Patent Publication Number: US-2015061508-A1

Title: Tuning of emitter with multiple leds to a single color bin

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. application Ser. No. 14/091,914, filed Nov. 27, 2013, entitled “Tuning of Emitter with Multiple LEDs to a Single Color Bin,” which is a continuation of U.S. application Ser. No. 13/106,808, filed May 12, 2011 (now U.S. Pat. No. 8,598,793, issued Dec. 3, 2013). The disclosures are also related to commonly-assigned U.S. application Ser. No. 13/106,810, filed on May 12, 2011 (now U.S. Pat. No. 8,513,900, issued on Aug. 20, 2013). All three disclosures are incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates in general to lamps based on light-emitting diodes (LEDs) and in particular to procedures for tuning the color of light produced by lamps that include multiple LEDs. 
     With the incandescent light bulb producing more heat than light, the world is eager for more efficient sources of artificial light. LEDs are a promising technology and are already widely deployed for specific purposes, such as traffic signals and flashlights. However, the development of LED-based lamps for general illumination has run into various difficulties. Among these is the difficulty of mass-producing lamps that provide a consistent color temperature. 
     As is known in the art, not all white light is the same. The quality of white light can be characterized by a color temperature, which ranges from the warm (slightly reddish or yellowish) glow of standard tungsten-filament light bulbs to the cool (bluish) starkness of fluorescent lights. Given existing processes for LED manufacture, mass-producing white LEDs with a consistent color temperature has proven to be a challenge. 
     Various solutions have been tried. For example, white LEDs can be binned according to color temperature and the LEDs for a particular lamp can be selected from the desired bin. However, the human eye is sensitive enough to color-temperature variation that a large number of bins is required, with the yield in any particular bin being relatively low. 
     Another solution relies on mixing different colors of light to produce a desired temperature. For example, an LED lamp can include a number of white LEDs plus some red LEDs. The brightness of the red LEDs can be increased to warm the light to the desired color temperature. Such lamps generally require an active feedback mechanism to maintain the color temperature, in part because the LEDs used are not stable in their color characteristics over time. The active feedback mechanism requires a sensor to detect the light being produced, an analyzer to determine whether the light is at the desired color, and an adjustment mechanism to adjust the relative brightness of the white and red LEDs as needed to maintain the desired color. These feedback-loop elements can be a weak point in the system; for example, if the light sensor drifts over time (as most do), so will the color of the light. In addition, incorporating active feedback components into a lamp drives up the cost of manufacturing (and operating) the lamp. 
     BRIEF SUMMARY OF THE INVENTION 
     Embodiments of the present invention relate to techniques for tuning the color of an LED-based lamp to a desired color or color temperature. Particular embodiments are adapted for use with lamps that include two or more independently addressable groups of LEDs that each produce light of a different color or color temperature. The lamps can also include a total-internal-reflection (TIR) color-mixing lens to produce light of a uniform color by mixing the light from the different groups of LEDs. The uniform color or color temperature output from the lamp is tuned by controllably dividing an input current among the groups of LEDs. For lamps using LEDs whose color is stable over time, the tuning can be performed once, e.g., during manufacture and/or factory testing of the lamp, and the lamp can thereafter operate at a stable color temperature without requiring active feedback components. 
     For example, in some embodiments a lamp includes two distinct groups of white LEDs: one group (“warm white”) that produces white light with a warmer color temperature than is desired and another group (“cool white”) that produces white light with a cooler color temperature than is desired. In such lamps, the color temperature can be tuned by controllably dividing an input current between the warm white group and the cool white group. In some embodiments, an optimal division of the input current can be determined based on a linear relationship between a shift in the fraction of current provided to each group and a shift in color-space coordinates (which correspond to color temperature) that obtains over the relevant (small) region in color space; the process is simple, requiring as few as three measurements, and can be highly automated to facilitate mass production of color-tuned lamps. 
     In other embodiments, a lamp includes three distinct groups of LEDs, for example, warm white, cool white, and red (other non-white colors can also be used). In some embodiments, tuning between the warm white and cool white groups is performed with the red (or other non-white) LED group turned off. Tuning between the “tuned white” light and the red LED group can then be performed, relying on the fact that as long as the current split between warm white and cool white LEDs does not change, the “tuned white” color will not shift with a shift in total current supplied to the white LEDs. Alternatively, triangular interpolation can be used for tuning, relying on the fact that over a small region in color space, the amount of change in the division of current between two groups of LEDs is linearly related to the amount of change in color-space coordinates. 
     In still other embodiments, a lamp includes four distinct groups of LEDs, for example, warm white, cool white, red, and green (other non-white colors can also be used; for producing white light, the non-white colors are advantageously complementary). Tuning between the warm white and cool white groups is performed with the non-white LED groups turned off. Tuning between the “tuned white” light and the red and/or green LED groups can then be performed, relying on the fact that as long as the current split between warm white and cool white LEDs does not change, the “tuned white” color will not shift with a shift in total current supplied to the white LEDs. Further tuning of the color can be achieved by adding green to the tuned white/red color. Again, triangular interpolation techniques or other linear interpolation can be used over a small region in color space. 
     Any number of groups of LEDs can be used. LEDs in different groups advantageously occupy non-overlapping regions of color space, and the target color is intermediate between the color-space regions occupied by the different groups. 
     Applying processes described herein across a number of lamps allows substantial reduction in the color variation from one lamp to the next. In addition, the tuning process can be confined to a relatively small region in color space such that color shift as a function of current shift from one group of LEDs to another can be modeled as a linear relation. Using linear modeling, the appropriate adjustment for a given lamp can be determined from a small number of measurements. Thus, tuning of a lamp can be accomplished quickly, allowing the tuning process to be incorporated into a mass-production environment. 
     Additional embodiments of the invention relate to tuning apparatus that provide a high degree of automation for the tuning process, suitable for use in mass-production environments. 
     One aspect of the invention relates to a method for tuning a color produced by a lamp having multiple groups of LEDs, where each group includes at least one LED. Each group of LEDs produces light having a different color, and a current applied to each group of LEDs is independently variable. According to one tuning method, at least two different testing distributions of a total current among the groups of LEDs are established. For each of the different testing distributions of the total current, a color of light produced by the lamp is measured. A target color is defined, and a desired distribution of the total current is determined based at least in part on the measured colors; the desired distribution of the total current produces light having the target color. 
     In some embodiments, the groups of LEDs can include a group of warm white LEDs and a group of cool white LEDs. Additional groups of LEDs, including groups of non-white LEDs, such as red and/or green LEDs, can also be included. In some embodiments, the groups of LEDs can include at least two groups of cool white LEDs and at least one group of warm white LEDs. 
     The lamp can include a total internal reflection lens to mix the light produced by the plurality of LEDs, and the measuring of the color of the light can be based on light exiting a front face of the total internal reflection lens. The measuring can be done by a spectrometer (or other color measuring device) external to the lamp, and the lamp itself need not include a spectrometer or other active feedback components for adjusting color. 
     Another aspect of the invention relates to a method for controlling a color produced by an emitter having independently-addressable warm white LEDs and cool white LEDs. A first value for a color property of the emitter can be measured under a first operating condition in which a maximum current is supplied to the warm white LEDs and a minimum current is supplied to the cool white LEDs. A second value for the color property of the emitter can be measured under a second operating condition in which the maximum current is supplied to the cool white LEDs and the minimum current is supplied to the cool white LEDs. A third value for the color property of the emitter can be measured under a third operating condition in which approximately half of a total current is delivered to the warm white LEDs and the rest of the total current is delivered to the cool white LEDs; the total current is advantageously equal to a sum of the maximum current and the minimum current. Based on the measured first, second, and third values of the color property and a target value of the color property, operating currents, including a first operating current to be supplied to the warm white LEDs and a second operating current to be supplied to the cool white LEDs, can be calculated. A current controller coupled to the emitter can be configured such that when the first operating current is supplied to the warm white LEDs, the second operating current is supplied to the cool white LEDs. 
     Another aspect of the invention relates to a method for controlling a color produced by a lamp having independently addressable warm white LEDs and cool white LEDs. A first value of a color property of the lamp can be measured while supplying a total current to the warm white LEDs and no current to the cool white LEDs. A second value of the color property of the lamp can be measured while supplying the total current to the cool white LEDs and no current to the warm white LEDs. A third value of the color property of the lamp can be measured while supplying half the total current to the warm white LEDs and half the total current to the cool white LEDs. A first operating current to be supplied to the warm white LEDs and a second operating current to be supplied to the cool white LEDs to achieve a target value of the color property can be determined, with the total current being equal to a sum of the first operating current and the second operating current. The determination of the first and second operating current can be based on the measured first, second and third values of the color property and a proportionality constant that linearly relates a unit of change in a difference between the first and second operating currents to an amount of change in the color property. A control circuit of the lamp can be configured such that when the first operating current is supplied to the warm white LEDs, the second operating current is supplied to the cool white LEDs. 
     The following detailed description together with the accompanying drawings will provide a better understanding of the nature and advantages of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a simplified cross-sectional side view of an LED-based lamp with tunable emitters according to an embodiment of the present invention. 
         FIG. 1B  is a top view of a substrate holding LEDs that may be used in the lamp of  FIG. 1A . 
         FIGS. 2A and 2B  illustrate examples of electrical connectivity that can be used to provide independent addressability of warm white and cool white LEDs. 
         FIG. 3  is a plot illustrating operating characteristics of lamps usable in some embodiments of the present invention. 
         FIG. 4  illustrates an operating principle for tuning a lamp according to an embodiment of the present invention. 
         FIG. 5  is a plot showing the effect on color temperature of a series of shifts in current for a number of lamps. 
         FIG. 6  is a flow diagram of a tuning process according to an embodiment of the present invention. 
         FIGS. 7A and 7B  illustrate a comparison of predicted and actual behavior of a group of LED-based lamps that were tuned in accordance with the process of  FIG. 6 . 
         FIG. 8  illustrates an operating principle relating to selection of LEDs to achieve a desired tuned color temperature according to an embodiment of the present invention. 
         FIG. 9  illustrates an operating principle for binning of lamps based on tuned color temperature according to an embodiment of the present invention. 
         FIG. 10  is a top view of an LED emitter package with three groups of LEDs according to an embodiment of the present invention. 
         FIG. 11  illustrates an operating principle for tuning a lamp that includes an emitter package with three groups of LEDs according to an embodiment of the present invention. 
         FIG. 12  illustrates a tuning process for a lamp with three groups of LEDs according to an embodiment of the present invention. 
         FIG. 13  illustrates an operating principle for tuning a lamp that includes an emitter package with three groups of LEDs according to another embodiment of the present invention. 
         FIG. 14  illustrates a process for tuning a lamp having the LED groups illustrated in  FIG. 13  according to an embodiment of the present invention. 
         FIG. 15  is a top view of an LED emitter package with four groups of LEDs according to an embodiment of the present invention. 
         FIG. 16  illustrates an operating principle for tuning a lamp with four groups of LEDs according to an embodiment of the present invention. 
         FIG. 17  illustrates a tuning process for a lamp with four groups of LEDs according to an embodiment of the present invention. 
         FIG. 18  is a simplified diagram of a tuning apparatus according to an embodiment of the present invention. 
         FIG. 19  shows a test apparatus that can be used to program potentiometers within a lamp according to an embodiment of the present invention. 
         FIG. 20  illustrates a tuning process according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiments of the present invention relate to techniques and apparatus for tuning the color of an LED-based lamp to a desired color temperature. Particular embodiments are adapted for use with lamps that include two or more independently addressable groups of LEDs that each produce light of a different color or color temperature. The lamps can also include a total-internal-reflection (TIR) color-mixing lens to produce light of a uniform color by mixing the light from the different groups of LEDs. The uniform color or color temperature output from the lamp is tuned by controllably dividing an input current among the groups of LEDs. For lamps using LEDs whose color is stable over time, the color tuning can be performed once, e.g., during manufacture and/or factory testing of the lamp, and the lamp can thereafter operate at a stable color temperature without requiring active feedback components. 
     Embodiments for tuning lamps with two independently addressable groups of LEDs will be considered first, after which extensions to lamps with larger numbers of groups. As used herein, a “group” of LEDs refers to any set of one or more LEDs that occupies a defined region in color space; the regions are defined such that regions occupied by different groups in the same lamp do not overlap. The lamp is advantageously designed such that the current supplied to each group of LEDs can be controlled independently of the current supplied to other LEDs, and the groups are thus said to be “independently addressable.” 
       FIG. 1A  is a simplified cross-sectional side view of an LED-based lamp  100  with tunable emitters according to an embodiment of the present invention. Lamp  100 , which can be cylindrical about an axis  101  (other shapes can also be used), has a housing  102 , which can be made of aluminum, other metals, plastic, and/or other suitable material. Housing  102  holds the various components of lamp  100  together and can provide a convenient structure for a user to grip lamp  100  during installation or removal from a light fixture. The exterior of housing  102  can include mechanical and/or electrical fittings (not shown) to secure lamp  100  into a light fixture and/or to provide electrical power for producing light. In some embodiments, housing  102  may include fins or other structures to facilitate dissipation of heat generated during operation of lamp  100 . 
     Within housing  102  is an LED package  104 . Package  104  includes a substrate  106  on which are mounted individual LEDs  108 . Each LED  108  can be a separate semiconductor die structure fabricated to produce light of a particular color in response to electrical current. In some embodiments, each LED  108  is coated with a material containing a color-shifting phosphor so that LED  108  produces light of a desired color. For example, a blue-emitting LED die can be coated with a material containing a yellow phosphor; the emerging mixture of blue and yellow light is perceived as white light having a particular color temperature. 
     In some embodiments, lamp  100  also includes a control circuit  116  that controls the power provided from an external power source (not shown) to LEDs  108 . As described below, control circuit  116  advantageously allows different amounts of power to be supplied to different LEDs  108 . 
     A primary lens  110 , which can be made of glass, plastic or other optically transparent material, is positioned to direct light emitted from LEDs  108  into secondary optics  112 . Secondary optics  112  advantageously include a total-internal-reflection (TIR) lens that also provides mixing of the colors of light emitted from LEDs  108  such that the light beam exiting through front face  114  has a uniform color. Examples of suitable lenses are described in U.S. Patent Application Pub. No. 2010/0091491; other color-mixing lens designs may also be used. As described below, tuning is advantageously performed based on the color of light exiting through front face  114  of TIR lens  112 . 
     In some embodiments LEDs  108  advantageously include both “warm” and “cool” white LEDs. An example is illustrated in  FIG. 1B , which is a top view of substrate  106  according to an embodiment of the present invention. As shown, twelve LEDs  108   a - l  are arranged within a recess  156  on substrate  106 . Six of the LEDs are cool white (“CW”) LEDs  108   a - f ; the other six are warm white (“WW”) LEDs  108   g - l . “Cool” white and “warm” white, as used herein, refer to the color temperature of the light produced. Cool white, for example, can correspond to a color temperature above, e.g., about 4000 K, while warm white can correspond to a color temperature below, e.g., about 3000 K. It is desirable that cool white LEDs  108   a - f  have a color temperature cooler than a target color temperature for lamp  100  while warm white LEDs  108   g - l  have a color temperature warmer than the target color temperature. When light from cool white LEDs  108   a - f  and warm white LEDs  108   g - l  is mixed by mixing lens  112 , the target temperature can be achieved. More generally, for purposes of providing a tunable lamp, the lamp can include LEDs belonging to any number of “groups,” with each group being defined as producing light within a different color or color temperature range (or “bin”); the ranges associated with different groups advantageously do not overlap, and the desired color or color temperature to which the lamp will be tuned is somewhere between the colors or color temperatures associated with the groups of LEDs. 
     To facilitate achieving a desired color temperature, the LEDs  108  of lamp  100  are advantageously connected such that cool white LEDs  108   a - f  and warm white LEDs  108   g - l  are independently addressable, i.e., different currents can be supplied to different LEDs.  FIGS. 2A and 2B  are simplified schematics illustrating examples of electrical connectivity that can be used to provide independent addressability of warm white and cool white LEDs. These electrical connections can be implemented, e.g., using traces disposed on the surface of substrate  106  and/or between electrically insulating layers of substrate  106 . Examples of substrates that provide independent addressability for groups of LEDs are described in U.S. Patent App. Pub. No. 2010/0259930; other substrates can also be used. 
     In  FIG. 2A , cool white LEDs  108   a - f  are connected in series between a first input node  202  and a first output node  204 ; warm white LEDs  108   g - l  are connected in series between a second input node  206  and a second output node  204 . Consequently, one current (I C ) can be delivered to cool white LEDs  108   a - f  while a different current (I W ) is delivered to warm white LEDs  108   g - l . The currents I C  and I W  can be independently controlled, thereby allowing the relative brightness of cool white LEDs  108   a - f  and warm white LEDs  108   g - l  to be controlled; this provides control over the color temperature of light produced by lamp  100 . For example, control circuit  116  ( FIG. 1A ) can be connected to nodes  202  and  206  and to nodes  204  and  208  to deliver the desired currents I C  and I W . 
       FIG. 2B  illustrates one specific technique for implementing per-group current control. As in  FIG. 2A , cool white LEDs  108   a - f  are connected in series, and warm white LEDs  108   g - l  are also connected in series. In  FIG. 2B , the last LEDs in each series (LEDs  108   f  and  108   l ) are connected to a common output node  228 . A common input node  222  receives a total current I TOT , which is divided between cool white LEDs  108   a - f  and warm white LEDs  108   g - l  using potentiometers (or variable resistors)  224 ,  226 . Potentiometer  224  can be set to a resistance R C  while potentiometer  226  can be independently set to a resistance R W ; as a result, a current I C  is delivered to cool white LEDs  108   a - g  while a current I W  is delivered to warm white LEDs  108   g - l . By controlling R W  and R C , I TOT  can be divided between I W  and I C  in a controllable proportion according to the property that I W /I C =R C /R W . Thus, as in  FIG. 2A , the relative brightness of cool white LEDs  108   a - f  and warm white LEDs  108   g - l  can be controlled, thereby providing control over the color temperature of light produced by lamp  100 . In one embodiment, control circuit  116  can be connected to nodes  222  and  228  to supply current I TOT , and further connected to control resistances R C  and R W . 
     Other addressing schemes can also be used; for example, each of the LEDS  108   a - l  can be independently addressable. 
     It will be appreciated that lamp  100  described herein is illustrative and that variations and modifications are possible. In one embodiment, lamp  100  can be similar to a LuxSpot™ lamp, manufactured and sold by LedEngin Inc., assignee of the present invention. Those skilled in the art with access to the present teachings will recognize that any lamp that has independently addressable warm white and cool white LEDs can also be used; thus, details of the lamp are not critical to understanding the present invention. 
     In accordance with some embodiments of the present invention, the currents I C  and I W  (shown in  FIGS. 2A and 2B ) can be efficiently tuned so that the light output from lamp  100  has a desired color temperature. The tuning process advantageously requires only a small number (e.g., three or four) of measurements and does not rely on trial-and-error. The process can also be automated to allow tuning of a large number of lamps in a mass-production environment; thus, color tuning can be incorporated into lamp production, e.g., as a stage in an assembly line. 
     Further, it should be noted that in the embodiment shown, lamp  100  does not include any active feedback components. As described below, lamp  100  can be placed into a tuning apparatus and color-tuned during production. Thereafter, lamp  100  can be configured to operate at the desired color temperature simply by maintaining the division (or distribution) of current determined in the tuning process. Provided that the LEDs in lamp  100  can maintain a stable color temperature over time, no further tuning or active feedback is needed during normal lamp operation. Since active feedback is not needed, the cost of manufacture can be reduced as compared to lamps that require active feedback to maintain a stable color temperature. 
     To understand the tuning process, it is useful to begin by considering the behavior of untuned lamps.  FIG. 3  is a plot illustrating operating characteristics of lamps usable in some embodiments of the present invention. The graph  300  represents a portion of CIE color space, which characterizes light in terms of luminance (CIE y) and chromaticity (CIE x) coordinates. The portion of the CIE color space represented encompasses much of the range associated with white light. The various data points (black diamonds) represent colors measured from a number of LED-based lamps having independently addressable warm white and cool white LED groups, e.g., as described above with reference to lamp  100 , under various operating conditions. 
     More specifically, for purposes of these measurements, a total current I TOT  of 1000 mA was supplied to the lamp, and the constraint I C +I W =I TOT  was maintained. “Cool white” data, represented by points  302 , was measured for each lamp by setting I C =I TOT  and I W =0. “Warm white” data, represented by points  304 , was measured for each lamp by setting I C =0 and I W =I TOT . “Balanced” data, represented by points  306 , was measured by setting I C =I W =0.5*I TOT.    
     A target color is represented by circle  308 , and the goal is to produce colors as close to this target as possible. As can be seen, merely applying equal current to the warm white and cool white LEDs results in balanced data points  306  being scattered about target  308 . While the balanced colors are more consistent across different lamps than can readily be obtained by using LEDs of a single white color, further improvement in color consistency can be achieved by tuning the relative currents I C  and I W  (and consequently the color) on a per-lamp basis. Such tuning in a typical case results in unequal currents being supplied to the warm white and cool white LEDs, with the currents being selected to reduce the lamp-to-lamp variation by bringing the light from each lamp closer to target  308 . 
       FIG. 4  illustrates an operating principle for tuning a lamp according to an embodiment of the present invention. Point  402 , at coordinates (x C , y C ) in CIE color space, represents the location of a “cool white” data point for a particular lamp (e.g., one of data points  302  in  FIG. 3 ). Similarly, point  404 , at coordinates (x W , y W ) in CIE color space, represents the location of a “warm white” data point for the same lamp (e.g., one of data points  304  in  FIG. 3 ). Point  406 , at coordinates (x B , y B ) represents the balanced data for that lamp (e.g., one of data points  306 ). Point  408 , at coordinates (x s , y s ), represents a single-color point to which it is desirable to tune the lamp. (This point, which can correspond to target  308  in  FIG. 3 , may be specified by the manufacturer of the lamp or any other entity who may be performing the tuning process.) 
     Blending light of the colors corresponding to points  402  and  404  results in a color somewhere along line  410 . Thus, it may not be possible to produce blended light with a color corresponding exactly to single-color point  408 . Accordingly, the aim instead is to reach the closest point to point  408  that is on line  410 , i.e., “tuned” point  412  at coordinates (x t , y t ). In a typical case (x t , y t ) and (x B , y B ) are not the same, and (x t , y t ) may be different for different lamps; thus, tuning on a per-lamp basis is desired. 
     In general, the relationship between a change in the relative currents (measured, e.g., as I W /I C ) supplied to the warm and cool LEDs and the resulting shift in color temperature is nonlinear. Further, the magnitude of the shift in color temperature resulting from a given change in relative current varies from one lamp to another. 
     However, as illustrated in  FIG. 5 , over a sufficiently narrow range of color space, the relationship can be approximated as linear.  FIG. 5  is a plot showing the effect on color temperature of a series of 50-mA shifts in current for a number of lamps. Data points  502  represent the cool white color (i.e., color when I C =I TOT ; I W =0) for a number of lamps of similar manufacture; and data points  504  represent the warm white color (i.e., color when I C =0; I W =I TOT ) for the same lamps. Data points  506   a - i  represent successive measurements at different relative currents. Specifically, each data point  506   a - i  represents a shift in current of ΔI=50 mA from I C  to I W . For example, if point  506   c  corresponds to (I C =I W =0.5*I TOT ), then point  506   b  would correspond to (I C =0.5*I TOT +ΔI; I W =0.5*I TOT −ΔI). Similarly, point  506   d  would correspond to (I C =0.5*I TOT −ΔI; I W =0.5*I TOT +ΔI), point  506   e  to (I C =0.5*I TOT −2*ΔI; I W =0.5*I TOT +2*ΔI), and so on. 
     As  FIG. 5  indicates, the shift in CIE x coordinate (Δx) resulting from a specific shift ΔI in relative current between cold and warm LEDs (with total current held constant) is approximately constant for a given lamp, at least over some range of CIE space. Although not explicitly shown, the magnitude of the constant CIE shift Δx is not constant from one lamp to another. However, for lamps in which the LEDs have a constant flux density, it has been found that the parameter 
     
       
         
           
             
               
                 
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     is very nearly constant for different lamps. In one embodiment, α is about 0.0008052 mA −1 . In other embodiments, the applicable ratio α can be determined by measuring a sampling of lamps. 
     Accordingly, referring to  FIG. 4 , given (c C , y C ) and (x W , y W ) for a particular lamp, and a desired color (x s , y s ), a tuned point (x t , y t ) on line  410  can be computed. If (x B , y B ) is also measured, then the desired shift in CIE x coordinate that will tune the lamp is (x t −x B ). The size of the current shift needed to produce this coordinate shift can be computed using: 
     
       
         
           
             
               
                 
                   
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     where α is the constant ratio defined in Eq. 1. Setting 
         I   C0 =0.5*( I   TOT   +I   δ )  (Eq. 3)
 
       and 
         I   W0 =0.5*( I   TOT   −I   δ )  (Eq. 4)
 
     can be expected to produce light of color (x t , y t ). 
     Based on the foregoing, a rapid tuning procedure can be applied to tune an LED lamp.  FIG. 6  is a flow diagram of a tuning process  600  according to an embodiment of the present invention. Process  600  can be applied to any lamp that incorporates independently addressable warm white and cool white LEDs and can be used to determine how to divide a fixed total current I TOT  between the warm white and cool white LEDs to best match a desired color (x s , y s ). Process  600  assumes that this desired color has been specified and that the constant ratio α defined above has been determined. 
     At block  602 , the input current to the LED lamp (or settings on potentiometers within the lamp) is adjusted such that I C =I TOT  and I W =0. At block  604 , the color of the resulting light is measured, e.g., as (x C , y C ). Conventional spectrometers or other known instruments can be used for this measurement and all color measurements described herein. 
     At block  606 , the input current to the LED lamp (or settings on potentiometers within the lamp) is adjusted such that I W =I TOT  and I C =0. At block  608 , the color of the resulting light is measured, e.g., as (x W , y W ). 
     At block  610 , the input current to the LED lamp (or settings on potentiometers within the lamp) is adjusted such that I C =I W =0.5*I TOT . At block  612 , the color of the resulting light can be measured, e.g., as (x B , y B ). 
     At block  614 , a current shift I δ  that will produce a tuned color (x t , y t ) is computed using the linear relation observed above. More specifically, (x t , y t ) can be computed as the nearest point to (x s , y s ) that is on the line between measured (x C , y C ) and (x W , y W ) (see  FIG. 4 ) using: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
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     Then, I δ  can be computed using Eq. 2. 
     At block  616 , the operating currents I C0  and I W0  can be determined using Eqs. 3 and 4. 
     At block  618 , to confirm the computation, operating currents I C0  and I W0  can be applied to the lamp. The resulting color can be measured and compared to the predicted (x t , y t ). 
     It will be appreciated that process  600  is illustrative and that variations and modifications are possible. Steps described as sequential may be executed in parallel, order of steps may be varied, and steps may be modified, combined, added or omitted. In addition, while the embodiment described takes the measurements used to calculate I δ  at the “extreme” points and the “mid” point of possible current splits, those skilled in the art will appreciate that other points could also be used. For example, if desired, measurements could be taken at 10/90 and 90/10 current splits, and at the midpoint some other intermediate point. As long as three distinct measurements at three distinct current splits are made, the process above can be used to determine a current split to achieve a desired tuned color temperature (or color). In some embodiments, the target value is advantageously close to the midpoint between the warm and cool color temperatures, as this allows the lamp to operate at highest efficiency (i.e., maximum lumens per LED die). This can be reliably achieved by selecting the warm white and cool white LEDs such that the target value is near the midpoint; in one embodiment, the warm white and cool white LEDs are selected such that the tuned color will always be reached with a warm/cool current split somewhere in the range between 30/70 and 70/30. However, no particular target value is required; tuning can be achieved at any point that lies between the two groups in color temperature space. 
     In some embodiments, process  600  can also include further fine-tuning of the color. For example, a least-squares fit can be used to determine the distance between the target point on the blackbody curve and the line between measured x C  and x W , and this can be used to modify the current split to fine-tune the color. 
       FIGS. 7A and 7B  illustrate a comparison of predicted and actual behavior of a group of LED-based lamps that were tuned in accordance with process  600 .  FIG. 7A  shows cool-white data points  702 , warm white data points  704 , and blended and tuned data points in area  706 , which is shown in an enlarged version in  FIG. 7B . 
     In  FIG. 7B , the “no tune” data points (diamonds) correspond to the color (x B , y B ) obtained by applying equal current to the warm-white and cool-white LEDs. As can be seen, the no-tune data points are scattered about the target point  720  (corresponding to (x s , y s )). “Theory” data points (squares) indicate the predicted color (x t , y t ) for each lamp when operating using currents I C0  and I W0  as determined in accordance with process  600 . “Real” data points (triangles) indicate the measured color (x 0 , y 0 ) when operating using I C0  and I W0 . As shown, the agreement of the data with theory is quite good, and a substantial improvement over the “no-tune” case (i.e., simply applying equal current to both LED groups) is observed. 
     It is noted that, based on the degree of scatter, the improvement is greater in the CIE-x coordinate than in CIE-y. Since the human eye is less sensitive to change in CIE-y, tuning based on CIE-x (e.g., using process  600 ) is found to yield satisfactory results. 
     Tuning as described herein can be practiced with any lamp with an emitter having independently addressable groups of warm white and cool white LEDs. In some embodiments, selection of the LEDs for the warm white and cool white groups can optimize tunability. For example,  FIG. 8  illustrates an operating principle relating to selection of LEDs to achieve a desired tuned color temperature according to an embodiment of the present invention. Represented in  FIG. 8  is the blackbody curve  800  in CIE color space. For existing white LED manufacturing processes, the color temperature of individual LEDs cannot be precisely controlled; however, it is possible to control the color temperature to within an elliptical region in CIE color space, producing LEDs within a generally elliptical “bin.”  FIG. 8  illustrates two different bins: bin  802 , which produces warm white light, and bin  804 , which produces cool white light. Bins  802  and  804  can be large enough in color space that that differences in color between different LEDs in the same bin are perceptible to the human eye. In some embodiments, for optimal tuning to a target color temperature chosen in advance, the manufacturer can select the warm white and cool white bins such that the major axes of the ellipses representing the bins are approximately aligned in color space, as is the case for bins  802  and  804 . 
     Using the processes described above, a lamp whose emitter contains warm white LEDs from bin  802  and cool white LEDs from bin  804  can be tuned, e.g., to a point along line  806 . The exact point will in general depend on the variations in particular LEDs in a given lamp; dotted lines  808  indicate some of the possibilities. As indicated, even with a relatively large manufacturing tolerance for the LEDs, a small tuned projection (line  806 ) can be achieved. 
     In other embodiments, rather than selectively choosing LEDs to produce a given color temperature, the manufacturer can produce an emitter with one group of LEDs above the blackbody curve and another group of LEDs below the blackbody curve without targeting a particular color temperature. The lamp can be tuned to a point on the blackbody curve using techniques described above, and thereafter the lamps can be binned according to their tuned color temperature. 
       FIG. 9  illustrates an operating principle for binning of lamps based on tuned color temperature according to an embodiment of the present invention. Represented therein is the blackbody curve  902  in CIE color space. The two groups of LEDs are represented by ellipse  904  located above the blackbody curve and ellipse  906  located below the blackbody curve. Each lamp can be tuned to a point on blackbody curve  902 , as can be inferred from the fact that any line joining a point in ellipse  904  and a point in ellipse  906  must cross curve  902 . Some specific examples are indicated by dotted lines  908 . 
     For purposes of providing lamps with a desired color, blackbody curve  902  can be segmented into a number of bins as indicated by boxes  910 . The size of the bins can be chosen such that variations in color are imperceptible or nearly so. Each lamp can be assigned to a bin based on the point on blackbody curve  902  to which it tunes. 
     In some embodiments, further improvements in tuning can be provided by using lamps that include more than two independently addressable groups of LEDs of different colors. For example, in addition to cool white and warm white, it is possible to include red and/or green LEDs in an emitter. 
     By way of illustration of a three-group embodiment,  FIG. 10  is a top view of an LED emitter package  1000 , in which a substrate  1001  has a recess  1002 . Within recess  1002  are mounted four cool white (CW) LEDs  1004   a - d , four warm white (WW) LEDs  1004   e - h , and one red LED  1004   i , arranged as shown. In this example, the red LED group contains a single LED. Those skilled in the art will appreciate that the number of LEDs in each group and/or the arrangement of LEDs can be modified as desired. Emitter package  1000  can be included in a lamp similar to lamp  100  of  FIG. 1 , with primary and secondary optics to provide color mixing. In this example, the control circuitry and electrical couplings are such that the cool-white group, warm-white group, and red group are each independently addressable, and the color of light emitted from the lamp can be tuned by adjusting the relative current delivered to each group. 
       FIG. 11  illustrates an operating principle for tuning a lamp that includes an emitter package with three groups of LEDs, such as emitter package  1000  of  FIG. 10 , according to an embodiment of the present invention. Point  1102 , at coordinates (x C , y C ) in CIE color space, represents the location of a “cool white” data point for a particular lamp. Similarly, point  1104 , at coordinates (x W , y W ) in CIE color space, represents the location of a “warm white” data point for the same lamp. Point  1106 , at coordinates (x R , y R ) in CIE color space, represents the color of the red LED group for the same lamp. Point  1108 , at coordinates (x s , y s ), represents a target point to which it is desirable to tune the lamp. (The target point may be specified by the manufacturer of the lamp or any other entity who may be performing the tuning process.) 
     Point  1110 , at coordinates (x t1 , y t1 ), represents a tuned color for the warm white and cool white LED groups. By performing process  600  described above (or a similar process), with no current supplied to the red LED group, a suitable division of current between the warm white and cool white groups (operating currents I W0  and I C0 ) can be determined, such that light of color (x t1 , y t1 ) is produced. Thereafter, current distribution between the white LEDs and the red LED can be tuned to bring the color closer to (x s , y s ), while maintaining the relative currents between the warm white and cool white LEDs. Specifically, a constant current I TOT  can be divided as follows: 
         I   TOT   =I   R +β( I   W0   +I   C0 ),  (Eq. 7)
 
     for 0≦β≦1. That is, during this phase of tuning, the currents supplied to the warm white and cool white LED groups are held in a fixed relation to each other (i.e., I W0 /I C0  is constant) so that the effective color temperature (“net white”) of the warm white and cool white groups is constant, and the total current to the white LED groups (i.e., β(I W0 +I C0 )) is adjusted relative to the current I R  to the red LED group, keeping I TOT  constant. A process similar to process  600  can be used to determine values for I R  and β such that the resulting color is at the closest point along line  1112  to point (x s , y s ), i.e., point  1114 , which has coordinates (x t2 , y t2 ). For tuning between the net white color and the red color, a different constant α′ would be used. 
       FIG. 12  illustrates a tuning process  1200  that can be used to determine I W0 , I C0 , β and I R  such that the resulting light has color-space coordinates (x t2 , y t2 ) according to an embodiment of the present invention. First, at block  1202 , with I R  held constant at zero, process  600  ( FIG. 6 ) can be used to determine I W0  and I C0 , i.e., the division of current between the warm white and cool white LED groups that produces a net white color (x t1 , y t1 ). 
     Next, tuning can be performed between the net white color and the red LED group. More specifically, at block  1204 , I R  in Eq. 7 is set to zero, β is set to 1, and a color (x β , y β ) is measured. (This may be the same color as (x t1 , y t1 ) in  FIG. 11 .) At block  1206 , I R  in Eq. 7 is set to I TOT , β is set to 0, and a color (x R , y R ) is measured. At block  1208 , I R  in Eq. 7 is set to 0.5*I TOT , β is set to 0.5, and a color (x B2 , y B2 ) is measured. At block  1210 , using similar linear interpolation to that described above, with an appropriate value of α, values I RO  and β 0  can be computed to produce the desired color (x t2 , y t2 ). At block  1212 , a current I RO  is supplied to the red LED group, current β 0 *I W0  is supplied to the warm white LED group, and current β 0 *I C0  is supplied to the cool white LED group; the resulting color temperature is measured to verify the color. As in process  600 , additional fine-tuning, e.g., with a least-squares fit, can be applied. 
     As with process  600 , it is not necessary to use the “endpoint” cases at blocks  1204  and  1206 . In a typical embodiment, the target color (x s , y s ) lies on the well-known blackbody curve in color space, line  1116  between points (x C , y C ), (x W , y W ) is close to the blackbody curve, and red color point (x R , y R ) is far from the blackbody curve. In such cases, (x t1 , y t1 ) is already quite close to (x s , y s ), and a small contribution from the red LED is used to fine-tune the color. Thus, a better linear interpolation may be obtained by using an intermediate value in place of the I R =1 endpoint at block  1206 . For example, it may be sufficient to use (I R =0.3*I TOT , β=0.7). 
     Process  1200  is particularly effective in embodiments where the red LED color is situated in color space such that moving the color along line  1112  in  FIG. 11  does not pull the color in the x direction significantly away from x s ; this is because the human eye is more sensitive to changes in the x direction in color space. For cases where (x s , y s ) is along the blackbody curve and (x R , y R ) is far off that curve, only a small amount of red light would be added and this will generally be the case. An alternative process can rely on triangular interpolation between three points corresponding to three different current distributions. For example, one could use the three points (x C , y C ), (x W , y W ) and (x R , y R ). Alternatively, one could use the points (x C , y C ), (x W , y W ) and a third point (x R′ , y R′ ) that can be defined, e.g., as the color obtained using Eq. 7 with (I R =0.3*I TOT , β0.7) or some other well-defined combination of currents. Here, one can first determine I W0  and I C0  using process  600 , then measure (x R′ , y R′ ), then interpolate. In yet another variation, triangular interpolation could be performed using as the three vertices the points (x t1 , y t1 ) (obtained with I W =I W0 , I C =I C0 , IR=0), (x B , y B ) (obtained with I W =I C =0.5*I TOT , IR=0), and (x R′ , y R′ ) (obtained with I W =0.7*I W0 , I C =0.7*I C0 , IR=0.3*I TOT , or some other combination of currents). In general, the closer the three vertex points are to each other in color space, the more reliable the triangular interpolation. 
     As  FIG. 11  suggests, adding red light can help tune the color in cases where the net white color is “above” the blackbody curve in color space and the target color (x s , y s ) is on the blackbody curve. Those skilled in the art will appreciate that a green LED group could be substituted for the red LED group in cases where the net white color tends to be “below” the blackbody curve; adding green light (which lies opposite red light in CIE color space) would then allow the color to be shifted closer to the blackbody curve. 
       FIG. 13  illustrates an operating principle for tuning a lamp that includes an emitter package with three groups of LEDs according to another embodiment of the present invention. In this embodiment, the three groups of LEDs include a first cool white group  1302  with a color temperature “above” the blackbody curve (dashed line  1308 ), a second cool white group  1304  with a color temperature “below” blackbody curve  1308 , and a warm white group  1306 . By adjusting the relative current distributed to LED groups  1302 ,  1304 , and  1306 , the color can be tuned to any point within triangle  1310 . In some embodiments, tuning to a range of points on blackbody curve  1308  (e.g., color temperatures of about 4500 K to about 2800 K) with high precision can be achieved. Thus, for example, a desired color temperature (x s , y s ) (point  1312 ) on blackbody curve  1308  can be produced by tuning. 
       FIG. 14  illustrates a process  1400  for tuning a lamp having the LED groups illustrated in  FIG. 13  according to an embodiment of the present invention. At block  1402 , the two cool-white LED groups  1302 ,  1304  are treated as a single group, and current is tuned between this “group” and warm-white LED group  1306  to produce a color temperature (x p , y p ) (point  1314 ) that is on the normal at point  1312  to blackbody curve  1308 . For example, if I C1  denotes the current delivered to cool white group  1302  and I C2  denotes the current delivered to cool white group  1304 , then at block  1402 , the total current to the cool white LEDs I C =I C1 +I C2  can be divided such that I C1 =I C2 =0.5*I C . A fixed total input current I TOT  can be adjustably divided between I C  and the current I W  supplied to warm white group  1306  until the color corresponding to (x p , y p ) is reached. This determines operating currents I CO  and I WO    
     Next, at block  1404 , a division of the cool-LED current I CO  between groups  1302  and  1304  is optimized. Holding I CO  and I WO  constant, I C1  and I C2  can be varied to shift the color toward the desired point (x s , y s ). 
     The embodiments of  FIGS. 13 and 14  provide tuning to a single point on the blackbody curve with very good CRI. It should be noted that alternative embodiments are also possible. For example, instead of a lamp with two cool white groups and one warm white group, another embodiment can use a lamp with two warm white groups bracketing the blackbody curve (i.e., one group above and one group below) and one cool white group; the tuning process can be similar to that of  FIG. 14 . 
     In some embodiments, more than three groups of LEDs can be used. For example, some embodiments may have two warm white groups (bracketing the blackbody curve) and two cool white groups (also bracketing the blackbody curve), for a total of four groups of LEDs. In still other embodiments, both red and green LED groups can be provided in addition to the warm white and cool white groups, thus providing four groups of LEDs.  FIG. 15  is a top view of an LED emitter package  1500 , in which a substrate  1501  has a recess  1502 . Within recess  1502  are mounted six cool white (CW) LEDs  1504   a - f , six warm white (WW) LEDs  1504   g - t , one red LED  1504   m , and four green LEDs  1504   n - q , arranged as shown, thus providing four groups of LEDs. Those skilled in the art will appreciate that the number of LEDs in each group and/or the arrangement of LEDs can be modified as desired. Emitter package  1500  can be included in a lamp similar to lamp  100  of  FIG. 1 . In this example, the control circuitry and electrical couplings are such that the cool-white group, warm-white group, red group, and green group are each independently addressable, and the color of light emitted from the lamp can be tuned by adjusting the relative current delivered to each group. 
       FIG. 16  illustrates an operating principle for tuning a lamp with a four-group emitter package according to an embodiment of the present invention. For a first lamp (lamp A), the cool white LEDs produce light at point  1602  in color space while the warm white LEDs produce light at point  1604 ; a net white color (x tA , y tA ) (point  1606 ) can be produced by tuning according to process  600 . Target color point  1608  (coordinates (x s , y s )) lies on the blackbody curve, which for lamp A is below the net-white tuning line  1610 . Thus, adding red to the net white color should bring it closer to point  1608 . For a second lamp (lamp B), the cool white LEDs produce light at point  1622  in color space while the warm white LEDs produce light at point  1624 ; a net white color (x tB , y tB ) (point  1626 ) can be produced by tuning according to process  600 . Target color point  1608  (coordinates (x s , y s )) lies on the blackbody curve, which for lamp B is above the net-white tuning line  1630 . Thus, adding green to the net white color should bring it closer to point  1608 . Accordingly, providing both red and green LED groups allows for greater flexibility in tuning. In some embodiments, both red and green light can be added to the net white light to further fine-tune the color. 
     The process for tuning with four groups can be similar to process  1200  ( FIG. 12 ).  FIG. 17  illustrates a process  1700  that can be used according to an embodiment of the present invention. At block  1702 , with I R  and I G  held constant at zero, process  600  ( FIG. 6 ) can be used to determine I W0  and I C0 , i.e., the division of current between the warm white and cool white LED groups that produces a net white color (x t1 , y t1 ). At block  1704 , by comparing (x t1 , y t1 ) to the target color (x s , y s ), a determination is made as to whether red or green light should be added to fine-tune the color. After decision  1706 , if red light is to be added, blocks  1708 - 1716  can be executed; these blocks can be similar to blocks  1204 - 1212  of process  1200  described above. If green light is to be added, blocks  1718 - 1726  can be executed. These blocks can be similar to blocks  1204 - 1212  of process  1200 , with green light used in place of red. 
     It will be appreciated that the tuning processes for multiple groups of LEDs described herein are illustrative and that variations and modifications are possible. Any number of groups of LEDs can be provided, and tuning can be done by successively adding the next group to an optimal blend of previous groups, or by interpolating between multiple vertex locations associated with different mixtures of light from the different groups. 
     In some embodiments described above, an assumption is made that the change in color is linearly related to the change in relative currents between groups of LEDs when total current to all groups is held constant. This assumption works well for small regions in color space, particularly if the LEDs are chosen to have equal flux densities. In this case, an approach to tuning with two groups can include defining at least two reference points in color space, corresponding to at least two different distributions of a fixed total current between the groups of LEDs in a lamp, where the reference points are chosen such that the target color is intermediate between them, then applying linear interpolation to tune the current distribution such that the resulting light closely approximates the target color. Where more than two groups of LEDs are provided, at least three reference points in color space can be chosen such that the target color lies within a polygon (e.g., a triangle) defined by the reference points, and triangular interpolation and/or other interpolation techniques can be used to tune the current distribution such that the resulting light closely approximates the target color. 
     More generally, the change in color need not be linearly related to change in relative currents between the LED groups. Blending of light from independently-addressable LED groups having different colors or color temperatures can be used to tune a lamp regardless of whether the assumption of a linear relationship holds. In some cases where the assumption of linearity does not hold, the actual nonlinear response can be modeled for a family of lamps. Alternatively, a tuning algorithm can proceed by a “search” strategy that tests different divisions (or distributions) of currents among the LED groups and adjusts the current division iteratively based on color measurements. One search strategy can include shifting the current division by a fixed step size (e.g., 50 mA) between color measurements. Another search strategy can be based on a half-interval search technique, similar to a binary search. Starting from an assumption that the extremes of the current distribution bracket the target color temperature, the color temperature with an equal distribution of current can be measured. The next measurement can be taken with a current distribution halfway between equal and the extreme that should pull the result closer to the desired temperature, and this can be repeated until the desired color temperature is reached. A particular search strategy is not critical to the present invention. 
     In order to facilitate tuning, the total current applied to all groups is advantageously held constant during tuning; tuning is achieved by varying the distribution of the fixed total current to different groups (or, equivalently, the fraction of total current applied to each group). 
     The tuning processes described herein are straightforward and predictable, allowing for automated implementation, e.g., in a manufacturing environment. Examples of apparatus capable of implementing the tuning processes described herein will now be described. 
       FIG. 18  is a simplified diagram of a tuning apparatus  1800  according to an embodiment of the present invention. Tuning apparatus  1800  includes an adjustment fixture  1802 , an optical fiber  1804 , a spectrometer  1806 , a control system  1808 , a programmable potentiometer  1810 , and a current source  1818 . 
     Adjustment fixture  1802  can incorporate mounting features for holding a lamp  1812  in place during tuning. Adjustment fixture  1802  also provides for delivery of light from lamp  1812  into optical fiber  1804  (e.g., a conventional optical fiber with a diameter of 100 microns). For example, adjustment fixture  1802  can include retention elements that hold optical fiber  1804  in position relative to lamp  1812  so that light from lamp  1812  falls onto the end of optical fiber  1804 . In some embodiments, adjustment fixture  1802  can provide lenses or other optical elements, e.g., to focus the light from lamp  1812 , thereby increasing the light incident on the end of optical fiber  1804 . 
     Spectrometer  1806  can be of conventional design, such as the commercially available Ocean Optic USB  4000  spectrometer. Any device capable of measuring light color and communicating its measurements to a computer can be used. 
     Programmable potentiometer  1810 , which can also be of conventional design, can be connected to current input points of lamp  1812 . Potentiometer  1810  can include variable resistors and the value of each resistor can be programmed, e.g., in response to a control signal. Potentiometer  1810  is advantageously arranged to apply resistances to divide an input current I TOT  provided by current source  1818  into a current distribution for each group of LEDs in lamp  1812 . For example, in the case where lamp  1812  includes cool white and warm white LEDs, I C  can be delivered to the cool white LEDs while I W  is delivered to the warm white LEDs in lamp  1812 . For example, as shown in  FIG. 2B , resistances R W  and R C  can be varied using a dual programmable potentiometer  1810 . In one embodiment, potentiometer  1810  is programmed with the desired R W  and R C  values based on control signals received from control system  1808 . Where lamp  1812  contains more than two groups, potentiometer  1810  can provide additional independently variable resistances so that the input current I TOT  can be distributed in any arbitrary manner among the groups of LEDs. Other devices and techniques capable of controlling the distribution of an input current among the groups of LEDs can also be used; a potentiometer is not required. 
     Control system  1808  can be implemented using, e.g., using a computer system of conventional design, including a central processor (CPU), memory (e.g., RAM), display device, user input devices (keyboard, mouse, etc.), magnetic storage media (e.g., a hard or fixed disk drive), removable storage media (e.g., optical disc, flash-based memory cards), and the like. (In the interest of simplicity, these conventional components are not illustrated.) In one embodiment, control system  1808  is based on a Linux platform; however, a particular platform is not required. Control system  1808  can implement a single-color adjustment algorithm  1822 , e.g., using program code that can be stored in memory and executed by the CPU. As described below, algorithm  1822  can implement aspects of process  600 . 
     Control system  1808  can also implement a spectrometer driver  1824  that can receive color data from spectrometer  1806 . In various embodiments, spectrometer driver  1824  can include a physical interface (e.g., Universal Serial Bus (USB) or the like) compatible with spectrometer  1806  and associated control software (executable by, e.g., a CPU or other processor of control system  1808 ) that can be used to direct the spectrometer to take readings and to provide data. In some embodiments, spectrometer driver  1824  in some embodiments can also provide code related to interpreting the data, e.g., converting measurements received from spectrometer  1806  into CIE color-space coordinates or other desired format. 
     Control system  1808  can also implement a potentiometer driver  1826  that can control operation of programmable potentiometer  1810 . In various embodiments, potentiometer driver  1826  can include a physical interface (e.g., Universal Serial Bus (USB), I 2 C or the like) compatible with potentiometer  1810  and associated control software (executable, e.g., by a CPU or other processor of control system  1808 ) that can be used to instruct the potentiometer to set its variable resistances to specified values. The values can be specified by single-color adjustment algorithm  1822 . 
     User interface  1828  can include standard interface components, such as a keyboard, mouse, track ball, track pad, touch pad, display screen, printer, etc., along with associated software executed by the CPU of control system  1808  to control and communicate with the interface components. Via user interface  1828 , a user can communicate with single-color adjustment algorithm  1822  to control operation thereof. For example, the user can control starting and stopping of a tuning process and view data associated with tuning processes (e.g., plots similar to those of  FIGS. 7A-7B ). 
     Operation of apparatus  1800  can proceed as follows. First, an LED-based lamp  1812  (e.g., corresponding to lamp  100  of  FIG. 1 ) is connected to potentiometer  1810  and placed into adjustment fixture  1802  such that light emitted by lamp  1812  is collected and delivered via optical fiber  1804  to spectrometer  1806 . Next, control system  1808  is instructed to execute the single-color adjustment algorithm. This can include executing any of the processes described above to determine and apply selected currents to different LED groups and to measure the resulting light color. This setup can be used with any lamp  1812  capable of receiving separate currents for warm-white and cool-white LEDs. Once the light color produced by the operating currents has been verified as matching the target color (within manufacturing tolerances that can be chosen by the operator of apparatus  1800 ), lamp  1812  can be reconfigured (e.g., by adding resistors) such that the desired current division is obtained. 
     Alternatively, in some embodiments, the lamp itself may include programmable potentiometers. For example,  FIG. 19  shows a test apparatus  1900  that can be used to program potentiometers within a lamp according to an embodiment of the present invention. As indicated, most of the components of apparatus  1900  can be similar (or identical) to those of apparatus  1800 . However, in this example, a lamp  1912 , which can be otherwise similar to lamp  1812 , includes potentiometer  1914  (or other control circuitry capable of controlling the amount of current delivered to each group of LEDs within lamp  1912 ), and an external adjustment interface  1910  replaces potentiometer  1810 . An external power source  1918  is provided to deliver operating current I TOT  to lamp  1912 . Potentiometer  1914  can be configured with a suitable number of independently variable resistances; for instance, if lamp  1912  includes two groups of LEDs, potentiometer  1914  can be configured with variable resistances R W  and R C , e.g., corresponding to variable resistors  224 ,  226  shown in  FIG. 2B . If lamp  1912  contains more than two groups, potentiometer  1914  can include additional independently variable resistances. Adjustment interface  1910  (which can be built into lamp  1912  or external to it) is capable of communicating with potentiometer  1914  to set the resistances to desired values in response to signals from potentiometer driver  1826 . 
     Apparatus  1900  also includes a robotic arm  1930  that is operable by robotic driver  1932  to pick up a lamp (e.g., lamp  1912 ) from a location holding lamps to be tuned and place lamp  1912  into adjustment fixture  1802 . Robotic arm  1930  is further operable by robotic driver  1932  to remove lamp  1912  from adjustment fixture  1802  after tuning and place lamp  1912  into a location designated for holding tuned lamps. Robotic driver  1932  can be controlled by a suitable robotic-control subsystem  1934 , which can be implemented using hardware and/or software incorporated into control system  1908 . Conventional techniques for robotic control systems can be used to implement robotic arm  1930 , driver  1932  and control subsystem  1934 . In some embodiments, adjustment fixture  1802  may include movable members that extend to hold lamp  1912  in place and retract to release lamp  1912 . Such members can also be operated under control of robotic driver  1932 , allowing full automation of the process of inserting lamps into the adjustment fixture for tuning and removing them when tuning is complete. 
     Apparatus  1900  allows for a fully automated tuning procedure, in which a lamp  1912  is inserted into adjustment fixture  1802  and connected to adjustment interface  1910 . Robotic arm  1930  can be used to remove human intervention from the process of inserting and removing lamps from the adjustment fixture. Control system  1908 , which can include components similar to those of control system  1808  of  FIG. 18  described above, can execute the tuning process to determine operating currents and program potentiometer  1914  with the appropriate resistances to produce the desired operating currents. Thereafter, lamp  1912  can be removed from apparatus  1900 . Again, robotic arm  1930  can be used to remove human intervention from this stage. Potentiometer  1914  advantageously retains its last programmed settings when disconnected from adjustment interface  1910 ; consequently, lamp  1912  will continue provide the desired operating currents to the warm-white and cool-white LEDs even after being removed from the test fixture. Thus, lamps can be tuned with little or no manual intervention, and multiple lamps can be tuned at once, e.g., by providing multiple copies of all or part of apparatus  1900 . 
       FIG. 20  illustrates a tuning process  2000  that can be implemented, e.g., in apparatus  1900  according to an embodiment of the present invention. Tuning process  2000  can be used to tune a single lamp or any number of lamps. At block  2002 , a user specifies the desired color (x s , y s ), e.g., by interacting with user interface  1828  of control system  1808 . In some embodiments, the user can specify a desired color temperature, which control system  1808  can convert to color-space coordinates. At block  2004 , a lamp (e.g., lamp  1912 ) is connected into adjustment fixture  1802 , e.g., by the user, by some other operator of apparatus  1900 , or by a robotic mechanism in an automated manufacturing plant. 
     At block  2006 , control system  1808  operates apparatus  1900  to determine a current distribution that produces the desired color. For example, single-color adjustment algorithm  1822 , which can implement any of the tuning processes described above, can be executed to determine a distribution of a total current among the groups of LEDs in lamp  1912  that produces the desired color. At block  2008 , operating resistances for potentiometer  1914  that produce the desired current distribution are determined. For example, in one embodiment with two groups of LEDs, the principle that I W /I C =R C /R W  can be used together with the operating currents I W0  and I C0  (determined at block  2006 ) to select appropriate resistances. This computation can be incorporated into single-color adjustment algorithm  1822 . At block  2010 , potentiometer  1914  is programmed with the operating resistances determined at block  2008 ; for instance, single-color adjustment algorithm  1822  can communicate the operating resistances to potentiometer driver  1826 , which communicates the resistances to potentiometer  1914  via adjustment interface  1910 . 
     At block  2012 , the operating currents can be tested by measuring the operating color (x 0 , y 0 ) while lamp  1912  remains in adjustment fixture  1802 . In some embodiments, at block  2014 , the color can be fine-tuned with a further adjustment, e.g., in response to the measurement at block  2012  and a least-squares fit to a blackbody curve. 
     At block  2016 , after the final tuning is completed, lamp  1912  can be removed from adjustment fixture  1802 . Potentiometer  1914  advantageously remains programmed with the operating resistances determined in process  2000  so that lamp  1912  will produce light of the tuned color whenever operating power is supplied. 
     After block  2016 , process  2000  can end. In some embodiments, additional lamps can be tuned to the same color temperature by repeating process  2000  (starting from block  2004 ) for each lamp. 
     It will be appreciated that the process  2000  described herein is illustrative and that variations and modifications are possible. Steps described as sequential may be executed in parallel, order of steps may be varied, and steps may be modified, combined, added or omitted. A similar process can be used with apparatus  1800  of  FIG. 18 . In some embodiments, it may be desirable to tune a single lamp for each of a number of different color temperatures and provide a control on the lamp that a user can operate to select among these color temperatures. This can be accomplished by repeating process  2000  for each desired color temperature and storing the operating resistances determined for each temperature (e.g., in a lookup table). When the user selects a color temperature by operating the control on the lamp, the corresponding resistances can be looked up and programmed into potentiometer  1914 . 
     It should be noted that in ordinary use (after process  2000 ), lamp  1912  does not require any feedback mechanism to preserve the color tuning. Potentiometer  1914  can remain in its programmed state for the life of the lamp, delivering the desired currents to keep the color tuned. The color will not shift as long as the LEDs within lamp  1912  remain color-stable throughout their lifetime. White LEDs capable of lifetime color stability to within acceptable tolerances are known and can be used in lamp  1912  or other lamps described here. Thus, there is no need for an active feedback process during ordinary use of the lamp and no need for a color sensor that is stable over the lifetime of the lamp. Accordingly, an external active feedback loop, e.g., as shown in  FIGS. 18 and 19 , can be used for initial tuning of the lamp, and the lamp can thereafter be operated without further feedback or tuning. 
     In some embodiments, lamp  1912  can include control circuitry to maintain a desired distribution of an input current to the different groups of LEDs. For example, programmable potentiometers can be used as described above. Once the current is tuned, the programmable potentiometers can store the resistance values corresponding to the desired color. In other embodiments, the lamp can include memory circuits (e.g., programmable read-only memory, flash memory or the like) that can store information indicating the desired distribution of current. Thus, for example, a fixture in which the lamp is installed can include a current controller capable of reading the stored information and providing input currents to each group of LEDs based on the desired distribution. Other techniques can also be used to store or retain the tuning information (e.g., the desired current distribution) within a lamp. In some embodiments, the lamp may be capable of operating at a user-selectable one of a number of different target colors (or color temperatures), e.g., by use of an external control switch to select a color or the like. The tuning process can be modified to determine a distribution of input current to produce each target color, and the lamp can store information indicating the distribution associated with each color; in operation, the lamp can retrieve the desired distribution based on the setting of the control switch. 
     Further, since ordinary use of lamp  1912  does not require a feedback loop, the various components of the feedback loop used for tuning can be external to lamp  1912  and removed after tuning, as is the case for apparatus  1900  of  FIG. 19 . This can reduce the costs of manufacture of the lamp relative to a lamp that relies on active feedback during ordinary use. Further, operating cost of the lamp may also be somewhat reduced, as there are no feedback components consuming power during ordinary use. 
     While the invention has been described with respect to specific embodiments, one skilled in the art will recognize that numerous modifications are possible. For example, the invention is not limited to a particular lamp geometry or form factor or as to the number and type of LEDs. The particular current values and tuning constant values mentioned herein are also illustrative, and other values may be substituted. The number of groups of LEDs, number of LEDs in any group, and/or the color of a group can be varied. In general, a tunable lamp will include at least two groups of LEDs, with each group occupying a non-overlapping region in color space. The size of the region will depend in part on the manufacturing processes and tolerances used to produce the different groups of LEDs; where a group includes multiple LEDs, those LEDs can be randomly scattered within the associated color-space region. The regions allowed for different groups are advantageously chosen such that the desired (tuned) color is intermediate between the regions occupied by the different LED groups. 
     Thus, although the invention has been described with respect to specific embodiments, it will be appreciated that the invention is intended to cover all modifications and equivalents within the scope of the following claims.