Abstract:
Systems and methods are provided related to a system for imaging an object and a fiducial reference pattern that is projected onto or beside the object. The captured image of the fiducial reference pattern is used to detect a distortion in the captured image of the object.

Description:
BACKGROUND  
       [0001]     There are a number of applications in which it is of interest to detect or image an object. Detecting an object determines the absence or presence of the object, while imaging results in a representation of the object. The object may be imaged or detected in daylight or in darkness, depending on the application.  
         [0002]     Wavelength-dependent imaging is one technique for imaging or detecting an object, and typically involves capturing one or more particular wavelengths that reflect off, or transmit through, an object. In some applications, only solar or ambient illumination is needed to detect or image an object, while in other applications additional illumination is required. But light is transmitted through the atmosphere at many different wavelengths, including visible and non-visible wavelengths. It can therefore be difficult to detect the wavelengths of interest because the wavelengths may not be visible.  
         [0003]      FIG. 1  illustrates the spectra of solar emission, a light-emitting diode, and a laser. As can be seen, the spectrum  100  of a laser is very narrow, while the spectrum  102  of a light-emitting diode (LED) is broader in comparison to the spectrum of the laser. And solar emission has a very broad spectrum  104  in comparison to both the LED and laser. The simultaneous presence of broad-spectrum solar radiation can make detecting light emitted from an eyesafe LED or laser and reflected off an object quite challenging during the day. Solar radiation can dominate the detection system and render the relatively weak scatter from the eyesafe light source small by comparison.  
         [0004]     Additionally, some filter materials exhibit a distinct absorption spectral peak with a tail extending towards a particular wavelength.  FIG. 2  depicts a filter spectrum  200  having an absorption peak  202  and a tail  204  towards the shorter wavelength side. When the wavelengths of interest (e.g., λ 1  and λ 2 ) are spaced closely together, it may be difficult to discriminate or detect one or more particular wavelengths. For example, in  FIG. 2 , the filter material effectively absorbs light at wavelength λ 2 . But it also partially absorbs light transmitting at wavelength λ 1 . This can make it difficult to detect the amount of light transmitting at wavelength λ 1 .  
       SUMMARY  
       [0005]     In accordance with the invention, a method and system for wavelength-dependent imaging and detection using a hybrid filter are provided. An object to be imaged or detected is illuminated by a single broadband light source or multiple light sources emitting light at different wavelengths. The light is received by a receiving module, which includes a light-detecting sensor and a hybrid filter. The hybrid filter includes a multi-band narrowband filter and a patterned filter layer. The patterned filter layer includes regions of filter material that transmit a portion of the light received from the narrowband filter and filter-free regions that transmit all of the light received from the narrowband filter. Because the regions of filter material absorb a portion of the light passing through the filter material, a gain factor is applied to the light that is transmitted through the regions of filter material. The gain factor is used to balance the scene signals in one or more images and maximize the feature signals in one or more images.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0006]     The invention will best be understood by reference to the following detailed description of embodiments in accordance with the invention when read in conjunction with the accompanying drawings, wherein:  
         [0007]      FIG. 1  illustrates the spectra for solar emission, a light-emitting diode, and a laser;  
         [0008]      FIG. 2  depicts a filter spectrum having an absorption peak and a tail extending towards the shorter wavelength side;  
         [0009]      FIG. 3  is a diagram of a first system for pupil detection that uses a hybrid filter in an embodiment in accordance with the invention;  
         [0010]      FIG. 4  is a diagram of a device that can be used in the system of  FIG. 3 ;  
         [0011]      FIG. 5  is a diagram of a second system for pupil detection in an embodiment in accordance with the invention;  
         [0012]      FIG. 6  is a diagram of a third system for pupil detection in an embodiment in accordance with the invention;  
         [0013]      FIG. 7A  illustrates an image generated in a first frame with an on-axis light source in accordance with the embodiments of  FIG. 3 ,  FIG. 5 , and  FIG. 6 ;  
         [0014]      FIG. 7B  depicts an image generated in a second frame with an off-axis light source in accordance with the embodiments of  FIG. 3 ,  FIG. 5 , and  FIG. 6 ;  
         [0015]      FIG. 7C  illustrates a difference image resulting from the subtraction of the image in the second frame in  FIG. 7B  from the image in the first frame in  FIG. 7A ;  
         [0016]      FIG. 8  is a top view of a sensor and a patterned filter layer in an embodiment in accordance with the invention;  
         [0017]      FIG. 9  is a cross-sectional view of a detector in an embodiment in accordance with the invention;  
         [0018]      FIG. 10  depicts spectra for the patterned filter layer and the narrowband filter shown in  FIG. 9 ;  
         [0019]      FIG. 11  is a diagram of a system for detecting wavelengths of interest that are transmitted through an object in an embodiment in accordance with the invention;  
         [0020]      FIG. 12  illustrates a Fabry-Perot resonator used in a first method for fabricating a dual-band narrowband filter in an embodiment in accordance with the invention;  
         [0021]      FIG. 13  depicts the spectrum for the Fabry-Perot resonator of  FIG. 12 ;  
         [0022]      FIG. 14  depicts a coupled-cavity resonator used in the first method for fabricating a dual-band narrowband filter in an embodiment in accordance with the invention;  
         [0023]      FIG. 15  depicts the spectrum for the coupled-cavity resonator of  FIG. 14 ;  
         [0024]      FIG. 16  illustrates a stack of three coupled-cavity resonators that form a dual-band narrowband filter in an embodiment in accordance with the invention;  
         [0025]      FIG. 17  depicts the spectrum for the dual-band narrowband filter of  FIG. 16 ;  
         [0026]      FIG. 18  illustrates a second method for fabricating a dual-band narrowband filter in an embodiment in accordance with the invention;  
         [0027]      FIG. 19  depicts the spectrum for the dual-band narrowband filter of  FIG. 18 ;  
         [0028]      FIG. 20  is a flowchart of a method for image processing of images captured by the detector of  FIG. 9 ;  
         [0029]      FIG. 21  depicts a histogram of pixel grayscale levels in a first image and a histogram of pixel grayscale levels in a second image in an embodiment in accordance with the invention;  
         [0030]      FIG. 22  illustrates spectra for a patterned filter layer and a tri-band narrowband filter in an embodiment in accordance with the invention; and  
         [0031]      FIG. 23  depicts a sensor in accordance with the embodiment shown in  FIG. 22 .  
     
    
     DETAILED DESCRIPTION  
       [0032]     The following description is presented to enable one skilled in the art to make and use the invention, and is provided in the context of a patent application and its requirements. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the generic principles herein may be applied to other embodiments. Thus, the invention is not intended to be limited to the embodiments shown, but is to be accorded the widest scope consistent with the appended claims and with the principles and features described herein. It should be understood that the drawings referred to in this description are not drawn to scale.  
         [0033]     Embodiments in accordance with the invention relate to methods and systems for wavelength-dependent imaging and detection using a hybrid filter. A technique for pupil detection is included in the detailed description as an exemplary system that utilizes a hybrid filter in accordance with the invention. Hybrid filters in accordance with the invention, however, can be used in a variety of applications where wavelength-dependent detection and/or imaging of an object or scene is desired. For example, a hybrid filter in accordance with the invention may be used to detect movement along an earthquake fault, to detect the presence, attentiveness, or location of a person or subject, and to detect or highlight moisture in a manufacturing subject. Additionally, a hybrid filter in accordance with the invention may be used in medical and biometric applications, such as, for example, systems that detect fluids or oxygen in tissue and systems that identify individuals using their eyes or facial features. In these biometric identification systems, pupil detection may be used to aim an imager accurately in order to capture required data with minial user training.  
         [0034]     With reference now to the figures and in particular with reference to  FIG. 3 , there is shown a diagram of a first system for pupil detection that uses a hybrid filter in an embodiment in accordance with the invention. The system includes detector  300  and light sources  302 ,  304 . Light sources  302 ,  304  are shown on opposite sides of detector  300  in the  FIG. 3  embodiment. In another embodiment in accordance with the invention, light sources  302 ,  304 , may be located on the same side of detector  300 . And in yet another embodiment in accordance with the invention, a set of light sources  302 ,  304  may be positioned on both sides of detector  300 . Light sources  302 ,  304  may also be replaced by a single broadband light source emitting light at two or more different wavelengths, such as the sun for example.  
         [0035]     In an embodiment for pupil detection, two images are taken of the face and/or eyes of subject  300  using detector  300 . One of the images is taken using light source  302 , which is close to or on axis  308  of the detector  300  (“on-axis light source”). The second image is taken using light source  304  that is located at a larger angle away from the axis  308  of the detector  300  (“off-axis light source”). When eyes of the subject  306  are open, the difference between the images highlights the pupils of the eyes. This is because specular reflection from the retina is detected only in the on-axis image. The diffuse reflections from other facial and environmental features are largely cancelled out, leaving the pupils as the dominant feature in the differential image. This can be used to infer the subject s  306  eyes are closed when the pupils are not detectable in the differential image.  
         [0036]     The amount of time eyes of subject  306  are open or closed can be monitored against a threshold in this embodiment in accordance with the invention Should the threshold not be satisfied (e.g. the percentage of time the eyes are open falls below the threshold), an alarm or some other action can be taken to alert subject  306 . The frequency or duration of blinking may be used as a criteria in other embodiments in accordance with the invention.  
         [0037]     Differential reflectivity off a retina of subject  306  is dependent upon angle  310  between light source  302  and axis  308  of detector  300 , and angle  312  between light source  304  and axis  308 . In general, making angle  310  smaller will increase the retinal return. As used herein, “retinal return” refers to the intensity (brightness) that is reflected off the back of the eye of subject  306  and detected at detector  300 . “Retinal return” is also used to include reflection from other tissue at the back of the eye (other than or in addition to the retina). Accordingly, angle  310  is selected such that light source  302  is on or close to axis  308 . In this embodiment in accordance with the invention, angle  310  is typically in the range from approximately zero to two degrees.  
         [0038]     In general, the size of angle  312  is chosen so that only low retinal return from light source  304  will be detected at detector  300 . The iris (surrounding the pupil) blocks this signal, and so pupil size under different lighting conditions should be considered when selecting the size of angle  312 . In this embodiment in accordance with the invention, angle  312  is in typically in the range from approximately three to fifteen degrees. In other embodiments in accordance with the invention, the size of angles  310 ,  312  may be different. For example, the characteristics of a particular subject may determine the size of angles  310 ,  312 .  
         [0039]     Light sources  302 ,  304  emit light at different wavelengths that yield substantially equal image intensity (brightness) in this embodiment in accordance with the invention. Even though light sources  302 ,  304  can be at any wavelength, the wavelengths selected in this embodiment are chosen so that the light will not distract the subject and the iris of the eye will not contract in response to the light. The selected wavelengths are typically in a range that allows the detector  300  to respond. In this embodiment in accordance with the invention, light sources  302 ,  304  are implemented as light-emitting diodes (LEDs) or multi-mode lasers having infrared or near-infrared wavelengths. Each light source  302 , 304  may be implemented as one, or multiple, sources.  
         [0040]     Controller  316  receives the images captured by detector  300  and processes the images. In the embodiment of  FIG. 3 , controller  316  determines and applies a gain factor to the images captured with the off-axis light source  304 . A method for processing the images is described in more detail in conjunction with  FIGS. 19 and 20 .  
         [0041]      FIG. 4  is a diagram of a device that can be used in the system of  FIG. 3 . Device  400  includes detector  300 , on-axis light sources  302 , and off-axis light sources  304 . In  FIG. 4 , light sources  302  are arranged in a circular pattern around detector  300  and are housed with detector  300 . In another embodiment in accordance with the invention, light sources  304  may be located in a housing separate from light sources  302  and detector  300 . In yet another embodiment in accordance with the invention, light sources  302  may be located in a housing separate from detector  300  by placing a beam splitter between detector  300  and the object, which has the advantage of permitting a smaller effective on-axis angle of illumination.  
         [0042]     Referring now to  FIG. 5 , there is a second system for pupil detection in an embodiment in accordance with the invention. The system includes detector  300 , on-axis light source  302 , off-axis light source  304 , and controller  316  from  FIG. 3 . The system also includes beam splitter  500 . In this embodiment, detector  300  is positioned adjacent to light source  304 . In other embodiments in accordance with the invention, the positioning of detector  300  and light source  302  may be interchanged, with light source  302  adjacent to light source  304 .  
         [0043]     On-axis light source  302  emits a beam of light towards beam splitter  500 . Beam splitter  500  splits the on-axis light into two segments, with one segment  502  directed towards subject  306 . A smaller yet effective on-axis angle of illumination is permitted when beam splitter  500  is placed between detector  300  and subject  306 .  
         [0044]     Off-axis light source  304  also emits beam of light  504  towards subject  306 . Light from segments  502 ,  504  reflects off subject  306  towards beam splitter  500 . Light from segments  502 ,  504  may simultaneously reflect off subject  306  or alternately reflect off subject  306 , depending on when light sources  302 ,  304  emit light. Beam splitter  500  splits the reflected light into two segments and directs one segment  506  towards detector  300 . Detector  300  captures two images of subject  306  using the reflected light and transmits the images to controller  316  for processing.  
         [0045]      FIG. 6  is a diagram of a third system for pupil detection in an embodiment in accordance with the invention. The system includes two detectors  300   a,    300   b,  two on-axis light sources  302   a,    302   b,  two off-axis light sources  304   a,    304   b,  and two controllers  316   a,    316   b.  The system generates a three-dimensional image of the eye or eyes of subject  306  by using two of the  FIG. 3  systems in an epipolar stereo configuration. In this embodiment, the comparable rows of pixels in each detector  300   a,    300   b  lie in the same plane. In other embodiments in accordance with the invention comparable rows of pixels do not lie in the same plane and adjustment values are generated to compensate for the row configurations.  
         [0046]     Each controller  316   a,    316   b  performs an independent analysis to determine the position of the subject&#39;s  306  eye or eyes in two-dimensions. Stereo controller  600  uses the data generated by both controllers  316   a,    316   b  to generate the position of the eye or eyes of subject  306  in three-dimensions. On-axis light sources  302   a,    302   b  and off-axis light sources  304   a,    304   b  may be positioned in any desired configuration. In some embodiments in accordance with the invention, an on-axis light source (e.g.  302   b ) may be used as the off-axis light source (e.g.  304   a ) for the opposite system.  
         [0047]      FIG. 7A  illustrates an image generated in a first frame with an on-axis light source in accordance with the embodiments of  FIG. 3 ,  FIG. 5 , and  FIG. 6 . Image  700  shows an eye that is open. The eye has a bright pupil due to a strong retinal return created by on-axis light source  302 . If the eye had been closed, or nearly closed, the bright pupil would not be detected and imaged.  
         [0048]      FIG. 7B  depicts an image generated in a first frame with an off-axis light source in accordance with the embodiments of  FIG. 3 ,  FIG. 5 , and  FIG. 6 . Image  702  in  FIG. 7B  may be taken at the same time as the image in  FIG. 7A , or it may be taken in an alternate frame (successively or non-successively) to image  700 . Image  702  illustrates a normal, dark pupil. If the eye had been closed or nearly closed, the normal pupil would not be detected and imaged.  
         [0049]      FIG. 7C  illustrates difference image  704  resulting from the subtraction of the image in the second frame in  FIG. 7B  from the image in the first frame in  FIG. 7A . By taking the difference between two images  700 ,  702 , relatively bright spot  706  remains against relatively dark background  708  when the eye is open. There may be vestiges of other features of the eye remaining in background  708 . However, in general, bright spot  706  will stand out in comparison to background  708 . When the eye is closed or nearly closed, there will not be bright spot  706  in differential image  704 .  
         [0050]      FIGS. 7A-7C  illustrate one eye of subject  306 . Those skilled in the art will appreciate that both eyes may be monitored as well. It will also be understood that a similar effect will be achieved if the images include other features of subject  306  (e.g. other facial features), as well as features of the environment of subject  306 . These features will largely cancel out in a manner similar to that just described, leaving either bright spot  706  when the eye is open (or two bright spots, one for each eye), or no spot(s) when the eye is closed or nearly closed.  
         [0051]     Referring now to  FIG. 8 , there is shown a top view of a sensor and a patterned filter layer in an embodiment in accordance with the invention. In this embodiment, sensor  800  is incorporated into detector  300  ( FIG. 3 ), and is configured as a complementary metal-oxide semiconductor (CMOS) imaging sensor. Sensor  800 , however, may be implemented with other types of imaging devices in other embodiments in accordance with the invention, such as, for example, a charge-coupled device (CCD) imager.  
         [0052]     A patterned filter layer  802  is formed on sensor  800  using filter materials that cover alternating pixels in the sensor  800 . The filter is determined by the wavelengths being used by light sources  302 ,  304 . For example, in this embodiment in accordance with the invention, patterned filter layer  802  includes regions (identified as 1) that include a filter material for blocking the light at the wavelength used by light source  302  and transmitting the light at the wavelength used by light source  304 . Other regions (identified as 2) are left uncovered and receive light from light sources  302 ,  304 .  
         [0053]     In the  FIG. 8  embodiment, patterned filter layer  802  is deposited as a separate layer of sensor  800 , such as, for example, on top of an underlying layer, using conventional deposition and photolithography processes while still in wafer form. In another embodiment in accordance with the invention, patterned filter layer  802  can be can be created as a separate element between sensor  800  and incident light. Additionally, the pattern of the filter materials can be configured in a pattern other than a checkerboard pattern. For example, the patterned filter layer can be formed into an interlaced striped or a non-symmetrical configuration (e.g. a 3-pixel by 2-pixel shape). The patterned filter layer may also be incorporated with other functions, such as color imagers.  
         [0054]     Various types of filter materials can be used in the patterned filter layer  802 . In this embodiment in accordance with the invention, the filter material includes a polymer doped with pigments or dyes. In other embodiments in accordance with the invention, the filter material may include interference filters, reflective filters, and absorbing filters made of semiconductors, other inorganic materials, or organic materials.  
         [0055]      FIG. 9  is a cross-sectional view of a detector in an embodiment in accordance with the invention. Only a portion of the detector is shown in this figure. Detector  300  includes sensor  800  comprised of pixels  900 ,  902 ,  904 ,  906 , patterned filter layer  908  including alternating regions of filter material  910  and alternating empty (i.e., no filter material) regions  912 , glass cover  914 , and dual-band narrowband filter  916 . Sensor  800  is configured as a CMOS imager and the patterned filter layer  908  as a polymer doped with pigments or dyes in this embodiment in accordance with the invention. Each filter region  910  in the patterned filter layer  908  (e.g. a square in the checkerboard pattern) overlies a single pixel in the CMOS imager.  
         [0056]     Narrowband filter  916  is a dielectric stack filter in this embodiment in accordance with the invention. Dielectric stack filters are designed to have particular spectral properties. In this embodiment in accordance with the invention, the dielectric stack filter is formed as a dual-band filter. Narrowband filter  916  (i.e., dielectric stack filter) is designed to have one peak at λ 1  and another peak at λ 2 . The shorter wavelength λ 1  is associated with the on-axis light source  302 , and the longer wavelength λ 2  with off-axis light source  304  in this embodiment in accordance with the invention. The shorter wavelength λ 1 , however, may be associated with off-axis light source  304  and the longer wavelength λ 2  with on-axis light source  302  in other embodiments in accordance with the invention.  
         [0057]     When light strikes narrowband filter  916 , the light at wavelengths other than the wavelengths of light source  302  (λ 1 ) and light source  304  (λ 2 ) are filtered out, or blocked, from passing through narrowband filter  916 . Thus, the light at visible wavelengths (λ VIS ) and at wavelengths (λ n ) are filtered out in this embodiment, while the light at or near the wavelengths λ 1  and λ 2  transmit through the narrowband filter  916 . Thus, only light at or near the wavelengths λ 1  and λ 2  pass through glass cover  914 . Thereafter, filter regions  910  transmit the light at wavelength λ 2  while blocking the light at wavelength λ 1 . Consequently, pixels  902  and  906  receive only the light at wavelength λ 2 .  
         [0058]     Filter-free regions  912  transmit the light at wavelengths λ 1  and λ 2 . In general, more light will reach uncovered pixels  900 ,  904  than will reach pixels  902 ,  906  covered by filter regions  910 . Image-processing software in controller  316  can be used to separate the image generated in the second frame (corresponding to covered pixels  902 ,  906 ) and the image generated in the first frame (corresponding to uncovered pixels  900 ,  904 ). For example, controller  316  may include an application-specific integrated circuit (ASIC) with pipeline processing to determine the difference image. And MATLAB®, a product by The MathWorks, Inc. located in Natick, Mass., may be used to design the ASIC.  
         [0059]     Narrowband filter  916  and patterned filter layer  908  form a hybrid filter in this embodiment in accordance with the invention.  FIG. 10  depicts spectra for the patterned filter layer and the narrowband filter shown in  FIG. 9 . As discussed earlier, narrowband filter  916  filters out all light except for the light at or near wavelengths λ 1  (spectral peak  916   a ) and λ 2  (spectral peak  916   b ). Patterned filter layer  908  blocks light at or near λ 1  (the minimum in spectrum  910 ) while transmitting light at or near wavelength λ 2 . Because the light at or near wavelength λ 2  passes through filter regions  910 , a gain factor is applied to the second frame prior to the calculation of a difference image in this embodiment in accordance with the invention. The gain factor compensates for the light absorbed by filter regions  910  and for differences in sensor sensitivity between the two wavelengths. Determination of the gain factor will be described in more detail in conjunction with  FIGS. 20 and 21 .  
         [0060]     Those skilled in the art will appreciate patterned filter layer  908  provides a mechanism for selecting channels at pixel spatial resolution. In this embodiment in accordance with the invention, channel one is associated with the on-axis image and channel two with the off-axis image. In other embodiments in accordance with the invention, channel one may be associated with the off-axis image and channel two with the on-axis image.  
         [0061]     Sensor  800  sits in a carrier (not shown) in this embodiment in accordance with the invention. Glass cover  914  typically protects sensor  800  from damage and particle contamination (e.g. dust). In another embodiment in accordance with the invention, the hybrid filter includes patterned filter layer  908 , glass cover  914 , and narrowband filter  916 . Glass cover  914  in this embodiment is formed as a colored glass filter, and is included as the substrate of the dielectric stack filter (i.e., narrowband filter  916 ). The colored glass filter is designed to have certain spectral properties, and is doped with pigments or dyes. Schott Optical Glass Inc., a company located in Mainz, Germany, is one company that manufactures colored glass that can be used in colored glass filters.  
         [0062]     Referring now to  FIG. 11 , there is shown a diagram of a system for detecting wavelengths of interest that are transmitted through an object in an embodiment in accordance with the invention. Similar reference numbers have been used for those elements that function as described in conjunction with earlier figures. Detector  300  includes sensor  800 , patterned filter layer  908 , glass cover  914 , and narrowband filter  916 .  
         [0063]     Broadband light source  1100  transmits light towards transparent object  1102 . Broadband light source  1100  emits light at multiple wavelengths, two or more of which are the wavelengths of interest detected by detector  300 . In other embodiments in accordance with the invention, broadband light source  1100  may be replaced by two light sources transmitting light at different wavelengths.  
         [0064]     Lens  1104  captures the light transmitted through transparent object  1102  and focuses it onto the top surface of narrowband filter  916 . For systems using two wavelengths of interest, detector  300  captures one image using light transmitted at one wavelength of interest and a second image using light transmitted at the other wavelength of interest. The images are then processed using the method for image processing described in more detail in conjunction with  FIGS. 20 and 21 .  
         [0065]     As discussed earlier, narrowband filter  916  is a dielectric stack filter that is formed as a dual-band filter. Dielectric stack filters can include any combination of filter types. The desired spectral properties of the completed dielectric stack filter determine which types of filters are included in the layers of the stack.  
         [0066]     For example, a dual-band filter can be fabricated by stacking three coupled-cavity resonators on top of each other, where each coupled-cavity resonator is formed with two Fabry-Perot resonators.  FIG. 12  illustrates a Fabry-Perot (FP) resonator used in a method for fabricating a dual-band narrowband filter in an embodiment in accordance with the invention. Resonator  1200  includes upper Distributed Bragg reflector (DBR)  1202  layer and lower DBR layer  1204 . The materials that form the DBR layers include N pairs of quarter-wavelength (mλ/4) thick low index material and quarter-wavelength (nλ/4) thick high index material, where the variable N is an integer number and the variables m and n are odd integer numbers. The wavelength is defined as the wavelength of light in a layer, which is equal to the freespace wavelength divided by the layer index of refraction.  
         [0067]     Cavity  1206  separates two DBR layers  1202 ,  1204 . Cavity  1206  is configured as a half-wavelength (pλ/2) thick cavity, where p is an integer number. The thickness of cavity  1206  and the materials in DBR layers  1202 ,  1204  determine the transmission peak for FP resonator  1200 .  FIG. 13  depicts the spectrum for the Fabry-Perot resonator of  FIG. 12 . FP resonator  1200  has a single transmission peak  1300 .  
         [0068]     In this first method for fabricating a dual-band narrowband filter, two FP resonators  1200  are stacked together to create a coupled-cavity resonator.  FIG. 14  depicts a coupled-cavity resonator used in the method for fabricating a dual-band narrowband filter in an embodiment in accordance with the invention. Coupled-cavity resonator  1400  includes upper DBR layer  1402 , cavity  1404 , strong-coupling DBR  1406 , cavity  1408 , and lower DBR layer  1410 . Strong-coupling DBR  1406  is formed when the lower DBR layer of top FP resonator (i.e., layer  1204 ) merges with an upper DBR layer of bottom FP resonator (i.e., layer  1202 ).  
         [0069]     Stacking two FP resonators together splits single transmission peak  1300  in  FIG. 13  into two peaks, as shown in  FIG. 15 . The number of pairs of quarter-wavelength thick index materials in strong-coupling DBR  1406  determines the coupling strength between cavities  1404 ,  1408 . And the coupling strength between cavities  1404 ,  1408  controls the spacing between peak  1500  and peak  1502 .  
         [0070]      FIG. 16  illustrates a stack of three coupled-cavity resonators that form a dual-band narrowband filter in an embodiment in accordance with the invention. Dual-band narrowband filter  1600  includes upper DBR layer  1602 , cavity  1604 , strong-coupling DBR  1606 , cavity  1608 , weak-coupling DBR  1610 , cavity  1612 , strong-coupling DBR  1614 , cavity  1616 , weak-coupling DBR  1618 , cavity  1620 , strong-coupling DBR  1622 , cavity  1624 , and lower DBR layer  1626 .  
         [0071]     Stacking three coupled-cavity resonators together splits each of the two peaks  1500 ,  1502  into a triplet of peaks  1700 ,  1702 , respectively.  FIG. 17  depicts the spectrum for the dual-band narrowband filter of  FIG. 16 . Increasing the number of mirror pairs in the coupling DBRs  1610 ,  1618  reduces the coupling strength in weak-coupling DBRs  1610 ,  1618 . The reduced coupling strength merges each triplet of peaks  1700 ,  1702  into a single broad, fairly flat transmission band. Changing the number of pairs of quarter-wavelength thick index materials in weak-coupling DBRs  1610 ,  1618  alters the spacing within the triplet of peaks  1700 ,  1702 .  
         [0072]     Referring now to  FIG. 18 , there is shown a second method for fabricating a dual-band narrowband filter in an embodiment in accordance with the invention. A dual-band narrowband filter is fabricated by combining two filters  1800 ,  1802  in this embodiment. Band-blocking filter  1800  filters out the light at wavelengths between the regions around wavelengths λ 1  and λ 2 , while bandpass filter  1802  transmits light near and between wavelengths λ 1  and λ 2 . The combination of filters  1800 ,  1802  transmits light in the hatched areas, while blocking light at all other wavelengths.  FIG. 19  depicts the spectrum for the dual-band narrowband filter in  FIG. 18 . As can be seen, light transmits through the combined filters only at or near the wavelengths of interest, λ 1  (peak  1900 ) and λ 2  Weak  1902 ).  
         [0073]      FIG. 20  is a flowchart of a method for image processing of images captured by detector  300  of  FIG. 9 . Initially a gain factor is determined and applied to some of the images captured by the detector. This step is shown in block  2000 . For example, in the embodiment of  FIG. 9 , the light transmitting at wavelength λ 2  passes through filter regions  910  in patterned filter layer  908 . Therefore, the gain factor is applied to the images captured at wavelength λ 2  in order to compensate for the light absorbed by the filter regions  910  and for differences in sensor sensitivity between the two wavelengths.  
         [0074]     Next, one or more difference images are generated at block  2002 . The number of difference images generated depends upon the application. For example, in the embodiment of  FIG. 7 , one difference image was generated by subtracting the image in the second frame ( FIG. 7B ) from the image in the first frame ( FIG. 7A ). In another embodiment in accordance with the invention, a system detecting K number of wavelengths may generate, for example, K!/2 difference images.  
         [0075]     Next, convolution and local thresholding are applied to the images at block  2004 . The pixel value for each pixel is compared with a predetermined value. The value given to the predetermined value is contingent upon the application. Each pixel is assigned a color based on the rank of its pixel value in relation to the predetermined value. For example, pixels are assigned the color white when their pixel values exceed the predetermined value. And pixels whose pixel values are less than the predetermined value are assigned the color black.  
         [0076]     Image interpretation is then performed on each difference image to determine where a pupil resides within the difference image. For example, in one embodiment in accordance with the invention, algorithms for eccentricity and size analyses are performed. The eccentricity algorithm analyzes resultant groups of white and black pixels to determine the shape of each group. The size algorithm analyzes the resultant groups to determine the number of pixels within each group. A group is determined to not be a pupil when there are too few or too many pixels within a group to form a pupil. A group is also determined to not be a pupil when the shape of the group does not correspond to the shape of a pupil. For example, a group in the shape of a rectangle would not be a pupil. In other embodiments in accordance with the invention, only one algorithm may be performed. For example, only an eccentricity algorithm may be performed on the one or more difference images. Furthermore, additional or different image interpretation functions may be performed on the images in other embodiments in accordance with the invention.  
         [0077]     The variables, equations, and assumptions used to calculate a gain factor depend upon the application.  FIG. 21  depicts a histogram of pixel grayscale levels in a difference image an embodiment in accordance with the invention. In one embodiment in accordance with the invention, the gain factor is calculated by first generating a histogram of the pixel grayscale levels in the difference image. The contrast between the pupils of the eyes when illuminated with the on-axis light source and when illuminated with the off-axis light source is high in this embodiment. One technique for obtaining high contrast differential images is to select two wavelength bands that reveal a feature of interest with a high degree of contrast between the two wavelength bands and portray the background scene with a low degree of contrast between the two wavelength bands. In order to obtain good contrast in a differential wavelength imager it is desirable to have a large difference between the feature signal levels in the two wavelength bands and a minimal difference between the background scene signal levels in the two wavelength bands. These two conditions can be described as  
         [0078]     (1) Maximize |feature signal in frame  1 —feature signal in frame  2 | 
         [0079]     (2) Balance scene signal in frame  1  with scene signal in frame  2  
 
 A pixel-based contrast can be defined from the expressions above as:  
         C   p     ≡              feature   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   1     -     feature   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   2           scene   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   1     -     scene   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   2                  
 
 In this case, maximizing C p  maximizes contrast. For the pixels representing the background scene, a mean difference in pixel grayscale levels over the background scene is calculated with the equation  
           M   A     =           ∑     i   =   1       r     ⁢     (       scene   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   1     -     scene   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   2       )       r       ,       
 
 where the index i sums over the background pixels and r is the number of pixels in the background scene. For the pixels representing the features of interest (e.g., pupil or pupils), a mean difference grayscale level over the features of interest is calculated with the equation  
           M   B     =         ∑     i   =   1     s     ⁢     (             feature   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   1     -               feature   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   2           )       s       ,       
 
 where the index i sums over pixels showing the feature(s) of interest and s is the number of pixels representing the feature(s) of interest. Each histogram in  FIG. 21  has a mean grayscale value M and standard deviation σ. 
 
         [0080]     In this embodiment |M B −M A | is large compared to (σ A +σ B ) by design. In spectral differential imaging, proper selection of the two wavelength bands yields high contrast to make |M B | large and proper choice of the gain will make |M A | small by balancing the background signal in the two frames. In eye detection, angle sensitivity of retinal reflection between the two channels will make |M B | large and proper choice of the gain will make |M A | small by balancing the background signal in the two frames. The standard deviations depend on a number of factors, including the source image, the signal gray levels, uniformity of illumination between the two channels, the gain used for channel two (e.g., off-axis image), and the type of interpolation algorithm used to represent pixels of the opposite frame.  
         [0081]     It is assumed in this embodiment that a majority of background scenes contain a wide variety of gray levels. Consequently, the standard deviation σ A  tends to be large unless the appropriate gain has been applied. In general, a larger value of the difference signal M A  will lead to a larger value of the standard deviation σ A , or 
 
σ A =αM A  
 
 where α is approximately constant and assumes the sign necessary to deliver a positive standard deviation σ A . In other embodiments in accordance with the invention, other assumptions may be employed. For example, a more complex constant may be used in place of the constant α. 
 
         [0082]     Contrast based on mean values can now be defined as  
         C   M     ≡              M   B     -     M   A              (       σ   B     +     σ   A       )           
 
 It is also assumed in this embodiment that σ A &gt;σ B , so C M  is approximated as  
           C   M     ≈              M   B     -     M   A              σ   A         =                M   B       α   ⁢           ⁢     M   A         -     1   α            =       1        α          ⁢              M   B       M   A       -   1                  
 
 To maximize  
         C   M     ,     the   ⁢           ⁢              M   B       M   A       -   1                
 
 portion of the equation is maximized by assigning the channels so that M B &gt;&gt;0 and M A  is minimized. The equation for C M  then becomes  
           C   M     ≡            M   B       M   A              =            r   s     ⁢         ∑     i   =   1     s     ⁢     (             feature   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   1     -               feature   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   2           )           ∑     i   =   1     r     ⁢     (             scene   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   1     -               scene   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   2           )                    
 
 with the above parameters defined as: 
    feature signal in frame  1 =∫(L 1 +A)P 1 T 1,1 S 1 dλ+∫(L 2 +A)P 2 T 1,2 S 2 dλ    feature signal in frame  2 =G└∫(L 2 +A)P 2 T 2 T 2,2 S 2 dλ+∫(L 1 +A)P 1 T 2,1 S 1 dλ┘    scene signal in frame  1 =└∫(L 1 +A)X x,y,1 T 1,1 S 1 dλ+∫(L 2 +A)X x,y,2 T 1,2 S 2 dλ┘    scene signal in frame  2 =G└∫(L 2 +A)X x,y,2 T 2,2 S 2 dλ+∫(L 1 +A)X x,y,1 T 2,1 S 1 dλ┘, 
 
 where: 
   
 
         [0087]     λ=wavelength;  
         [0088]     L m (λ) is the power per unit area per unit wavelength of light source m of the differential imaging system at the object, where m represents one wavelength band. Integrating over wavelength band m, L m =∫L m (λ)dλ;  
         [0089]     A(λ) is the ambient light source power per unit area per unit wavelength Integrating over wavelength band m, A m =∫A(λ)dλ;  
         [0090]     P m (λ) is the reflectance (diffuse or specular) of the point (part of the feature) of interest at wavelength λ per unit wavelength, for wavelength band m. Integrating over wavelength band m, P m =∫P m (λ)dλ;  
         [0091]     X x,y,m (λ) is the background scene reflectance (diffuse or specular) at location x,y on the imager per unit wavelength as viewed at wavelength band m;  
         [0092]     T m,n (λ) is the filter transmission per unit wavelength for the pixels associated with wavelength band m measured at the wavelengths of band n. Integrating over wavelength for the case m=n, T m,m ∫T m,m (λ)dλ;  
         [0093]     S(λ) is the sensitivity of the imager at wavelength λ; and  
         [0094]     G is a gain factor which is applied to one frame.  
         [0095]     In this embodiment, T m,n (λ) includes all filters in series, for example both a dual-band narrowband filter and a patterned filter layer. For the feature signal in frame  1 , if the wavelength bands have been chosen correctly, P 1 &gt;&gt;P 2  and the second integral on the right becomes negligible. And the relatively small size of P 2  makes the first integral in the equation for the feature signal in frame  2  negligible. Consequently, by combining integrands in the numerator, condition (1) from above becomes 
 
Maximize |∫(L 1 +A)P 1 (T 1,1 −GT 2,1 )S 1 dλ|. 
 
         [0096]     To meet condition (1), L 1 , P 1 , and S 1  are maximized within eye safety/comfort limits in this embodiment in accordance with the invention. One approach maximizes T 1,1,  while using a smaller gain G in the wavelength band for channel two and a highly discriminating filter so that T 2,1  equals or nearly equals zero. For eye detection in the near infrared range, P 1  is higher when the shorter wavelength channel is the on-axis channel, due to water absorption in the vitreous humor and other tissues near 950 nm. S 1  is also higher when the shorter wavelength channel is the on-axis channel due to higher detection sensitivity at shorter wavelengths.  
         [0097]     Note that for the scene signal in frame  1 , the second integral should be small if T 1,2  is small. And in the scene signal in frame  2 , the second integral should be small if T 2,1  is small. More generally, by combining integrands in the denominator, condition (2) from above becomes 
 
minimize |∫(L 1 +A)X x,y,1 (T 1,1 −GT 2,1 )S 1 dλ−∫(L 2 +A)X x,y,2 (GT 2,2 −T 1,2 )S 2 dλ|. 
 
         [0098]     To meet condition (2), the scene signal levels in the two frames in the denominator are balanced in this embodiment in accordance with the invention. Therefore, 
 
∫(L 1 +A)X x,y,1 (T 1,1 −GT 2,1 )S 1 dλ=∫(L 2 +A)X x,y,2 (GT 2,2 −T 1,2 )S 2 dλ. 
 
 Solving for gain G,  
       G   =         ∫       (         (       L   1     +   A     )     ⁢     X     x   ,   y   ,   1       ⁢     T     1   ,   1       ⁢     S   1       +       (       L   2     +   A     )     ⁢     X     x   ,   y   ,   2       ⁢     T     1   ,   2       ⁢     S   2         )     ⁢     ⅆ   λ           ∫       (         (       L   2     +   A     )     ⁢     X     x   ,   y   ,   2       ⁢     T     2   ,   2       ⁢     S   2       +       (       L   1     +   A     )     ⁢     X     x   ,   y   ,   1       ⁢     T     2   ,   1       ⁢     S   1         )     ⁢     ⅆ   λ           .         
 
 It is assumed in this embodiment that X≡X x,y,1 ≈X x,y,2  for most cases, so the equation for the gain is reduced to  
       G   ≈         ∫       (         (       L   1     +   A     )     ⁢     T     1   ,   1       ⁢     S   1       +       (       L   2     +   A     )     ⁢     T     1   ,   2       ⁢     S   2         )     ⁢     ⅆ   λ           ∫       (         (       L   2     +   A     )     ⁢     T     2   ,   2       ⁢     S   2       +       (       L   1     +   A     )     ⁢     T     2   ,   1       ⁢     S   1         )     ⁢     ⅆ   λ           .         
 
         [0099]     Filter crosstalk in either direction does not exist in some embodiments in accordance with the invention. Consequently, T 1,2 ,T 2,1 =0, and the equation for the gain is  
         G   noXtalk     ≈         ∫       (       L   1     +   A     )     ⁢     T     1   ,   1       ⁢     S   1     ⁢     ⅆ   λ           ∫       (       L   2     +   A     )     ⁢     T     2   ,   2       ⁢     S   2     ⁢     ⅆ   λ           .         
 
 When a dielectric stack filter is used in series with other filters, the filter transmission functions may be treated the same, as the peak levels are the same for both bands. Thus, the equation for the gain becomes  
         G   noXtalk     ≈           (         L   1     ⁡     (     λ   1     )       +     A   1       )     ⁢       T     1   ,   1       ⁡     (     λ   1     )       ⁢       S   1     ⁡     (     λ   1     )             (         L   2     ⁡     (     λ   2     )       +     A   2       )     ⁢       T     2   ,   2       ⁡     (     λ   2     )       ⁢       S   2     ⁡     (     λ   2     )           .         
 
 Defining  
       S   ≡         S   1     ⁡     (     λ   1     )           S   2     ⁡     (     λ   2     )             
 
 the gain equation is  
         G   noXtalk     ≈       (           L   1     ⁡     (     λ   1     )       +     A   1             L   2     ⁡     (     λ   2     )       +     A   2         )     ⁢   S   ⁢           T     1   ,   1       ⁡     (     λ   1     )           T     2   ,   2       ⁡     (     λ   2     )         .           
 
 If the sources are turned off, L 1 , L 2 =0 and  
           G   AnoXtalk     ≈           A   1     ⁢       T     1   ,   1       ⁡     (     λ   1     )             A   2     ⁢       T     2   ,   2       ⁡     (     λ   2     )           ⁢   S       ,       
 
 where G AnoXtalk  is the optimal gain for ambient lighting only. In this embodiment, the entire image is analyzed for this calculation in order to obtain relevant contrasts. The entire image does not have to be analyzed in other embodiments in accordance with the invention. For example, in another embodiment in accordance with the invention, only a portion of the image near the features of interest may be selected. 
 
         [0100]     Since the ambient spectrum due to solar radiation and the ratio of ambient light in the two channels change both over the course of the day and with direction, the measurements to determine gain are repeated periodically in this embodiment. The ratio of measured light levels is calculated by taking the ratio of the scene signals in the two channels with the light sources off and by applying the same assumptions as above:  
           R   AnoXtalk     ≡       scene   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   subframe   ⁢           ⁢   1       scene   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   subframe   ⁢           ⁢   2         =           A   1     ⁢     T     1   ,   1       ⁢     S   1           A   2     ⁢     T     2   ,   2       ⁢     S   2         .         
 
 Solving for the ratio of the true ambient light levels A 1 /A 2  the equation becomes  
           A   1       A   2       =       R   AnoXtalk     ⁢           T     2   ,   2       ⁢     S   2           T     1   ,   1       ⁢     S   1         .           
 
 Substituting this expression into the equation for G AnoXtalk  yields 
 
G AnoXtalk =R AnoXtalk . 
 
 Thus the gain for ambient lighting can be selected as the ratio of the true ambient light levels in the two channels (A 1 /A 2 ) as selected by the dielectric stack filter. 
 
         [0101]     When the light sources are driven relative to the ambient lighting, as defined in the equation  
               L   1     ⁡     (     λ   1     )           L   2     ⁡     (     λ   2     )         =       A   1       A   2         ,       
 
 the gain expressions for both the ambient- and intentionally-illuminated no-crosstalk cases will be equal, i.e. G noXtalk =G AnoXtalk , even in dark ambient conditions where the system sources are more significant. Thus the gain is constant through a wide range of ambient light intensities when the sources are driven at levels whose ratio between the two channels matches the ratio of the true ambient light levels. 
 
         [0102]     In those embodiments with crosstalk in only one of the filters, the expression for the gain can be written as  
         G   =       ∫       (         (       L   1     +   A     )     ⁢     X     x   ,   y   ,   1       ⁢     T     1   ,   1       ⁢     S   1       +       (       L   2     +   A     )     ⁢     X     x   ,   y   ,   2       ⁢     T     1   ,   2       ⁢     S   2         )     ⁢     ⅆ   λ           ∫       (       L   2     +   A     )     ⁢     X     x   ,   y   ,   2       ⁢     T     2   ,   2       ⁢     S   2     ⁢     ⅆ   λ             ,       
 
 where T 2,1 =0, thereby blocking crosstalk at wavelength band 1 into the pixels associated with wavelength band 2. Assuming X x,y,1 ≈X x,y,2 , this expression can also be written as  
       G   ≈         ∫       (       L   1     +   A     )     ⁢     T     1   ,   1       ⁢     S   1     ⁢     ⅆ   λ           ∫       (       L   2     +   A     )     ⁢     T     2   ,   2       ⁢     S   2     ⁢     ⅆ   λ           +         ∫       (       L   2     +   A     )     ⁢     T     1   ,   2       ⁢     S   2     ⁢     ⅆ   λ           ∫       (       L   2     +   A     )     ⁢     T     2   ,   2       ⁢     S   2     ⁢     ⅆ   λ           .           
 
 The filter transmission functions are treated similar to delta functions (at the appropriate wavelengths multiplied by peak transmission levels) in this embodiment, so the equation for the gain becomes  
       G   ≈           (         L   1     ⁡     (     λ   1     )       +     A   1       )     ⁢       T     1   ,   1       ⁡     (     λ   1     )       ⁢       S   1     ⁡     (     λ   1     )             (         L   2     ⁡     (     λ   2     )       +     A   2       )     ⁢       T     2   ,   2       ⁡     (     λ   2     )       ⁢       S   2     ⁡     (     λ   2     )           +           (         L   2     ⁡     (     λ   2     )       +     A   2       )     ⁢       T     1   ,   2       ⁡     (     λ   2     )       ⁢       S   2     ⁡     (     λ   2     )             (         L   2     ⁡     (     λ   2     )       +     A   2       )     ⁢       T     2   ,   2       ⁡     (     λ   2     )       ⁢       S   2     ⁡     (     λ   2     )           .           
 
 Defining  
         S   ≡         S   1     ⁡     (     λ   1     )           S   2     ⁡     (     λ   2     )           ,       
 
 the equation simplifies to  
       G   ≈         (           L   1     ⁡     (     λ   1     )       +     A   1             L   2     ⁡     (     λ   2     )       +     A   2         )     ⁢   S   ⁢         T     1   ,   1       ⁡     (     λ   1     )           T     2   ,   2       ⁡     (     λ   2     )           +           T     1   ,   2       ⁡     (     λ   2     )           T     2   ,   2       ⁡     (     λ   2     )         .           
 
 The ratio of the true ambient light levels is calculated by taking the ratio of the scene signals in the two channels with light sources off and applying the same assumptions as above. Therefore, the ratio of the measured signal levels is  
           R   A     ≡       scene   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   1       scene   ⁢           ⁢   signal   ⁢           ⁢   in   ⁢           ⁢   frame   ⁢           ⁢   2         =           A   1     ⁢     T     1   ,   1       ⁢     S   1           A   2     ⁢     T     2   ,   2       ⁢     S   2         +         T     1   ,   2         T     2   ,   2         .           
 
 Solving for A 1 /A 2 , the equation becomes  
           A   1       A   2       =       (       R   A     -       T     1   ,   2         T     2   ,   2           )     ⁢         T     2   ,   2       ⁢     S   2           T     1   ,   1       ⁢     S   1               
 
 and again G A =R A . Thus, in the embodiments with crosstalk the ambient gain is set as the ratio of the measured ambient light levels. Similar to the no-crosstalk embodiment above, the illumination levels are set in proportion to the ratio of the true ambient light levels. The system then operates with constant gain over a wide range of illumination conditions. 
 
         [0103]     In practice, for some applications, the feature signal fills so few pixels that the statistics for the entire subframes can be used to determine the gain factor. For example, for pupil detection at a distance of sixty centimeters using a VGA imager with a twenty-five degree full angle field of view, the gain can be set as the ratio of the mean grayscale value of channel one divided by the mean grayscale value of channel 2. Furthermore, those skilled in the art will appreciate that other assumptions than the ones made in the above calculations can be made when determining a gain factor. The assumptions depend on the system and application in use.  
         [0104]     Although a hybrid filter and the calculation of a gain factor has been described with reference to detecting light at two wavelengths, λ 1  and λ 2 , hybrid filters in other embodiments in accordance with the invention may be used to detect more than two wavelengths of interest.  FIG. 22  illustrates spectra for a patterned filter layer and a tri-band narrowband filter in an embodiment in accordance with the invention. A hybrid filter in this embodiment detects light at three wavelengths of interest, λ 1 , λ 2  and λ 3 . Spectra  2200 ,  2202 , and  2204  at wavelengths λ 1 , λ 2 , and λ 3 , respectively, represent three signals to be detected by an imaging system. Typically, one wavelength is chosen as a reference, and in this embodiment wavelength λ 2  is used as the reference.  
         [0105]     A tri-band narrowband filter transmits light at or near the wavelengths of interest (λ 1  λ 2 , and λ 3 ) while blocking the transmission of light at all other wavelengths in this embodiment in accordance with the invention. Photoresist filters in a patterned filter layer then discriminate between the light received at wavelengths λ 1  λ 2 , and λ 3 .  FIG. 23  depicts a sensor in accordance with the embodiment shown in  FIG. 22 . A patterned filter layer is formed on sensor  2300  using three different filters. Each filter region transmits only one wavelength. For example, in one embodiment in accordance with the invention, sensor  2300  may include a color three-band filter pattern. Region 1 transmits light at λ 1 , region 2 at λ 2 , and region 3 at λ 3 .  
         [0106]     Determining a gain factor for the sensor of  FIG. 23  begins with  
         [0107]     (1) Maximizing |feature signal in frame  1 —feature signal in frame  2 | 
         [0108]     (2) Maximizing |feature signal in frame  3 —feature signal in frame  2 | and  
         [0109]     (3) Balance scene signal in frame  1  with scene signal in frame  2   
         [0110]     (4) Balance scene signal in frame  3  with scene signal in frame  2   
         [0000]     which becomes 
 
Maximize=|∫( L   1   +A ) P   1   T   1,1   S   1   dλ−G   1,2 ∫( L   2   +A ) P   2   T   2,2   S   2   dλ| 
 
Maximize=|∫( L   3   +A ) P   3   T   3,3   S   3   dλ−G   3,2 ∫( L   2   +A ) P   2   T   2,2   S   2   dλ| 
 
and 
 
∫( L   1   +A ) X   x,y,1   T   1,1   S   1   dλ=G   1,2 ∫( L   2   +A ) X   x,y,2   T   2,2   S   2   dλ 
 
∫( L   3   +A ) X   x,y,3   T   3,3   S   3   dλ=G   3,2 ∫( L   2   +A ) X   x,y,2   T   2,2   S   2   dλ 
 
 where G 1,2  is the gain applied to the reference the channel at (λ 2 ) in order to match channel 1 (e.g., λ 1 ) and G 3,2  is the gain applied to the reference channel 2 (λ 2 ) in order to match channel 3 (e.g., λ 3 ). Following the calculations from the two-wavelength embodiment (see  FIG. 21  and its description), the gain factors are determined as  
         G     1   ,   2       ≈         A   1     ⁢       T     1   ,   1       ⁡     (     λ   1     )       ⁢       S   1     ⁡     (     λ   1     )             A   2     ⁢       T     2   ,   2       ⁡     (     λ   2     )       ⁢       S   2     ⁡     (     λ   2     )               
 
 where G 1,2 =R 1,2 , the ratio of the scene signals. And  
         G     3   ,   2       ≈         A   3     ⁢       T     3   ,   3       ⁡     (     λ   3     )       ⁢       S   3     ⁡     (     λ   3     )             A   2     ⁢       T     2   ,   2       ⁡     (     λ   2     )       ⁢       S   2     ⁡     (     λ   2     )               
 
 where G 3,2 =R 3,2 , the ratio of the scene signals. 
 
         [0111]     Like the two-channel embodiment of  FIG. 8 , one of the three channels in  FIG. 23  (e.g. channel 2) may not be covered by a pixel filter. The gain factor may be calculated similarly to the embodiment described with reference to  FIG. 21 .