currently being formed and other layers L(i+1), . . . , L(N′) remaining to be formed with the new target thicknesses t″(i), t″(i+1), . . . , t″(N′)—is minimum and does not exceed the maximum allowed SEC max , SEC′ t (i;N′;T op )≦SEC max . 
     Once the previous instance of the ICE design is updated with specification of the new total number of layers N′ and the new target thicknesses t″(i), t″(i+1), . . . , t″(N′)—which are used to form the current layer L(i) and the remaining layers L(i+1), . . . , L(N′) and correspond to the new target SEC′ t (i;N′;T op ) at T op —the forming of the current layer L(i) is completed in accordance with its new target thickness t″(i) and a next iteration of the loop  615  will be triggered to form the next layer L(i+1) from the new total number of layers N′ to its new target thickness t″(i+1). In this manner, the remaining layers of the ICE will be formed based on the updated ICE design, at least until another update is performed. 
     Some embodiments have been described in detail above, and various modifications are possible. While this specification contains many specifics, these should not be construed as limitations on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the embodiments described above should not be understood as requiring such separation in all embodiments. 
     Other embodiments fall within the scope of the following claims.